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Federal Reserve Bank
of Chicago
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81999
RB RESEARCH I IRRAR\
Third Quarter 1999
Economic..
perspectives
2
State budgets and the business cycle: Implications
for the federal balanced budget amendment debate
18
Birth, growth, and life or death of newly chartered banks
36
New facts in finance
59
Portfolio advice for a multifactor world
79
Audio tapes for 1999 Bank Structure Conference
Economic .
perspectives
President
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Senior Vice President and Director of Research
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ISSN 0164-0682
Contents
Third Quarter 1999, Volume XXIII, Issue 3
2
State budgets and the business cycle: Implications for the
federal balanced budget amendment debate
Leslie McGranahan
Balanced budget amendment proponents often use the experience of the states with
balanced budget restrictions as an argument in favor of a federal balanced budget
amendment. However, the state experience is not directly relevant to the federal
government. State restrictions are more lenient than those considered at the federal
level, and many of the techniques used by the states to balance their budgets over the
business cycle are not available to the federal government.
18
Birth, growth, and life or death of newly chartered banks
Robert DeYoung
Thousands of new commercial banks have been chartered in the U.S. over the past two
decades. This article documents how the financial characteristics of new banks evolve
over time, develops a simple theory of why and when new banks fail, and tests the
theory using a variety of methods.
36
New facts in finance
John H. Cochrane
In the last 15 years, the cherished “random walk” view that stock returns are unpre
dictable, the “CAPM” view that the market is the only benchmark and market
exposure the only source of returns, and the “expectations hypothesis” relating
interest rates of various maturities and countries have all been abandoned. This article
surveys this revolution in finance, explaining and integrating the new view of the facts.
59
Portfolio advice for a multifactor world
John H. Cochrane
How does traditional portfolio theory adapt to the new facts? The old “two-fund”
theorem becomes a “many-fund” theorem; some investors can improve returns by
investing in portfolio strategies that let them take on nonmarket sources of risk; and
other investors can shed nonmarket risks in the same way. Investors can, if willing to
take on the risks, improve returns by some modest market timing. However, the
average investor must always hold the market, so only investors who are different
from average can benefit from holding new and unusual portfolios.
79
Audio tapes for 1999 Bank Structure Conference
State budgets and the business cycle: Implications
for the federal balanced budget amendment debate
Leslie McGranahan
Introduction and summary
A proposal to amend the U.S. Constitution to require
that the federal budget be balanced has been a part
of the national debate for over 25 years. Following its
inclusion as one of the central planks of the Republican Contract with America in 1994, the balanced budget
amendment became a prominent item on the congressional agenda. The amendment easily passed the
House by a vote of 300 to 132 in January 1995, but
failed to achieve the two-thirds majority required in
the Senate to send it back to the states. Since the
proposals most recent failure in the Senate, by one
vote on March 4, 1997, it has been a less important
agenda item because of the strength of the economy
and the surplus in the federal budget. However, the
issue is by no means dead. In January 1999, the
amendment was again proposed in the House with
the cosponsorship of 117 representatives.
Balanced budget amendment supporters frequently
cite the experience of the states, most of which have
statutory or constitutional balanced budget restrictions.1 In this article, I question how the state experience
with balanced budget restrictions can inform the federal debate on a balanced budget amendment. First,
I address how the longstanding state restrictions
compare with those contemplated at the federal level.
I then investigate how state government revenues,
expenditures, debt issuance, and asset holdings have
responded to changes in the states economic conditions, as measured by the unemployment rate, during
the last two decades. I use regression analysis to ask
how, controlling for a time trend and state fixed effects,
state finances have reacted to fiscal year state unemployment rates from 1977 to 1997. I further question
whether similar responses on the part of the federal
government would be either feasible or prudent.
In my investigation of how state finances respond
to business cycle conditions, I discover that states
use four main mechanisms to maintain budget balances
2
during downturns: they issue more short- and longterm debt; they rely more heavily on the federal
government for funds while giving less to local governments; they increase tax rates; and they lower
capital spending. This is not a feasible policy combination for the federal government for a number of
reasons. Most importantly, the provisions of the balanced budget amendment would not allow the federal
government to issue any new debt without a legislative supermajority. In this way, the federal balanced
budget amendment differs significantly from the restrictions in place in the states. While the states use the issuance of debt as an important safety valve, this option
would not be available to the federal government.
Of course, the opportunity to receive more from
a higher level of government would also not be available to the federal government. However, the federal
government could follow the states lead by transferring less money to the states during difficult times.
This would reverse the current relationship between
federal government intergovernmental spending and
the business cycle and would make it more difficult
for the state governments to balance their budgets.
Importantly, this suggests that one of the reasons
that the states are able to balance their budgets is that
the federal government does not.
The federal government could follow the states
by increasing tax rates during economic downturns.
This would be an unpopular policy for two main reasons. First, tax increases are always unpopular and
difficult to pass. Second, unlike the state governments,
the federal government is responsible for the condition
Leslie McGranahan is an economist in the Economic
Research Department of the Federal Reserve Bank of
Chicago. The author would like to thank Loula Sassaris
for research assistance and colleagues at the Federal
Reserve Bank of Chicago for help and comments.
Economic Perspectives
of the macroeconomy. Tax increases during recessions would further depress disposable incomes and
consumption and could prolong downturns.
The other state behavior open to the federal
government would be to decrease capital spending
during economic downturns. States get a lot of leverage out of their ability to cut capital spending during
difficult times; my results show that this is among the
most pronounced state responses to a deteriorating
economic situation. The federal government may be
unwilling to follow the states lead by cutting capital
spending during recessions because the bulk of federal capital spending, over 80 percent, is in the area
of national defense (U.S. Government, Office of Management and Budget, 1999). By contrast, the majority
of state capital spending is on highways (57 percent)
and institutions of higher education (14 percent)
(U.S. Department of Commerce, Bureau of the Census,
197787 and 198897). Whether it is prudent for the
federal government to structure defense capital
spending to maintain budget balance during downturns is an open question.
Because of the differences in the proposed federal balanced budget amendment and the measures in
place in the states and the different responsibilities
of the federal versus state governments, none of the
four methods used by state governments during economic downturns is an obvious choice for the federal
government. In summary, my results suggest that the
ability of the states to function under their current
balanced budget restrictions should not be used to
argue in favor of the balanced budget amendment
most recently proposed in Congress. However, this
does not necessarily imply that other reasons advanced in favor of a balanced budget amendment are
invalid or that the amendment should not be justified
on other grounds.
Comparing state and federal balanced
budget requirements
The provisions of the proposed federal balanced
budget amendment are quite basic. The amendment
as voted on in 1997 simply states that [t]otal outlays
for any fiscal year shall not exceed total receipts for
that fiscal year, unless three-fifths of the whole number of each House of Congress shall provide by law
for a specific excess of outlays over receipts by a rollcall vote. Additional provisions require a three-fifths
majority to increase the debt limit or to increase revenues (U.S. Senate, 1997).
The amendment does not provide for separate
funds to finance capital projects and, therefore, in the
absence of a super-majority vote, does not allow the
Federal Reserve Bank of Chicago
government to issue any new debt. In addition, the
amendment does not provide for a reserve fund that
can be used to carry over surpluses from one year to
the next. Instead, surpluses that were neither spent
nor returned to citizens would be used to reduce the
existing debt. This arises from the provisions that
outlays must be financed by total receipts from the
same fiscal yearit does not allow for the use of
receipts from previous years. Both of these features
would be in contrast to the provisions in the states.
In short, the amendment simply requires that the budget be balanced every year.
State balanced budget restrictions are far more
complex than the federal proposal. There is no prototypical requirement at state level; each state has a
unique set of provisions. However, the following state
provisions are comparable to the federal proposal: balanced budget requirements, restrictions on deficit carryovers, and restrictions on long-term debt issuance.
Before addressing how these three types of
restrictions interact to affect state behavior, it is important to briefly explain the role of capital budgeting
in the states. Most states have capital budgets that
are separate from their operating budgets.2 The construction of new facilities and the repair, maintenance,
remodeling, and rehabilitation of existing facilities are
funded separately.3 One important feature that distinguishes state balanced budget requirements from
those at the federal level is that most of these requirements only mandate that the operating budget be balanced. In cases where the capital budget also needs
to be balanced, proceeds from the issuance of debt
are counted as revenues. Therefore, the balanced
budget restrictions do not stop states from issuing
debt. This contrasts with the federal proposal, which
explicitly excludes receipts derived from borrowing
from government revenues. The ability of states to
borrow for capital projects reconciles the common
perception that states have balanced budgets with
a thriving and substantial municipal bond market.
Submitting, passing, or signing a balanced budget
When commentators write that most states have
balanced budget restrictions, they are usually referring
to constitutional or statutory provisions that require
that the governor must submit, the legislature must
pass, or the governor must sign a balanced budget.
These provisions do not explicitly require that the
year-end budget end up balanced, but rather that the
budget as proposed, passed, or signed be balanced
in expectation. For example, the Illinois constitution
requires that the governor submit and the legislature
pass a balanced budget. The document states, [t]he
Governor shall prepare and submit to the General
3
Assembly, at a time prescribed by law, a State budget
for the ensuing fiscal year. ... Proposed expenditures
shall not exceed funds estimated to be available for
the fiscal year as shown in the budget. It further
states that [a]ppropriations for a fiscal year shall not
exceed funds estimated by the General Assembly to
be available during that year (italics added) (State of
Illinois, 1970, Article 8, Section 2). Note that in both
cases expenditures cannot exceed estimated revenues.
Deficit carryover provisions
In the event that circumstances change during
the year and a budget that was expected or estimated
to be balanced was not, state provisions either allow
or do not allow deficits to be carried over from one
fiscal year to the next. If the state does not allow
deficits to be carried over, the state must either cut
spending or increase revenues to eradicate the deficit
by fiscal year-end. Such deficit carryover provisions
represent the teeth of the balanced budget requirements, because they prohibit the state from issuing
debt to finance a shortfall. The National Conference
of State Legislatures reports that 13 states have no
restriction on carrying over a deficit and a total of 21
may carry over a deficit if necessary (Snell, 1999).
Illinois is one of the states allowed to carry over deficits. The Illinois constitution states that [s]tate debt
may be incurred by law in an amount not exceeding
15 percent of the States appropriations for that fiscal
year to meet deficits caused by emergencies or failures
of revenue (State of Illinois, 1970, Article 9, Section 9).4
Note that all states do allow surpluses to be carried over
from one year to the next and 45 states have special
rainy day funds for surplus carryovers (Eckl, 1998).
State long-term debt provisions
The final parts of states budget restrictions are
provisions limiting their ability to issue long-term
debt. Nearly all long-term debt is used to finance specific capital projects in conjunction with the states
capital budget. While federal Treasury bonds, notes,
and bills are very general in nature, most state government debt is very specific and is issued to benefit
particular capital projects. State debt can be backed
by either the full faith and credit or the taxing power
of the government, and can be redeemed from general
revenues or be nonguaranteed and be backed by
specific income streams.
Most states have a restriction limiting the issuance
of long-term debt. Some state constitutions require
that debt cannot be issued until it receives majority
support in a statewide referendum; in some states
debt can only be issued up to a prespecified limit;
and other states allow no debt to be issued at all.5
4
However, state courts have interpreted these constitutional requirements as only applying to debt backed
by the full faith and credit of the government. As a
result, states can issue nonguaranteed debt limited
only by the constraints of the capital market. In fact,
despite restrictions on long-term debt that in some
cases seem quite severe, in every year since 1977
every state has issued some long-term debt.
In sum, the restrictions on the states are far
more lenient than that contemplated for the federal
government. In particular, all states can and do issue
long-term debt and many states can issue debt to
finance deficits.
Nonetheless, the states experience with budget
restrictions is frequently used to support balanced
budget restrictions at the federal level. For example,
Michigans Governor John Engler in his State of the
State Address in 1997 said, I support the balanced
budget amendment and so do Michigan voters. When
Congress takes up this historical amendment next
month, I urge them to pass it and submit it to the states.
I invite this legislature to join the debate, call upon
your colleagues in Congress to act and help the
federal budget look more like Michigans budget
balanced (Engler, 1997). Similarly, in his 1997 State of
the State address Oklahoma Governor Frank Keating
stated that We Oklahomans know the wisdom of a
constitutional mandate for fiscal common sense. Lets
send some Oklahoma values to Washington by being
the first to ratify this vital amendment (Keating, 1997).
While the current state restrictions and the contemplated federal restrictions are quite different, the
general perception that states are more fiscally responsible is warranted. States do a better job on two
dimensions. First, they have a lower level of overall
debt relative to their financial obligations. Between
1977 and 1997, net interest payments on the federal
debt averaged 12.7 percent of outlays and 15.0 percent of receipts (U.S. Government, Office of Management and Budget, 1999), while state interest payments
averaged 3.7 percent of expenditures and 3.4 percent
of revenues (U.S. Department of Commerce, Bureau
of the Census, 197787 and 198897).6 Similarly, gross
federal debt outstanding averaged 2.3 times outlays
and 2.7 times receipts, while state gross debt outstanding averaged 0.5 times revenues and 0.6 times
outlays over the same period. Second, the states do
a better job of smoothing over the business cycle.
A 1 percentage point increase in the state unemployment rate increases the average states budget deficit
(expenditures revenues) by $23 per capita or about
9 percent (relative to the mean), while a 1 percentage
Economic Perspectives
point increase in the national unemployment rate
increases the federal government deficit by $134 or
about 16 percent.
Next, I investigate how state budget items respond
to business cycle conditions. If a federal balanced
budget amendment were to pass, the federal government would need to find ways to either raise additional
funds or cut expenditures to compensate for the
decline in tax revenues that accompanies downturns.
The assumption that the federal government could
mimic the cyclical behavior of the states is implicit in
the argument that state experience is a valid example
for the federal government. I ask what the states do
and whether the state experience could or should be
mimicked by the federal government.
Data and methodology
To look at how state finances change over the
business cycle, I need data on both business cycle
conditions within a state and on various attributes
of state government finances.
Measuring the business cycle
To measure business conditions in the state,
I use the average monthly state unemployment rate
during the fiscal year for which the state finance data
are collected. For the most part, the analysis focuses
on state fiscal years (FY) 197797. Most states fiscal
year begins on July 1 and ends on June 30. 7 Since
January 1978, the Bureau of Labor Statistics has calculated a monthly unemployment rate for every state
(expect California, first calculated in 1980). Since FY
1979, I calculate the fiscal year unemployment rate as
the average monthly unemployment rate during the
fiscal year. Prior to FY 1979, I calculate the fiscal year
unemployment rate as a weighted average of the
unemployment rates in the state in the two calendar
years that comprise the fiscal years. The weights
depend on the fraction of months for which the fiscal
and calendar years overlap.
While the national business cycle is usually discussed in terms of changes in gross domestic product
(GDP), the unemployment rate is a better measure of
economic conditions in the state than gross state
product (GSP). There are problems concerning the
accuracy of GSP numbers. GSP is gross output minus
the value of intermediate inputs. Evaluating the worth
of intermediate inputs for the same company across
different states is surely a daunting task. While such
transfer pricing issues also arise for GDP, linkages
across nations are both weaker and more carefully
monitored than those across states. The final advantage of the unemployment rate is that during most of
Federal Reserve Bank of Chicago
the period of study, it was measured monthly. This
allows me to calculate a measure that corresponds in
timing to the state financial year. By contrast, GSP is
measured only yearly and is therefore more difficult
to match accurately with the financial data. However,
if I were to use the percentage change in GSP per capita
as the measure of state fiscal condition instead of the
fiscal year unemployment, I would arrive at a set of
results broadly similar to those discussed below.8
Fiscal data
The data I use to measure state financial variables
come from the annual survey of state government
finances conducted by the U.S. Census Bureau (U.S.
Department of Commerce, Bureau of the Census,
197787 and 198897). The survey measures approximately 450 different aspects of state revenues, expenditures, debts, and assets. I use the survey data from
197797; the 1998 data have not yet been released
and the data prior to 1977 are not available in electronic
form. Importantly, this is not accounting data drawn
from state budgets, but is statistical in nature. Budgetary data would not be as comparable across states
or over time. The variables measured over this period
have been relatively consistent. One important exception is that major changes in measurement of debt
occurred in 1988. (Throughout, dollar numbers are in
GDP-deflated 1997 dollars.)
Methodology
In analyzing state fiscal behavior, I look at how a
change in the fiscal year unemployment rate changes
a variable measuring a fiscal outcome. I measure all
fiscal outcomes in per capita terms to make the numbers comparable across states. Throughout, the unit
of analysis is an individual state and states are not
weighted in terms of population. I look at how a 1
percentage point change in the fiscal year unemployment rate (say, a jump from 4.2 percent to 5.2 percent)
affects the per capita measure of a fiscal variable.
Throughout the remainder of the analysis, I omit the
state of Alaska. Alaskas fiscal behavior differs drastically from that of the other 49 states, mainly due to
the revenues Alaska receives from oil production.
I also include a series of state fixed effects. This
allows the average value of a variable to differ across
states. This is especially important when looking at
state expenditure patterns because the role of the
local governments in service provision differs quite
dramatically across states. Importantly, I do not include any measures of the nature or severity of state
balanced budget requirements. One might want to
include these interacted with the unemployment rate
5
to investigate whether fiscal variables in states with
stricter requirements are more responsive to changes
in the unemployment than states with more lax requirements; however, I do not do so here. I believe that
the issuance of debt by all states implies that their
provisions are more similar than different.9 I am more
interested in how all states behave because states as
a whole are perceived as being more fiscally responsible than the federal government. I also include both
a linear and a quadratic time trend to account for the
fact that there was an upward secular trend in state
spending during this entire period.
The regression estimated for each fiscal
variable is:
fiscal variablest
= a + b unemployment ratest
populationst
+ c year -1977 t
1
6
+ d 1year -19776
2
t
+ f state dummiess + e.
In the tables, I only present the coefficient on
the unemployment rate, β. This coefficient can be
interpreted as the effect of a 1 percentage point
increase in the unemployment rate on the per capita
amount of the fiscal variable. Note that the typical
peak to trough difference in the unemployment rate
is greater than 1 percent. For example, the average
fiscal year state unemployment rate rose from 6.0 percent in 1981 to 9.8 percent in 1983. In the milder 1991
recession, the average fiscal year state unemployment rate increased from 5.2 percent in 1990 to 6.7
percent in 1992; it retreated to 5.0 percent in FY 1997.
In some places I compare the behavior of the states
to the behavior of the federal government. To do so, I
use federal data from the Budget of the United States
(U.S. Government, Office of Management and Budget, 1999). This is accounting data,
unlike the state data. In the case of the federal data, I
estimate the same regression presented above, excluding the series of state dummies.
I break the analysis into four partsfirst, I look
at the gap between state expenditures and revenues
(the deficit or surplus); second, at state revenues;
third, at expenditures; and finally, at state indebtedness and asset accumulation. In each section, I look
separately at finances inside and outside the insurance
trust funds run by the states. The states administer a
number of different insurance trust systems, including
employee retirement systems, unemployment compensation, workers compensation, and other smaller funds
(including disability and sickness policies). The budget items outside the insurance trust system are
considered general budget items.10
Responsiveness of the surplus
to the business cycle
Between 1977 and 1997, average state general
fund revenues exceeded average state general fund
expenditures by almost $64 per capita while average
state insurance trust fund revenues exceeded average
state insurance trust fund expenditures by nearly
$189 per capita (see table 1, column 1). While these
calculations imply that states operate with a general
fund surplus on average, this is somewhat misleading
because state expenditure data exclude state payments
into their insurance trust systems. State contributions
to their insurance trust systems average just over
$70 per capita yearly. These contributions are almost
TABLE 1
Per capita budget deficit or surplus, 197797
(dollars)
Average
per capita value
Effect of 1 percentage
point increase in
unemployment rate
Total surplus (revenues – expenditures)
General fund surplus
Insurance trust surplus
252.00
63.50
188.50
–23.03 (6.943)
–10.85 (4.642)
–12.18 (5.822)
General fund surplus net of interest payments
163.87
–10.92 (4.526)
Budget category
Notes: Absolute t-statistics are in parentheses. The final column of each row represents the
coefficient on the unemployment rate in a separate regression. Other variables included in all
regressions are a linear and quadratic time trend, a constant, and a series of state fixed effects.
Source: Author’s calculations from U.S. Department of Commerce, Bureau of the Census, 1977–87 and 1988–99,
State Government Finances.
6
Economic Perspectives
exclusively payments by states into their employee retirement systems. If these intragovernmental transfers
were included as general fund expenditures and insurance trust revenues, the average general surplus would
become slightly negative and the average insurance
trust surplus would increase.
When I run the regression specified above to
look at how state surpluses are affected by changes
in the unemployment rate, I find that a 1 percentage
point increase in the unemployment rate decreases
state surpluses by $23.03 per capita, 11 as shown in
the last column of table 1. This combines a $10.85
($2.34)number in parentheses indicates the standard
errorper capita drop in the general fund surplus with
a $12.18 ($2.09) per capita drop in the insurance trust
surplus. This result suggests that state budgets as a
whole do respond to the business cycle. Below, I investigate the sources of this business cycle variation by
exploring revenues and expenditures separately.
FIGURE 1
Expenditures and revenues, 197797
dollars per capita
Total revenue
Total expenditures
Note: Dollars are measured in 1997 dollars.
Source: Author’s calculations from U.S. Department of
Commerce, Bureau of the Census, 1977–87, Survey of State
Government Finances, Washington, DC: Government Printing
Office, and U.S. Department of Commerce, Bureau of the
Census, 1988–97, Survey of State Government Finances,
available on the Internet at www.census.gov/govs/state/
www.census.gov/govs/state/.
Responsiveness of revenues to
business cycle
Between 1977 and 1997 average state yearly revenues per capita were $2,893. This breaks down into
$2,448 raised by the general fund and $445 raised by
the insurance trust systems. Total revenues per capita were growing rather steadily over the period, from
$2,220 in 1977 to $3,908 in 1997 (see figure 1). These
revenues come from five distinct sources: taxes, intergovernmental transfers from both the federal government and local governments, government charges for
service provision, 12 funds from miscellaneous other
sources including lotteries and property sales, and
contributions to the trust systems run by the state.
Table 2 presents both totals and the breakdown of
average yearly per capita revenues during this period
and the responsiveness of budget items to the unemployment rate. Figure 2 depicts the percentage contribution to total revenues from each of these sources.
The table and figure demonstrate that the great majority of state government funds come from taxes, intergovernmental transfers from the federal government,
and insurance trust contributions.
Overall per capita revenues are somewhat responsive to changes in the fiscal condition in the state as
measured by the state fiscal year unemployment rate.
In particular, as presented in table 2, I find that a 1
percentage point increase in the state unemployment
rate decreases total state revenues by $13.80 ($4.16)
per capita. This combines a $20.08 ($3.47) decrease in
general revenues with a $6.28 ($2.12) increase in the
revenues of the insurance trust funds. The changes
mask considerable variation within the various categories in the budget.
Federal Reserve Bank of Chicago
Taxes
Not surprisingly, taxes are among the most fiscally
sensitive of state revenue sources. Although the lions
share of such revenues comes from sales and income
taxes, state governments also assess license taxes
and taxes on miscellaneous items such as stock
transfers. Table 2 shows the breakdown in per capita
tax revenues into these three categories and their responsiveness to a 1 percentage point change in the
FIGURE 2
State revenue sources, 197797
Miscellaneous
general
7%
Insurance
trust
15%
Taxes
46%
Charges
9%
Intergovernmental
from local
governments 1%
Intergovernmental
from federal
government
22%
Source: Author’s calculations from U.S. Department of Commerce,
Bureau of the Census, 1977–87, Survey of State Government
Finances, Washington, DC: Government Printing Office, and U.S.
Department of Commerce, Bureau of the Census, 1988–97,
Survey of State Government Finances, available on the Internet at
www.census.gov/govs/state/www.census.gov/govs/state/.
7
TABLE 2
Average yearly revenue per capita, 197797
(dollars)
Budget category
Average
per capita value
Effect of 1 percentage
point increase in
unemployment rate
Total revenues
2,892.54
–13.80 (3.313)
General fund revenues
Tax revenues
Sales taxes
Income taxes
Other taxes
Intergovernmental revenues
Federal intergovernmental revenues
Public welfare
Education
Other
State intergovernmental revenues
Charges
Miscellaneous general revenues
2,447.97
1,318.45
662.80
460.83
194.82
649.95
625.70
276.85
111.96
236.88
24.26
261.09
218.47
–20.08
–21.04
–10.90
–10.50
0.36
3.24
2.74
4.51
–1.27
–0.50
0.50
–2.01
–0.26
Insurance trust
Contributions
Investment revenue
Federal unemployment
insurance advances
(5.788)
(8.728)
(7.524)
(7.331)
(0.270)
(2.040)
(1.850)
(4.047)
(4.707)
(0.513)
(1.409)
(2.898)
(0.188)
444.57
223.68
208.22
6.28 (2.958)
0.55 (0.669)
–2.73 (1.390)
12.67
8.46(12.479)
Notes and source: See table 1.
unemployment rate. 13 Some tax revenues are more
sensitive to the business cycle than others. As table
2 indicates, sales and income tax receipts are far more
sensitive to the business cycle than other taxes.
While I find that income and sales taxes are
equally sensitive to the business cycle, I would
expect income taxes to be far more sensitive. This
expectation arises from the fact that while income is
highly sensitive to the unemployment rate, individuals
dip into savings in order to smooth consumption during downturns. As a result of this smoothing, total
sales, and hence sales tax receipts, are not thought to
be as sensitive as income taxes to the business cycle.
The lower than expected income tax numbers can
be explained by the fact that these numbers represent
the change in actual tax collections and do not account
for the fact that states often make statutory changes
in their tax structures to counteract the effects of the
business cycle. In particular, states tend to raise tax
rates during times of economic difficulty and lower
taxes in times of economic strength. In the absence
of such statutory changes, the cyclicality of state
revenues would be more pronounced.14 One potential
8
explanation for the income tax number not being larger
than the sales tax number is that income tax levels are
more often statutorily adjusted than sales tax levels
in response to economic conditions. This conjecture
certainly holds true of the current economic expansion.
In their yearly reports on State Tax Actions from 1995
to 1998, the National Conference of State Legislatures
(NCSL) reported that income tax reductions and, in
particular, reductions in the personal income tax
dominated state tax reduction efforts (NCSL, 1995);
were the primary focus of state tax cuts (NCSL, 1996);
dominated legislative tax actions (NCSL, 1997); and
were the main focus of cuts (NCSL, 1998). In contrast, in most years excise and sales tax changes were
relatively small. In total, the tax reductions put into
effect between 1995 and 1998 reduced state taxes by
a staggering $16.8 billion dollars.
Even though states counteract some of the effects of the business cycle on tax receipts by changing
tax rates, states are still faced with declining resources
during times of economic difficulty. The tax rate
changes do not totally counteract the fiscal effects
of recession.
Economic Perspectives
Intergovernmental revenues
Intergovernmental transfers are the second major
source of state revenue. While states receive payments
from both the federal and local governments, the
amount from the federal government far exceeds the
amount from the local governments (see table 2). As
shown in table 2, intergovernmental revenues are relatively unresponsive to business cycle conditions.
Looking at the breakdown into local and federal intergovernmental revenues yields a similar picture
in both categories per capita revenues increase
slightly when the unemployment rate increases.
To look at the relationship between federal intergovernmental revenues and the business cycle a bit
more closely, I break revenues into three categories
education, public welfare and other. Public welfare
consists of grants for income support and medical
assistance programs. I expect intergovernmental
spending on public welfare revenues to be more cyclically sensitive than spending in the other categories.
The results in table 2 support this picture. Intergovernmental revenues for public welfare increase when
the economy worsens, while spending in the other two
categories declines. Importantly, the welfare reform
legislation passed in 1996 will reduce the cyclicality
of public welfare grants because it replaced an openended matching grant with a fixed block grant.15
Charges
Charges include government fees for service
provision and revenues from the sale of products in
connection with general government activities. For
example, the air transportation measure of charges
includes landing fees at airports and rents for concession stands. I also include the revenues of public
utilities and liquor stores in this category. As is shown
in table 2, revenues from charges only decline slightly
during a downturn.
Miscellaneous revenue sources
Miscellaneous revenue sources consist of monies coming into the state that cannot be easily categorized elsewhere. These include proceeds from special
assessments and property sales and monies from
interest earnings, rents, royalties, fines, forfeits, and
state lotteries. The analysis of miscellaneous revenues
differs from that of other revenue sources because a
major code change in FY 1988 makes a couple of the
subcategories noncomparable before and after this
date. Since 1988, a 1 percentage point change in the
unemployment rate has increased miscellaneous revenues by $4.82 ($2.06), while prior to 1988, a 1 percentage point change in the unemployment rate decreased
revenues by $3.39 ($1.88). (I present the regressions
Federal Reserve Bank of Chicago
for the entire period in table 2 so that the subcategories can add up to the total). The more recent experience suggests that state governments can expect
revenues to go up slightly in the future when the
economy worsens.
One argument regarding how the federal government might adjust its budgeting in order to achieve
budget balance in times of economic stress is that it
might engage in increased sales of public lands
(Eisner et al., 1997). I explore whether the state governments engage in the analogous activity by increasing
property sales during times of high unemployment.
Because the category property sales did not experience a definitional change in 1988, I look at behavior
over the entire sample period.16 I find no evidence of
increased property sales during times of economic
stress. While this does not mean that the federal government, with its far more extensive land holdings,
would not engage in this behavior, it does suggest
that states do not sell property to compensate for
budget shortfalls.17
Insurance trust revenues
Revenues for insurance trust programs come from
three different sources (aside from within the state itself): contributions from employees, contributions
from other governments (both local and federal), and
interest revenues.18 As shown in table 2, overall insurance trust revenues are countercyclical, increasing
$6.28 ($2.13) when the unemployment rate increases
by 1 percentage point.
Not surprisingly, most of the variation within this
category over the business cycle occurs in unemployment compensation. In particular, federal advance
contributions, the amounts credited to the states
when contributions and interest cannot pay unemployment benefits due, increase by $8.46 ($0.68) per
capita when the unemployment rate increases by 1
percentage point. By contrast, contributions and
investment revenues are much less sensitive to the
state of the economy.
Revenue results and implications
During times of economic difficulty, state revenues
drop by about $23 per capita. This drop is mostly
driven by declining tax revenues and in particular by
declining income and sales tax receipts. There are
three principal reasons that this decline is not more
pronounced. First, state income tax rates are often
increased when times are bad. Although this does
not emerge directly from this analysis, the recent
declines in state tax rates highlight this phenomenon.
Second, the states get more money from the federal
government during downturns, particularly in terms
9
of intergovernmental funds for public welfare and
federal advances from the unemployment insurance
system. Third, state governments rely on a number
of income sources that are fairly acyclical. Only 44
percent of state revenues come from taxes and only
15 percent come from the highly sensitive income tax.
By contrast, 53 percent of federal government revenues came from taxes in 1991 and 47 percent came from
income taxes (U.S. Department of Commerce, Bureau
of the Census, 1994).
While state revenues decline in recessions, federal government revenues have historically declined
even more. Between 1977 and 1997, a 1 percentage
point increase in the national unemployment rate
reduced federal government revenues per capita by
$115.75 ($30.00), 2.5 percent of the mean federal revenue level of $4,674.06; by contrast the drop in state
revenues is about 0.8 percent of mean revenues ($23.03
of $2,892.54).
The methods that states use to mitigate this decline, heavier reliance on the federal government, tax
increases, and use of less cyclically sensitive revenue
sources, would not be as readily available to the federal government. Heavier reliance on a higher level of
government is obviously not an option for the federal
government. Tax increases during downturns are a possibility but would aggravate recessions by decreasing
disposable income and consumption during recessions. States are able to increase tax rates because
they are not responsible for the condition of the macroeconomy. Eventually the federal government may
want to seek out less cyclically sensitive revenue
sources. One such possibility would be a national
sales tax that could be less sensitive than the income
tax to downturns.
Because of the super-majority requirement for
revenue increases enshrined in most balanced budget
proposals, it is unlikely that much of the adjustment
in recessions would occur via revenues. Indeed, this
is exactly the point for some proponents of the measurethey seek an amendment that would force
Congress to cut spending during difficult times. Next,
I investigate what happens to state expenditures during recessions.
Responsiveness of expenditures to
business cycle
State government expenditure is divided into
five different categoriescurrent spending, capital
spending, intergovernmental expenditures, interest
on the debt, and insurance trust expenditures. The
breakdown of expenditures is presented in the first
column of table 3 and in figure 3. Like revenues, state
10
per capita expenditures have been steadily increasing
since 1977 (see figure 1).
Overall expenditures are somewhat sensitive to
business cycle conditions, although less so than
revenues. The first row of table 3 shows that a 1 percentage point increase in the unemployment rate
increases overall expenditures by $9.23 ($4.14) per
capita. This is the combination of a $9.23 ($3.75) decline in general fund expenditures with an $18.46
($0.95) increase in insurance trust expenditures. Falling general fund expenditures are more than offset
by rising insurance trust spending.
Current expenditure
Current expenditure represents the biggest portion of state government expenditure at just over half
of the entire category. Current operations include
spending on a vast array of goods and services including transportation, hospitals, state educational institutions, and public welfare.19 As shown in table 3, current
expenditure is rather flat over the business cycle,
increasing by an insignificant amount when the unemployment rate rises.
Breaking current operations expenditures down
by the function they support, I find that during downturns public welfare spending increases, while spending on education (mostly higher education) and other
services falls. The increase in public welfare is not
surprising given that during downturns a greater
fraction of the population relies on the government
for support.
Capital expenditure
Capital expenditure is much more sensitive to the
business cycle than current expenditure. Table 3 shows
that capital expenditure per capita drops by $6.94
($1.23) when the unemployment rate increases by 1
percentage point. This drop is evenly split between
a decline in spending on construction and a decline
in other capital outlay (mostly comprising land and
equipment).20
Given that the benefits of capital projects are less
immediately apparent, spending on capital projects
may be politically easier to cut. In addition, states
have more discretion over capital spending because
it is less likely than current spending to arise from entitlement programs. Capital spending is also naturally
less persistent. Although a state cannot easily close a
university to bring about budget balance, it can slow
down major capital projects or wait to begin new ones.
The role of this reduction in capital spending is
interesting in light of the fact that state capital budgets are outside the operating budgets directly affected by balanced budget restrictions. It suggests that
Economic Perspectives
TABLE 3
Average yearly expenditure per capita, 197797
(dollars)
Average
per capita value
Effect of 1 percentage
point increase in
unemployment rate
Total expenditures
2,640.54
9.23 (2.232)
General fund expenditures
Current operations
Education
Public welfare
Other current operations
Capital expenditure
Construction
Other capital outlay
Intergovernmental expenditures
To school districts
To other local
To federal government
To education
To public welfare
To other
Interest payments on the debt
2,384.47
1,349.71
358.64
404.66
586.41
239.85
192.98
46.88
694.54
386.76
302.19
5.59
464.57
43.42
186.55
100.37
Budget category
Insurance trust expenditure
Unemployment benefits
Other trust payments
256.07
99.23
156.84
–9.23
2.75
–2.43
7.09
–1.91
–6.94
–3.57
–3.37
–4.97
–4.22
–0.77
0.02
–3.74
2.00
–3.23
–0.07
(2.462)
(1.102)
(4.190)
(4.776)
(1.288)
(5.640)
(3.398)
(7.996)
(3.180)
(3.158)
(0.648)
(0.294)
(3.077)
(4.254)
(4.248)
(0.118)
18.46 (19.500)
17.71 (28.736)
0.75 (1.039)
Notes and source: See table 1.
FIGURE 3
State expenditure areas
Interest payments
on the debt 4%
Insurance
trust
10%
Intergovernmental
to other local
governments
11%
Intergovernmental
to school districts
15%
Current
operations
51%
Capital
9%
Source: Author’s calculations from U.S. Department of
Commerce, Bureau of the Census, 1977–87, Survey of State
Government Finances, Washington, DC: Government Printing
Office, and U.S. Department of Commerce, Bureau of the
Census, 1988–97, Survey of State Government Finances ,
available on the Internet at www.census.gov/govs/state/
www.census.gov/govs/state/.
Federal Reserve Bank of Chicago
states reduce pressure on their operating budget
by reducing capital spending. When I compare debt
issuance to capital spending, I find that if all revenues
from debt issuance were spent on capital projects,
only 60 percent of the money for capital projects
would be financed by debt.21 This indicates that
states finance a large portion of capital expenditure
out of current revenues.
Intergovernmental expenditure
States transfer money to local governments and
to the federal government. The great majority of these
funds go to school districts and to general-purpose
local governments, such as county, municipal, and
township governments. Only a small sum is transferred to the federal government. As shown in table 3,
overall intergovernmental expenditures fall when the
economy worsens.
I break up intergovernmental expenditures in two
different ways. First, I divide them by recipient government: school districts, other local governments,
and federal government. Second, I divide them by
11
function: education, public welfare, and other. While
transfers to the federal government and to local governments are relatively flat over the business cycle,
transfers to school districts drop off significantly
when the economy worsens. The functional breakdown yields the same picture, with declines in education spending being the main explanation for the
overall reduction in intergovernmental revenues. By
contrast, as with federal intergovernmental revenues
and current operations, public welfare intergovernmental spending increases during downturns as
states transfer more money to localities to support
swelling public assistance rolls.
Interest expenditures
States pay interest on general debt and interest
on the debts of public utilities, with the general debt
accounting for the bulk of interest paid. As shown in
table 3, interest expenditures are largely acyclical.
Although state debt may increase during difficult
economic times, as explained further below, the stock
of debt and, hence, interest payments are quite flat
over time.
Insurance trust
Insurance trust expenditures are benefit payments
to recipients under the states employee retirement,
workers compensation, unemployment insurance,
and other trust funds. In total, as shown in table 3,
insurance trust expenditures are highly procyclical,
increasing by $18.46 ($0.95) or about 7 percent of the
mean when the unemployment rate increases by 1
percentage point.
Given that unemployment benefits are one source
of insurance trust expenditures, the size of this increase
is not surprising. During times of high unemployment,
unemployment benefit benefits greatly increase. In
fact, all of the increase in insurance trust spending
that occurs when unemployment is high can be attributed to increases in spending for unemployment benefits.
Expenditure results and implications
During times of economic difficulty, states are
able to decrease their general fund expenditures by
$9 per capita in spite of increasing pressure on public
welfare spending. States do this in three ways: They
decrease higher education current expenditure; they
drastically reduce capital expenditure; and they cut
the funds going to school districts.
The implications of this for the federal government are mixed. There is no reason to believe that the
federal government would not be able to cut current
expenditure in some areas in response to recessions.
While the size of federal government entitlement
12
programs limits government flexibility, the federal
government has some areas of responsibility that are
akin to state governments higher education responsibilities. The most obvious area is that of education,
training, employment, and social services, but cuts in
other areas would also be possible.
The states ability to decrease capital spending
is important in helping them to achieve budget balance.
In fact, the drop in state capital spending almost totally
offsets the increase in current public welfare expenditure brought about by a 1 percentage point increase
in the unemployment rate. However, whether the federal budget would or should follow the states lead in
this arena is a difficult question. Some of the same
factors causing the states to decrease capital spending during recessions may also affect the federal government. In particular, because capital spending has
current costs and longer term benefits, cuts in capital
spending may be politically easier to swallow than
cuts in federal spending on education or job training.
In addition, the absence of a federal capital budget
may make federal capital spending even more responsive to economic conditions. It is possible that states
do not reduce their capital spending further because
they can issue debt for capital projects. Therefore,
their ability to alleviate general budget pressures is
limited by the portion of capital spending that is being
financed by current revenues.
However, there is one important reason that federal capital spending may not be as susceptible to the
business cycle as state capital spending. While the
majority of state capital spending is for highways and
higher education, projects that may be easy to delay,
the great majority of federal capital expenditure goes
to finance defense. Between 1977 and 1997, 82 percent
of the money spent on direct federal capital expenditure was used for defense.22 In no year did defense
spending drop below 70 percent of total direct capital
expenditure. It seems unlikely that federal defense
spending would or should be a function of business
cycle conditions. A brief glance at the numbers demonstrates that, historically, defense capital spending
has been more a function of the political climate and
whether the nation is at war than of the unemployment
situation. For example, from 194346, at the height of
U.S. involvement in World War II, defense capital
goods represented about 99 percent of federal capital
expenditure on average. The federal government
could cut capital spending in other areas, but nondefense capital spending is a very small part of the budgetaveraging only 1.6 percent between 1977 and
1997 (total capital spending averaged 9 percent of the
federal budget over the same period).
Economic Perspectives
In addition to reducing current spending for education and capital expenditure, state governments
reduce overall intergovernmental grants, especially
those to school districts. In general the states take
advantage of their unique position in the intergovernmental structure by procuring additional grants
from the federal government while sending less money to the local governments. The federal government
could follow the states lead here by reducing intergovernmental expenditures to the states during times
of economic stress. While this may improve the federal governments budgeting position, it would make
it more difficult for the states to balance their budgets.
Part of the reason state governments are able to come
close to balancing their budgets is that the federal
government does not achieve a balanced budget.
The federal government could not avail of the
overall expenditure strategy relied on in the states
because of its unique responsibility to provide for
national defense. By contrast, the federal government
may be able to follow the states lead in cutting current
expenditure and in cutting grants to lower levels of
government. The wording of the federal balanced
budget amendment implies that the government would
need to cut spending to compensate for the entire
drop in revenues. However, state governments have
an important safety valve in their ability to issue debt
to fund capital projects. Next, I investigate the extent
to which they take advantage of this safety valve.
What happens to debt and assets?
The combination of the revenue and expenditure
pictures for both the general and insurance trust funds
is not very consistent with the common notion of
budget balance. During difficult times, general fund
revenues fall more than expenditures, and trust fund
expenditures increase more than revenues. This implies that states must either deplete assets or issue
debt when the economy deteriorates. In other words,
their net asset position must worsen. Below, I look
at what happens to state debt issuance and state
reserve funds, both inside and outside the insurance
trust system.
Short-term debt
Short-term debt is issued to account for unexpected shortfalls. This category includes debt payable
within one year of issuance or debt backed by taxes
to be collected in the same year. It includes items
such as tax anticipation notes and short-term warrants
and obligations, but excludes accounts payable and
similar less formal non-interest-bearing obligations.
States that are not allowed to carry over deficits still
Federal Reserve Bank of Chicago
sometimes have short-term debt in the form of tax
obligation notes and similar liabilities.
The Census Bureau only collects two short-term
debt items (in stark contrast to the approximately 50
different measures of long-term debt)the amounts
outstanding at the beginning and the end of the fiscal
year. I use the amount outstanding at the end of the
year; given that most short-term debt has a maturity
of under one year, this is a reasonably good proxy for
issuance. 23 As table 4 shows, short-term debt is fairly
responsive to the business cycle, increasing by about
$2.41 ($0.56) for a 1 percentage point increase in the
unemployment rate. However, this only goes part of
the way in explaining how states finance the growing
gap between revenues and expenditures during
downturns. States also rely on additional long-term
debt issuance.
Long-term debt and government assets
Because long-term debt and asset data before
and after 1988 are not comparable (due to a classification change in 1988), I use data from 1989 onwards.
State government long-term debt and asset data are
far more complicated than other financial data for
three main reasons. First, over 40 percent of state
government debt is public debt for private purposes. This debt is issued using the tax-exempt status
of state governments to finance expenditures by private firms. I analyze this debt separately from government purpose debt.24 Second, not all debt issuance
funds contemporaneous expenditures. Some debt is
issued to refund previously issued debt. Because a
lot of state debt is callable (that is, it can be redeemed
prior to maturity for a prespecified premium), when
interest rates are falling, states can realize savings if
they call debt and refund it at a lower interest rate.
Because I am interested in debt issuance that contributes to the states concurrent fiscal situation, I would
ideally like to look only at new government purpose
debt issued, that is, net of refunding. Unfortunately,
I cannot do this because debt issued for refunding
cannot be separated into public and private purpose
debt. Third, an analysis of debt cannot be separated
from an analysis of government assets because two
of the three state government asset measures are
directly related to debt. The sinking fund contains
money explicitly saved for debt redemption, while
the bond fund contains the proceeds of bond issuance prior to disbursement. Only the other funds
category contains assets not explicitly linked to debt.
Because these assets are all stocks rather than flows,
I look at the change in value per capita from one
year to the next as the appropriate measure of government assets.25
13
TABLE 4
Debts and assets, 198997
(dollars)
Budget category
Short-term debt, 1977–97
Outstanding at end
Long-term debt, 1989–97
Issuance
Governmental purposes
Private purposes
Refunding
Redemption/retirement
Governmental purposes
Private purposes
Retired by refunding
Government assets, 1989–97
Change in sinking fund
Change in bond fund
Change in other funds
Insurance trust assets, 1978–97
Change in employee retirement
Change in unemployment insurance
Change in worker’s compensation
Change in other trust assets
Average
per capita value
Effect of 1 percentage
point increase in
unemployment rate
14.94
2.41 (4.299)
155.86
145.37
37.50
16.06 (2.604)
10.90 (1.755)
10.89 (2.680)
104.77
109.64
36.11
18.99 (4.228)
8.26 (1.815)
9.93 (2.619)
–8.10
0.71
35.83
–10.97 (2.553)
–7.51 (2.432)
3.61 (0.489)
183.01
7.43
8.35
0.11
2.84 (0.466)
–8.54 (7.730)
–0.33 (0.268)
0.04 (0.524)
Notes and source: See table 1.
Table 4 shows the relationship between the state
unemployment rate and the state long-term debt issuance, redemption, and asset measures. The first thing
to notice is that all measures of debt issuance increase
significantly during downturns. Because nearly all
long-term debt is used to finance capital projects and
because capital spending drops off quite significantly during downturns, the increase in debt issuance
suggests that state governments finance a higher percent of their capital spending with debt during recessions. This implies that states use debt issuance as
an important safety valve during recessions. The decrease in the state bond fund, also shown in table 4,
supports this finding. Although states spend less on
capital projects, they both draw down unspent monies
from previous bond issuance and issue more bonds.
As with issuance, all three measures of debt
redemption also increase during downturns (also in
table 4). This result is more intuitive than it may appear
when combined with the information on the change
in the value of the sinking fund.26 States redeem more
debt during downturns, but it appears that this extra
money is coming from a combination of debt refunding
14
(which increases by $9.93 per capita) and a drop in
the value of the sinking fund (which decreases by
$10.97 per capita) rather than from current revenue
sources. The transfers from the sinking fund probably
occur because of cyclical changes in financial market
conditions. In particular, states have an incentive to
pay off debt using sinking fund assets when they are
paying more interest on existing debt than they are
receiving from fund assets. In short, during good
times, states accumulate assets in their sinking funds
that are then spent to call bonds when the economy
worsens and interest rates fall. Finally, there is no
evidence of changes in the assets of non-bondrelated funds.
Assets of the trust funds
One of the most frequently articulated worries
about a balanced budget requirement is that it would
lead to the depleting of social security reserves in
a downturn. Do state government deplete the assets
of state managed trust funds in downturns? I look
at the change in the assets of all four types of government trust fundsemployee retirement, workers
Economic Perspectives
compensation, unemployment insurance, and others.
The employee retirement trust fund is the only one
that is directly comparable to social security. The other funds, particularly the unemployment insurance
trust fund, are supposed to fall during recessions.
Table 4 shows that there is little evidence of systematic raiding of the trust funds. While state unemployment insurance trust funds decline dramatically
during downturns, there is no evidence that the assets
of other trust funds fall.
Debt and assets results
I find that states issue more short-term and longterm debt during recessions. As mentioned above, the
federal balanced budget amendment does not allow
any new debt issuance short of a super-majority
vote. Therefore, this avenue would not be open to
the federal government. Instead, the federal government would be compelled to find areas in which to
cut spending in order to confront revenue declines.
Conclusion
Both state and national balanced budget supporters frequently cite the experience of the states to demonstrate the feasibility of a federal balanced budget
amendment. State governors and U.S. presidents alike
have claimed that the state experience is a relevant
example to the federal government. In this analysis of
the way that state budgets respond to the business
cycle, I find few examples of methods for budget balance used by the states that are directly relevant to
the federal government. This is the case for four principal reasons.
First, state balanced budget requirements differ
in one major way from the amendment currently contemplated at the federal level. State governments can
and do issue both short-term and long-term debt to
finance shortfalls and capital projects, respectively.
The states are able to issue long-term debt because
state capital projects are outside the restrictions
imposed by the balanced budget amendments.
Second, despite the fact that state capital budgets
are separate, states cut capital spending quite drastically during downturns in order to relax budgetary
pressures. The current costs and delayed benefits of
capital spending make it politically easier to cut. The
federal government may not find capital spending so
easy a target because most federal capital spending
is for defense.
Third, states take advantage of their unique position in the federal system to cut funds going to local
governments while drawing on increased funds from
the federal government. The federal government can
not draw down more money from a higher level of
government, but could potentially decrease the money
it sends to the states.
Finally, states increase tax rates during downturns and decrease them during booms. The states
are able to engage in this behavior because, unlike
the federal government, they are not perceived as
being responsible for the macroeconomy.
Overall, the state experience with budget balance
and business cycles is not a very relevant model for
the federal government. State governors are not responsible for the macroeconomy or for national defense
and, in general, confront a more relaxed budget restriction than that proposed for the federal government.
Policymakers need to consider carefully how budget
balance at the federal level could be achieved during
an economic downturn under a balanced budget
restrictionfor example, which taxes could be increased, which programs could be cut, or which
assets could be sold.
NOTES
Briffault (1996) provides an interesting set of quotations
suggesting that the state experience is relevant to the federal
government.
1
For a further discussion of limits on long-term debt, see
McGranahan (1999b).
5
These comparisons actually underestimate the difference
between the states and the federal government because, while
the federal numbers are net of trust fund interest revenues, the
state numbers are gross. I do not net out state interest revenues
because the definition of interest revenues changed in 1988 to
include revenues from public debt for private purposes. Therefore, it is impossible to calculate a net number for the states
that is consistent over time. The gross numbers for the federal
government would be 18 percent for expenditures and 21 percent for revenues.
6
The National Association of State Budget Officers (1997)
states that 40 of 48 states that responded to a survey report
that their capital planning occurs in a capital budget.
2
The exact definition of what capital spending consists of differs
by state. This is the most common definition.
3
Forty-eight states have either a constitutional or statutory
balanced budget requirement. One state that does not is not
permitted to carry over deficits. These combine to generate
the frequently cited figure that 49 states have balanced budget
restrictions. The exception is Vermont.
4
Federal Reserve Bank of Chicago
The year refers to the calendar year in which the fiscal year ends,
so fiscal 1999 ended in most states on June 30, 1999. Some states
7
15
have different fiscal years. I take these differences into
account when calculating the fiscal year unemployment rate.
One disadvantage of using the unemployment rate is that it
is often viewed as a lagging indicator of economic activity.
Contributions by the state to its own insurance trust systems
are considered within government transfers and do not enter
the revenue tabulations.
18
8
For a discussion of the effects of different balanced budget
restrictions in the states, see Poterba (1994).
9
This division is analogous to the separation between onbudget and off-budget in the federal context, because the federal
budget excludes most social security funds.
I include spending on assistance and subsidies in the current
expenditure category. It is only a small portion of total current
expenditure. In published Census tables, assistance and subsidies
(which include scholarships, veterans benefits, and some welfare
payments) are usually presented separately.
19
10
With a standard error of $3.32; note that table 1 shows
t-statistics rather than standard errors.
11
I include receipts of utilities and liquor stores run by the state
in charges. In Census Bureau statistics, these are treated separately. They are generally very small and do not warrant separate treatment.
12
Sales taxes refer to all sales and gross receipt taxes, including
general sales, gas, and tobacco taxes. Income taxes refer to
both individual and corporate income tax collections.
13
For a discussion of tax revenue changes taking statutory
changes into account, see Dye and McGuire (1998).
14
15
For further discussion of this issue, see McGranahan (1999a).
The classification manual defines property sales as amounts
received from sale of real property, buildings, improvements
to them, land easements, rights-of-way, and other capital assets
(buses, automobiles, etc.), including proceeds from sale of
operating and nonoperating property of utilities. Includes
sale of property to other governments.
16
Interestingly, the historical relationship between federal
property sales and the unemployment rate has been negative,
indicating that the federal government sells less when the
economy is bad.
There were some minor changes in coding of some of the
capital outlay variables in 1988. Looking only at data from
after this change yields very similar conclusionscapital
expenditure falls off, mostly driven by changes in spending
on equipment and existing land and structures.
20
The 60 percent number represents the average of debt issuance
divided by capital spending from 198897. Debt issuance
excludes debt for private purposes but is not net of refunding.
21
Direct capital expenditure excludes grants. Many grants are
to state governments for highways and other programs.
22
The U.S. Department of Commerce, Bureau of the Census
(1995) reports that obligations having no fixed maturity date
(even where outstanding for more than one year if payable
from a tax levied for collection in the same year it was issued)
are included in short-term debt.
23
The major reclassification in 1988 pertains to changes in
the categorization of public debt for private purposes. Prior
to 1988 it is not possible to fully separate it from other debts.
The spending supported by public debt for private purposes
does not show up in the states expenditure measures.
24
This is not the per capita change, but the change per capita
where the population is the population in the second year.
25
17
I subtract the value of public debt for private purposes outstanding from the sinking fund numbers to account for the fact
that the value of collateral pledged for private purpose debt is
included in the sinking fund numbers.
26
REFERENCES
Bond Market Association, The, 1999, Daily report of
municipal bond transactions available on the Internet
at www.investinginbonds.com/, accessed April 20.
Branstad, Terry E., 1997, Balancing the budget:
What Washington can learn from the states, Heritage
Lecture, No. 586, available on the Internet at www.
heritage.org/library/categories/budgettax/hl586.html,
May 13.
Briffault, Richard, 1996, Balancing Acts: The Reality
Behind State Balanced Budget Requirements, New
York: The Twentieth Century Fund Report.
Dye, Richard F., and Therese J. McGuire, 1998,
Block grants and the sensitivity of state revenues to
recession, in National Tax Association Proceedings
of the Annual Conference on Taxation, Washington,
DC, pp. 1523.
16
Eckl, Corina, 1998, States broaden the scope of
rainy day funds, Washington, DC: National Association of State Legislatures, available on the Internet
at www.ncsl.org/programs/fiscal/rdf97.htm.
Eisner, Robert, with Robert M. Solow, and James Tobin, 1997, Petition in opposition to Balanced Budget
Amendment, in Economists Oppose the Balanced
Budget Amendment, Max Sawicky (lead contributor),
Internet discussion board of Communications for a
Sustainable Future, available at http://csf.colorado.
edu/mail/pkt/jan97/0338.html, January 16.
Engler, John, 1997, Text of the State of the State
address, The Detroit News, available on the
Internet at http://detnews.com/1997/metro/9701/29/
01290057.htm, January 29.
Economic Perspectives
Illinois, State of, 1970, Constitution of the State of
Illinois, adopted at special election on December 15,
available on the Internet at www.legis.state.il.us/
commission/lrb/conmain.htm.
Keating, Frank, 1997, The State of the State, available on the Internet at www.oklaosf.state.ok.us/
osfdocs/sos97.html, February 3.
McGranahan, Leslie, 1999a, Welfare reform and state
budgets, Chicago Fed Letter, Federal Reserve Bank
of Chicago, No. 137, January.
__________, 1999b, Voter preferences for capital
and debt spending: Evidence from state debt referenda, Proceedings of the Ninety First Annual Conference on Taxation, Washington, DC: National Tax
Association, forthcoming
National Association of State Budget Officers, 1997,
Capital budgeting in the states: Paths to success,
available on the Internet at www.nasbo.org/pubs/
capbud97/capbud97.htm/.
National Conference of State Legislatures (NCSL),
1998, State Tax Actions 1998, Washington, DC:
National Conference of State Legislatures, available
on the Internet at www.ncsl.org/programs/fiscal/
sta97sum.htm, accessed April 1, 1999.
__________, 1997a, Capital Budgeting in the
States, Washington, DC: National Association of
State Budget Officers, September.
__________, 1997b, State Tax Actions 1997, Washington, DC: National Conference of State Legislatures,
available on the Internet at www.ncsl.org/programs/
fiscal/sta97sum.htm, accessed April 1, 1999.
Poterba, J., 1994, State responses to fiscal crises: The
effects of budgetary institutions and politics, Journal
of Political Economy, Vol. 102, No. 4, pp. 799821.
Snell, Ronald K., 1999, State balanced budget requirements: Provisions and practice, National Conference of State Legislatures Fiscal Letter, available
on the Internet at www.ncsl.org/programs/fiscal/
0796fl.htm.
U.S. Department of Commerce, Bureau of the Census, 1999, Governments Finance and Employment
Classification Manual, Washington, DC, available
on the Internet at www.census.gov/govs/www/
class.html/.
__________, 1998, 1997 State Government Finance
Tables by State, available on the Internet at
www.census.gov/govs/www/stsum97.html.
__________, 1994, Government Finances: Summary
of Federal Government Finances1991 to 1994,
available on the Internet tat www.census.gov/govs/
fedfin/federal.txt.
__________, 1990, State Government Finances in
1989, Washington, DC: U.S. Government Printing
Office, Series GF-89-3.
__________, 198897, State Government Finances,
available on the Internet at www.census.gov/govs/
state/.
__________, 197787, State Government Finances,
Washington, DC: U.S. Government Printing Office,
electronic data provided by the Census Bureau Governments Division, Series GF-Year-3.
__________, 1996, State Tax Actions 1996, Washington, DC: National Conference of State Legislatures,
available on the Internet at www.ncsl.org/programs/
fiscal/STAEX.HTM, accessed April 1, 1999.
U.S. Government, Office of Management and Budget,
1999, Budget of the United States government, fiscal
year 2000, historical tables, Washington, DC: U.S.
Government Printing Office, available on the Internet
at www.access.gpo.gov/usbudget/fy2000/.
__________, 1995, State Tax Actions 1995, Washington, DC: National Conference of State Legislatures,
available on the Internet at www.ncsl.org/programs/fiscal/STA95P1.HTM, accessed April 1, 1999.
U.S. Senate, 1997, S.J. Res. 1, proposing an amendment to the Constitution of the United States to
require a balanced budget, available on the Internet
at http://thomas.loc.gov/, accessed April 19, 1999.
Federal Reserve Bank of Chicago
17
Birth, growth, and life or death of
newly chartered banks
Robert DeYoung
Introduction and summary
Thousands of new commercial banks have been chartered in the U.S. over the past two decades. As the
U.S. banking industry continues to consolidate, these
de novo banks are potentially important for preserving competition and providing credit in local markets.
However, like other new business ventures, newly
chartered banks initially struggle to earn profits, and
this financial fragility makes them especially prone to
failure. In this article, I document the financial evolution of the typical de novo bank and develop and test
a simple theory of why and when new banks fail.
Recent decades have seen an upsurge in the number of mergers and failures among new banks. Figure 1,
panel A shows the annual change in the number of
commercial bank charters in the U.S. since 1966. Prior
to 1980, the reduction in bank charters due to mergers
and failures was relatively stable at about 100 charters
per year, or about 1 percent of the industry total (figure 1, panel B). The pace accelerated greatly after 1980,
and since 1986 about 600 charters, or 5 percent to 6
percent of the industry total, have disappeared each
year due to mergers and failures.
To a large extent, this tremendous consolidation
can be explained by the repeal of federal and state
laws that restricted branch banking and interstate
banking. As these restrictions gradually were relaxed,
banking companies expanded their geographic reach
by acquiring thousands of other banks, and reduced
their overhead expenses by converting thousands of
affiliate banks into branch offices. This geographic
expansion, combined with newly deregulated deposit
rates, increased competition between commercial banks
just when new information technology was allowing
mutual funds, insurance companies, and the commercial paper market to compete for banks traditional loan
and deposit businesses. Under these new competitive
conditions, many commercial banks became more vulnerable to economic downturns, and thousands of
18
banks failed during the 1980s and early 1990s. Over the
past two decades, the combined effect of these mergers and failures has reduced the number of commercial
banks in the U.S. by nearly 40 percent.
This consolidation has been partially offset by
a recurring wave of new bank charters. As shown in
figure 1, panel A, over 3,000 de novo commercial banks
have been chartered by state and federal banking authorities since 1980. It is generally believed that these
newly chartered banks can help restore competition
in local markets that have experienced a large amount
of consolidation. It is also commonly believed that
these newly chartered banks can help replace credit
relationships for small businesses whose banks failed
or were acquired or reorganized. However, before a
newly chartered bank can provide strong competition
for established banks and before it can be a dependable
source of credit for small businesses, it must survive
long enough to become financially viable.
I begin by examining the conditions under which
investors are likely to start up new banks, including
the influence of business cycles, merger activity in
local banking markets, and the policies of federal and
state chartering authorities. Next, I track the evolution
of profits, growth rates, capital levels, asset quality,
overhead costs, and funding mix at more than 1,500
commercial banks chartered between 1980 and 1994.
These data suggest that newly chartered banks pass
through a period of financial fragility during which
they are more vulnerable to failure than established
Robert DeYoung is a senior economist and economic
advisor at the Federal Reserve Bank of Chicago. The
author thanks Iftekhar Hasan and Curt Hunter for their
advice; Richard Cahill, Philip Jackson, and participants at a Federal Reserve Bank of Chicago seminar for
helpful comments; Eli Brewer and David Marshall for
reading an earlier draft of this article; and especially,
Nancy Andrews for outstanding data support.
Economic Perspectives
FIGURE 1
Entry and exit of commercial banks
A. Change in number of U.S. commercial bank charters
number
New charters
Failed banks
Merged banks
B. Change in number of U.S. commercial bank charters, as a percent of total charters
percent
New charters
Failed banks
Merged banks
Source: Federal Deposit Insurance Corporation, 1966–98, “Change in number of insured commercial banks,”
available on the Internet at www2.fdic.gov/hsob/.
banks. Specifically, new bank capital ratios quickly
decline to established bank levels, but new bank
profits improve more slowly over time before attaining
established bank levels.
Based on these empirical observations, I develop
a simple life-cycle theory of de novo bank failure, in
which the probability of failure at first rises, and then
declines with the age of the new bank. I use hazard
function analysis to test this simple theory for 303
new commercial banks chartered in 1985, just as the
wave of bank failures shown in figure 1 was picking
up steam. The tests offer support for the simple theory.
On average, the results suggest that newly chartered
banks are less likely to fail than established banks
during the first few years of their lives; however, new
banks quickly become substantially more likely to fail
than established banks; and, over an extended period
of time, new bank failure rates gradually converge to
the failure rates of established banks.
What are the implications of these results for
bank supervision and bank competition policy? The
results suggest that the policies in place during the
1980s successfully insulated new banks from economic
Federal Reserve Bank of Chicago
disruptions early in their lives, but were less successful in preventing new banks from failing after the initial years. Clearly, de novo bank failure rates could be
reduced by requiring investors to supply higher
amounts of start-up capital or by requiring banks to
maintain extranormal capital-to-asset ratios in the early
yearsindeed, the latter policy option was adopted
by federal bank supervisors during the 1990s. However, failure-proofing de novo banks is not an optimal
policy. The social costs of small bank failure are relatively low, and setting higher capital requirements
would at some point discourage investment in new
banks and thereby limit the competitive benefits of
de novo entry.
Birth of new banks
As illustrated in figure 1, panel A, the number of
new banks started up each year has ebbed and flowed
over the past three decades. There are a number of
explanations for these patterns. Like all new business
ventures, new banks are more likely to form when
business conditions are good. For example, new bank
charters bulged to well over 250 per year during the
19
general economic expansion of the mid-1980s. This
high rate of bank start-ups also coincided with the
relaxation of unit banking laws in a number of states,
laws that had prevented banking companies from
operating affiliates in multiple locations. The steady
decline in new charters during the late 1980s and early
1990s, which bottomed out at about 50 new banks per
year, also had multiple causes. Difficult times in regional
banking markets made new bank start-ups unprofitable in many regions (bank failures reached their peak
in 1988), and a national recession in the early 1990s
reinforced this trend. New bank charters have been
on the increase since then, reaching over 100 per year
in 1997 and 1998, in large part due to the extended
economic expansion of the 1990s.
Conditions in local banking markets also influence
bank start-ups. Moore and Skelton (1998) find that
there are more de novo banks 1) in markets that are
experiencing healthy economic growth, 2) in highly
concentrated banking markets in which competition
among existing banks is weak, and 3) in markets where
small banks are under-represented and, hence, small
businesses are not being adequately served. These
results imply that new banks will be more likely to start
up in local markets where mergers have reduced the
number of competing banks, and where the resulting
market power has reduced the level of banking services. In such markets, new banks should receive a
profitable welcome from customers unhappy with
paying high prices for financial services or from businesses whose credit relationships were disrupted
when their bank was acquired or failed. Researchers
only recently began investigating these phenomena,
so there is not yet a consensus on the results. In a
study of de novo bank entry in all U.S. markets between 1980 and 1998, Berger, Bonime, Goldberg, and
White (1999) find that the probability of de novo entry
is higher in local markets that have experienced mergers
or acquisitions during the previous three years, particularly mergers and acquisitions involving large banking organizations. In contrast, Seelig and Critchfield
(1999) find that local market entry by acquisition deters
entry by de novo banks and thrifts.1 Their results
are based on a study of de novo banks and thrifts
between 1995 and 1997, a time when banking conditions were exceptional and restrictions on geographic
mobility were virtually nonexistent.
Differences in the policies of the legal authorities
that grant commercial bank charters can also affect the
rate and location of new bank start-ups. A de novo
national bank receives its charter from the Office of
the Comptroller of the Currency (OCC), while a de novo
state bank receives its charter from the banking
20
commission of the home state. The OCC has historically been more liberal in granting charters than most
state authorities. Its policy has been that market forces,
not the chartering authority, should determine which
local markets need and can support new commercial
banks. In contrast, many state chartering authorities
have historically applied convenience and needs tests
when considering applications for new bank charters,
denying applications if they judge that the convenience and needs of the banking public are already
adequately served. Although this federalstate difference in chartering philosophy has diminished over
time, DeYoung and Hasan (1998) find that national
banks were chartered with greater frequency than
state banks during the 1980s and early 1990s, and that
the financial performance of de novo national banks
initially lagged that of de novo state chartered banks.2
This suggests that national banks chartered during
the 1980s were likely to have had a higher probability
of failure than newly chartered state banks operating
under similar economic and market conditions.
A concern shared by all chartering authorities is
that newly chartered banks start out with enough
equity capital to survive through the several years
of negative earnings and rapid asset growth that is
typical of de novo banks. The dollar amount of startup financial capital required for approval might be $3
million, $10 million, or even as much as $20 million, depending on the proposed location and business plan
of the prospective bank. Larger amounts of start-up
capital are generally required for urban banks, for
banks locating in vibrant economic markets, and for
banks with business strategies that feature fast growth
(for example, a new Internet bank).
Once a new bank opens its doors for business,
regulatory scrutiny shifts from the applications staff
to the examination staff. Bank supervisors pay closer
attention to newly chartered banks than to similarly
situated established banks, although the difference in
treatment varies depending on the new banks primary regulator. Federal Reserve supervisors will conduct
full scope examinations for safety and soundness at
a newly chartered bank at six-month intervals (established banks are examined every 12 to 18 months) and
will continue to schedule exams at this frequency
until the bank receives a strong composite CAMEL
rating (that is, a rating of 1 or 2) in two consecutive
exams. The Federal Deposit Insurance Corporation
requires that all newly chartered state and national
banks maintain an 8 percent tier 1 equity capital-to-riskbased assets ratio for their first three years of operation, while the Federal Reserve requires new state
chartered Fed member banks to hold this ratio above
Economic Perspectives
9 percent for three years. These temporary extranormal capital requirements for new banks (the tier 1
requirement for established banks to be considered
adequately capitalized is only 4 percent) are a relatively recent supervisory response to de novo failure
experience of the 1980s. Bank supervisors also prohibit
new banks from paying out dividends for several
years and, in some cases, require new banks to maintain minimum levels of loan loss reserves.
Evolution of new banks
Relatively few research studies have examined
how banks grow and evolve in the years immediately
after they receive their charters.3 Brislin and Santomero
(1991) show that the financial statements of a new
bank can fluctuate rapidly and dramatically during its
first year. A handful of studies have examined how the
profitability of de novo banks grows over time (for example, Hunter and Srinivasan, 1990, and DeYoung
and Hasan, 1998). Another strand of research documents how small business lending becomes less important to de novo banks as they mature (for example,
DeYoung, Goldberg, and White, 1999). In this section,
I analyze how a broad group of de novo bank characteristics not typically considered in the literature evolve
over time, including de novo bank profits, growth rates,
capital ratios, sources of income, financing mix, overhead ratios, and loan quality.
Each of the eight panels in figure 2 examines a
different financial ratio and compares its average value for a sample of de novo commercial banks to its average value for a sample of established commercial
banks. The de novo bank sample includes 4,305 observations of commercial banks that were chartered between 1980 and 1994, were between one and 14 years
old when they were observed, and were located in
urban banking markets. The established bank sample
includes 4,305 observations of commercial banks that
were at least 14 years old when they were observed,
operated in urban banking markets, and were similar
to the de novo banks in terms of asset size. These
two samples of banks were originally constructed by
DeYoung and Hasan (1998). Box 1 contains additional
details about the two bank samples.
To construct each of the graphs in figure 2, I divided the de novo banks into 14 separate age groups
(one-year old banks, two-year old banks, etc.). I then
calculated the median average for the financial ratio
in questionsay, return on assets (ROA)for each
age group. Plotting these 14 average values in chronological order creates a time path showing how ROA
evolves as the typical de novo bank matures. Finally,
I superimposed the value of ROA at the 25th, 50th,
Federal Reserve Bank of Chicago
and 75th percentiles of the established bank sample
as horizontal lines over the de novo bank time path.
These horizontal lines serve as maturity benchmarks
against which to compare the progress of de novo
banks over time. The rate at which the de novo time
path converges with the maturity benchmarks indicates the speed at which the de novo banks mature.
While each of the individual graphs in figure 2
has a straightforward interpretation when considered
in isolation, these eight panels reveal a richer story
when they are interpreted in conjunction with each
other. For example, by itself the return on assets (ROA)
graph (panel A) merely confirms the results of existing
studies of de novo bank profitability, that is, that the
typical new bank loses money until it is about 18
months old and continues to underperform the average established bank for about a decade. But when
the ROA graph is considered together with the assetgrowth (panel B) and equity-to-asset (panel C) graphs,
a simple theory of de novo failure begins to emerge.
De novo banks average an extraordinary 20 percent
annual rate of growth during the first three years of
their lives. While this fast growth rate is increasing
the amount of assets against which new banks need
to hold equity capital, the losses suffered during the
first and second years of these banks lives are depleting their equity capital. Despite initially high capital
levels, the equity-to-asset ratio of the typical new
bank declines very quickly, entering the established
bank range after just three years. Thus, panels A, B,
and C suggest the probability of failure should increase as new banks pass their third year of life
their capital has declined to established bank levels
by year three, but their asset growth and profitability
do not converge with those of established banks
until at least year ten.
The remaining five panels in figure 2 are consistent with the simple theory of de novo bank failure
suggested by the ROA, asset growth, and equity-toasset panels. For example, newly chartered banks initially have almost no nonperforming loans (panel D).
This is because these banks loan portfolios are composed disproportionately of unseasoned loans made
recently to borrowers who demonstrated strong financial fundamentals. However, as time passes some
of these new borrowers will naturally run into trouble,
and the quality of de novo banks loan portfolios will
naturally decline. This happens quite quickly for the
typical de novo bank, as its level of nonperforming
loans rises slightly above the median level for established banks after three yearsjust as de novo
banks are depleting their excess capital cushions and
well before new bank profitability rates have matured.
21
FIGURE 2
Financial ratio time paths for de novo banks
A. Return on assets
B. Annual asset-growth rate
percent
percent
years
years
C. Equity-to-asset ratio
D. Ratio of nonperforming banks
percent
percent
years
years
E. Ratio of interest-bearing assets
F. Fee income ratio
percent
percent
years
years
G. Ratio of large deposits
H. Accounting efficiency ratio
percent
percent
years
years
Notes: The data are described in box 1. The three colored horizontal bands are maturity benchmarks that indicate the twenty-fifth, fiftieth, and seventyfifth percentiles of the distribution of the ratio in question for the established bank sample. The black line plots the median value of the ratio in
question for the banks of various ages in the de novo bank sample. Return on assets is net income divided by total assets. Annual asset-growth rate
is the percent increase in total assets over the previous year-end total. Equity-to-asset ratio is the book value of equity divided by total assets. Ratio
of nonperforming loans is loans past due 90 or more days plus nonaccruing loans divided by total loans. Ratio of interest-bearing assets is total
performing loans plus total securities divided by total assets. Fee income ratio is noninterest income divided by net interest income plus noninterest
income. Ratio of large deposits is deposits in accounts greater than $100,000 divided by total deposits. Accounting efficiency ratio is noninterest
expense divided by net interest income plus noninterest income.
Source: National Information Center, 1988, 1990, 1992, and 1994, “Report of income and condition,” selected banks, December 31.
22
Economic Perspectives
The slow rate at which de novo bank profitability
improves appears to be attributable more to cost factors
than to revenue factors. Although the percentage of
de novo bank assets invested in interest-bearing
assets, such as loans and securities, starts out relatively
low and increases only slowly over time (panel E), the
typical de novo bank outperforms one-quarter of the
established banks in this area after only three years.
(De novo bank ROA does not reach the 25th percentile benchmark until year six.) Even more impressive is
the speed at which new banks develop the ability to
generate fee income (panel F). The typical de novo
bank outstrips the average established bank in feebased revenues after only three years, and outperforms three-quarters of the older banks in this area
after about nine years. By virtue of their newness, de
novo banks may be less constrained by the inertia of
existing customer relationships and existing employee habits and, therefore, may be better able to impose
fees on retail customers or to enter into less traditional
BOX 1
Financial ratio time path data
Both the de novo bank sample and the established
bank sample were taken from a primary data set
used originally in a study by DeYoung and Hasan
(1998). For the current study, I added variables
from the Reports of income and condition (call
reports). The primary dataset is an unbalanced
panel consisting of 16,282 observations of 5,435
small, urban commercial banks at year-end 1988,
1990, 1992, and 1994. Not all of the banks are present
in each of the four years because some banks failed,
were acquired, or received their charters during
the sample period. There are 2,611 banks present
in all four years, 977 banks in three of the four years,
1,005 banks in two years only, and 842 banks in just
one year.
Banks had to meet a number of conditions to
be included in the primary dataset. First, banks
had to have less than $500 million of assets (in 1994
dollars). By definition, newly chartered banks are
small, and established banks that are large will not
serve as good benchmarks against which to judge
the progress of young banks. Large banks have
access to production methods, risk strategies,
distribution channels, and managerial talent not
available to small banks. Second, all banks had to
be headquartered in metropolitan statistical areas
(MSAs). Demand for banking products, as well
as competitive rivalry among banks, can be quite
different in rural and urban markets, and may cause
young banks to develop differently in these two
environments. Third, banks had to be at least 12
months old at the time of observation. For example,
a bank that was chartered during 1993, but was
observed at year-end 1994, is referred to as a oneyear old bank. Brislin and Santomero (1991) find
that financial statements are quite volatile during
the first year of a banks operations, which makes
performance difficult to measure. Fourth, all banks
had to make loans and take deposits, eliminating
special purpose banks such as credit card banks.
Fifth, banks that were 14 years old or less (that is,
Federal Reserve Bank of Chicago
banks that would be in the de novo sample) were
excluded if they held more than $50 million in assets at the end of their first year. This filter prevents established banks that received new charters
as part of regulatory reorganizations and established thrift institutions converting to bank charters from being identified as de novo banks.
The resulting de novo sample comprises
4,305 observations of 1,579 different banks 14
years old or younger. Roughly 47 percent of these
de novo banks hold federal charters and roughly
21 percent are affiliates in multibank holding companies. The established bank sample was constructed by choosing 4,305 observations of 1,514
different banks, each more than 14 years old, from
the primary dataset. Roughly 25 percent of these
established banks hold federal charters and
roughly 27 percent are affiliates in multibank
holding companies. The established banks were
chosen to have roughly the same asset-size distribution as the de novo bank sample, as follows:
Banks more than 14 years old were grouped into
ten asset categories ($0$50 million, $50$100
million, ..., $450$500 million). Established banks
were drawn at random from each of these size categories, depending on the number of de novo banks
of each asset size. The assets of the resulting established bank sample average $55.97 million with a
standard deviation of $49.64 million, compared
with the de novo bank sample average of $54.39
million and standard deviation of $48.70 million.
Obviously, there is no bright line that separates de novo banks from established banks. I chose
the 14-year old threshold for two reasons. First,
it is the maximum age at which previous studies
refer to commercial banks as de novo (see Huyser,
1986, and DeYoung and Hasan, 1998). Second,
choosing a relatively large number for this threshold ensures that the maturity benchmarks in figure
2 contain only banks that are fully mature.
23
fee-generating lines of business. In addition, de novo
banks tend to start up in markets where business
conditions are strong, and selling fee-based financial
services may be easier in these markets.
In contrast to their reasonably strong ability to
generate revenue, newly chartered banks have a difficult time controlling expenses. De novo banks initially
use large deposits twice as intensively as do established banks, and this disparity only slowly disappears (panel G). This suggests that de novo banks
tend to finance their fast asset growth by purchasing
funds rather than by growing their core deposit base.
All else being equal, this is an expensive and potentially risky financing strategy, because large depositors
are more sensitive to changes in interest rates than are
retail depositors and require higher rates to leave their
funds in the bank. The accounting efficiency ratio
graph (panel H) indicates that newly chartered banks
also have relatively high levels of overhead expenses
(for example, branch locations, labor expenses, and
computer equipment) and that these fixed factors of
production are not used at near full capacity for a
number of years. Excess overhead capacity not only
depresses bank profitability but, by increasing operating leverage, it makes bank profits more sensitive
to fluctuations in bank revenues.
Note that each of the panels in figure 2 exhibits
what is known as survivor bias, because some de novo
banks fail before they are 14 years old. For example,
average de novo ROA equals approximately 0.4 percent
for the three-year old banks, which is about twice as
large as the average ROA of 0.2 percent for the twoyear old banks. For the most part, this substantial improvement can be attributed to better performance as
young banks grow older and larger. But some amount
of this improvement occurs because some of the most
unprofitable de novo banks failed between years two
and three and dropped out of the sample. Although
this second explanation is responsible for only a small
amount of the large increase in ROA (as we shall see,
very few de novo banks fail after only two years of
operation), it is a good illustration of how survivor
bias can affect our results. Thus, the most exact way
to interpret the ROA time path is as follows: If a newly chartered bank survives to be three years old, one
would expect its ROA to be about 0.4 percent. I revisit
the issue of survivor bias when I estimate time to failure models in a later section (see Estimating hazard
functions section, starting on page 26).
Hypothetical hazard rates
likely to fail than established banks. Despite the losses
typically incurred during their first year of operation,
de novo banks initially have very high cushions of
equity capital and very low levels of nonperforming
loans. But the time paths in figure 2 also imply that
de novo banks become dramatically more likely to fail
as time passes, and quickly may become more likely
to fail than established banks. As de novo banks age,
their initially high capital cushions and low nonperforming loan ratios move rapidly toward established
bank levelsmuch more rapidly than their profitability reaches established bank levels.
The combined effect of these financial ratio time
paths on the timing and probability of de novo bank
failure is suggested by the hypothetical hazard functions in figure 3. A hazard function tracks changes over
time in the hazard rate, which is simply the probability
that a bank will fail at a particular time, given that it
has survived through all of the previous periods
leading up to that time.4 The horizontal line at P* represents the hypothetical hazard rate for established
banks, and the curved line plots the hypothetical hazard rate for newly chartered banks. Although this figure is highly stylized, the relative shapes of the two
functions are consistent with the combined financial
ratio time paths shown in figure 2.
The constant, non-zero hazard rate depicted in
figure 3 for established banks is an obvious simplification. Historically, established banks are more prone
to failure during recessionary periods, and almost
completely unlikely to fail during expansionary periods.
This simplification focuses attention on the issue of primary interest here, the failure rate of newly chartered
banks relative to the failure rate of established banks.
The hypothetical hazard rate for newly chartered
banks starts out at zero in figure 3, which makes sense
because these banks are so heavily capitalized at the
outset. But, as we saw in figure 2, de novo bank capital
FIGURE 3
Hypothetical probabilities of failure
New bank
P*
Established bank
0
time
The time paths in figure 2 imply that de novo banks
will at first be very unlikely to fail, perhaps even less
24
Economic Perspectives
percent with a standard deviation of 1 percent, then
its Z-score would equal 6.00. In this case, the banks
ROA would have to decline by 6 standard deviations
below its average (to 5 percent) for its losses to exhaust its capital cushion. Thus, the higher a banks
Z-score, the lower its probability of failure. Z will increase (that is, the probability of failure will decrease)
with higher levels of average ROA; Z will increase with
higher levels of equity to assets; and Z will increase
with lower variability in ROA.5
Table 1 displays Z-scores for the established
bank sample, for the de novo bank sample, and for
several subsamples of de novo banks. All of these
calculations employ the data used to construct the
graphs in figure 2. For each sample or subsample of
banks, Z is calculated using the median average of
ROA, the mean average of equity/assets, and the crosssectional standard deviation of ROA. (I use the median
ROA because the mean ROA is skewed downward
by banks that incurred large losses.) Because these
Z-scores are averages, they represent the likelihood
of failure for the typical bank in each sample.
In general, the calculations shown in table 1 suggest that becoming insolvent is a relatively unlikely
event for the typical bank in these samples. For example, the lowest Z-score (highest probability of insolvency) is 3.01, or about 3 standard deviations, for the
average three- to five-year old bank. Assuming that Z
is normally distributed, this implies only a 13 in 1,000
(0.13 percent) chance of becoming insolvent. Given
the large number of bank failures during the sample
period (see figure 1, panel A), the level of the failure
ratios decline to established bank averages after
about three years, while de novo bank profits, asset
quality, and growth rates do not reach (or return to)
established bank levels for around ten years. When
these time paths are considered simultaneously, they
imply the hypothetical patterns displayed in figure 3.
The hypothetical hazard rate for new banks increases
at first (for example, between ages one and three) as
new banks become increasingly vulnerable to economic fluctuations; it exceeds the established bank hazard
rate for a time (for example, after year three); and it
eventually declines to converge with established
bank levels (for example, around year ten). Regardless
of the exact shape and timing of the de novo bank
hazard function, it must eventually converge with the
established bank hazard function, because by definition new banks that survive eventually turn into established banks.
A rough way to check the relative accuracy of
the hypothetical hazard functions drawn in figure 3 is
to calculate Z-score probabilities of failure for de
novo banks and established banks. The Z-scores are
constructed as follows:
Z =
ROA + equity / assets
.
standard deviation of ROA
The Z-score indicates the number of standard deviations that ROA would have to fall below its average
value in order to wipe out 100 percent of the banks
equity capital. For example, if a bank has 5 percent
equity capital and, on average, it earns ROA of 1
TABLE 1
Average Z-scores
Components of average Z-score
Number
of banks
Median ROA
De novo banks
1 to 14 years old
Less than 3 years old
3 to 5 years old
6 to 10 years old
11 to 14 years old
4,305
667
1,424
1,570
644
.0057
.0006
.0050
.0074
.0089
Established banks
More than 14 years old
4,305
.0097
Cross-sectional
standard
deviation of ROA
Average
Z-score
.0957
.1231
.0814
.0762
.0795
.0230
.0206
.0287
.0195
.0155
3.97
6.00
3.01
4.28
5.70
.0867
.0129
7.48
Mean capitalto-assets ratio
Notes: Z-scores were calculated using formula described in the text and data described in box 1.
The selected commercial banks are also described in box 1.
Source: Author’s calculations based on year-end data from the National Information Center,
1988, 1990, 1992, and 1994, “Report of income and condition,” selected banks.
Federal Reserve Bank of Chicago
25
probabilities implied by these Z-scores is probably
too low.6 However, these Z-scores are still useful,
because they summarize the information in figure 2
into a single number that ranks the probability of failure across banks of different ages.
Overall, the analysis suggests that newly chartered banks are more likely to fail than established
banks: The average de novo Z-score of 3.97 is considerably smaller than the average established bank
Z-score of 7.48. On average, de novo banks and established banks have nearly identical capital-to-asset
ratios, so any difference in their implied failure rates
must be due to the level and variability of ROA. Indeed,
the median de novo bank ROA is only about half as
large as the median established bank ROA (.0057 versus .0097), and ROA is nearly twice as variable across
the de novo banks than across the established banks
(.0230 versus .0129).
Analyzing the Z-scores across de novo banks
of different ages provides some support for the shape
of the de novo bank hazard function in figure 3. The
implied probability of failure is relatively low for banks
less than three years old (Z = 6.00); is substantially
higher for three- to five-year old banks (Z = 3.01); and
then gradually declines toward established bank levels
for banks that survive beyond five years (Z = 4.28)
and beyond ten years (Z = 5.70). Looking at the components of these average Z-scores reveals why the
probability of failure changes as new banks mature.
The youngest group of de novo banks are the least
likely to fail because their earnings are relatively stable
(although they average near zero) and their capital
cushions are large. The three- to five-year old de novo
banks are more likely to fail because, although they
have higher average earnings, their capital cushions
have been depleted and their earnings are highly variable. Once banks are five to ten years old, increasing
earnings, increasing capital, and declining earnings
volatility all contribute to a reduced probability of
bank failure.
Estimating hazard functions
Next, I test whether the hypothetical hazard functions in figure 3 accurately depict the relative rates at
which newly chartered banks and established banks
fail. The Z-score analysis discussed above provides
some support for these hypothetical hazard functions,
but that evidence is crude at best and suffers from
survivor bias in the data. In this section, I employ
more sophisticated techniques to estimate hazard
functions for both newly chartered and established
banks. These techniques explicitly account for survivor
26
bias caused by failures and acquisitions during the
sample period. In addition, these techniques generate
continuous (or nearly continuous) hazard functions
that can be plotted against time, making them easy to
compare with the shape of the hypothetical hazard
functions in figure 3. Finally, one of these techniques
tests whether differences in de novo and established
bank failure rates are caused by differences in these
banks locational, regulatory, or organizational characteristics.
Data on bank failures
Table 2 displays some summary statistics for a
bank failure dataset Federal Reserve Bank of Chicago
staff created for the purpose of this study. This dataset
contains 56 quarters of information on 2,653 banks
from 1985 through 1998, and is constructed from the
Reports of income and condition (call reports) and
from the failures, transformations, and attributes tables
in the National Information Center database. The
dataset includes 303 newly chartered commercial
banks that opened their doors during 1985 and 2,350
established commercial banks that had been in operation for at least 25 years in 1985. The established
banks each had less than $25 million in assets (1985
dollars); had equity capital equal to at least 5 percent
of their assets; and were located in states in which
at least four de novo banks started up in 1985. The
dataset tracks each of these 2,653 banks across time
and records the quarters in which banks left the
dataset because they either failed or were acquired
by another bank.
These data cover a period during which there
were economic disruptions of sufficient magnitude to
cause a statistically meaningful number of bank failures.
Commercial bank failures were extremely rare in the
U.S. during the 1950s, 1960s, and 1970s, due to generally good economic times, regulatory limits on the risks
that banks could take, and legal entry barriers that
protected banks from competition. But the combination
of banking deregulation and volatile interest rates
during the 1970s and 1980s exposed banks to greater
risks and more competition. As seen in figure 1, panel
A, bank failures accelerated from near zero in 1980 to
over 100 failures per year from the mid-1980s through
the early 1990s. The catalyst for these bank failures
was a series of substantial economic disruptions,
including a general recession in the early 1990s and
a number of regional recessions in the mid- to late
1980s, the most disruptive of which was due to land
price deflations in Texas and other oil-producing states.
For the purposes of this article, I consider a bank
to have failed when at least one of the following
Economic Perspectives
TABLE 2
Descriptive statistics for hazard function data sets
characteristics affect the probability of
bank failure.
Nonparametric hazard functions
I use the bank failure data, summarized in table 2, to estimate separate hazNumber of banks
303
2,350
ard functions for newly chartered banks
and established banks, and then compare
<1
> 25
Age of banks in 1985 (years)
these estimated hazard functions with
43.23
84.17
Federal charters (%)
the hypothetical hazard functions in
78.55
18.81
Urban locations (%)
figure 3. I employ two different hazard
32.34
11.62
Multibank holding company (%)
function techniques to produce these
Southwest states (%),
estimatesa nonparametric, or actuarial,
(Texas, Louisiana, Oklahoma)
32.67
10.68
approach, and a parametric, or duration
Mean equity/assets
0.368
0.098
model, approach.
Median assets
An actuarial hazard function is sim(current dollars in thousands)
6,204
14,415
ply a series of actuarial hazard rates
Outcome
strung together in chronological order.
(number and % of sample)
Calculating the actuarial hazard rates is
Failed before 1999
50 (16.5)
185 (7.9)
straightforward and intuitive. For example,
Acquired before 1999
144 (47.5)
302 (12.9)
to calculate the 1990 hazard rate for a set
Survived to 1999
109 (36.0)
1,863 (79.2)
of banks that were chartered in 1985, one
Notes: The de novo banks began operations during 1985. The established
simply divides the number of these banks
banks were operating in the same states as the de novo banks and were
at least 25 years old in 1985. For further details of the data sources and
that failed during 1990 by the number of
data selection process, see “Estimating hazard functions” section of the
the banks that still existed at the begintext. These data are used to estimate the hazard functions shown in
figures 4 and 5.
ning of 1990. Thus, the hazard rate tells
Sources: Federal Deposit Insurance Corporation, 1985–98, “Report of
us the probability of failure in 1990 conincome and condition,” Washington, DC, and National Information Center,
1988, 1990, 1992, and 1994, “Report of income and condition.”
ditional on having survived for five years.
The following, more exact, formula can
be used to calculate the actuarial hazard
rate
for
any
time
period, T:
occurs: 1) the bank is declared insolvent by its regulator; 2) the bank receives regulatory assistance (for
example, a capital injection) without which it would
no. of bank failures during T
hazard(T) =
become insolvent; or 3) the bank is acquired soon
no. of banks surviving at start of T
after its net worth has declined to less than 1 percent
of assets. In terms of raw percentages, 16.5 percent
f(T)
£
,
of the de novo banks failed before the end of the 14T -1
1
n(t = 0) - Í f(t)+ m(t) - m(T)
year sample period. While this is over twice the 7.9
2
t=0
percent failure rate for the established banks in the
sample, it is well below the reported failure rates for
where n(t = 0) is the number of banks present at the
new (nonbank) business ventures. (See box 2 for a
beginning of the analysis; f(t) represents the number
short discussion of new bank failures versus new
of these banks that failed during time period t; m(t)
business failures.)
represents the number of these banks that were acBoth the sample de novo banks and the sample
quired in mergers during time period t, and T indicates
established banks were more likely to be acquired
the current time period. Note the subtle adjustment to
than to fail during the sample period. The new banks
the denominator in the second line of this formula:
were more likely to hold state charters; to be located
The denominator is reduced by one-half the number
in urban areas; to be located in the Southwest (primaof banks that were acquired during the current time
rily Texas, but also Louisiana and Oklahoma); and to
period. These banks clearly did not survive until the
be affiliates in multibank holding companies. Some of
end of time period T, and subtracting some portion of
the hazard functions I estimate below include tests of
these banks from the denominator acknowledges the
whether these locational, organizational, and regulatory
possibility that they might have failed during time T
De novo
banks
Established
banks
1
Federal Reserve Bank of Chicago
6
27
BOX 2
New bank failures and new business failures
During the 14 years covered by the bank failure
dataset (see table 2), 16.5 percent of the newly
chartered banks failed, compared with only 7.9
percent of the established banks of comparable
size and location. To put these new bank failure
rates into perspective, note that a 16.5 percent failure rate over 14 years is substantially lower than
the failure rates typically reported for business
start-ups in general. Raw data reported by the
U.S. Small Business Administration (1992) suggest
that at least 60 percent of new business ventures
with less than 500 employees that started in 197778
failed within six years. Kirchhoff (1994, pp. 153169)
argues convincingly that these raw data overstate
the new business failure rate because, among other things, the data in many instances define firms
that changed owners or voluntarily shut down as
having failed. After adjusting for these and other
had they not been acquired. Although weighting
these banks by one-half is a crude and ad hoc adjustment, it is important to make some kind of adjustment
because, as shown in table 2, acquired banks greatly
outnumbered failed banks between 1985 and 1998.
I use the above formula to calculate 14 separate
hazard rates (one rate for each of the 14 years from
1985 through 1998) for the 303 newly chartered banks.
I repeat this exercise for the 2,350 established banks.
Plotting the resulting hazard rates in chronological
order generates two nonparametric hazard functions,
which are displayed in figure 4.
In general, the nonparametric hazard functions in
figure 4 resemble the hypothetical hazard functions
posited in figure 3. The hazard rate for newly chartered banks is initially zero, and it remains below the
established bank hazard rate for several years. As
discussed above, this is most likely because the typical new bank holds a healthy equity cushion at the
outset. After year three, the new bank hazard rate
exceeds the established bank hazard rate, and it remains substantially higher than the established bank
hazard rate until year eight. The hazard rate for newly
chartered banks peaks in years five, six, and seven at
about 1.2 percentthat is, if a newly chartered bank
reaches the beginning of any of these years without
failing or being acquired, it has about a 1.2 percent
chance of failing before the year is out. At this point,
the typical new banks capital ratio has declined to
established bank levels, but its profitability has not
28
factors, Kirchhoff concludes that, in a best case
scenario, 18 percent of new business ventures fail
within eight years of start-upabout the same
rate of failure as the de novo banks but in half the
number of years. Furthermore, the 16.5 percent failure rate for new banks occurred during the worst
period of bank failures since the Great Depression.
It should not be surprising that new banks
have a better rate of survival than other new businesses. Both federal and state bank regulators
deny charters to applicants with questionable financial credentials, restrict business activities, require
high amounts of capital, apply regular scrutiny via
on-site exams, and have the power to revoke bank
charters. Banking start-ups face more severe entry
barriers and ongoing scrutiny than new businesses in most other industries, and this selection bias
naturally leads to a higher survival for new banks.
yet attained the level or degree of stability found at
established banks. After year eight, the new bank
hazard rate approaches the established bank hazard
rate from above, suggesting that the maturation of
new banks is well under way at this point.
The results displayed in figure 4 are consistent
with the simple life-cycle theory of de novo bank failure. The nonparametric techniques used to generate
figure 4 paint a good general picture of the rate at
which new banks fail relative to established banks.
But these nonparametric techniques do not control
for the survivor bias in the data and, as a result, they
understate the hazard rate at any given point in time.
FIGURE 4
Nonparametric hazard rates
percent
De novo
banks
Established
banks
years after 1985
Economic Perspectives
Furthermore, these techniques are not useful for testing how much, if any, of the difference between the new
bank and established bank failure rates is caused by
the economic, regulatory, and organizational conditions under which newly chartered banks operate.
In the final step in this analysis, I use econometric
duration analysis to estimate hazard functions. These
parametric methods account for survivor bias and
control for environmental conditions that can affect
the probability of failure.
Parametric hazard functions
Duration analysis is a statistical regression approach. The dependent variable in these regressions
is t, the length of time that passes between a new
banks start-up date and its subsequent failure. For
established banks, t is the length of time between its
first observation in the dataset (in this case, the first
quarter of 1985) and its subsequent failure. The period
measured by t is often referred to as a banks duration.
Because the banks in this dataset are observed quarterly, duration will range from t = 1 for banks that fail
during the quarter in which they begin operations, to
t = 56 for banks that fail in the fourth quarter of 1998.
The simplest duration approach includes no
explanatory variables. The analyst starts by selecting
a probability distribution formula that has a shape
that is roughly similar to the actual distribution of the
duration variable t, and uses maximum likelihood techniques to estimate parameter values that shape that
probability distribution formula more exactly to the
actual duration data. Here, I use a log-logistic distribution formula, because this is capable of producing
hazard functions that have shapes similar to the hazard
functions in figures 3 and 4. (Details of these duration
model procedures can be found in the appendix to this
article or in Greene, 1997). Once the parameters of the
distribution formula have been estimated, they can be
used to construct hazard functions as follows:
hazard(T) =
f(T)
,
1 – F(T)
where f(T) is the probability that a bank fails at time T
(that is, the log-logistic probability density) and F(T)
is the probability that a bank fails before time T (that
is, the log-logistic cumulative probability distribution).
The denominator, 1 F(T), is the log-logistic survival
function, which is the probability that a bank neither
fails nor is acquired before time T. This parametric
hazard function has the same general interpretation
as the nonparametric hazard function calculated in
the previous sectionthey are both estimates of the
Federal Reserve Bank of Chicago
probability that a bank will fail at time T given that it
has survived until time T. One difference is that the
hazard function generated by this parametric approach
will be a smooth and continuous function of time similar to the hypothetical hazard functions in figure 3,
as opposed to the segmented nonparametric hazard
function in figure 4.
The duration models I estimate here control for
survivor problems in the data. Recall that many of the
sample banks either survived beyond the end of the
sample period or were acquired during the sample period. These banks are known as censored observations.
We cannot assign a duration value t to these banks
because we cannot observe their ultimate fate (failure
or survival). Furthermore, history suggests that very
few of these banks will eventually fail, so including
them in hazard rate calculations creates a downward
bias by inflating the survival function 1 F(t). Duration models can adjust for this problem by estimating
the probability that censored banks will eventually
fail, and then weighting the censored observations by
this probability before estimating the parameters of the
hazard function. (See the appendix for more details.)
The sample banks differ in terms of their geographic location, their organizational form, and their
primary regulator. These characteristics could make
a bank more or less likely to fail, or given that a bank
does fail, these characteristics could influence how
quickly it fails. For example, banks located in depressed
economic regions will be more likely to fail and, absent
regulatory intervention, will fail more quickly than
banks located in economically healthy markets. Duration models can include a vector of independent variables, typically known as covariates, measuring the
characteristics that vary across banks but remain
constant for each bank over the sample period. I use
a split population approach which estimates two regression coefficients for each of the covariates in the
duration model. The first coefficient measures the
covariates impact on the probability that a bank will
survivea negative coefficient indicates that the
covariate is associated with a lower probability of
survival (higher probability of failure). The second
coefficient measures the covariates impact on a
banks durationgiven that a bank will eventually
fail, a negative coefficient indicates that the covariate
is associated with a shorter duration (a faster failure).
The duration models I estimate include four covariates, each of which is expressed as a (0, 1) dummy
variable. OCC = 1 if the bank holds a federal charter
(as opposed to a state charter). The OCC has traditionally practiced a more lenient chartering policy than
most state chartering authorities, relying on market
29
forces rather than administrative rules to determine
the number of banks a market could support.7 A negative coefficient on OCC would suggest that this policy caused new national banks to fail more often and/
or more quickly, on average, than new state-chartered
banks. INDEPENDENT = 1 if the bank is either a freestanding business or a one-bank holding company
(as opposed to being an affiliate of a multibank holding company) throughout the sample period. A negative coefficient on INDEPENDENT would suggest
that banks not having access to the financial strength
and managerial expertise of a multibank holding company tend to fail more often and/or more quickly.
MSA = 1 if the bank is located in an urban area. Banks
in urban areas face greater competition than rural
banks, but also may have greater opportunities for
diversification. A negative coefficient on MSA would
suggest that, on balance, these conditions cause
banks in urban areas to fail more often and/or more
quickly than rural banks. SW = 1 if the bank is located
in the southwestern states of Louisiana, Texas, or
Oklahoma, which experienced large numbers of bank
failures during the mid- to late 1980s due to disruptions
in energy-related industries. One would expect the
coefficients on SW to be negative, reflecting lower
survival probabilities and shorter duration times for
banks in this region.
I add these four covariates to the duration model
merely to illustrate how conditions and events external to the bank can affect its probability of failure and
its time to failure. These four variables are not meant
to be an exhaustive list of such conditions. Similarly,
the duration model I estimate here is by no means definitive of the duration model techniques available to
researchers. Other duration approaches do exist, including those that allow for time-varying covariates
(for example, changes in economic, regulatory, or
competitive conditions during each banks duration).
However, the multiple approaches I employ (including
the Z-score and actuarial hazard function analysis
conducted above) serve the purpose of this study,
which is to test the simple life-cycle theory of de novo
bank failure summarized in figure 3.
Table 3 displays the results of the duration models
estimated separately for newly chartered banks and
established banks. The estimated probability that the
average bank will eventually fail is 19.65 percent for
de novo banks and 8.93 percent for established banks.
Note that these estimated failure probabilities are somewhat higher than the raw failure percentages shown
at the bottom of table 2. In each case, the estimated
probability is higher than the raw percentage because
of the possibility that some of the censored observations will eventually fail.
30
Although established banks are less likely to fail,
those that do fail have relatively short durations. Of
the established banks that are expected to eventually
fail, half of them will fail within an estimated 9.8 quarters (about 2.5 years) after the beginning of the sample
period. Consistent with the life-cycle theory, newly
chartered banks fail more slowly than established
banks. It takes an estimated 21.1 quarters (about 5.25
years) for half of the de novo banks that are expected
to fail to do so.
These differences in average duration can be
seen clearly in figure 5, which charts the estimated
hazard rates from the de novo and established bank
duration models. Each of these functions is plotted
based on the estimated coefficients shown in table 3
and the average values of the covariates for each
sample. In general, these two estimated hazard functions resemble the shapes displayed above in figures
3 and 4. Thus, after controlling for censored data and
a variety of environmental conditions, the failure patterns of newly chartered banks still differ substantially from the failure patterns of established banks.
The estimated probability of failure for established
banks starts out above zero; peaks at about 8 percent
for banks that survive for two years; and then slowly
declines as the bank failure wave dissipates (see figure 1). In contrast, the estimated probability of failure
for de novo banks starts out at zero and remains lower
than the established bank hazard rate for three years;
increases rapidly and peaks at nearly 14 percent for
banks the survive for seven years; and then declines
relatively quickly and begins to approach the established bank hazard rate. Note that both of these hazard
functions peak much higher on the vertical scale than
did the actuarial hazard functions plotted in figure 4.
Thus, by not controlling for censored observations
and the overall low probability of eventual failure, the
actuarial model substantially understated the hazard
rates. Also, note that the hazard rates in figure 5 are
in decline but are still positive at year 14, which reflects
the non-zero probability of failure for the censored
observations.
As expected, being located in one of the southwestern states reduces the probability of survival (or
increases the probability of failure) for both de novo
and established banks. Failing de novo banks also
failed more quickly in this region, but failing established
banks had longer than average durations. The latter
result may indicate that regulators allowed troubled
banks with longstanding business relationships (and,
hence, more franchise value) more time to recover
before stepping in to resolve them.8 Being located in
a metropolitan statistical area reduced the probability
Economic Perspectives
TABLE 3
Selected results from parametric duration models
De novo banks
Number of banks in sample
Established banks
303
2,350
Average predicted failure probability
19.65%
8.93%
Predicted time for 50 percent of banks to fail
21.1 quarters
9.8 quarters
1.2930**
(0.5144)
1.2475***
(0.2145)
0.0197
(0.2242)
–0.1296
(0.1117)
Probability of survival parameter estimates
Constant
OCC (= 1 if national bank)
SW (= 1 if in Louisiana, Oklahoma, or Texas)
–0.3928*
(0.2219)
–0.7419***
(0.0992)
MSA (= 1 if urban bank)
–0.5266*
(0.3205)
0.2530**
(0.1163)
–0.5265**
(0.2386)
#
INDEPENDENT (= 1 if independent or sole bank in
a one-bank holding company)
Survival time parameter estimates
Constant
OCC
3.3045***
(0.6124)
2.3369***
(0.4489)
0.0075
(0.1376)
0.1354
(0.2339)
SW
–0.3243**
(0.1386)
0.4753**
(0.1971)
MSA
–0.2204
(0.5318)
0.5391**
(0.2699)
INDEPENDENT
–0.1195
(0.1547)
#
*, **, and *** indicate significance at the 10 percent, 5 percent, and 1 percent levels, respectively.
Notes: Both models are estimated using the data sets described in table 2. Standard errors are in
parentheses. # indicates that it was necessary to exclude the variable INDEPENDENT to make the
established bank model converge. Further details on these models can be found in the appendix to this article.
FIGURE 5
Parametric hazard functions
percent
De novo
banks
Established
banks
years after 1985
Federal Reserve Bank of Chicago
of survival for de novo banks, but increased both the
probability of survival for established banks and the
survival time for established banks likely to eventually fail. Recall that intense competitive rivalry can cause
banks to fail in urban markets, and that the lack of diversification opportunities can cause banks to fail in
rural markets. The results suggest that these two
phenomena affect de novo banks and established
banks differentlyon balance, de novo banks may
be more sensitive to competition than to diversification risk, while small established banks may be more
affected by a lack of diversification than by competitive rivalry. Being an independent bank or banking
organization also reduces the probability of survival
for de novo banks, which suggests that having access
to the resources of multibank holding companies helps
31
new banks survive. (I excluded this covariate from the
established bank model because its presence prevented the model from converging.) The identity of
a banks primary regulator (OCC or state) is not a significant determinant of the probability of survival or
the survival time for either set of banks.
Conclusion
Like all new business ventures, banks start with
a business plan but no guarantee of success. So,
despite the regulatory safeguards of on-site examinations, capital requirements, and other risk controls, we
should not be surprised to find that new banks are
more likely to fail than established banks. This article
offers a simple framework that explains not only why
but also when new banks are likely to fail.
My results suggest that the primary determinant
of new bank failure is how new the bank is. Ironically,
de novo banks are relatively unlikely to fail during
their first few years of operation when they are earning negative profits. They are relatively more likely to
fail during the years of positive profits that follow.
Brand new, but unprofitable, banks are typically protected from failure by large initial capital cushions.
However, equity cushions at de novo banks typically
decline to established bank levels several years before
their earnings become stable enough to justify these
relatively low levels of capital.
What are the implications of this result for capital
regulation at newly chartered banks? If ensuring a
high rate of survival for de novo banks is a regulatory
objective, then this result offers support for requiring
high levels of start-up capital for new banks, and for
holding young banks to higher capital requirements.
Higher levels of required capital will make newly chartered banks less vulnerable to failure. Under such
policies, de novo entrants might be a more credible
long-run deterrent to market power in consolidating
local markets. Indeed, in the wake of the wave of de
novo bank failures during the 1980s, federal bank
supervisory agencies did impose higher capital requirements on newly chartered banks.
32
On the other hand, promoting the safety and
soundness of the banking system does not require
that regulators prevent all bank failures, much less
all failures of new banks. At some point, attempting
to improve the survival rate of de novo banks by increasing the amount of capital necessary for investors
to secure the charter will act as an entry barrier. Similarly, increasing the required capital ratios for young
banks with charters already in hand will, at some
point, depress investors expected rates of return and
discourage investment in new banks. Higher capital
requirements for young banks could also slow the rate
at which they can grow their balance sheets, hampering the beneficial impact of new banks in markets
where existing banks (perhaps with market power)
are not adequately serving the banking public.
What are the implications of this study for the
bank chartering decision? During the period covered
by this study, some state chartering authorities would
approve or deny a charter application only after considering whether a local market needed an additional
bank, based on the number of banks already serving
the market and the expected rate of local economic
growth. These restrictive chartering policies sought
to reduce bank failure rates, and the financial disruptions that accompany them, by limiting competition
in local banking markets. In contrast, the federal chartering authority practiced a liberal entry policy that
explicitly ignored these convenience and needs
issues, stressing instead the potential procompetitive
benefits of de novo entry. My results indicate that
the de novo national banks chartered in 1985 were no
more likely to fail, or to fail quickly, than the de novo
state banks chartered in that same year. This suggests
that the benefits of a liberal chartering policy can be
achieved without substantial increases in de novo
bank failure rates. Additional research might confirm
whether these findings, which are based on data from
just 303 new banks chartered in a single year, also
hold for banks chartered in other years and/or under
different economic and regulatory circumstances.
Economic Perspectives
APPENDIX
Split population duration models
The parametric hazard functions described in the text
begin with the assumption that a population of N
banks will fail over time period (0,t) according to
some probability distribution:
1 6 I f (t )dt ,
t
F t =
0
where t represents time and f(t) is the probability density function associated with F(t). The hazard function
h(t) can then be written as a function of F(t) and f(t)
as follows:
h( T ) =
f (T )
f (T )
=
,
1 - F (T )
S (T )
where S(t) = 1 F(t) is the survival function and
0<T<t. Thus, h(T) gives the probability (that is, the
hazard rate) that a bank will fail at T conditional on
surviving until T.
The general shape of the estimated hazard function will depend on the underlying probability distribution chosen to fit the data. I use the log-logistic
distribution because it is capable of producing the
hazard function shapes hypothesized in figure 3. The
log-logistic distribution imposes the following functional forms on the hazard and survival functions:
h( t ) =
lp(lp) p -1
1 + (lt ) p
S (t ) =
1
,
1 + (lt ) p
where the parameters p and λ give the hazard function
its exact shape. The parameter p captures duration
dependence or whether the hazard rate increases or
decreases across time. The parameter λ captures the
portion of the hazard rate that is time-invariant. This
parameter, which can take on different values for different banks, is expressed as follows:
li = e-bXi ,
where the bank index i ranges from 1 to N, and Xi is a
vector of bank-specific covariates that do not vary
over time. Table 3 reports the estimated values of β
under the heading survival time parameter estimates.
I use these β estimates to evaluate the above expression at the means of the covariates, which results in
Federal Reserve Bank of Chicago
λ = 0.0474 for the average de novo bank and 0.1019
for the average established bank. The parameter p is
a constant that does not vary across banks; it equals
5.0175 for the de novo bank model and 1.6333 for the
established bank model.
All of the parameters of the duration models in
this study were estimated using maximum likelihood
techniques. The standard estimation procedure for
duration models starts with the following likelihood
function:
N
L = ½ f (t i | p, b)
i =1
Qi
S (ti | p, b)
1- Qi
,
where Qi = 1 if bank i failed during the sample period
(an uncensored observation) and Qi = 0 if bank i
survived or was acquired during the sample period
(a censored observation). Substituting h(t)/S(t) for
f(t) and performing a log transformation produces the
log-likelihood function to be maximized:
UC
N
i =1
i =1
lnL = Í lnh(t i | p, b) + Í lnS (ti | p, b) ,
where i≤UC are the uncensored observations. Once I
have estimated the parameters p and β, I can calculate
the median time to failure by setting S(t) = 0.50 and
solving for t.
This standard approach is based on the assumption that all of the censored banks will eventually fail
(or would have eventually failed had they not been
acquired). This assumption is inappropriate for the
data used here, however, because over 80 percent of
the de novo banks were censored observations, and
over 90 percent of the established banks were censored observations. Given the nature of the data, I
use a more general framework that avoids making this
assumption. In the split population duration model,
an additional estimable parameter δ, the probability
that a bank eventually fails, enters the likelihood
function as follows:
N
L = ½ df (t i | p, b)
i =1
Qi
(1 - d) + dS (ti | p, b)
1- Qi
.
Both Cole and Gunther (1995) and Hunter,
Verbrugge, and Whidbee (1996) estimate split population models of financial institution failure. Note that
this formulation collapses to the standard framework
when δ = 1. But when δ<1, the functions S(t) and f(t)
become conditional on the bank eventually failing.
Thus, the estimated hazard function h(t) = f(t)/S(t)
33
will not be unduly influenced by censored observations of banks that have little chance of ever failing.
The parameter δ can vary across banks as a function
of a banks covariate values:
di =
1
.
1 + e a X i
Table 3 reports the estimated values of α under
the heading is probability of survival parameter estimates. I use these α estimates to evaluate the above
expression at the means of the covariates, which results
in δ = 0.1965 for the average de novo bank and 0.0893
for the average established bank.
The hazard functions plotted in figure 5 show
the probability that the average bank will fail at time t,
given that the bank has not yet failed but will eventually fail. Thus, the shapes of the plotted hazard
functions are based on the estimated values of λ and
p, but not on the estimated values of δ.
NOTES
Note that such ambiguity is largely absent from studies that
examine the determinants of local market entry by already
established banks. For a recent example, see Amel and Liang
(1997). In general, these studies tend to find that established
banks are more likely to enter highly profitable local banking
markets, but less likely to enter highly concentrated local
banking markets. Of course, the causes and consequences of a
new bank start-up may be quite different from the causes and
consequences of market entry by an already established bank.
1
Seelig and Critchfield (1999) find that, on average, the state
chartering authorities remain relatively more likely than the
OCC to consider the ability of local banking markets to support
an additional bank when evaluating a charter application. The
authors show that income per capita per branch in the local
banking market was a substantially stronger predictor of de
novo state bank entry than of de novo national bank entry
between 1995 and 1997.
2
There are a number of possible reasons for this. In general,
Z-score analysis performs best when used to represent the
likelihood that an individual firm will become insolvent and,
as such, Z-scores are typically constructed based on the known
distribution (the mean and standard deviation) of ROA for an
individual firm. In contrast, these average Z-scores are constructed for groups of banks, and rely on the cross-sectional
distribution (the median and standard deviation) of ROA for
each group of banks. As mentioned in the text, the distribution
of ROA is not normally distributed, but rather is relatively
skewed. Hence, it would be inappropriate to use the absolute
levels of these average Z-scores to draw statistical inferences
about the probability of bank failure.
6
See Hunter and Srinivasan (1990) and DeYoung and Hasan
(1998) for discussions that compare historical federal and
state chartering policies.
7
There are many potential reasons for the high bank failure
rates in Texas, and for the relatively shorter durations for de
novo banks in Texas, during the 1980s and 1990s. These reasons
include unexpected economic shocks, unit banking restrictions
that limited geographic diversification, a relatively undiversified regional economy, and regulatory failure.
8
See DeYoung and Hasan (1998) for a more complete review of
this literature.
3
Examples of studies that have used hazard rates to analyze
financial institution failure include Whalen (1991); Wheelock
and Wilson (1995); Cole and Gunther (1995); Helwege (1996);
and Hunter, Verbrugge, and Whidbee (1996).
4
The Z-score is a measure of the probability that a firms losses
(negative profits) will exceed its equity capital. See Brewer
(1989) for a discussion of the Z-score and its use in banking
research.
5
REFERENCES
Amel, Dean F., and J. Nellie Liang, 1997, Determinants of entry and profits in local banking markets,
Review of Industrial Organization, Vol. 12, No. 1,
pp. 5978.
Brewer III, Elijah, 1989, Relationships between
bank holding company risk and nonbank activity,
Journal of Economics and Business, Vol. 41, November, pp. 337353.
Berger, Allen N., Seth D. Bonime, Lawrence G.
Goldberg, and Lawrence J. White, 1999, The dynamics of market entry: The effects of mergers and
acquisitions on de novo entry and customer service
in banking, Proceedings from a Conference on
Bank Structure and Regulation, Federal Reserve
Bank of Chicago, forthcoming.
Brislin, Patricia, and Anthony Santomero, 1991,
De novo banking in the Third District, Business
Review, Federal Reserve Bank of Philadelphia, January,
pp. 312.
34
Economic Perspectives
Cole, Rebel A., and Jeffery W. Gunther, 1995, Separating the likelihood and timing of bank failure, Journal
of Banking and Finance, Vol. 19, No. 6, September,
pp. 10731089.
DeYoung, Robert, Lawrence G. Goldberg, and
Lawrence J. White, 1999, Youth, adolescence, and
maturity of banks: Credit availability to small business in an era of banking consolidation, Journal
of Banking and Finance, Vol. 23, No. 2-4, February,
pp. 463492.
DeYoung, Robert, and Iftekhar Hasan, 1998, The
performance of de novo commercial banks: A profit
efficiency approach, Journal of Banking and
Finance, Vol. 22, May, pp. 565587.
Greene, William H., 1997, Econometric Analysis,
Upper Saddle River, NJ: Prentice Hall.
Helwege, Jean, 1996, Determinants of savings and
loan failure, Journal of Financial Services Research,
Vol. 10, No. 4, pp. 373392.
Hunter, William C. and Aruna Srinivasan, 1990,
Determinants of de novo bank performance,
Economic Review, Federal Reserve Bank of Atlanta,
March, pp. 1425.
Hunter, William C., James A. Verbrugge, and David
A. Whidbee, 1996, Risk taking and failure in de novo
savings and loans in the 1980s, Journal of Financial
Services Research, Vol. 10, No. 3, pp. 235272.
Federal Reserve Bank of Chicago
Huyser, Daniel, 1986, De novo bank performance in
the Seventh District states, Banking Studies, Federal
Reserve Bank of Kansas City, pp. 1322.
Kirchhoff, Bruce A., 1994, Entrepreneurship and
Dynamic Capitalism, Westport, CT and London:
Greenwood, Praeger.
Moore, Robert R., and Edward C. Skelton, 1998,
New banks: Why enter when others exit?, Financial Industry Issues, Federal Reserve Bank of Dallas,
First Quarter, pp. 17.
Seelig, Stephen, and Timothy Critchfield, 1999,
Determinants of de novo entry in banking, Federal
Deposit Insurance Corporation, working paper, No.
99-1, January.
U.S. Small Business Administration, 1992, The State
of Small Business, Washington, DC: U.S. Government
Printing Office.
Whalen, Gary, 1991, A proportional hazards model
of bank failure: An examination of its usefulness as
an early warning tool, Economic Review, Federal
Reserve Bank of Cleveland, Vol. 27, No. 1, First Quarter,
pp. 2031.
Wheelock, David C., and Paul W. Wilson, 1995,
Explaining bank failures: Deposit insurance, regulation, and efficiency, Review of Economics and Statistics, November, pp. 689700.
35
New facts in finance
John H. Cochrane
Introduction and summary
The last 15 years have seen a revolution in the way
financial economists understand the investment world.
We once thought that stock and bond returns were
essentially unpredictable. Now we recognize that
stock and bond returns have a substantial predictable
component at long horizons. We once thought that
the capital asset pricing model (CAPM) provided a
good description of why average returns on some
stocks, portfolios, funds, or strategies were higher than
others. Now we recognize that the average returns of
many investment opportunities cannot be explained
by the CAPM, and multifactor models are used in
its place. We once thought that long-term interest
rates reflected expectations of future short-term rates
and that interest rate differentials across countries
reflected expectations of exchange rate depreciation.
Now, we see time-varying risk premiums in bond and
foreign exchange markets as well as in stock markets.
We once thought that mutual fund average returns
were well explained by the CAPM. Now, we see that
funds can earn average returns not explained by the
CAPM, that is, unrelated to market risks, by following
a variety of investment styles.
In this article, I survey these new facts, and I show
how they are variations on a common theme. Each
case uses price variables to infer market expectations
of future returns; each case notices that an offsetting
adjustment (to dividends, interest rates, or exchange
rates) seems to be absent or sluggish. Each case suggests that financial markets offer rewards in the form
of average returns for holding risks related to recessions and financial distress, in addition to the risks
represented by overall market movements. In a companion article in this issue, Portfolio advice for a multifactor world, I survey and interpret recent advances
in portfolio theory that address the question, What
should an investor do about all these new facts?
First, a slightly more detailed overview of the
facts then and now. Until the mid-1980s, financial
36
economists view of the investment world was based
on three bedrocks:
1. The CAPM is a good measure of risk and thus
a good explanation of the fact that some assets (stocks,
portfolios, strategies, or mutual funds) earn higher
average returns than others. The CAPM states that
assets can only earn a high average return if they
have a high beta, which measures the tendency
of the individual asset to move up or down with the
market as a whole. Beta drives average returns because
beta measures how much adding a bit of the asset to
a diversified portfolio increases the volatility of the
portfolio. Investors care about portfolio returns, not
about the behavior of specific assets.
2. Returns are unpredictable, like a coin flip. This
is the random walk theory of stock prices. Though
there are bull and bear markets; long sequences of
good and bad past returns; the expected future return
is always about the same. Technical analysis that
tries to divine future returns from patterns of past
returns and prices is nearly useless. Any apparent
predictability is either a statistical artifact which will
quickly vanish out of sample or cannot be exploited
after transaction costs.
Bond returns are not predictable. This is the
expectations model of the term structure. If long-term
bond yields are higher than short-term yieldsif the
yield curve is upward slopingthis does not mean
that you expect a higher return by holding long-term
bonds rather than short-term bonds. Rather, it means
John H. Cochrane is the Sigmund E. Edelstone
Professor of Finance in the Graduate School of
Business at the University of Chicago, a consultant to
the Federal Reserve Bank of Chicago, and a research
associate at the National Bureau of Economic Research
(NBER). The author thanks Andrea Eisfeldt for research
assistance and David Marshall, John Campbell, and
Robert Shiller for comments. The authors research is
supported by the Graduate School of Business and by
a grant from the National Science Foundation,
administered by the NBER.
Economic Perspectives
that short-term interest rates are expected to rise in
the future. Over one year, the rise in interest rates will
limit the capital gain on long-term bonds, so they earn
the same as the short-term bonds over the year. Over
many years, the rise in short rates improves the rate
of return from rolling over short-term bonds to equal
that of holding the long-term bond. Thus, you expect
to earn about the same amount on short-term or longterm bonds at any horizon.
Foreign exchange bets are not predictable. If a
country has higher interest rates than are available in
the U.S. for bonds of a similar risk class, its exchange
rate is expected to depreciate. Then, after you convert your investment back to dollars, you expect to
make the same amount of money holding foreign or
domestic bonds.
In addition, stock market volatility does not
change much through time. Not only are returns close
to unpredictable, they are nearly identically distributed
as well. Each day, the stock market return is like the
result of flipping the same coin, over and over again.
3. Professional managers do not reliably outperform simple indexes and passive portfolios once one
corrects for risk (beta). While some do better than the
market in any given year, some do worse, and the
outcomes look very much like luck. Funds that do well
in one year are not more likely to do better than average the next year. The average actively managed fund
performs about 1 percent worse than the market index.
The more actively a fund trades, the lower the returns
to investors.
Together, these views reflect a guiding principle
that asset markets are, to a good approximation, informationally efficient (Fama, 1970, 1991). Market prices
already contain most information about fundamental
value and, because the business of discovering information about the value of traded assets is extremely
competitive, there are no easy quick profits to be made,
just as there are not in any other well-established
and competitive industry. The only way to earn large
returns is by taking on additional risk.
These views are not ideological or doctrinaire
beliefs. Rather, they summarize the findings of a quarter century of careful empirical work. However, every
one of them has now been extensively revised by a
new generation of empirical research. The new findings need not overturn the cherished view that markets
are reasonably competitive and, therefore, reasonably
efficient. However, they do substantially enlarge our
view of what activities provide rewards for holding
risks, and they challenge our understanding of those
risk premiums.
Federal Reserve Bank of Chicago
Now, we know that:
1. There are assets whose average returns can
not be explained by their beta. Multifactor extensions
of the CAPM dominate the description, performance
attribution, and explanation of average returns. Multifactor models associate high average returns with a
tendency to move with other risk factors in addition
to movements in the market as a whole. (See box 1.)
2. Returns are predictable. In particular: Variables
including the dividend/price (d/p) ratio and term premium can predict substantial amounts of stock return
variation. This phenomenon occurs over business
cycle and longer horizons. Daily, weekly, and monthly
stock returns are still close to unpredictable, and technical systems for predicting such movements are still
close to useless.
Bond returns are predictable. Though the expectations model works well in the long run, a steeply
upward sloping yield curve means that expected
returns on long-term bonds are higher than on shortterm bonds for the next year. These predictions are not
guaranteesthere is still substantial riskbut the
tendency is discernible.
Foreign exchange returns are predictable. If you
put your money in a country whose interest rates are
higher than usual relative to the U.S., you expect to
earn more money even after converting back to dollars.
Again, this prediction is not a guaranteeexchange
rates do vary, and a lot, so the strategy is risky.
Volatility does change through time. Times of
past volatility indicate future volatility. Volatility also
is higher after large price drops. Bond market volatility is higher when interest rates are higher, and possibly when interest rate spreads are higher as well.
3. Some mutual funds seem to outperform simple
indexes, even after controlling for risk through market
betas. Fund returns are also slightly predictable: Past
winning funds seem to do better than average in the
future, and past losing funds seem to do worse than
average in the future. For a while, this seemed to indicate that there is some persistent skill in active management. However, multifactor models explain most
fund persistence: Funds earn persistent returns by
following fairly mechanical styles, not by persistent
skill at stock selection.
Again, these statements are not dogma, but a
cautious summary of a large body of careful empirical
work. The strength and usefulness of many results
are hotly debated, as are the underlying reasons for
many of these new facts. But the old world is gone.
37
BOX 1
The CAPM and multifactor models
The CAPM uses a time-series regression to measure beta, β, which quantifies an assets or portfolios tendency to move with the market as a whole,
Rti - Rt f = ai + bim ( Rtm - Rtf ) + eit ;
t = 1, 2 ... T for each asset i.
Then, the CAPM predicts that the expected
excess return should be proportional to beta,
E ( Rti - Rtf ) = biml m for each i.
λm gives the price of beta risk or market risk premiumthe amount by which expected returns
must rise to compensate investors for higher beta.
Since the model applies to the market return as
well, we can measure λm via
l m = E ( Rtm - Rt f ).
The CAPM and multifactor models
The CAPM
The CAPM proved stunningly successful in a
quarter century of empirical work. Every strategy that
seemed to give high average returns turned out to
have a high beta, or a large tendency to move with
the market. Strategies that one might have thought
gave high average returns (such as holding very volatile stocks) turned out not to have high average
returns when they did not have high betas.
Figure 1 presents a typical evaluation of the
CAPM. I examine 10 portfolios of NYSE stocks sorted
by size (total market capitalization), along with a portfolio of corporate bonds and long-term government
bonds. As the vertical axis shows, there is a sizable
spread in average returns between large stocks (lower
average return) and small stocks (higher average
return) and a large spread between stocks and bonds.
The figure plots these average returns against market
betas. You can see how the CAPM prediction fits: Portfolios with higher average returns have higher betas.
In fact, figure 1 captures one of the first significant failures of the CAPM. The smallest firms (the far
right portfolio) seem to earn an average return a few
percent too high given their betas. This is the celebrated small-firm effect, (Banz, 1981) and this deviation is statistically significant. Would that all failed
economic theories worked so well! However, the plot
shows that this effect is within the range that statisticians can argue about. Estimating the slope of the
38
Multifactor models extend this theory in a
straightforward way. They use a time-series multiple regression to quantify an assets tendency to
move with multiple risk factors FA, FB, etc.
3)
Rti - Rtf = ai + bim ( Rtm - Rtf ) + biA Ft A + biB Ft B
+ ... + eit ; t = 1, 2 ... T for each asset i.
Then, the multifactor model predicts that the
expected excess return is proportional to the betas
4) E( Rti - Rtf ) = bimlm + biAl A + biBlB + ...
for each i.
The residual or unexplained average return in
either case is called an alpha,
ai ¢ E ( Rti - Rtf ) - (biml m + biAl A + biB l B + ...).
line by fitting a cross-sectional regression (average
return against beta), shown in the colored line, rather
than forcing the line to go through the market and
Treasury bill return, shown in the black line, halves
FIGURE 1
CAPMMean excess returns vs. beta, version 1
mean excess returns, percent
18
Means and betas
Fitted market premium
Direct market premium
14
10
6
2
–2
0.0
0.2
0.4
0.6
0.8
betas
1.0
1.2
1.4
Notes: Average returns versus betas on the NYSE value-weighted
portfolio for ten size-sorted stock portfolios, government bonds,
and corporate bonds. Sample period 1947–96. The black line
draws the CAPM prediction by fitting the market proxy and
Treasury bill rates exactly (a time-series test) and the colored line
draws the CAPM prediction by fitting an OLS cross-sectional
regression to the displayed data points (a second-pass or crosssectional test). The small-firm portfolios are at the top right.
Moving down and to the left, one sees increasingly large-firm
portfolios and the market index. The points far down and to the
left are the government bond and Treasury bill returns.
Economic Perspectives
FIGURE 2
CAPMMean excess returns vs. beta, version 2
mean excess returns, percent
16
Means and betas
Direct market premium
Fitted market premium
12
8
4
0
0.0
0.2
0.4
0.6
0.8
betas
1.0
1.2
1.4
Notes: CAPM using the equally weighted NYSE as the “market
portfolio.” Otherwise, this figure is identical to figure 1.
the small-firm effect. Figure 2 uses the equally weighted
portfolio as market proxy, and this change in specification eliminates the small-firm effect, making the line of
average returns versus betas if anything too shallow
rather than too steep.
Why we expect multiple factors
In retrospect, it is surprising that the CAPM
worked so well for so long. The assumptions on which
it is built are very stylized and simplified. Asset pricing
theory recognized at least since Merton (1973, 1971)
the theoretical possibility, indeed probability, that we
should need factors, state variables or sources of
priced risk, beyond movements in the market portfolio to explain why some average returns are higher
than others. (See box 1 for details of the CAPM and
multifactor models.)
Most importantly, the average investor has a
job. The CAPM (together with the use of the NYSE
portfolio as the market proxy) simplifies matters by
assuming that the average investor only cares about
the performance of his investment portfolio. While
there are investors like that, for most of us eventual
wealth comes both from investment and from earning
a living. Importantly, events like recessions hurt the
majority of investors. Those who dont actually lose
jobs get lower salaries or bonuses. A very limited number of people actually do better in a recession.
With this fact in mind, compare two stocks. They
both have the same sensitivity to market movements.
However, one of them does well in recessions, while
the other does poorly. Clearly, most investors prefer
the stock that does well in recessions, since its performance will cushion the blows to their other income.
Federal Reserve Bank of Chicago
If lots of people feel that way, they bid up the price of
that stock, or, equivalently, they are willing to hold it
at a lower average return. Conversely, the procyclical
stocks price will fall or it must offer a higher average
return in order to get investors to hold it.
In sum, we should expect that procyclical stocks
that do well in booms and worse in recessions will have
to offer higher average returns than countercyclical
stocks that do well in recessions, even if the stocks
have the same market beta. We expect that another
dimension of riskcovariation with recessions
will matter in determining average returns.1
What kinds of additional factors should we look
for? Generally, asset pricing theory specifies that
assets will have to pay high average returns if they
do poorly in bad timestimes in which investors
would particularly like their investments not to perform
badly and are willing to sacrifice some expected return
in order to ensure that this is so. Consumption (or,
more generally, marginal utility) should provide the
purest measure of bad times. Investors consume less
when their income prospects are low or if they think
future returns will be bad. Low consumption thus
reveals that this is indeed a time at which investors
would especially like portfolios not to do badly, and
would be willing to pay to ensure that wish. Alas,
efforts to relate asset returns to consumption data
are not (yet) a great success. Therefore, empirically
useful asset pricing models examine more direct measures of good times or bad times. Broad categories
of such indicators are
1. The market return. The CAPM is usually
included and extended. People are unhappy if the
market crashes.
2. Events, such as recessions, that drive investors noninvestment sources of income.
3. Variables, such as the p/d ratio or slope of
the yield curve, that forecast stock or bond returns
(called state variables for changing investment
opportunity sets).
4. Returns on other well-diversified portfolios.
One formally justifies the first three factors by
stating assumptions under which each variable is related to average consumption. For example, 1) if the
market as a whole declines, consumers lose wealth
and will cut back on consumption; 2) if a recession
leads people to lose their jobs, then they will cut back
on consumption; and, 3) if you are saving for retirement, then news that interest rates and average stock
returns have declined is bad news, which will cause
you to lower consumption. This last point establishes
a connection between predictability of returns and the
presence of additional risk factors for understanding
39
the cross-section of average returns. As pointed out
by Merton (1971), one would give up some average
return to have a portfolio that did well when there
was bad news about future market returns.
The fourth kind of factoradditional portfolio
returnsis most easily defended as a proxy for any of
the other three. The fitted value of a regression of any
pricing factor on the set of all asset returns is a portfolio that carries exactly the same pricing information as
the original factora factor-mimicking portfolio.
It is vital that the extra risk factors affect the
average investor. If an event makes investor A worse
off and investor B better off, then investor A buys
assets that do well when the event happens and investor B sells them. They transfer the risk of the event,
but the price or expected return of the asset is unaffected. For a factor to affect prices or expected returns,
it must affect the average investor, so investors collectively bid up or down the price and expected return of
assets that covary with the event rather than just transferring the risk without affecting equilibrium prices.
Inspired by this broad direction, empirical researchers have found quite a number of specific factors that
seem to explain the variation in average returns across
assets. In general, empirical success varies inversely
with theoretical purity.
Small and value/growth stocks
The size and book to market factors advocated
by Fama and French (1996) are one of the most popular additional risk factors.
Small-cap stocks have small market values (price
times shares outstanding). Value (or high book/market)
stocks have market values that are small relative to
the value of assets on the companys books. Both
categories of stocks have quite high average returns.
Large and growth stocks are the opposite of small
and value and seem to have unusually low average
returns. (See Fama and French, 1993, for a review.)
The idea that low prices lead to high average returns
is natural.
High average returns are consistent with the
CAPM, if these categories of stocks have high sensitivity to the market, high betas. However, small and
especially value stocks seem to have abnormally
high returns even after accounting for market beta. Conversely, growth stocks seem to do systematically worse
than their CAPM betas suggest. Figure 3 shows this
valuesize puzzle. It is just like figure 1, except that the
stocks are sorted into portfolios based on size and
book/market ratio2 rather than size alone. The highest
portfolios have three times the average excess return
of the lowest portfolios, and this variation has nothing
at all to do with market betas.
40
FIGURE 3
Mean excess returns vs. market beta,
FamaFrench portfolios
mean excess returns
1.25
1.00
0.75
0.50
0.25
0.00
0.0
0.2
0.4
0.6
0.8
1.0
market beta
1.2
1.4
Notes: Average monthly returns versus market beta for 25 stock
portfolios sorted on the basis of size and book/market ratio.
In figure 4, I connect portfolios of different sizes
within the same book/market category (panel A). Variation in size produces a variation in average returns
that is positively related to variation in market betas,
as shown in figure 1. In panel B, I connect portfolios
that have different book/market ratios within size categories. Variation in book/market ratio produces a
variation in average return that is negatively related to
market beta. Because of this value effect, the CAPM is
a disaster when confronted with these portfolios.
To explain these facts, Fama and French (1993,
1996) advocate a multifactor model with the market
return, the return of small less big stocks (SMB), and
the return of high book/market less low book/market
stocks (HML) as three factors. They show that variation in average returns of the 25 size and book/market
portfolios can be explained by varying loadings (betas)
on the latter two factors.
Figure 5 illustrates Fama and Frenchs results.
As in figure 4, the vertical axis is the average returns
of the 25 size and book/market portfolios. Now, the
horizontal axis is the predicted values from the Fama
French three-factor model. The points should all lie
on a 45 degree line if the model is correct. The points
lie much closer to this prediction in figure 5 than in
figures 3 and 4. The worst fit is for the growth stocks
(lowest line, panel A), for which there is little variation
in average return despite large variation in size beta
as one moves from small to large firms.
What are the size and value factors?
One would like to understand the real, macroeconomic, aggregate, nondiversifiable risk that is proxied
by the returns of the HML and SMB portfolios. Why
Economic Perspectives
FIGURE 4
Mean excess returns vs. market beta, varying size and book/market ratio
A. Changing size within book/market category
B. Changing book/market within size category
mean excess return
1.25
mean excess return
1.25
1.00
1.00
0.75
0.75
0.50
0.50
0.25
0.25
0.00
0.0
0.2
0.4
0.6
0.8
1.0
market beta
1.2
0.00
0.0
1.4
0.2
0.4
0.6
0.8
1.0
market beta
1.2
1.4
Notes: Average returns versus market beta for 25 stock portfolios sorted on the basis of size and book/market ratio.
The points are the same as figure 3. In panel A, lines connect portfolios as size varies within book/market categories;
in panel B, lines connect portfolios as book/market ratio varies within size categories.
are investors so concerned about holding stocks that
do badly at the times that the HML (value less growth)
and SMB (small-cap less large-cap) portfolios do badly,
even though the market does not fall? The answer to
this question is not yet totally clear.
Fama and French (1995) note that the typical value
stock has a price that has been driven down due to
financial distress. The stocks of firms on the verge
of bankruptcy have recovered more often than not,
which generates the high average returns of this
strategy.3 This observation suggests a natural interpretation of the value premium: In the event of a credit
crunch, liquidity crunch, or flight to quality, stocks in
financial distress will do very badly, and this is precisely when investors least want to hear that their portfolio is losing money. (One cannot count the distress
of the individual firm as a risk factor. Such distress
is idiosyncratic and can be diversified away. Only
aggregate events that average investors care about
can result in a risk premium.)
FIGURE 5
Mean excess return vs. three-factor model predictions
A. Changing size within book/market category
B. Changing book/market within size category
actual mean excess return, E(R i – R f )
1.2
actual mean excess return, E(R i – R f )
1.2
0.9
0.9
0.6
0.6
0.3
0.3
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
predicted, β i , m E(R m – R f ) + βi , h E(HML) +β i ,s E(SMB)
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
predicted, β i , m E(R m – R f) + β i ,h E(HML) +β i ,sE(SMB)
Notes: Average returns versus market beta for 25 stock portfolios sorted on the basis of size and book/market ratio versus
predictions of Fama–French three-factor model. The predictions are derived by regressing each of the 25 portfolio returns, R it ,
on the market portfolio, R mt, and the two Fama–French factor portfolios, SMBt (small minus big) and HMLt (high minus low
book/market). (See equation 4 in box 1.)
Federal Reserve Bank of Chicago
41
Heaton and Lucass (1997) results add to this
story for the value effect. They note that the typical
stockholder is the proprietor of a small, privately held
business. Such an investors income is, of course,
particularly sensitive to the kinds of financial events
that cause distress among small firms and distressed
value firms. Therefore, this investor would demand a
substantial premium to hold value stocks and would
hold growth stocks despite a low premium.
Liew and Vassalou (1999), among others, link value
and small-firm returns to macroeconomic events. They
find that in many countries, counterparts to HML and
SMB contain supplementary information to that contained in the market return for forecasting gross domestic product (GDP) growth. For example, they report
a regression
GDPt→ t+4 = a + 0.065 MKTt4→ t
+ 0.058 HMLt4→ t + εt+4,
where GDPt→ t+4 denotes the following years GDP
growth and MKTt4→t and HMLt4→t denote the previous
years return on the market index and HML portfolio.
Thus, a 10 percent HML return raises the GDP forecast
by 0.5 percentage points. (Both coefficients are significant with t-statistics of 3.09 and 2.83, respectively.)
The effects are still under investigation. Figure 6
plots the cumulative return on the HML and SMB
portfolios; a link between these returns and obvious
macroeconomic events does not jump out. Both portfolios have essentially no correlation with the market
return, though HML does seem to move inversely with
large market declines. HML goes down more than the
market in some business cycles, but less in others.
On the other hand, one can ignore Fama and
Frenchs motivation and regard the model as an arbitrage pricing theory (APT) following Ross (1976). If
the returns of the 25 size and book/market portfolios
could be perfectly replicated by the returns of the
three-factor portfoliosif the R2 values in the timeseries regressions of the 25 portfolio on the three
factors were 100 percentthen the multifactor model
would have to hold exactly, in order to preclude arbitrage opportunities. To see this, suppose that one of
the 25 portfolioscall it portfolio Agives an average
return 5 percent above the average return predicted
by the FamaFrench model, and its R2 is 100 percent.
Then, one could short a combination of the threefactor portfolios, buy portfolio A, and earn a completely
riskless profit. This logic is often used to argue that
a high R2 should imply an approximate multifactor
model. If the R2 were only 95 percent, then an average
return 5 percent above the factor model prediction
42
FIGURE 6
Cumulative returns on market portfolios
cumulative return
8
6
HML
Market
4
SMB
2
0
1945
‘55
‘65
‘75
‘85
‘95
Notes: Cumulative returns on the market RMRF, SMB, and
HML portfolios. The SMB return is formed by R TB
+ aSMBt ;
t
a = σ(RMRF)/σ(SMB). In this way it is a return that can be
cumulated rather than a zero-cost portfolio, and its standard
deviation is equal to that of the market return. HML is adjusted
similarly. The vertical axis is the log base 2 of the cumulative
return or value of $1 invested at the beginning of the sample
period. Thus, each time a line increases by 1 unit, the value
doubles.
would imply that the strategy long portfolio A and
short a combination of the three-factor portfolios
would earn a very high average return with very little,
though not zero, riska very high Sharpe ratio.
In fact, the R2 values of Fama and Frenchs (1993)
time-series regressions are all in the 90 percent to 95
percent range, so extremely high risk prices for the
residuals would have to be invoked for the model not
to fit well. Conversely, given the average returns from
HML and SMB and the failure of the CAPM to explain
those returns, there would be near-arbitrage opportunities if value and small stocks did not move together
in the way described by the FamaFrench model.
One way to assess whether the three factors
proxy for real macroeconomic risks is by checking
whether the multifactor model prices additional portfolios, especially portfolios whose ex-post returns are
not well explained by the factors (portfolios that do
not have high R2 values in time-series regressions).
Fama and French (1996) find that the SMB and HML
portfolios comfortably explain strategies based on
alternative price multiples (price/earnings, book/market),
five-year sales growth (this is the only strategy that
does not form portfolios based on price variables),
and the tendency of five-year returns to reverse. All
of these strategies are not explained by CAPM betas.
However, they all also produce portfolios with high
R2 values in a time-series regression on the HML and
SMB portfolios. This is good and bad news. It might
Economic Perspectives
mean that the model is a good APT, and that the size
and book/market characteristics describe the major
sources of priced variation in all stocks. On the other
hand, it might mean that these extra ways of constructing portfolios just havent identified other sources of
priced variation in stock returns. (Fama and French,
1996, also find that HML and SMB do not explain
momentum, despite high R2 values. I discuss this
anomaly below.) The portfolios of stocks sorted by
industry in Fama and French (1997) have lower R2
values, and the model works less well.
A final concern is that the size and book/market
premiums seem to have diminished substantially in
recent years. The sharp decline in the SMB portfolio
return around 1980 when the small-firm effect was first
popularized is obvious in figure 6. In Fama and Frenchs
(1993) initial samples, 196090, the HML cumulative
return starts about one-half (0.62) below the market
and ends up about one-half (0.77) above the market.
On the log scale of the figure, this corresponds to Fama
and Frenchs report that the HML average return is
about double (precisely, 20.62+0.77 = 2.6 times) that of
the market. However, over the entire sample of the
plot, the HML portfolio starts and ends at the same
place and so earns almost exactly the same as the
market. From 1990 to now, the HML portfolio loses
about one-half relative to the market, meaning an investor in the market has increased his money one and a
half times as much as an HML investor. (The actual
number is 0.77 so the market return is 20.77 = 1.71 times
better than the HML return.)
Among other worries, if the average returns decline
right after publication it suggests that the anomalies
may simply have been overlooked by a large fraction
of investors. As they move in, prices go up further,
helping the apparent anomaly for a while. But once a
large number of investors have moved in to include
small and value stocks in their portfolios, the anomalous high average returns disappear.
However, average returns are hard to measure.
There have been previous ten- to 20-year periods in
which small stocks did very badly, for example the
1950s, and similar decade-long variations in the HML
premium. Also, since SMB and HML have a beta of
essentially zero on the market, any upward trend is a
violation of the CAPM and says that investors can
improve their overall meanvariance tradeoff by taking
on some of the HML or SMB portfolio.
Macroeconomic factors
I focus on the size and value factors because they
provide the most empirically successful multifactor
model and have attracted much industry as well as
Federal Reserve Bank of Chicago
academic attention. Several authors have used macroeconomic variables as factors. This procedure examines
directly whether stock performance during bad macroeconomic times determines average returns. Jagannathan and Wang (1996) and Reyfman (1997) use
labor income; Chen, Roll, and Ross (1986) look at
industrial production and inflation among other variables; and Cochrane (1996) looks at investment growth.
All these authors find that average returns line up
with betas calculated using the macroeconomic indicators. The factors are theoretically easier to motivate,
but none explains the value and size portfolios as
well as the (theoretically less solid, so far) size and
value factors.
Mertons (1973, 1971) theory says that variables
which predict market returns should show up as factors that explain cross-sectional variation in average
returns. Campbell (1996) is the lone test I know of to
directly address this question. Cochrane (1996) and
Jagannathan and Wang (1996) perform related tests in
that they include scaled return factors, for example,
market return at t multiplied by d/p ratio at t 1; they
find that these factors are also important in understanding cross-sectional variation in average returns.
The next step is to link these more fundamentally
determined factors with the empirically more successful value and small-firm factor portfolios. Because of
measurement difficulties and selection biases, fundamentally determined macroeconomic factors will never
approach the empirical performance of portfolio-based
factors. However, they may help to explain which portfolio-based factors really work and why.
Predictable returns
The view that risky asset returns are largely unpredictable, or that prices follow random walks, remains
immensely successful ( Malkiel, 1990, is a classic and
readable introduction). It is also widely ignored.
Unpredictable returns mean that if stocks went
up yesterday, there is no exploitable tendency for them
to decline today because of profit taking or to continue to rise today because of momentum. Technical
signals, including analysis of past price movements
trading volume, open interest, and so on are close to
useless for forecasting short-term gains and losses.
As I write, value funds are reportedly suffering large
outflows because their stocks have done poorly in
the last few months, leading fund investors to move
money into blue-chip funds that have performed better (New York Times Company, 1999). Unpredictable
returns mean that this strategy will not do anything
for investors portfolios over the long run except rack
up trading costs. If funds are selling stocks, then
43
contrarian investors must be buying them, but unpredictable returns mean that this strategy can not
improve performance either. If one can not systematically make money, one can not systematically
lose money either.
As discussed in the introduction, researchers
once believed that stock returns (more precisely, the
excess returns on stocks over short-term interest
rates) were completely unpredictable. It now turns
out that average returns on the market and individual
securities do vary over time and that stock returns
are predictable. Alas for would-be technical traders,
much of that predictability comes at long horizons
and seems to be associated with business cycles and
financial distress.
Market returns
Table 1 presents a regression that forecasts returns. Low pricesrelative to dividends, book value,
earnings, sales, or other divisorspredict higher subsequent returns. As the R2 values in table 1 show,
these are long-horizon effects: Annual returns are
only slightly predictable and month-to-month returns
are still strikingly unpredictable, but returns at five-year
horizons seem very predictable. (Fama and French, 1989,
is an excellent reference for this kind of regression).
The results at different horizons are reflections
of a single underlying phenomenon. If daily returns
are very slightly predictable by a slow-moving variable, that predictability adds up over long horizons.
For example, you can predict that the temperature in
Chicago will rise about one-third of a degree per day
in spring. This forecast explains very little of the day
to day variation in temperature, but tracks almost all
of the rise in temperature from January to July. Thus,
the R2 rises with horizon.
Precisely, suppose that we forecast returns with
a forecasting variable x, according to
1)
Rt +1 - R
2)
x t +1 = c + rxt + d t +1 .
TB
t +1
= a + bx t + e t +1
Small values of b and R in equation 1 and a large
coefficient ρ in equation 2 imply mathematically that
the long-horizon regression as in table 1 has a large
regression coefficient b and large R2.
This regression has a powerful implication: Stocks
are in many ways like bonds. Any bond investor understands that a string of good past returns that pushes the price up is bad news for subsequent returns.
Many stock investors see a string of good past returns
and become elated that we seem to be in a bull
2
44
market, concluding future stock returns will be good
as well. The regression reveals the opposite: A string
of good past returns which drives up stock prices
is bad news for subsequent stock returns, as it is
for bonds.
Long-horizon return predictability was first documented in the volatility tests of Shiller (1981) and
LeRoy and Porter (1981). They found that stock prices vary far too much to be accounted for by changing expectations of subsequent cash flows; thus
changing discount rates or expected returns must
account for variation in stock prices. These volatility
tests turn out to be almost identical to regressions
such as those in table 1 (Cochrane, 1991).
Momentum and reversal
Since a string of good returns gives a high price,
it is not surprising that individual stocks that do
well for a long time (and reach a high price) subsequently do poorly, and stocks that do poorly for a
long time (and reach a low price, market value, or market to book ratio) subsequently do well. Table 2, taken
from Fama and French (1996) confirms this hunch.
(Also, see DeBont and Thaler, 1985, and Jegadeesh
and Titman, 1993.)
The first row in table 2 tracks the average monthly
return from the reversal strategy. Each month, allocate
all stocks to ten portfolios based on performance
from year 5 to year 1. Then, buy the best-performing portfolio and short the worst-performing portfolio.
This strategy earns a hefty 0.74 percent monthly
return.4 Past long-term losers come back and past
winners do badly. Fama and French (1996) verify that
these portfolio returns are explained by their threefactor model. Past winners move with value stocks,
TABLE 1
OLS regression of excess returns on
price/dividend ratio
Horizon k
1 year
2 years
3 years
5 years
b
Standard error
R2
–1.04
–2.04
–2.84
–6.22
0.33
0.66
0.88
1.24
0.17
0.26
0.38
0.59
Notes: OLS regressions of excess returns (value-weighted
NYSE–Treasury bill rate) on value-weighted price/dividend
ratio.
TB
RtVW
t +k - Rt t +k = a + b( Pt / Dt ) + et +k .
Rt→t+k indicates the k year return. Standard errors use GMM
to correct for heteroskedasticity and serial correlation.
Economic Perspectives
results of table 2. The key is the large
standard deviation of individual stock
Average monthly returns, reversal and momentum strategies
returns, typically 40 percent or more on
Portfolio
Average
an annual basis. The average return of
Strategy
Period
formation return, 10–1
the best performing decile of a normal
(months)
(monthly %)
distribution is 1.76 standard deviations
above the mean,5 so the winning momenReversal
July 1963–Dec. 1993
60–13
–0.74
tum portfolio went up about 80 percent
Momentum July 1963–Dec. 1993
12–2
+1.31
Reversal
Jan. 1931–Feb. 1963
60–13
–1.61
in the previous year and the typical losMomentum Jan. 1931–Feb. 1963
12–2
+0.38
ing portfolio went down about 60
percent. Only a small amount of continuNotes: Each month, allocate all NYSE firms to 10 portfolios
based on their performance during the “portfolio formation months”
ation will give a 1 percent monthly return
interval. For example, 60–13 forms portfolios based on returns from 5
when multiplied by such large past
years ago to 1 year, 1 month ago. Then buy the best-performing decile
portfolio and short the worst-performing decile portfolio.
returns. To be precise, the monthly indiSource: Fama and French (1996, table 6).
vidual stock standard deviation is about
40% / 12 £ 12%. If the R2 is 0.0025,
the standard deviation of the predictand so inherit the value stock premium. (To compare
able part of returns is .0025 12% £ 0.6%. Hence,
the strategies, the table always buys the winners and
the decile predicted to perform best will earn
shorts the losers. In practice, of course, you buy the
176
. 0.6% £ 1% above the mean. Since the strategy
losers and short the winners to earn +0.71 percent
buys the winners and shorts the losers, an R2 of
monthly average return.)
0.0025 implies that one should earn a 2 percent monthly
The second row of table 2 tracks the average
return by the momentum strategy.
monthly return from a momentum strategy. Each
We have known at least since Fama (1965) that
month, allocate all stocks to ten portfolios based on
monthly and higher frequency stock returns have
performance in the last year. Now, the winners conslight, statistically significant predictability with R2
tinue to win and the losers continue to lose, so that
about 0.01. Campbell, Lo, and MacKinlay (1997, table
buying the winners and shorting the losers generates
2.4) provide an updated summary of index autocorrelaa positive 1.31 percent monthly return.
tions (the R2 is the squared autocorrelation), part of
Momentum is not explained by the FamaFrench
which I show in table 3. Note the correlation of the equal(1996) three-factor model. The past losers have low
ly weighted portfolio, which emphasizes small stocks.6
prices and tend to move with value stocks. Hence, the
However, such small, though statistically signifimodel predicts that they should have high average
cant, high-frequency predictability has thus far failed
returns, not low average returns.
to yield exploitable profits after one takes into account
Momentum stocks move together, as do value
transaction costs, thin trading of small stocks, and
and small stocks, so a momentum factor works to
high short-sale costs. The momentum strategy for exexplain momentum portfolio returns (Carhart, 1997).
ploiting this correlation may not work in practice for
This step is so obviously ad hoc (that is, an APT facthe same reasons. Momentum does require frequent
tor that will only explain returns of portfolios orgatrading. The portfolios in table 2 are re-formed every
nized on the same characteristic as the factor rather
than a proxy for macroeconomic risk) that most peoTABLE 3
ple are uncomfortable adding it. We obviously do not
want to add a new factor for every anomaly.
First-order autocorrelation, CRSP value- and
Is momentum really there, and if so, is it exploitable
equally weighted index returns
after transaction costs? One warning is that it does not
Frequency
Portfolio
Correlation ρ1
seem stable over subsamples. The third and fourth
lines in table 2 show that the momentum effect essenDaily
Value-weighted
0.18
tially disappears in the earlier data sample, while reversal
Equally weighted
0.35
is even stronger in that sample.
Monthly
Value-weighted
0.043
Momentum is really just a new way of looking at
Equally weighted
0.17
an old phenomenon, the small apparent predictability
of monthly individual stock returns. A tiny regression
Note: Sample 1962–94.
Source: Campbell, Lo, and MacKinlay (1997).
R2 for forecasting monthly returns of 0.0025 (0.25 percent) is more than adequate to generate the momentum
TABLE 2
Federal Reserve Bank of Chicago
45
month. Annual winners and losers will not change
that often, but the winning and losing portfolio must
be turned over at least once per year. In a quantitative
examination of this effect, Carhart (1997) concludes
that momentum is not exploitable after transaction
costs are taken into account. Moskowitz and Grinblatt
(1999) note that most of the apparent gains from the
momentum strategy come from short positions in
small illiquid stocks. They also find that a large part
of momentum profits come from short positions taken
in November. Many investors sell losing stocks toward
the end of December to establish tax losses. By shorting illiquid losing stocks in November, an investor
can profit from the selling pressure in December. This
is also an anomaly, but it seems like a glitch rather than
a central principle of risk and return in asset markets.
Even if momentum and reversal are real and as
strong as indicated by table 2, they do not justify much
of the trading based on past results that many investors seem to do. To get the 1 percent per month
momentum return, one buys a portfolio that has typically gone up 80 percent in the last year, and shorts a
portfolio that has typically gone down 60 percent.
Trading between stocks and fund categories such as
value and blue-chip with smaller past returns yields
at best proportionally smaller results. Since much of
the momentum return seems to come from shorting
small illiquid stocks, mild momentum strategies may
yield even less. And we have not quantified the substantial risk of momentum strategies.
Bonds
The venerable expectations model of the term
structure specifies that long-term bond yields are
equal to the average of expected future short-term bond
yields (see box 2). For example, if long-term bond yields
are higher than short-term bond yieldsif the yield
curve is upward slopingthis means that short-term
rates are expected to rise in the future. The rise in future short-term rates means that investors can expect
BOX 2
Bond definitions and expectations hypothesis
Let pt( N ) denote the log of the N year discount
bond price at time t. The N period continuously
1
compounded yield is defined by yt( N ) = - pt( N ) .
N
The continuously compounded holding period
return is the selling price less the buying price,
hprt(+N1 ) = pt(+N1-1) - pt( N ) . The forward rate is the rate
at which an investor can contract today to borrow
money N 1 years from now, and repay that money
N years from now. Since an investor can synthesize a forward contract from discount bonds, the
forward rate is determined from discount bond
prices by
f t ( N ) = pt( N –1) – pt( N ) .
The spot rate refers, by contrast with a forward rate, to the yield on any bond for which the
investor take immediate delivery. Forward rates
are typically higher than spot rates when the yield
curve rises, since the yield is the average of intervening forward rates,
yt( N ) =
1 (1)
( f t + f t ( 2 ) + f t ( 3) + ... + f t ( N ) ).
N
The expectations hypothesis states that the
expected log or continuously compounded return
should be the same for any bond strategy. This
statement has three mathematically equivalent
expressions:
46
1. The forward rate should equal the expected
value of the future spot rate,
f t( N ) = Et ( yt(+1)N -1 ).
2. The expected holding period return should be
the same on bonds of any maturity
Et (hprt(+N1 ) ) = Et ( hprt(+M1 ) ) = yt(1) .
3. The long-term bond yield should equal the
average of the expected future short rates,
yt( N ) =
1
Et ( yt(1) + yt(1+)1 + ... + yt(+1)N -1 ).
N
The expectations hypothesis is often amended to allow a constant risk premium of undetermined sign in these equations. Its violation is then
often described as evidence for a time-varying
risk premium.
The expectations hypothesis is not quite the
same thing as risk-neutrality, because the expected
log return is not equal to the log expected return.
However, the issues here are larger than the difference between the expectations hypothesis and
strict risk-neutrality.
Economic Perspectives
TABLE 4
Zero-coupon bond returns
Maturity Average holding
N
period return
1
2
3
4
5
5.83
6.15
6.40
6.40
6.36
Standard
error
0.42
0.54
0.69
0.85
0.98
Standard
deviation
2.83
3.65
4.66
5.71
6.58
Note: Continuously compounded one-year holding period
returns on zero-coupon bonds of varying maturity. Annual
data from CRSP 1953–97.
the same rate of return whether they hold a long-term
bond to maturity or roll over short-term bonds with
initially low returns and subsequent higher returns.
As with the CAPM and the view that stock returns
are independent over time, a new round of research
has significantly modified this traditional view of
bond markets.
Table 4 calculates the average return on bonds
of different maturities. The expectations hypothesis
seems to do pretty well. Average holding period returns
do not seem very different across bond maturities,
despite the increasing standard deviation of longermaturity bond returns. The small increase in average
returns for long-term bonds, equivalent to a slight
average upward slope in the yield curve, is usually
excused as a liquidity premium. Table 4 is just the
tip of an iceberg of successes for the expectations
model. Especially in times of significant inflation and
exchange rate instability, the expectations hypothesis
has done a very good first-order job of explaining the
term structure of interest rates.
However, if there are times when long-term bonds
are expected to do better and other times when shortterm bonds are expected to do better, the unconditional
averages in table 4 could still show no pattern. Similarly, one might want to check whether a forward rate
that is unusually high forecasts an unusual increase
in spot rates.
Table 5 updates Fama and Blisss (1987) classic
regression tests of this idea. Panel A presents a regression of the change in yields on the forward-spot
spread. (The forward-spot spread measures the slope
of the yield curve.) The expectations hypothesis predicts a slope coefficient of 1.0, since the forward rate
should equal the expected future spot rate. If, for
example, forward rates are lower than expected future
spot rates, traders can lock in a borrowing position
with a forward contract and then lend at the higher
spot rate when the time comes.
Instead, at a one-year horizon we find slope coefficients near zero and a negative adjusted R2. Forward rates one year out seem to have no predictive
power whatsoever for changes in the spot rate one
year from now. On the other hand, by four years out,
we see slope coefficients within one standard error of
1.0. Thus, the expectations hypothesis seems to do
poorly at short (one-year) horizons, but much better
at longer horizons.
If the expectations hypothesis does not work at
one-year horizons, then there is money to be made
one must be able to foresee years in which short-term
bonds will return more than long-term bonds and vice
versa, at least to some extent. To confirm this implication, panel B of table 5 runs regressions of the one-year
excess return on long-term bonds on the forwardspot spread. Here, the expectations hypothesis predicts a coefficient of zero: No signal (including the
TABLE 5
Forecasts based on forward-spot spread
A.
N
Change in yields
Intercept
Standard
error,
intercept
Slope
B.
Standard
error,
slope
Adjusted
R2
Holding period returns
Intercept
Standard
error,
intercept
Slope
Standard
error,
slope
Adjusted
R2
1
0.10
0.3
–0.10
0.36
–0.020
–0.1
0.3
1.10
0.36
0.16
2
–0.01
0.4
0.37
0.33
0.005
–0.5
0.5
1.46
0.44
0.19
3
–0.04
0.5
0.41
0.33
0.013
–0.4
0.8
1.30
0.54
0.10
4
–0.30
0.5
0.77
0.31
0.110
–0.5
1.0
1.31
0.63
0.07
Notes: OLS regressions, 1953–97 annual data. Panel A estimates the regression y – y = a +b ( ft
– y ) + ε t+N
and panel B estimates the regression hpr (N)
–yt(1) = a + b (f t( N+1) – y (1)
) + ε t+1, where y denotes the N-year bond yield at
t+1
t
date t; f t( N) denotes the N-period ahead forward rate; and hpr (Nt+)1 denotes the one-year holding period return at date t + 1
on an N-year bond. Yields and returns in annual percentages.
(1)
t+ n
(N)
t
Federal Reserve Bank of Chicago
(1)
t
(N +1)
(1)
t
47
forward-spot spread) should be able to tell you that
this is a particularly good time for long bonds versus
short bonds, as the random walk view of stock prices
says that no signal should be able to tell you that
this is a particularly good or bad day for stocks versus
bonds. However, the coefficients in panel B are all
about 1.0. A high forward rate does not indicate that
interest rates will be higher one year from now; it
seems to indicate that investors will earn that much
more by holding long-term bonds.7
Of course, there is risk. The R2 values are all 0.1
0.2, about the same values as the R 2 from the d/p regression at a one-year horizon, so this strategy will
often go wrong. Still, 0.10.2 is not zero, so the strategy does pay off more often than not, in violation of
the expectations hypothesis. Furthermore, the forward-spot spread is a slow-moving variable, typically
reversing sign once per business cycle. Thus, the R2
builds with horizon as with the d/p regression, peaking in the 30 percent range (Fama and French, 1989).
Foreign exchange
making tidy sums borrowing at 5 percent in dollars to
lend at 20 percent in local currencies. This suggests
that traders were anticipating a 15 percent devaluation, or a smaller chance of a larger devaluation, which
is exactly what happened. Many observers attribute
high nominal interest rates in troubled economies to
tight monetary policy aimed at defending the currency. In reality, high nominal rates reflect a large probability of inflation and devaluationloose monetary
policyand correspond to much lower real rates.
Still, does a 5 percent interest rate differential
correspond to a 5 percent expected depreciation, or
does some of it represent a high expected return from
holding debt in that countrys currency? Furthermore, while expected depreciation is clearly a large
part of the interest rate story in high-inflation economies, how does the story play out in economies like
the U.S. and Germany, where inflation rates diverge
little but exchange rates still fluctuate a large amount?
The first row of table 6 (from Hodrick, 2000, and
Engel, 1996) shows the average appreciation of the
dollar against the indicated currency over the sample
period. The dollar fell against the deutschemark, yen,
and Swiss franc, but appreciated against the pound
sterling. The second row gives the average interest
rate differentialthe amount by which the foreign
interest rate exceeds the U.S. interest rate.9 According to the expectations hypothesis, these two numbers should be equalinterest rates should be
higher in countries whose currencies depreciate
against the dollar.
Suppose interest rates are higher in Germany
than in the U.S. Does this mean that one can earn
more money by investing in German bonds? There
are several reasons that the answer might be no.
First, of course, is default risk. Governments have
defaulted on bonds in the past and may do so again.
Second, and more important, is the risk of devaluation. If German interest rates are 10 percent and U.S.
interest rates are 5 percent, but the euro falls 5 percent relative to the dollar during the year, you make
no more money holding the German bonds
despite their attractive interest rate. Since
TABLE 6
lots of investors are making this calculaForward discount puzzle
tion, it is natural to conclude that an interest rate differential across countries on
DeutschePound
Swiss
bonds of similar credit risk should reveal
mark
sterling
Yen
franc
an expectation of currency devaluation.
Mean appreciation
–1.8
3.6
–5.0 –3.0
The logic is exactly the same as that of the
Mean interest differential
–3.9
2.1
–3.7 –5.9
expectations hypothesis in the term strucb, 1975–89
–3.1
–2.0
–2.1 –2.6
ture. Initially attractive yield or interest rate
R2
.026
.033
.034 .033
differentials should be met by an offsetting
b, 1976–96
–0.7
–1.8
–2.4 –1.3
event so that you make no more money
b, 10-year horizon
0.8
0.6
0.5
–
on average in one maturity or currency
Notes: The first row gives the average appreciation of the dollar against the
versus another.8
indicated currency, in percent per year. The second row gives the average
interest differential—foreign interest rate less domestic interest rate,
As with the expectations hypothesis
measured as the forward premium—the 30-day forward rate less the spot
in the term structure, the expected depreciexchange rate. The third through sixth rows give the coefficients and R2 in a
regression of exchange rate changes on the interest differential,
ation view still constitutes an important
first-order understanding of interest rate
st+1 – st = a + b ( rtf – rtd) + ε t+1,
differentials and exchange rates. For examwhere s = log spot exchange rate, r f = foreign interest rate, and
r d = domestic interest rate.
ple, interest rates in east Asian currencies
Source: Hodrick (2000), Engel (1996), and Meredith and Chinn (1998).
were very high on the eve of the recent
currency tumbles, and many banks were
48
Economic Perspectives
The second row shows roughly the expected pattern. Countries with steady long-term inflation have
steadily higher interest rates and steady depreciation.
The numbers in the first and second rows are not
exactly the same, but exchange rates are notoriously
volatile so these averages are not well measured. Hodrick (2000) shows that the difference between the
first and second rows is not statistically different
from zero. This fact is analogous to the evidence in
table 4 that the expectations hypothesis works well
on average for U.S. bonds.
As in the case of bonds, however, we can ask
whether times of temporarily higher or lower interest
rate differentials correspond to times of above- and
below-average depreciation as they should. The third
and fifth rows of table 6 update Famas (1984) regression tests. The number here should be +1.0 in each
case1 percentage point extra interest differential
should correspond to 1 percentage point extra expected depreciation. On the contrary, as table 6 shows,
a higher than usual interest rate abroad seems to lead
to further appreciation. This is the forward discount
puzzle. See Engel (1996) and Lewis (1995) for recent
surveys of the avalanche of academic work investigating whether this puzzle is really there and why.
The R2 values shown in table 6 are quite low.
However, like d/p and the term spread, the interest differential is a slow-moving forecasting variable, so the
return forecast R2 builds with horizon. Bekaert and
Hodrick (1992) report that the R2 rises to the 30 percent
to 40 percent range at six-month horizons and then
declines. Thats high, but not 100 percent; taking
advantage of any predictability strategy is quite risky.
The puzzle does not say that one earns more by
holding bonds from countries with higher interest
rates than others. Average inflation, depreciation,
and interest rate differentials line up as they should.
The puzzle does say that one earns more by holding
bonds from countries whose interest rates are higher
than usual relative to U.S. interest rates (and vice
versa). The fact that the usual rate of depreciation
and interest differential changes through time will, of
course, diminish the out-of-sample performance of
these trading rules.
One might expect that exchange rate depreciation
works better for long-run exchange rates, as the expectations hypothesis works better for long-run interest
rate changes. The last row of table 6, taken from
Meredith and Chinn (1998) verifies that this is so.
Ten-year exchange rate changes are correctly forecast
by the interest differentials of ten-year bonds.
Federal Reserve Bank of Chicago
Mutual funds
Studying the returns of funds that follow a specific strategy gives us a way to assess whether that
strategy works in practice, after transaction costs
and other trading realities are taken into account.
Studying the returns of actively managed funds tells
us whether the time, talent, and effort put into picking
securities pays off. Most of the literature on evaluating
fund performance is devoted to the latter question.
A large body of empirical work, starting with
Jensen (1969), finds that actively managed funds, on
average, underperform the market index. I use data
from Carhart (1997), whose measures of fund performance account for survivor bias. Survivor bias arises
because funds that do badly go out of business.
Therefore, the average fund that is alive at any point
in time has an artificially good track record.
As with the stock portfolios in figure 1, the fund
data in figure 7 show a definite correlation between
beta and average return: Funds that did well took on
more market risks. A cross-sectional regression line is
a bit flatter than the line drawn through the Treasury
bill and market return, but this is a typical result of
measurement error in the betas. (The data are annual,
and many funds are only around for a few years, contributing to beta measurement error.) The average fund
underperforms the line connecting Treasury bills and
the market index by 1.23 percent per year (that is, the
average alpha is 1.23 percent).
The wide dispersion in fund average returns in
figure 7 is a bit surprising. Average returns vary across
funds almost as much as they do across individual
stocks. This fact implies that the majority of funds
are not holding well-diversified portfolios that would
reduce return variation, but rather are loading up on
specific bets.
Initially, the fact that the average fund underperforms the market seems beside the point. Perhaps the
average fund is bad, but we want to know whether
the good funds are any good. The trouble is, we must
somehow distinguish skill from luck. The only way
to separate skill from luck is to group funds based
on some ex-ante observable characteristic, and then
examine the average performance of the group. Of
course, skillful funds should have done better, on
average, in the past, and should continue to do better
in the future. Thus, if there is skill in stock picking,
we should see some persistence in fund performance.
However, a generation of empirical work found no persistence at all. Funds that did well in the past were no
more likely to do well in the future.
49
French (1993) report that the HML portfolio alone gives nearly double the market
Average returns of mutual funds vs. market betas
Sharpe ratiothe same average return at
half the standard deviation. Why dont
average return
funds cluster around a risk/reward line
0.25
= value
significantly above the markets?
= neutral
Of course, we should not expect all
0.20
= growth
funds to cluster around a higher risk/re0.15
ward tradeoff. The average investor
holds the market, and if funds are large
0.10
enough, so must the average fund. Index
funds, of course, will perform like the in0.05
dex. Still, the typical actively managed
0.00
fund advertises high mean and, perhaps,
low variance. No fund advertises cutting
–0.05
average returns in half to spare investors
exposure to nonmarket sources of risk.
–0.10
Such funds, apparently aimed at mean
variance investors, should cluster
–0.50
0.00
0.50
1.00
1.50
around the highest risk/reward tradeoff
beta
available from mechanical strategies
Notes: Average returns of mutual funds over the Treasury bill rate versus their
(and more, if active management does
market betas. Sample consists of all funds with average total net assets
greater than $25 million and more than 25 percent of their assets in stocks,
any good). Most troubling, funds who
in the Carhart (1996) database. Data sample 1962–96. The average excess
return is computed as E (R – R ) = a + β x 9%. a and β are computed from a
say they follow value strategies dont
time-series regression of fund annual excess returns on market annual excess
returns over the life of the fund. The o, +, and x labels in the figure sort funds
outperform the market either. For example,
into thirds based on their regression coefficient h on the Fama–French value
Lakonishok, Shleifer, and Vishny (1992,
(HML) portfolio. The breakpoints are h = –0.084, 0.34. The dashed line gives
the fit of a cross-sectional ordinary least squares regression of a on β ; The
table 3) find that the average value fund
solid line connects the Treasury bill (β and excess return = 0) and the market
return (β = 1, excess return = 9%).
underperforms the S&P500 by 1 percent
just like all the others.
We can resolve this contradiction if
we
think
that
fund
managers were simply unaware of
Since the average fund underperforms the market,
the
possibilities
offered
by our new facts, and so
and fund returns are not predictable, we conclude
(despite
the
advertising)
were not really following
that active management does not generate superior
them.
That
seems
to
be
the
implication of figure 7,
performance, especially after transaction costs and
which
sorts
funds
by
their
HML
beta. One would exfees. This fact is surprising. Professionals in almost
pect
the
high-HML
beta
funds
to
outperform the marany field do better than amateurs. One would expect
ket
line.
But
the
cutoff
for
the
top
one-third of funds
that a trained experienced professional who spends
is
only
a
HML
beta
of
0.3,
and
even
that may be high
all day reading about markets and stocks should be
(many
funds
dont
last
long,
so
betas
are poorly meaable to outperform simple indexing strategies. Even if
sured;
the
distribution
of
measured
betas
is wider
entry into the industry is so easy that the average
than
the
actual
distribution).
Thus,
the
value
funds
fund does not outperform simple indexes one would
were
really
not
following
the
value
strategy
that
expect a few stars to outperform year after year, as
earns the HML returns; if they were doing so they
good teams win championship after championship.
would have HML betas of 1.0. Similarly, Lakonishok,
Alas, the contrary fact is the result of practically every
Shleifer, and Vishnys (1992) documentation of value
investigation, and even the anomalous results docufunds underperformance reveals that their market
ment very small effects.
beta is close to 1.0. These results imply that value
Funds and value
funds are not really following a value strategy, since
Given the value, small-firm, and predictability
their returns correlate with the market portfolio and not
effects, the idea that funds cluster around the market
the value portfolio.
line is quite surprising. All of these new facts imply
Interestingly, the number of value and small-cap
inescapably that there are simple, mechanical stratefunds (as revealed by their betas, not their marketing
gies that can give a risk/reward ratio greater than that
claims) is increasing quickly. Before 1990, 14 percent
of buying and holding the market index. Fama and
of funds had measured SMB betas greater than 1.0,
FIGURE 7
i
f
i
i
i
i
i
50
i
Economic Perspectives
and 12 percent had HML betas greater than 1.0. In
the full sample, both numbers have doubled to 22
percent and 23 percent. This trend suggests that
funds will, in the future, be much less well described
by the market index.
The view that funds were unaware of value strategies, and are now moving quickly to exploit them,
can explain why most funds still earn near the market
return, rather than the higher value return. However,
this view contradicts the view that the value premium
is an equilibrium risk premium, that is, that everyone
knew about the value returns but chose not to invest
all along because they feared the risks of value strategies. If it is not an equilibrium risk premium, it wont
last long.
individual fund returns. This result verifies that mutual
fund performance is persistent.
Perhaps the funds that did well took on more
market risks, raising their betas and, hence, average
returns in the following year. The third column in table
7 shows that this is not the case. The cross-sectional
variation in fund average returns has nothing to do
with market betas. Just as in the case of individual
stock returns, we have to understand fund returns
with multifactor models, if at all.
The last column of table 7 presents alphas (intercepts, the part of average return not explained by the
model) from a model with four factorsthe market,
the FamaFrench HML and SMB factors, and a momentum factor, PR1YR, that is long NYSE stocks that did
well in the last year and short NYSE stocks that did
Persistence in fund returns
poorly in the last year. In general, one should object
The fund counterpart to momentum in stock reto the inclusion of so many factors and such ad-hoc
turns has been more extensively investigated than
factors. However, this is a performance attribution
the value and size effects. Fund returns have also
rather than an economic explanation use of a multibeen found to be persistent. Since such persistence
factor model. We want to know whether fund perforcan be interpreted as evidence for persistent skill in
mance, and persistence in fund performance in
picking stocks, it is not surprising that it has attractparticular, is due to persistent stock-picking skill or
ed a great deal of attention, starting with Hendricks,
to mechanical strategies that investors could just as
Patel, and Zeckhauser (1993).
easily follow on their own, without paying the manTable 7, taken from Carhart (1997), shows that a
agement costs associated with investing through a
portfolio of the best-performing one-thirtieth of funds
fund. For this purpose, it does not matter whether the
last year outperforms a portfolio of the worst-performfactors represent true, underlying sources of macroing one-thirtieth of funds by 1 percent per month
economic risks.
(column 2). This is about the same size as the momenThe alphas in the last column of table 7 are almost
tum effect in stocks, and similarly results from a small
all about 1 percent to 2 percent per year negative. Thus,
autocorrelation plus a large standard deviation in
Carharts model explains that the persistence in fund
performance is due to persistence in the
underlying stocks, not persistent stockTABLE 7
picking skill. These results support the
Portfolios of mutual funds formed on previous years return
old conclusion that actively managed
funds underperform mechanical indexing
Average
4-factor
Last year rank
return
CAPM alpha
alpha
strategies. There is some remaining puzzling persistence, but it is all in the large
( - - - - - - - - - - - - - - - - - - - percent -- - - - - - - - - - - - - - - - - -)
negative alphas of the bottom one-tenth
1/30
0.75
0.27
–0.11
to bottom one-thirtieth of performers,
1/10
0.68
0.22
–0.12
which lose money year after year. Car5/10
0.38
–0.05
–0.14
hart also shows that the persistence of
9/10
0.23
–0.21
–0.20
fund performance is due to momentum in
10/10
0.01
–0.45
–0.40
the underlying stocks, rather than mo30/30
–0.25
–0.74
–0.64
mentum funds. If, by good luck, a fund
Notes: Each year, mutual funds are sorted into portfolios based on the
happened to pick stocks that went up
previous year’s return. The rank column gives the rank of the selected
portfolio. For example, 1/30 is the best performing portfolio when funds are
last year, the portfolio will continue to
divided into 30 categories. Average return gives the average monthly return
go up a bit this year.
in excess of the T-bill rate of this portfolio of funds for the following year.
Four-factor alpha gives the average return less the predictions of a
In sum, the new research does nothmultifactor model that uses the market, the Fama–French HML and SMB
ing
to
dispel the disappointing view of
portfolios, and portfolio PR1YR which is long NYSE stocks that did well in
the last year and short NYSE stocks that did poorly in the last year.
active management. However, we disSource: Carhart (1997).
cover that passively managed style
Federal Reserve Bank of Chicago
51
portfolios can earn returns that are not explained by
the CAPM.
Catastrophe insurance
A number of prominent funds have earned very
good returns (and others, spectacular losses) by following strategies such as convergence trades and
implicit put options. These strategies may also reflect
high average returns as compensation for nonmarket
dimensions of risk. They have not been examined at
the same level of detail as the value and small-cap
strategies, so I offer a possible interpretation rather
than a documented one.
Convergence trades take strong positions in very
similar securities that have small price differences.
For example, a 29.5-year Treasury bond typically
trades at a slightly higher yield (lower price) than a
30-year Treasury bond. (This was the most famous
bet placed by LTCM. See Lewis, 1999.) A convergence
trade puts a strong short position on the expensive
security and a strong long position on the cheap security. This strategy is often mislabeled an arbitrage.
However, the securities are similar, not identical. The
spread between 29.5- and 30-year Treasury bonds
reflects the lower liquidity of the shorter maturity
and the associated difficulty of selling it in a financial
panic. It is possible for this spread to widen. Nonetheless, panics are rare, and the average returns in
all the years when they do not happen may more than
make up for the spectacular losses when they do.
Put options protect investors from large price
declines. The volatility smile in put option prices
reflects the surprisingly high prices of such options,
compared with the small probability of large market
collapses (even when one calibrates the probability
directly, rather than using the log-normal distribution
of the BlackScholes formula). Writers of out-of-themoney puts collect a fee every month; in a rare market
collapse they will pay out a huge sum, but if the probability of the collapse is small enough, the average
returns may be quite good.
All of these strategies can be thought of as catastrophe insurance (Hsieh and Fung, 1999). Most of
the time they earn a small premium. Once in a great
while they lose a lot, and they lose a lot in times of
financial catastrophe, when most investors are really
anxious that the value of their investments not evaporate. Therefore, it is economically plausible that
these strategies can earn positive average returns,
even when we account for stock market risk via the
CAPM and we correctly measure the small probabilities
of large losses.
The difficulty in empirically estimating the true
average return of such strategies, of course, is that
52
rare events are rare. Many long samples will give a
false sense of security because the big one that
justifies the premium happened not to hit.
The value, yield curve, and foreign exchange
strategies I survey above also exhibit features of
catastrophe insurance. Value stocks may earn high
returns because distressed stocks will all go bankrupt
in a financial panic. Buying bonds of countries with
high interest rates leaves one open to the small chance
of a large devaluation, and such devaluation is
especially likely to happen in a global financial panic.
Similarly, buying long-term bonds in the depth of a
recession when the yield curve is upward sloping
may expose one to a small risk of a large inflation.
If these interpretations bear out, they also suggest that the premiumsthe average returns from
holding stocks sensitive to HML or from following
the bond and foreign exchange strategiesmay be
overstated in the data. The markets have had an unusually good 50 years, and devastating financial
panics have not happened.
Implications of the new facts
While the list of new facts appears long, similar
patterns show up in every case. Prices reveal slowmoving market expectations of subsequent returns,
because potential offsetting events seem sluggish
or absent. The patterns suggest that investors can
earn substantial average returns by taking on the
risks of recession and financial stress. In addition,
there is a small positive autocorrelation of highfrequency returns.
The effects are not completely new. We have
known since the 1960s that high-frequency returns
are slightly predictable, with R2 of 0.01 to 0.1 in daily
to monthly returns. These effects were dismissed
because there didnt seem to be much one could do
about them. A 51/49 bet is not very attractive, especially if there is any transaction cost. Also, the increased
Sharpe ratio (mean excess return/standard deviation)
from exploiting predictability is directly related to the
forecast R2, so a tiny R2, even if exploitable, did not
seem important. Now, we have a greater understanding of the potential importance of these effects and
their economic interpretations.
For price effects, we now realize that the R2 rises
with horizon when the forecasting variables are slowmoving. Hence, a small R2 at short horizons can mean a
really substantial R2 in the 30 percent to 50 percent
range at longer horizons. Also, the nature of these
effects suggests the kinds of additional sources of
priced risk that theorists had anticipated for 20 years.
For momentum effects, the ability to sort stocks and
Economic Perspectives
funds into momentum-based portfolios means that very
small predictability times portfolios with huge past returns gives important subsequent returns, though it is
not totally clear that this amplification of the small predictability really does survive transaction costs.
Price-based forecasts
If expected returns rise, prices are driven down,
since future dividends or other cash flows are discounted at a higher rate. A low price, then, can reveal a market expectation of a high expected or required return.10
Most of our results come from this effect. Low
price/dividend, price/earnings, or price/book values
signal times when the market as a whole will have high
average returns. Low market value (price times shares)
relative to book value signals securities or portfolios
that earn high average returns. The small-firm effect derives from low pricesother measures of size
such as number of employees or book value alone
have no predictive power for returns (Berk, 1997).
The five-year reversal effect derives from the fact
that five years of poor returns lead to a low price. A
high long-term bond yield means that the price of longterm bonds is low, and this seems to signal a time
of good long-term bond returns. A high foreign interest rate means a low price on foreign bonds, and this
seems to indicate good returns on the foreign bonds.
The most natural interpretation of all these effects
is that the expected or required returnthe risk premiumon individual securities as well as the market
as a whole varies slowly over time. Thus we can track
market expectations of returns by watching price/dividend, price/earnings, or book/market ratios.
Absent offsetting events
In each case, an apparent difference in yield
should give rise to an offsetting movement, but does
not seem to do so. Something should be predictable
so that returns are not predictable, and it is not. Figure
8 provides a picture of the results in table 5. Suppose
that the yield curve is upward sloping as in panel A.
What does this mean? If the expectations model were
true, the forward rates plotted against maturity would
translate one for one to the forecast of future spot
rates in panel B, as plotted in the black line marked
Expectations model. A high long-term bond yield
relative to short-term bond yields should not mean a
higher expected long-term bond return. Subsequent
short rates should rise, cutting off the one-period
advantage of long-term bonds and raising the multiyear advantage of short-term bonds.
In figure 8, panel b, the colored line marked Estimates shows the actual forecast of future spot interest rates from the results in table 5. The essence of the
phenomenon is sluggish adjustment of the short
rates. The short rates do eventually rise to meet the
forward rate forecasts, but not as quickly as the forward rates predict they should. Short-term yields
should be forecastable so that returns are not forecastable. In fact, yields are almost unforecastable,
so, mechanically, bond returns are. The roughly 1.0
coefficients in panel B of table 5 mean that a 1 percentage point increase in the forward rate translates
into a 1 percentage point increase in expected return.
It seems that old fallacy of confusing bond yields
with their expected returns for the first year contains
a grain of truth.
FIGURE 8
Yield curve and forecast one-year interest rates
A. Current yield curve
B. Forecast one-year interest rates
percent
7.0
forecast interest rate
7.0
Forward rate
6.5
Expectations
model
6.5
Yield
6.0
6.0
Estimates
5.5
5.5
5.0
5.0
4.5
4.5
1
2
3
maturity, years
4
5
1
2
3
4
time in the future, years
5
Notes: Assuming that the current yield curve is as shown in panel A, the black line in panel
B gives the forecast from the expectations hypothesis, in which case forward rates today are
the forecast of future spot rates. The colored line in panel B gives the actual forecast of future
spot rates, constructed from the estimates in table 5.
Federal Reserve Bank of Chicago
53
In the same way, a high dividend yield on a stock
or portfolio should mean that dividends grow more
slowly over time, or, for individual stocks, that the firm
has taken on more market risk and will have a higher
market beta. These tendencies seem to be completely
absent. Dividend/price ratios do not seem to forecast
dividend growth and, hence, (mechanically) they
forecast returns. The one-year coefficient in table 1 is
very close to 1.00, meaning that a 1 percentage point
increase in the dividend yield translates into a 1 percentage point increase in return. It seems that the old
fallacy of confusing increased dividend yield with increased total return does contain a grain of truth.
A high foreign interest rate relative to domestic
interest rates should not mean a higher expected return. We should see, on average, an offsetting depreciation. But here, the coefficients are even larger than
1.0. An interest rate differential seems to predict a further appreciation. It seems that the old fallacy of
confusing interest rate differentials across countries
with expected returns, forgetting about depreciation,
also contains a grain of truth.
Economic interpretation
The price-based predictability patterns suggest
a premium for holding risks related to recession and
economy-wide financial distress. Stock and bond predictability are linked: The term spread (forward-spot,
or long yieldshort yield) forecasts stock returns as
well as bond returns (Fama and French, 1989). Furthermore, the term spread is one of the best variables
for forecasting business cycles. It rises steeply at the
bottom of recessions and is inverted at the top of a
boom. Return forecasts are high at the bottom of a
business cycle and low at the top of a boom. Value
and small-cap stocks are typically distressed. Empirically successful economic models of the recession and
distress premiums are still in their infancy (Campbell
and Cochrane, 1999, is a start), but the story is at
least plausible and the effects have been expected
by theorists for a generation.
To make this point come to life, think concretely
about what you have to do to take advantage of the
predictability strategies. You have to buy stocks or
long-term bonds at the bottom, when stock prices are
low after a long and depressing bear market, in the
bottom of a recession or the peak of a financial panic.
This is a time when few people have the guts or the
wallet to buy risky stocks or risky long-term bonds.
Looking across stocks rather than over time, you have
to invest in value or small-cap companies, with years
of poor past returns, poor sales, or on the edge of
bankruptcy. You have to buy stocks that everyone
else thinks are dogs. Then, you have to sell stocks
54
and long-term bonds in good times, when stock prices
are high relative to dividends, earnings, and other
multiples and the yield curve is flat or inverted so
that long-term bond prices are high. You have to sell
the popular growth stocks, with good past returns,
good sales, and earnings growth.
You have to sell now, and the stocks that you
should sell are the blue-chips that everyone else seems
to be buying. In fact, the market timing strategies said
to sell long ago; if you did so, you would have missed
much of the runup in the Dow past the 6,000 point. Value stocks too have missed most of the recent market
runup. However, this shouldnt worry youa strategy
that holds risks uncorrelated with the market must underperform the market close to half of the time.
If this feels uncomfortable, what youre feeling
is risk. If youre uncomfortable watching the market
pass you by, perhaps you dont really only care about
long-run mean and variance; you also care about
doing well when the market is doing well. If you want
to stay fully invested in stocks, perhaps you too feel
the time-varying aversion to or exposure to risk that
drives the average investor to stay fully invested
despite low prospective returns.
This line of explanation for the foreign exchange
puzzle is still a bit farther off (see Engel, 1996, for a
survey; Atkeson, Alvarez, and Kehoe, 1999, offer a
recent stab at an explanation). The strategy leads investors to invest in countries with high interest rates.
High interest rates are often a sign of monetary instability or other economic trouble, and thus may mean
that the investments are more exposed to the risks of
global financial stress or a global recession than are
investments in the bonds of countries with low interest
rates, which are typically enjoying better times.
Return correlation
Momentum and persistent fund performance
explained by a momentum factor are different from the
price-based predictability results. In both cases, the
underlying phenomenon is a small predictability of
high-frequency returns. The price-based predictability strategies make this predictability important by
showing that, with a slow-moving forecasting variable,
the R2 builds over horizon. Momentum, however, is
based on a fast-moving forecast variablethe previous years return. Therefore, the R2 declines rather
than building with horizon. Momentum makes the
small predictability of high-frequency returns significant in a different way, by forming portfolios of extreme
winners and losers. The large volatility of returns means
that the extreme portfolios will have extreme past
returns, so only a small continuation of past returns
gives a large current return.
Economic Perspectives
It would be appealing to understand momentum
as a reflection of slowly time-varying average expected
returns or risk premiums, like the price-based predictability strategies. If a stocks average return rises for
a while, that should make returns higher both today
and tomorrow. Thus, a portfolio of past winners will
contain more than its share of stocks that performed
well because their average returns were higher, along
with stocks that performed well due to luck. The
average return of such a portfolio should be higher
tomorrow as well.
Unfortunately, this story has to posit a substantially different view of the underlying process for
varying expected returns than is needed to explain
everything else. The trouble is that a surprise increase
in expected returns means that prices will fall, since
dividends are now discounted at a greater rate. This
is the phenomenon we have relied on to explain why
low price/dividend, price/earnings, book/market,
value, and size forecast higher subsequent returns.
Therefore, positive correlation of expected returns
typically yields a negative correlation of realized
returns. To get a positive correlation of realized returns
out of slow expected return variation, you have to
imagine that an increase in average returns today is
either highly correlated with a decrease in expected
future dividend growth or with a decrease in expected
returns in the distant future (an impulse response
that starts positive but is negative at long horizons).
Campbell, Lo, and MacKinlay (1997) provide a quantitative exposition of these effects.
Furthermore, momentum returns have not yet
been linked to business cycles or financial distress in
even the informal way that I suggested for price-based
strategies. Thus, momentum still lacks a plausible
economic interpretation. To me, this adds weight to
the view that it isnt there, it isnt exploitable, or it
represents a small illiquidity (tax-loss selling of small
illiquid stocks) that will be quickly remedied once a
few traders understand it.
Remaining doubts
The size of all these effects is still somewhat
in question. It is always hard to measure average
returns of risky strategies. The standard formula
s / T for the standard error of the mean, together
with the high volatility σ of any strategy, means that
one needs 25 years of data to even start to measure
average returns. With σ = 16 percent (typical of the
index), even T = 25 years means that one standard
error is 16/5 ≅ 3 percent per year, and a two-standard
error confidence interval runs plus or minus 6 percentage points. This is not much smaller than the average
returns we are trying to measure. In addition, all of
Federal Reserve Bank of Chicago
these facts are highly influenced by the small probability of rare events, which makes measuring average
returns even harder.
Finally, viewed the right way, we have very few
data points with which to evaluate predictability. The
term premium and interest rate differentials only change
sign with the business cycle, and the dividend/price
ratio only crosses its mean once every generation.
The history of interest rates and inflation in the U.S.
is dominated by the increase, through two recessions,
to a peak in 1980 and then a slow decline after that.
Many of the anomalous risk premiums seem to
be declining over time. Figure 6 shows the decline in
the HML and SMB premiums, and the same may be
true of the predictability effects. The last three years
of high market returns have cut the estimated return
predictability from the dividend/price ratio in half.
This fact suggests that at least some of the premium
the new strategies yielded in the past was due to the
fact that they were simply overlooked.
Was it really clear to average investors in 1947 or
1963 (the beginning of the data samples) that stocks
would earn 9 percent over bonds, and that the strategy of buying distressed small stocks would double
even that return for the same level of risk? Would average investors have changed their portfolios with this
knowledge? Or would they have stayed pat, explaining that these returns are earned as a reward for risk
that they were not willing to take? Was it clear that
buying stocks at the bottom in the mid-1970s would
yield so much more than even that high average return? If we interpret the premiums measured in sample as true risk premiums, the answer must be yes.
If the answer is no, then at least some part of the
premium was luck and will disappear in the future.
Since the premiums are hard to measure, one is
tempted to put less emphasis on them. However, they
are crucial to our interpretation of the facts. The
CAPM is perfectly consistent with the fact that there
are additional sources of common variation. For example, it was long understood that stocks in the same
industry move together; the fact that value or small
stocks also move together need not cause a ripple.
The surprise is that investors seem to earn an average
return premium for holding these additional sources
of common movement, whereas the CAPM predicts
that (given beta) they should have no effect on a
portfolios average returns.
The behavior of funds also suggests the overlooked strategy interpretation. As explained earlier,
fund returns still cluster around the market line. It turns
out that very few fund returns actually followed the
value or other return-enhancing strategies. However,
the number of small, value, and related fundsfunds
55
that actually do follow the strategieshas increased
dramatically in recent years. It might be possible to
explain this in a way consistent with the idea that investors knew the premiums were there all along, but
such an argument is obviously strained.
Conclusion
In sum, it now seems that investors can earn a
substantial premium for holding dimensions of risk
unrelated to market movements, such as recessionrelated or distress-related risk. Investors earn these
premiums by following strategies, such as value and
growth, market-timing possibilities generated by return
predictability, dynamic bond and foreign exchange
strategies, and maybe even a bit of momentum. The
exact size of the premiums and the economic nature
of the underlying risks is still a bit open to question,
but researchers are unlikely to go back to the simple
view that returns are independent over time and that
the CAPM describes the cross section.
The next question is, What should investors do
with this information? The article, Portfolio advice
for a multifactor world, also in this issue, addresses
that question.
NOTES
The market also tends to go down in recessions; however
recessions can be unusually severe or mild for a given level of
market return. What counts here is the severity of the recession
for a given market return. Technically, we are considering
betas in a multiple regression that includes both the market
return and a measure of recessions. See box 1.
1
2
I thank Gene Fama for providing me with these data.
The rest of the paragraph is my interpretation, not Fama and
Frenchs. They focus on the firms financial distress, while I
focus on the systematic distress, since idiosyncratic distress
cannot deliver a risk price.
3
Fama and French do not provide direct measures of standard deviations for these portfolios. One can infer, however, from the
betas, R2 values, and standard deviation of the market and factor
portfolios that the standard deviations are roughly one to two
times that of the market return, so Sharpe ratios of these strategies are comparable to that of the market return in sample.
4
The index autocorrelations suffer from some upward bias
since some stocks do not trade every day. Individual stock
autocorrelations are generally smaller, but are enough to
account for the momentum effect.
6
Panel B is really not independent evidence, since the coefficients in panels A and B of table 5 are mechanically linked. For
example, 1.14 + (0.14) = 1.0, and this holds as an accounting
identity. Fama and Bliss (1987) call them complementary
regressions.
7
As with bonds, the expectations hypothesis is slightly different
from pure risk neutrality since the expectation of the log is
not the log of the expectation. Again, the size of the phenomena we study swamps this distinction.
8
The data are actually the spread between the forward exchange
rate and the spot exchange rate, but this quantity must equal
the interest rate differential in order to preclude arbitrage.
9
This effect is initially counterintuitive. One might suppose
that a higher average return would attract investors, raising
prices. But the higher prices, for a given dividend stream, must
reduce subsequent average returns. High average returns persist,
in equilibrium, when investors fear the increased risks of an
asset and try to sell, lowering prices.
10
5
We are looking for
I rf (r)dr
E(r|r x) = x
,
I x f (r)dr
where x is defined as the top one-tenth cutoff,
f ( r ) dr = 1 .
I x
10
With a normal distribution, x = 1.2816σ and E(r|r≥x) = 1.755σ.
REFERENCES
Atkeson, Andrew, Fernando Alvarez, and Patrick
Kehoe, 1999, Volatile exchange rates and the forward
premium anomaly: A segmented asset market view,
University of Chicago, working paper.
Banz, R. W., 1981, The relationship between return
and market value of common stocks, Journal of
Financial Economics, Vol. 9, No. 1, pp. 318.
Bekaert, Geert, and Robert J. Hodrick, 1992, Characterizing predictable components in excess returns
56
on equity and foreign exchange markets, Journal of
Finance, Vol. 47, No. 2, June, pp. 467509.
Berk, Jonathan, 1997, Does size really matter?,
Financial Analysts Journal, Vol. 53, September/
October, pp. 1218.
Campbell, John Y., 1996, Understanding risk and return, Journal of Political Economy, Vol. 104, No. 2,
April, pp. 298345.
Economic Perspectives
Campbell, John Y., and John H. Cochrane, 1999, By
force of habit: A consumption-based explanation of
aggregate stock market behavior, Journal of Political
Economy, Vol. 107, No. 2, April, pp. 205251.
Fama, Eugene F., and Robert R. Bliss, 1987, The
information in long-maturity forward rates, American
Economic Review, Vol. 77, No. 4, September,
pp. 680692.
Campbell, John Y., Andrew W. Lo, and A. Craig
MacKinlay, 1997, The Econometrics of Financial
Markets, Princeton, NJ: Princeton University Press.
Fama, Eugene F., and Kenneth R. French, 1997, Industry costs of equity, Journal of Financial Economics,
Vol. 43, No. 2, February, pp. 153193.
Carhart, Mark M., 1997, On persistence in mutual
fund performance, Journal of Finance, Vol. 52, No.
1, March, pp. 5782.
, 1996, Multifactor explanations of assetpricing anomalies, Journal of Finance, Vol. 51, No. 1,
March, pp, 5584.
Chen, Nai-Fu, Richard Roll, and Stephen A. Ross,
1986, Economic forces and the stock market, Journal
of Business, Vol. 59, No. 3, July, pp. 383403.
, 1995, Size and book-to-market factors in
earnings and returns, Journal of Finance, Vol. 50,
No.1, March, pp. 131155.
Cochrane, John H., 1997, Where is the market going?
Uncertain facts and novel theories, Economic
Perspectives, Federal Reserve Bank of Chicago, Vol.
21, No. 6, November/December, pp. 337.
, 1993, Common risk factors in the returns
on stocks and bonds, Journal of Financial Economics, Vol. 33, No. 1, February, pp. 356.
, 1996, A cross-sectional test of an investment-based asset pricing model, Journal of Political
Economy, Vol. 104, No. 3, June, pp. 572621.
, 1991, Volatility tests and efficient markets: Review essay, Journal of Monetary Economics; Vol. 27, No. 3, June, pp. 463-485.
Daniel, Kent, David Hirshleifer, and Avanidhar
Subrahmanyam, 1998, Investor psychology and
security market under- and overreactions, Journal
of Finance, Vol. 3, No. 6, December, pp. 18391885.
DeBondt, Werner F. M., and Richard H. Thaler,
1985, Does the stock market overreact?, Journal
of Finance, Vol. 40, No. 3, pp. 793805.
Engel, Charles, 1996, The forward discount anomaly
and the risk premium: A survey of recent evidence,
Journal of Empirical Finance, Vol. 3, pp. 123192.
Fama, Eugene F. 1991, Efficient markets II, Journal
of Finance, Vol. 46, No. 5, December, pp. 15751617.
, 1984, Forward and spot exchange
rates, Journal of Monetary Economics, Vol. 14,
No. 3, November, pp. 319338.
, 1970, Efficient capital markets: A review
of theory and empirical work, Journal of Finance,
Vol. 25, No. 2, May, pp. 383417.
, 1965, The behavior of stock market prices,
Journal of Business, Vol. 38, No. 1, pp. 34105.
Federal Reserve Bank of Chicago
, 1989, Business conditions and expected
returns on stocks and bonds, Journal of Financial
Economics, Vol. 25, No. 1, November, pp. 2349.
Heaton, John, and Deborah Lucas, 1997, Portfolio
choice and asset prices: The importance of entrepreneurial risk, Northwestern University, manuscript.
Hendricks, Darryll, Jayendu Patel, and Richard
Zeckhauser, 1993, Hot hands in mutual funds:
Short-term persistence of performance, Journal of
Finance, Vol. 48, No. 1, March, pp. 93130.
Hodrick, Robert, 2000, International Financial
Management, Englewood Cliffs, NJ: Prentice-Hall,
forthcoming.
Hsieh, David, and William Fung, 1999, Hedge fund
risk management, Duke University, working paper.
Jagannathan, Ravi, and Zhenyu Wang, 1996, The
conditional CAPM and the cross-section of expected
returns, Journal of Finance, Vol. 51, No. 1, March,
pp. 353.
Jegadeesh, Narasimham, and Sheridan Titman,
1993, Returns to buying winners and selling losers:
Implications for stock market efficiency, Journal of
Finance, Vol. 48, No. 1, March, pp. 6591.
Jensen, Michael C., 1969, The pricing of capital
assets and evaluation of investment portfolios,
Journal of Business, Vol. 42, No. 2, April, pp. 167247.
57
Lakonishok, Josef, Andrei Shleifer, and Robert W.
Vishny, 1992, The structure and performance of the
money management industry, Brookings Papers on
Economic Activity: Microeconomics 1992, Washington, DC, pp. 339391
LeRoy, Stephen F., and Richard D. Porter, 1981, The
present-value relation: Tests based on implied variance bounds, Econometrica, Vol. 49, No. 3, May, pp.
555574.
Lewis, Karen, K., 1995, Puzzles in international
financial markets, in Handbook of International
Economics, Vol. 3, G. Grossman and K. Rogoff (eds.),
Amsterdam, New York, and Oxford: Elsevier Science
B.V, pp. 19131971.
, 1971, Optimum consumption and portfolio rules in a continuous time model, Journal of
Economic Theory, Vol. 3, No. 4, pp. 373413.
, 1969, Lifetime portfolio selection under
uncertainty: The continuous time case, Review of
Economics and Statistics, Vol. 51, No. 3, August,
pp. 247257.
Moskowitz, Tobias, and Mark Grinblatt, 1999, Tax
loss selling and return autocorrelation: New evidence,
University of Chicago, working paper.
, 1998, Do industries explain momentum?, University of Chicago, CRSP working paper,
No. 480.
Lewis, Michael, 1999, How the eggheads cracked,
New York Times Magazine, January 24,
pp. 2442.
New York Times Company, 1999, Mutual funds
report: Whats killing the value managers?, New
York Times, April 4, Section 3, p. 29.
Liew, Jimmy, and Maria Vassalou, 1999, Can book-tomarket, size and momentum be risk factors that predict economic growth?, Columbia University,
working paper.
Reyfman, Alexander, 1997, Labor market risk and
expected asset returns, University of Chicago,
Ph.D. thesis.
MacKinlay, A. Craig, 1995, Multifactor models do
not explain deviations from the CAPM, Journal of
Financial Economics, Vol. 38, No. 1, pp. 328.
Malkiel, Burton, 1990, A Random Walk Down Wall
Street, New York: Norton.
Markowitz, H., 1952, Portfolio selection, Journal
of Finance, Vol. 7, No. 1, March, pp. 7799.
Meredith, Guy, and Menzie D. Chinn, 1998, Longhorizon uncovered interest rate parity, National Bureau of Economic Research, working paper, No. 6797.
Merton, Robert C., 1973, An intertemporal capital
asset pricing model, Econometrica, Vol. 41, No. 5,
September, pp. 867887.
58
Ross, S. A., 1976, The arbitrage theory of capital
asset pricing, Journal of Economic Theory, Vol. 13,
No. 3, December, pp. 341360.
Samuelson, Paul A., 1969, Lifetime portfolio selection by dynamic stochastic programming, Review
of Economics and Statistics, Vol. 51, No. 3, August,
pp. 239246.
Sargent, Thomas J., 1993, Bounded Rationality in
Macroeconomics, Oxford: Oxford University Press.
Shiller, Robert J., 1981, Do prices move too much
to be justified by subsequent changes in dividends?, American Economic Review, Vol. 71, No. 3,
June, pp. 421436.
Economic Perspectives
Portfolio advice for a multifactor world
John H. Cochrane
Introduction and summar
y
summary
A companion article in this issue, New facts in
finance, summarizes the revolution in how financial
economists view the world. Briefly, there are strategies
that result in high average returns without large betas,
that is, with no strong tendency for the strategys
returns to move up and down with the market as a
whole. Multifactor models have supplanted the capital
asset pricing model (CAPM) in describing these phenomena. Stock and bond returns, once thought to be
independent over time, turn out to be predictable at
long horizons. All of these phenomena seem to reflect
a premium for holding macroeconomic risks associated
with the business cycle and for holding assets that
do poorly in times of financial distress. They also all
reflect the information in priceshigh prices lead to
low returns and low prices lead to high returns.
The world of investment opportunities has also
changed. Where once an investor faced a fairly straightforward choice between managed mutual funds, index
funds, and relatively expensive trading on his own
account, now he must choose among a bewildering
variety of fund styles (such as value, growth, small
cap, balanced, income, global, emerging market, and
convergence), as well as more complex claims of active
fund managers with customized styles and strategies,
and electronic trading via the Internet. (Msn.coms
latest advertisement suggests that one should sign
up in order to check the hours hottest stocks. Does
a beleaguered investor really have to do that to earn
a reasonable return?) The advertisements of investment advisory services make it seem important to tailor
an investment portfolio from this bewildering set of
choices to the particular circumstances, goals, and
desires of each investor.
What should an investor do? An important current of academic research investigates how portfolio
theory should adapt to our new view of the financial
Federal Reserve Bank of Chicago
world. In this article, I summarize this research and I
distill its advice for investors. In particular, which of
the bewildering new investment styles seem most
promising? Should you attempt to time stock, bond,
or foreign exchange markets, and if so how much?
To what extent and how should an investment portfolio be tailored to your specific circumstances? Finally,
what can we say about the future investment environment? What kind of products will be attractive to
investors in the future, and how should public policy
react to these financial innovations?
I start by reviewing the traditional academic portfolio advice, which follows from the traditional view
that the CAPM is roughly correct and that returns are
not predictable over time. In that view, all investors
(who do not have special information) should split
their money between risk-free bonds and a broadbased passively managed index fund that approximates
the market portfolio. More risk-tolerant investors
put more money into the stock fund, more risk averse
investors put more money into the bond fund, and
that is it.
The new academic portfolio advice reacts to the
new facts. An investor should hold, in addition to the
market portfolio and risk-free bonds, a number of passively managed style funds that capture the broad
(nondiversifiable) risks common to large numbers
John H. Cochrane is the Sigmund E. Edelstone
Professor of Finance in the Graduate School of
Business at the University of Chicago, a consultant to
the Federal Reserve Bank of Chicago, and a research
associate at the National Bureau of Economic Research
(NBER). The author thanks Andrea Eisfeldt for research
assistance and David Marshall, John Campbell, and
Robert Shiller for comments. The authors research is
supported by the Graduate School of Business and by
a grant from the National Science Foundation,
administered by the NBER.
59
of investors. In addition to the overall level of risk
aversion, his exposure to or aversion to the various
additional risk factors matters as well. For example,
an investor who owns a small steel company should
shade his investments away from a steel industry
portfolio, or cyclical stocks in general; a wealthy investor with no other business or labor income can afford
to take on the value and other stocks that seem to
offer a premium in return for potentially poor performance in times of financial distress. The stock market
is a way of transferring risks; those exposed to risks
can hedge them by proper investments, and those
who are not exposed to risks can earn a premium by
taking on risks that others do not wish to shoulder.
Since returns are somewhat predictable, investors
can enhance their average returns by moving their
assets around among broad categories of investments.
However, the market timing signals are slow-moving,
and I show that the uncertainty about the nature and
strength of market timing effects dramatically reduces
the optimal amount by which investors can profit
from them.
I emphasize a cautionary fact: The average investor must hold the market. You should only vary from
a passive market index if you are different from everyone else. It cannot be the case that every investor
should tilt his portfolio toward value or other highyield strategies. If everybody did it, the phenomenon
would disappear. Thus, if such strategies will persist
at all, it must be the case that for every investor who
should take advantage of them, there is another investor who should take an unusually low position,
sacrificing the good average returns for a reduction
in risk. It cannot be the case that every investor
should market time, buying when prices are low
and selling when prices are high. If everyone did it,
that phenomenon would also disappear. The phenomenon can only persist if, for every investor who should
enhance returns by such market-timing, there is another investor who is so exposed to or averse to the
time-varying risks that cause return predictability,
that he should buy high and sell low, again earning
a lower average return in exchange for avoiding risks.
We have only scratched the surface of asset
markets usefulness for sharing risks. As often in economics, what appears from the outside to be greedy
behavior is in fact socially useful.
The traditional view
The new portfolio theory really extends rather
than overturns the traditional academic portfolio theory. Thus, its useful to start by reminding ourselves
what the traditional portfolio theory is and why. The
traditional academic portfolio theory, starting from
60
Markowitz (1952) and expounded in every finance
textbook, remains one of the most useful and enduring
bits of economics developed in the last 50 years.
Two-fund theorem
The traditional advice is to split your investments
between a money-market fund and a broad-based,
passively managed stock fund. That fund should concentrate on minimizing fees and transaction costs,
period. It should avoid the temptation to actively
manage its portfolio, trying to chase the latest hot
stock or trying to foresee market movements. An index
fund or other approximation to the market portfolio
that passively holds a bit of every stock is ideal.
Figure 1 summarizes the analysis behind this
advice. The straight line gives the mean-variance
frontierthe portfolios that give the highest mean
return for every level of volatility. Every investor
should pick a portfolio on the mean-variance frontier.
The upward-curved lines are indifference curves that
represent investors preference for more mean return
and less volatility. The indifference curve to the lower
left represents a risk-averse investor, who chooses a
portfolio with less mean return but also less volatility;
the indifference curve to the upper right represents a
more risk-tolerant investor who chooses a portfolio
with more mean return but also higher risk.
This seems like a lot of person-specific portfolio
formation. However, every portfolio on the mean-variance frontier can be formed as a combination of a
risk-free money-market fund and the market portfolio
of all risky assets. Therefore, every investor need only
hold different proportions of these two funds.
Bad portfolio advice
The portfolio advice is not so remarkable for what
it does say, which given the setup is fairly straightforward, as for what it does not say. Compared with
common sense and much industry practice, it is radical advice.
One might have thought that investors willing to
take on a little more risk in exchange for the promise
of better returns should weight their portfolios to
riskier stocks, or to value, growth, small-cap, or other
riskier fund styles. Conversely, one might have thought
that investors who are willing to forego some return
for more safety should weight their portfolios to safer
stocks, or to blue-chip, income, or other safer fund
styles. Certainly, some professional advice in deciding
which style is suited for an investors risk tolerance,
if not a portfolio professionally tailored to each investors circumstances, seems only sensible and prudent.
The advertisements that promise we build the portfolio thats right for you cater to this natural and
sensible-sounding idea.
Economic Perspectives
Figure 1 proves that nothing of the sort is true.
All stock portfolios lie on or inside the curved risky
asset frontier. Hence, an investor who wants more
return and is willing to take more risk than the market
portfolio will do better by borrowing to invest in the
marketincluding the large-cap, income, and otherwise safe stocksthan by holding a portfolio of riskier stocks. An investor who wants something less
risky than the market portfolio will do better by splitting his investment between the market and a moneymarket fund than by holding only safe stocks, even
though his stock portfolio will then contain some of
the small-cap, value, or otherwise risky stocks. Everyone holds the same market portfolio; the only decision
is how much of it to hold.
The two-fund theorem in principle still allows for
a good deal of customized portfolio formation and
active management if investors or managers have
different information or beliefs. For example, if an investor knows that small-cap stocks are ready for a
rebound, then the optimal (or tangency) portfolio that
reflects this knowledge will be more heavily weighted
toward small-cap stocks than the market portfolio held
by the average investor. All the analysis of figure 1
holds, but this specially constructed tangency portfolio goes in the place indicated by the market portfolio in the figure. However, the empirical success of
market efficiency, and the poor performance of professional managers relative to passive indexation, strongly
suggests that these attempts will not pay off for most
investors. For this reason, the standard advice is to
hold passively managed funds that concentrate on
minimizing transaction costs and fees, rather than a
carefully constructed tangency portfolio that reflects
an investors or managers special insights. However,
a quantitative portfolio management industry tries
hard to mix information or beliefs about the behavior
of different securities with the theory of figure 1 (for
example, see Black and Litterman, 1991).
The two-fund theorem leaves open the possibility
that the investors horizon matters as well as his risk
aversion. What could be more natural than the often
repeated advice that a long-term investor can afford
to ride out all the markets short-term volatility, while
a short-term investor should avoid stocks because he
may have to sell at the bottom rather than wait for the
inevitable recovery after a price drop? The fallacy
lies in the inevitable recovery. If returns are close
to independent over time (like a coin flip), and prices
are close to a random walk, a price drop makes it no
more likely that prices will rise more in the future. This
view implies that stocks are not safer in the long run,
and the stock/bond allocation should be independent
of investment horizon.
This proposition can be shown to be precisely
true in several popular mathematical models of the
portfolio decision. If returns are independent over
time, then the mean and variance of continuously
compounded returns rises in proportion to the horizon:
The mean and variance of ten-year returns are ten
times those of one-year returns, so the ratio of mean
to variance is the same at all horizons. More elegantly,
Merton (1969) and Samuelson (1969) show that an
investor with a constant relative risk aversion utility
who can continually rebalance his portfolio between
stocks and bonds will always choose the same stock/
bond proportion regardless of investment horizon,
when returns are independent over time.
Taking the advice
This advice has had a sizable impact on portfolio
practice. Before this advice was widely popularized in
the early 1970s, the proposition that professional active
management and stock selection could outperform
blindly holding an index seemed selfevident, and passively managed index
FIGURE 1
funds were practically unknown. They
have exploded in size since then. The
Mean-variance frontier, optimal portfolios
remaining actively managed funds clearly
and two-fund theorem
feel the need to defend active management
average return E(R)
Mean-variance
in the face of the advice to hold passive
frontier
Investors want
index funds and the fact that active managers selected on any ex-ante basis underRisky-asset
Optimal portfolios
frontier
perform indexes ex-post.
Market portfolio
The one input to the optimal portfoOriginal assets
lio advice is risk tolerance, and many providers of investment services have started
Rf
thinking about how to measure risk tolerance using a series of questionnaires.
This is the trickiest part of the convenvolatility σ (R)
tional advice, in part since conventional
Federal Reserve Bank of Chicago
61
measures of risk tolerance often seem quite out of
whack with risk aversion displayed in asset markets.
(This is the equity premium puzzle; see Cochrane,
1997, for a review.) However, the basic question is
whether one is more risk tolerant or less risk tolerant
than the average investor. This question is fairly easy
to conceptualize and can lead to a solid qualitative,
if not quantitative, answer.
One might object to the logical inconsistency of
providing portfolio advice based on a view of the
world in which everyone is already following such
advice. (This logic is what allowed me to identify the
mean-variance frontier with the market portfolio.)
However, this logic is only wrong if other investors
are systematically wrong. If some investors hold too
much of a certain stock, but others hold too little of
it, market valuations are unaffected and the advice to
hold the market portfolio is still valid.
New portfolio theory
Multiple factors: An N-fund theorem
Figure 2 shows how the simple two-fund theorem
of figure 1 changes if there are multiple sources of
priced risk. This section is a graphical version of Famas
(1996) analysis. Much of the theory comes from
Merton (1969, 1971, 1973).
To keep the figure simple I consider just one additional factor. For concreteness, think of an additional
recession factor. Now, investors care about three
attributes of their portfolios: 1) They want higher
average returns; 2) they want lower standard deviations or overall risk; and 3) they are willing to accept
a portfolio with a little lower mean return or a little
higher standard deviation of return if the portfolio
does not do poorly in recessions. In the context of
figure 2, this means that investors are happier with
portfolios that are higher up (more mean), more to the
left (less standard deviation), and farther out (lower
recession sensitivity). The indifference curves of
figure 1 become indifference surfaces. Panel A of figure 2 shows one such surface curving upwards.
As with figure 1, we must next think about what
is available. We can now calculate a frontier of portfolios based on their mean, variance, and recession
sensitivity. This frontier is the multifactor efficient
frontier. A typical investor then picks a point as shown
in panel A of figure 2, which gives him the best possible
portfoliotrading off mean, variance, and recession
sensitivitythat is available. Investors want to hold
multifactor efficient, rather than mean-variance efficient, portfolios. As the mean-variance frontier of figure 1 is a hyperbola, this frontier is a revolution of a
hyperbola. The appendix summarizes the mathematics
behind this figure.
Panel B of figure 2 adds a risk-free rate. As the
mean-variance frontier of figure 1 was the minimal V
shape emanating from the risk-free rate (Rf) that includes
the hyperbolic risky frontier, now the multifactor efficient frontier is the minimum cone that includes the
hyperbolic risky multifactor efficient frontier, as shown.
FIGURE 2
Portfolio theory in a multifactor world
A. No risk-free rate
B. Risk-free rate
E(R)
E(R)
σ (R)
σ (R)
β
β
Notes: Panel A shows an indifference surface and optimal portfolio in the case with no risk-free rate.
The dot marks the optimal portfolio where the indifference surface touches the multifactor efficient
frontier. Panel B shows the set of multifactor efficient portfolios with a risk-free rate. The two coneshaped surfaces intersect on the black line with two dots. The two dots are the market portfolio and an
additional multifactor-efficient portfolio; all multifactor-efficient portfolios on the outer cone can be
reached by combinations of the risk-free rate, the market, and the extra multifactor-efficient portfolio.
62
Economic Perspectives
As every point of the mean-variance frontier of
figure 1 can be reached by some combination of two
fundsa risk-free rate and the market portfolionow
every point on the multifactor efficient frontier can
be reached by some combination of three multifactor
efficient funds. The most convenient set of portfolios
is the risk-free rate (money-market security), the market
portfolio (the risky portfolio held by the average investor), and one additional multifactor efficient portfolio
on the tangency region as shown in panel B of figure
2. It is convenient to take this third portfolio to be a
zero-cost, zero-beta portfolio, so that it isolates the
extra dimension of risk.
Investors now may differ in their desire or ability
to take on recession-related risk as well as in their tolerance for overall risk. Thus, some will want portfolios
that are farther in and out, while others will want portfolios that are farther to the left and right. They can
achieve these varied portfolios by different weights in
the three multifactor efficient portfolios, or three funds.
Implications for mean-variance investors
The mean-variance frontier still existsit is the
projection of the cone shown in figure 2 on the meanvariance plane. As the figure shows, the average investor is willing to give up some mean or accept more
variance in order to reduce the recession-sensitivity
of his portfolio. The average investor must hold the
market portfolio, so the market return is no longer
on the mean-variance frontier.
Suppose, however, that you are concerned only
with mean and varianceyou are not exposed to the
recession risk, or the risks associated with any other
factor, and you only want to get the best possible mean
return for given standard deviation. If so, you still
want to solve the mean-variance problem of figure 1,
and you still want a mean-variance efficient portfolio.
The important implication of a multifactor world is that
you, the mean-variance investor, should no longer
hold the market portfolio.
You can still achieve a mean-variance efficient
portfolio just as in figure 1 by a combination of a
money market fund and a single tangency portfolio,
lying on the upper portion of the curved risky-asset
frontier. The tangency portfolio now takes stronger
positions than the market portfolio in factors such as
value or recession-sensitive stocks that the average
investor fears.
Predictable returns
The fact that returns are in fact somewhat predictable modifies the standard portfolio advice in three
ways. It introduces horizon effects, it allows markettiming strategies, and it introduces multiple factors
Federal Reserve Bank of Chicago
via hedging demands (if expected returns vary over
time, investors may want to hold assets that protect
them against this risk).
Horizon effects
Recall that when stock returns are independent
over time (like coin flips), the allocation between stocks
and bonds does not depend at all on the investment
horizon, since mean returns (reward) and the variance
of returns (risk) both increase in proportion to the
investment horizon. But if returns are predictable, the
mean and variance may no longer scale the same way
with horizon. If a high return today implies a high return
tomorrowpositive serial correlationthen the variance of returns will increase with horizon faster than
does the mean return. In this case, stocks are worse
in the long run. If a high return today implies a lower
return tomorrownegative serial correlation or mean
reversionthen the variance of long-horizon returns
is lower than the variance of one-period returns times
the horizon. In this case, stocks are more attractive
for the long run.1 For example, if the second coin flip
is always the opposite of the first coin flip, then two
coin flips are much less risky than they would be if
each flip were independent, and a long-run coin
flipper is more likely to take the bet.
Which case is true? Overall, the evidence suggests that stock prices do tend to come back slowly
and partially after a shock, so return variances at
horizons of five years and longer are about one-half
to two-thirds as large as short-horizon variances suggest. Direct measures of the serial correlation of stock
returns, or equivalent direct measures of the mean
and variance of long-horizon returns, depend a lot on
the period studied and the econometric method. Multivariate methods give somewhat stronger evidence.
Intuitively, the price/dividend (p/d) ratio does not
explode. Hence, the long-run variance of prices must
be the same as the long-run variance of dividends,
and this extra piece of information helps to measure the
long-run variance of returns. (Cochrane and Sbordone,
1986, and Cochrane, 1994, use this idea. See Campbell,
Lo, and MacKinlay, 1997, for a summary of these issues
and of the extensive literature.)
How big are the horizon effects? Barberis (1999)
calculates optimal portfolios for different horizons
when returns are predictable. Figure 3 presents some
of his results.
We start with a very simple setup: The investor
allocates his portfolio between stocks and bonds and
then holds it without rebalancing for the indicated
horizon. His objective is to maximize the expected utility of wealth at the indicated horizon. The flat line in
figure 3 shows the standard result: If returns are not
63
predictable, then the allocation to stocks does not
depend on horizon.
The top (black) line in figure 3 adds the effects of
return predictability on the investment calculation. The
optimal allocation to stocks increases sharply with
horizon, from about 40 percent for a monthly horizon
to 100 percent for a ten-year horizon. To quantify the
effects of predictability, Barberis uses a simple model,
1)
2)
Rt +1 - RtTB
+1 = a + bx t + e t +1
Allocation to stocks, different
investment horizons
percent allocation to stocks
100
80
Predictable
Predictable,
uncertain parameters
60
x t +1 = c + rxt + d t +1 ,
using the d/p ratio for the forecasting variable x.
(Whether or not one includes returns in the right
hand side makes little difference.) Barberis estimates
significant mean-reversion: In Barberiss regressions,
the implied standard deviation of ten-year returns is
23.7 percent, just more than half of the 45.2 percent
value implied by the standard deviation of monthly
returns. Stocks are indeed safer in the long run, and
the greater allocation to stocks shown in figure 3 for
a long-run investor reflects this fact.
Uncertainty about predictability
This calculation ignores the fact that we do not
know how predictable returns really are. One could
address this fact by calculating standard errors for
portfolio computations; and such standard errors do
indicate substantial uncertainty. However, standard
error uncertainty is symmetricreturns might be more
predictable than we think or they might be less predictable. This measure of uncertainty would say that we
are just as likely to want an even greater long-run
stock allocation as we are to shade the advice back
to a constant allocation.
Intuitively, however, uncertainty about predictability should lead us to shade the advice back toward
the standard advice. Standard errors do not capture
the uncertainties behind this (good) intuition for at
least two reasons.
First, the predictability captured in Barberiss
regression of returns on dividend/price ratios certainly
results to some extent from data-dredging. Thousands
of series were examined by many authors, and we have
settled on the one or two that seem to predict returns
best in sample. The predictability will obviously be
worse out of sample, and good portfolio advice should
account for this bias. Standard errors take the set of
forecasting variables and the functional form as given.
Second, the portfolio calculation assumes that
the investor knows the return forecasting process
perfectly. Standard errors only reflect the fact that we
do not know the return forecasting process, so we
64
FIGURE 3
40
Unpredictable
Unpredictable, uncertain parameters
20
0
2
4
6
horizon, years
8
10
Notes: The investor maximizes the utility of terminal wealth via
a buy-and-hold investment in stocks versus bonds. The investor
has constant relative risk aversion utility with a risk aversion
coefficient of 10. The top calculation (black) includes predictable
returns modeled by a regression on d/p ratios (equation 1). The
second calculation (color) includes predictable returns and the
effects of parameter uncertainty. The third calculation (black dash)
assumes unpredictable returns, and no parameter uncertainty. The
bottom calculation (color dash) assumes unpredictable returns, but
adds parameter uncertainty. All distributions are conditional on a
dividend/price ratio equal to its historical mean.
Source: Barberis (1999).
are unsure about what investors want to do.2 What
we would like to do is to solve a portfolio problem in
which investors treat uncertainty about the forecastability of returns as part of the risk that they face, along
with the risks represented by the error terms of the
statistical model. Kandel and Stambaugh (1996) and
Barberis (1999) tackle this important problem.
Figure 3 also gives Barberiss calculations of the
effects of parameter uncertainty on the stock/bond
allocation problem. (See box 1 for a description of how
these calculations are made.) The lowest (dotted) line
considers a simple case. The investor knows, correctly,
that returns are independent over time (not predictable) but he is not sure about the mean return. Without parameter uncertainty, this situation gives rise to
the constant stock allocationthe flat line. Adding
parameter uncertainty lowers the allocation to stocks
for long horizons; it declines from 34 percent to about
28 percent at a ten-year horizon.
The reason is simple. If the investor sees a few
good years of returns after making the investment,
this raises his estimate of the actual mean return and,
thus, his estimate of the returns over the rest of the
investment period. Conversely, a few bad years will
lower his estimate of the mean return for remaining
years. Thus, learning about parameters induces a
Economic Perspectives
BOX 1
How to include model uncertainty in portfolio problems
A statistical model, such as equations 1 and 2,
tells us the distribution of future returns once we
know the parameters θ, f (Rt +1 q, x1 , x2 , ..., xt ), where
xt denotes all the data used (returns, d/p, etc.).
We would like to evaluate uncertainty by the
distribution of returns conditional only on the history available to make guesses about the future,
f ( Rt +1 x 1 , x2 ... x t ). We can use Bayesian analysis
to evaluate this concept. If we can summarize the
information about parameters given the historical
data as f (q x1 , x2 .... xt ), then we can find the distribution we want by
f ( Rt +1 x1 , x2 ... xt ) =
I f (R
t +1
q) f (q x1 , x2 ... xt )d q.
f ( x1 , x2 ... xt q) via the standard law for conditional probabilities,
f ( q x 1 , x2 ... xt ) =
f ( x1 , x2 ... xt ) =
I
f ( x1 , x2 ... xt q ) f (q )
f ( x1 , x2 ... x t )
f ( x1 , x2 ... xt q ) f ( q ) d q.
Barberis (1999), Kandel and Stambaugh
(1996), Brennan, Schwartz, and Lagnado (1997)
use these rules to compute f ( Rt +1 x 1 , x2 ... xt ),
and solve portfolio problems with this distribution over future returns.
In turn, we can construct f (q x1 , x2 .... xt ),
from a prior f (q) and the likelihood function
positive correlation between early returns and later
returns. Positive correlation makes long-horizon returns
more than proportionally risky and reduces the optimal allocation to stocks.
The colored line in figure 3 shows the effects of
parameter uncertainty on the investment problem,
when we allow return predictability as well. As the
figure shows, uncertainty about predictable returns
cuts the increase in stock allocation from one to ten
years in half. In addition to the positive correlation of
returns due to learning about their mean mentioned
above, uncertainty about the true amount of predictability adds to the risk (including parameter risk) of
longer horizon returns.
Market timing
Market-timing strategies are the most obvious
implication of return predictability. If there are times
when expected returns are high and other times when
they are low, you might well want to hold more stocks
when expected returns are high, and fewer when expected returns are low. Of course, the crucial question is,
how much market-timing should you engage in? Several authors have recently addressed this technically
challenging question.
Much of the difficulty with return predictability
(as with other dynamic portfolio questions) lies in computing the optimal strategyexactly how should you
adjust your portfolio as the return prediction signals
change? Gallant, Hansen, and Tauchen (1990) show
how to measure the potential benefits of market-timing
without actually calculating the market-timing strategy.
Federal Reserve Bank of Chicago
The meanstandard deviation tradeoff or Sharpe
ratiothe slope of the frontier graphed in figure 1
is a convenient summary of any strategy. If the riskfree rate is constant and known, the square of the
maximum unconditional Sharpe ratio is the average
of the squared conditional Sharpe ratios. (The appendix details the calculation.) Since we take an average
of squared conditional Sharpe ratios, volatility in
conditional Sharpe ratiostime-variation in expected
returns or return volatilityis good for an investor
who cares about the unconditional Sharpe ratio. By
moving into stocks in times of high Sharpe ratio and
moving out of the market in times of low Sharpe ratio,
the investor does better than he would by buying
and holding. Furthermore, the best unconditional
Sharpe ratio is directly related to the R2 in the return-forecasting regression.
The buy-and-hold Sharpe ratio has been about
0.5 on an annual basis in U.S. datastocks have
earned an average return of about 8 percent over
Treasury bills, with a standard deviation of about 16
percent. Table 1 presents a calculation of the increased
Sharpe ratio one should be able to achieve by markettiming, based on regressions of returns on dividend/
price ratios. (I use the regression estimates from table
1 of New facts in finance.)
As table 1 indicates, market-timing should be a
great benefit. Holding constant the portfolio volatility,
market-timing should raise average returns by about
two-fifths at an annual horizon and it should almost
double average returns at a five-year horizon.
65
TABLE 1
Maximum unconditional Sharpe ratios
Horizon k (years)
Buy & hold
1
2
3
5
R2
Annualized
Sharpe ratio
0.17
0.26
0.38
0.59
0.50
0.71
0.72
0.78
0.95
Notes: Maximum unconditional Sharpe ratios available
from market-timing based on regressions of value-weighted
NYSE index returns on the dividend/price ratio. The table
reports annualized Sharpe ratios corresponding to each R2.
The formula is
S*
k
= 05
. 2+
R2
/ 1 - R 2 and is derived in
k
the appendix.
FIGURE 4
Optimal allocation to stocks
fraction wealth in equities
Optimal market-timing:
An Euler equation approach
Brandt (1999) presents a clever way to estimate a
market-timing portfolio rule without solving a model.
Where standard asset pricing models fix the consumption or wealth process and estimate preference parameters, Brandt fixes the preference parameters (as one
does in a portfolio question) and estimates the portfolio decision, that is, he estimates the optimal consumption or wealth process.3 This calculation is very
clever because it does not require one to specify a
statistical model for the stock returns (like equations
12), and it does not require one to solve
the economic model.
Figure 4 presents one of Brandts results. The figure shows the optimal allocation to stocks as a function of investment
horizon and of the dividend/price ratio,
which forecasts returns. There is a mild
2.5
horizon effect, about in line with Barberiss
results of figure 3 without parameter uncer2.0
tainty: Longer term investors hold more
1.5
stocks. There is also a strong market-timing
effect. The fraction of wealth invested in
1.0
stocks varies by about 200 percentage
0.5
points for all investors. For example, long0.0
term investors vary from about 75 percent
48
to 225 percent of wealth invested in stocks
as the d/p ratio rises from 2.8 percent to
5.5 percent.
who desire lifetime consumption4 rather than portfolio
returns at a fixed horizon. They model the time-variation in expected stock returns via equation 1 on d/p
ratios. Their investors live only off invested wealth
and have no labor income or labor income risk. Thus,
these investors are poised to take advantage of business cycle related variation in expected returns.
As one might expect, the optimal investment strategy takes strong advantage of market-timing possibilities. Figure 5 reproduces Campbell and Viceras optimal
allocation to stocks as a function of the expected
return, forecast from d/p ratios via equation 1. A risk
aversion coefficient of 4 implies that investors roughly want to be fully invested in stocks at the average
expected excess return of 6 percent, so this is a sensible risk aversion value to consider. Then, as the d/p
ratio ranges from minus two to plus one standard
deviations from its mean, these investors range from
50 percent in stocks to 220 percent in stocks. This
is aggressive market-timing indeed.
Figure 6 presents the calculation in a different
way: It gives the optimal allocation to stocks over
time, based on dividend/price ratio variation over
time. The high d/p ratios of the 1950s suggest a
strong stock position, and that strong position profits
from the high returns of the late 1950s to early 1960s.
The low d/p ratios of the 1960s suggest a much smaller
position in stocks, and this smaller position avoids
the bad returns of the 1970s. The high d/p ratios of
the 1970s suggest strong stock positions again, which
benefit from the good return of the 1980s; current
Optimal market-timing: A solution
Campbell and Vicera (1999) actually
calculate a solution to the optimal markettiming question. They model investors
66
26
hor
izo
n (m24
ont 12
hs)
0
2.8
3.3
3.9
e
divid
4.9
4.4
ratio
e
ric
nd/p
5.5
Notes: Optimal allocation to stocks as a function of horizon and dividend yield.
Source: Brandt (1999).
Economic Perspectives
FIGURE 5
Optimal allocation to stocks
Campbell and Vicera also present achieved utility
calculations that mirror the lesson of table 1: Failing
to time the market seems to impose a large cost.
allocation to stocks, percent
220
Doubts
One may be understandably reluctant to take on
quite
such strong market-timing positions as indicated
140
by
figures
5 and 6, or to believe table 1 that market
100
timing
can
nearly double five-year Sharpe ratios. In
60
particular,
one
might question advice that would have
20
meant missing the dramatic runup in stock values of
–20
the late 1990s. Rather than a failure of nerve, perhaps
–60
such reluctance reveals that the calculations do not
–100
yet include important considerations and, therefore,
–5
–4
–2
0
2
4
6
8
10
12
overstate the desirable amount of market-timing and
log expected gross excess return, percent
its benefits.
Notes: Optimal allocation to stocks as a function of the expected
return implied by a regression that forecasts stock returns from
First, the unconditional Sharpe ratio as reported
dividend/price ratios. The line extends from a d/p ratio two
in
table
1 for, say, five-year horizons answers the quesstandard deviations above its mean (low expected returns) to
one standard deviation below its mean (high expected returns).
tion,
Over
very long periods, if an investor follows
Risk aversion is 4.0.
Source: Campbell and Vicera (1999).
the best possible market-timing strategy and evaluates
his portfolio based on five-year returns, what Sharpe
ratio does he achieve? It does not answer the question, Given todays d/p, what is the best Sharpe raunprecedented high prices suggest the lowest stock
tio you can achieve for the next five years by
positions ever. The optimal allocation to stocks again
following market-timing signals? The latter question
varies wildly, from 0 (now) to over 300 percent.
characterizes the return distribution conditional on toCampbell and Viceras calculations are, if anything,
days d/p. It is harder to evaluate; it depends on the
conservative compared with others in this literature.
initial d/p level, and it is lower, especially for a slowOther calculations, using other utility functions, somoving signal such as d/p.
lution techniques, and calibrations of the forecasting
To see the point, suppose that the d/p ratio is
process often produce even more aggressive marketdetermined
on day one, is constant thereafter, and intiming strategies. For example, Brennan, Schwartz, and
dicates
high
or low returns in perpetuity. Conditional
Lagnado (1997) make a similar calculation with two
on
the
d/p
ratio,
one cannot time the market at all. But
additional forecasting variables. They report marketsince
the
investor
will invest less in stocks in the lowtiming strategies that essentially jump back and forth
return
state
and
more
in the high-return state, he will
between constraints at 0 percent in stocks and 100
unconditionally
time
the
market (that is, adjust his
percent in stocks.
portfolio based on day one information)
and this gives him a better date-zero (unconditional) Sharpe ratio than he would
FIGURE 6
obtain by fixing his allocation at date zero.
Optimal allocation to stocks based on dividend/price ratio
This fact captures the intuition that there
allocation to stocks, percent
is a lot more money to be made from a 50
400
percent R2 at a daily horizon than at a five320
year horizon, where the calculations in
table 1 are not affected by the persistence
240
of the market-timing signal. Campbell and
Viceras (1999) utility calculations are also
160
based on the unconditional distribution,
80
so the optimal degree and benefit of market-timing might be less, conditional on
0
1940
1950
1960
1970
1980
1990
2000
the observed d/p ratio at the first date.
Notes: Risk aversion γ = 4.00 (black line) and γ = 20.00 (colored dashed line).
Second, there are good statistical
Source: Campbell and Vicera (1999).
reasons to think that the regressions
overstate the predictability of returns.
180
Federal Reserve Bank of Chicago
67
1) Figure 6 emphasizes one reason: The d/p ratio signal
has only crossed its mean four times in the 50 years
of postwar history. You have to be very patient to
profit from this trading rule. Also, we really have only
four postwar data points on the phenomenon. 2) The
dividend/price ratio was selected, in sample, among
hundreds of potential forecasting variables. It has
not worked well out of samplethe last two years of
high market returns with low d/p ratios have cut the
estimated predictability in half! 3) The model imposes
a linear specification, where the actual predictability
is undoubtedly better modeled by some unknown
nonlinear function. In particular, the linear specification implies negative expected stock returns at many
points in the sample, and one might not want to take
this specification seriously for portfolio construction.
4) The d/p ratio is strongly autocorrelated, and estimates of this autocorrelation are subject to econometric
problems. For this reason, long-horizon return properties inferred from a regression such as equations 1 and
2 are often more dramatic and apparently more precisely measured than direct long-horizon estimates.
The natural next step is to include this parameter
uncertainty in the portfolio problem, as I did above
for the case of independent returns. While this has
not been done yet in a model with Campbell and Viceras (1999) level of realism (and for good reasons
Campbell and Viceras non-Bayesian solution is
already a technical tour de force), Barberis (1999)
makes such calculations in his simpler formulation. He
uses a utility of terminal wealth and no intermediate
trading, and he forces the allocation to stocks to be
less than 100 percent.
Figure 7 presents Barberiss (1999) results.5 As
the figure shows, uncertainty about the parameters of
the regression of returns on d/p almost eliminates the
usefulness of market-timing.
Third, it is uncomfortable to note that fund returns
still cluster around the (buy-and-hold) market Sharpe
ratio (see figure 7 of New facts in finance). Here is
a mechanical strategy that supposedly earns average
returns twice those of the market with no increase in
risk. If the strategy is real and implementable, one
must argue that funds simply failed to follow it.
Market-timing, like value, does requires patience
and the willingness to stick with a portfolio that departs
from the indexing crowd. For example, a market-timer
following Campbell and Viceras rules in figures 5 and
6 would have missed most of the great runup in stocks
of the last few years. Fund managers who did that are
now unemployed. On the other hand, if an eventual
crash comes, the market timer will look wise.
Finally, ones reluctance to take such strong
market-timing advice reflects the inescapable fact
that getting more return requires taking on more, or
different, kinds of risk. A market-timer must buy at
the bottom, when everyone else is in a panic; he
must sell at the top (now) when everyone else is feeling flush. His portfolio will have a greater mean for a
given level of variance over very long horizons, but
it will do well and badly at very different times from
everyone elses portfolio. He will often underperform
a benchmark.
Hedging demands
Market-timing addresses whether you should
change your allocation to stocks over time as a return
signal rises or falls. Hedging demands address whether
your overall allocation to stocks, or to specific
portfolios, should be higher or lower as a result of
FIGURE 7
Allocation to stocks as a function of dividend/price ratio, with parameter uncertainty
A. Risk aversion coefficient 10
B. Risk aversion coefficient 20
allocation to stocks, percent
100
allocation to stocks, percent
100
No uncertainty
80
80
No uncertainty
60
60
Parameter uncertainty
40
40
20
20
0
Parameter uncertainty
0
2.06
3.75
d/p, percent
5.43
2.06
3.75
d/p, percent
5.43
Notes: The colored line ignores parameter uncertainty, as in Campbell and Vicera (1999).
The black line includes parameter uncertainty, as in Barberis (1999). Data sample is in months (523).
68
Economic Perspectives
return predictability, in order to protect you against
reinvestment risk.
A long-term bond is the simplest example. Suppose
you want to minimize the risk of your portfolio ten
years out. If you invest in apparently safe short-term
risk-free assets like Treasury bills or a money-market
fund, your ten-year return is in fact quite risky, since
interest rates can fluctuate. You should hold a tenyear (real, discount) bond. Its price will fluctuate a lot
as interest rates go up and down, but its value in ten
years never changes.
Another way of looking at this situation is that,
if interest rates decline, the price of the ten-year bond
will skyrocket; it will skyrocket just enough so that,
reinvested at the new lower rates, it provides the same
ten-year return as it would have if interest rates had
not changed. Changes in the ten-year bond value
hedge the reinvestment risk of short-term bonds. If
lots of investors want to secure the ten-year value
of their portfolios, this will raise demand for ten-year
bonds and lower their prices.
In general, the size and sign of a hedging demand
depend on risk aversion and horizon and, thus, will
be different for different investors. If the investor is
quite risk averseinfinitely so in my bond example
he wants to buy assets whose prices go up when expected returns decline. But an investor who is not so
risk averse might want to buy assets whose prices
go up when expected returns rise. If the investor is
sitting around waiting for a good time to invest, and
is willing to pounce on good (high expected return)
investments, he would prefer to have a lot of money
to invest when the good opportunity comes around.
It turns out that the dividing line in the standard
(CRRA) model is logarithmic utility or a risk aversion
coefficient of 1investors more risk averse than this
want assets whose prices go up when expected returns decline, and vice versa. Most investors are undoubtedly more risk averse than this, but not
necessarily all investors. Horizon matters as well. A
short horizon investor cares nothing about reinvestment risk and, therefore, has zero hedging demand.
In addition, the relationship between price and
expected returns is not so simple for stocks as for
bonds and must be estimated statistically. The predictability evidence reviewed above suggests that
high stock returns presage lower subsequent returns.
High returns drive up price/dividend, price/earnings,
and market/book ratios, all of which have been strong
signals of lower subsequent returns. Therefore, stocks
are a good hedge against their own reinvestment
riskthey act like the long-term assets that they are.
This consideration raises the attractiveness of stocks
Federal Reserve Bank of Chicago
for typical (risk aversion greater than 1) investors.
Precisely, if the two-fund analysis of figure 1 suggests
a certain split between stocks and short-term bonds
for a given level of risk aversion and investment horizon, then return predictability, a long horizon, and
typical risk aversion greater than 1 will result in a
higher fraction devoted to stocks. Again, exactly how
much more one should put into stocks in view of this
consideration is a tough question.
(In this case, the hedging demand reduces to
much the same logic as the horizon effects described
above. The market portfolio is a good hedge against
its own reinvestment risk, and so its long horizon
variance is less than its short horizon variance would
suggest. More generally, hedging demands can tilt a
portfolio toward stocks whose returns better predict
and, hence, better hedge the expected return on the
market index, but this long-studied possibility from
Merton [1971a, 1971b] has not yet been implemented
in practice.)
Campbell and Viceras (1999) calculations address
this hedging demand as well as market-timing demand,
and figure 5 also illustrates the strength of the hedging demand for stocks. Campbell and Viceras investors want to hold almost 30 percent of their wealth in
stocks even if the expected return of stocks is no
greater than that of bonds. Absent the hedging motive,
of course, the optimal allocation to stocks would be
zero with no expected return premium. Almost a 2 percent negative stock return premium is necessary to
dissuade Campbell and Viceras investors from holding
stocks. At the average (roughly 6 percent) expected return, of the roughly 130 percent of wealth that the risk
aversion 4 investors want to allocate to stocks, nearly
half is due to hedging demand. Thus, hedging demands
can importantly change the allocation to stocks.
However, hedging demand works in opposition
to the usual effects of risk aversion. Usually, less risk
averse people want to hold more stocks. However,
less risk averse people have lower or even negative
hedging demands, as explained above. It is possible
that hedging demand exactly offsets risk aversion;
everybody holds the same mean allocation to stocks.
This turns out not to be the case for Campbell and
Viceras numerical calibration; less risk averse people
still allocate more to stocks on average, but the effect
depends on the precise specification.
Choosing a risk-free rate
Figure 1 describes a portfolio composed of the
market portfolio and the risk-free rate. But the riskfree rate is not as simple as it once was either. For a
consumer or an institution6 with a one-year horizon,
69
one-year bonds are risk-free, while for one with a tenyear horizon, a ten year zero-coupon bond is risk-free.
For a typical consumer, whose objective is lifetime consumption, an interest-only strip (or real level annuity) is
in fact the risk-free rate, since it provides a riskless
coupon that can be consumed at each date. Campbell
and Vicera (1998) emphasize this point. Thus, the
appropriate bond portfolio to mix with risky stocks in
the logic of figure 1 is no longer so simple as a shortterm money market fund.
Of course, these comments refer to real or indexed bonds, which are only starting to become easily
available. When only nominal bonds are available,
the closest approximation to a risk-free investment
depends additionally on how much interest rate variability is due to real rates versus nominal rates. In the
extreme case, if real interest rates are constant and
nominal interest rates vary with inflation, then rolling
over short-term nominal bonds carries less long-term
real risk than holding long-term nominal bonds. In the
past, inflation was much more variable than real interest
rates in the U.S., so the fact that portfolio advice paid
little attention to the appropriate risk-free rate may
have made sense. We seem to be entering a period
in which inflation is quite stable, so real interest rate
fluctuations may dominate interest rate movements.
In this case, longer term nominal bonds become more
risk-free for long-term investors, and inflation-indexed
bonds open up the issue in any case. Once again,
new facts are opening up new challenges and opportunities for portfolio formation.
Notes of caution
The new portfolio theory can justify all sorts of
interesting new investment approaches. However,
there are several important qualifications that should
temper ones enthusiasm and that shade portfolio advice back to the traditional view captured in figure 1.
The average investor holds the market
The portfolio theory that I have surveyed so far
asks, given multiple factors or time-varying investment
opportunities, How should an investor who does not
care about these extra risks profit from them? This
may result from intellectual habit, as the past great
successes of portfolio theory addressed such investors, or it may come from experience in the money
management industry, where distressingly few investors
ask about additional sources of risk that multifactor
models and predictable returns suggest should be
a major concern.
Bear in mind, however, that the average investor
must hold the market portfolio. Thus, multiple factors
and return predictability cannot have any portfolio
70
implications for the average investor. In addition, for
every investor who should follow a value strategy or
time the market for the extra returns offered by those
extra risks, there must be an investor who should follow the exact opposite advice. He should follow a
growth strategy or sell stocks at the bottom and buy
at the top, because he is unusually exposed to or
averse to the risks of the value or market-timing strategies in his business or job. He knows that he pays a
premium for not holding those risks, but he rationally
chooses this course just as we all choose to pay a
premium for home insurance.
Again, dividend/price, price/earnings, and book/
market ratios forecast returns, if they do, because the
average investor is unwilling to follow the value and
market-timing strategies. If everyone tries to time the
market or buy more value stocks, the premiums from
these strategies will disappear and the CAPM, random
walk view of the market will reemerge. Market-timing
can only work if it involves buying stocks when
nobody else wants them and selling them when everybody else wants them. Value and small-cap anomalies
can only work if the average investor is leery about
buying financially distressed and illiquid stocks. Portfolio advice to follow these strategies must fall on
deaf ears for the average investor, and a large class
of investors must want to head in exactly the other
direction. If not, the premiums from these strategies
will not persist.
One can see a social function in all this: The stock
market acts as a big insurance market. By changing
weights in, say, recession-sensitive stocks, people
whose incomes are particularly hurt by recessions
can purchase insurance against that loss from people
whose incomes are not hurt by recessions. They pay
a premium to do so, which is why investors are willing
to take on the recession-related risk.
The quantitative portfolio advice is all aimed at
the providers of insurance, which may make sense if
the providers are large wealthy investors or institutions.
But for each provider of insurance, there must be a
purchaser, and his portfolio must take on the opposite characteristics.
Are the effects real or behavioral, and will they last?
So far, I have emphasized the view that the average
returns from multifactor or market-timing strategies are
earned as compensation for holding real, aggregate
risks that the average investor is anxious not to hold.
This view is still debated. Roughly half of the academic studies that document such strategies interpret
them this way, while the other half interpret them as
evidence that investors are systematically irrational.
This half argues that a new behavioral finance
Economic Perspectives
should eliminate the assumption of rational consumers
and investors that has been at the core of all economics
since Adam Smith, in order to explain these asset
pricing anomalies.
For example, I have followed Fama and Frenchs
(1993, 1996) interpretation that the value effect exposes
the investor to systematic risks associated with economywide financial distress. However, Lakonishok,
Shleifer, and Vishny (1994) interpret the same facts as
evidence for irrationality: Investors flock to popular
stocks and away from unpopular stocks. The prices
of the unpopular stocks are depressed, and their average returns are higher as the fad slowly fades. Fama
and French point out that the behavioral view cannot
easily account for the comovement of value stocks;
the behavioral camp points out that the fundamental
risk factor is still not determined.
Similarly, the predictability of stock returns over
time is interpreted as waves of irrational exuberance
and pessimism as often as it is interpreted as timevarying, business cycle related risk or risk aversion.
Those who advocate an economic interpretation
point to the association with business cycles (Fama
and French, 1989) and to some success for explicit
models of this association (Campbell and Cochrane,
1999); those who favor the irrational investors view
point out that the rational models are as yet imperfect.
While this academic debate is entertaining, how
does it affect a practical investor who is making a
portfolio decision? At a basic level, it does not. If you
are not exposed to the risk a certain investment represents, it does not matter why other investors shy away
from holding it.
Analogously, to decide what to buy at the grocery
store, you only have to know how you feel about
various foods and what their prices are. You do not
have to understand the economic determinants of
food prices: You do not need to know whether a sale on
tomatoes represents a real factor like good weather in
tomato growing areas, or whether it represents an
irrational fear or fad.
Will they last?
Investments do not come with average returns
as clearly marked as grocery prices, however. Investors
have to figure out whether an investment opportunity that did well in the past will continue to do well.
This is one reason that it is important to understand
whether average returns come from real or irrational
aversion to risk.
If it is real, it is most likely to persist. If a high
average return comes from exposure to risk, well understood and widely shared, that means all investors
understand the opportunity but shrink from it. Even if
Federal Reserve Bank of Chicago
the opportunity is widely publicized, investors will
not change their portfolio decisions, and the relatively
high average return will remain.
On the other hand, if it is truly irrational, or a
market inefficiency, it is least likely to persist. If a high
average return strategy involves no extra exposure to
real risks and is easy to implement (it does not incur
large transaction costs), that means that the average
investor will immediately want to invest when he hears
of the opportunity. News travels quickly, investors
react quickly, and such opportunities vanish quickly.
Recent work in behavioral finance tries to document a way that irrational phenomena can persist
in the face of the above logic. If an asset-pricing
anomaly corresponds to a fundamental, documented,
deeply formed aspect of human psychology, then the
average investor may not pounce on the strategy the
minute he hears of it, and the phenomenon may last
(DeBondt and Thaler, 1985, and Daniel, Hirshleifer,
and Subrahmanyam, 1998). For example, many people
systematically overestimate the probability that airplanes crash, and make wrong decisions resulting
from this belief, such as choosing to drive instead.
No amount of statistics changes this view. Most such
people readily admit that a fear of flying is irrational
but persist in it anyway. If an asset-pricing anomaly
results from such a deep-seated misperception of
risk, then it could in fact persist.
A final possibility is that the average return premiums are the result of narrowly held risks. This view
is (so far) the least stressed in academic analysis. In
my opinion, it may end up being the most important.
It leads to a view that the premiums will be moderately persistent. Catastrophe-insurance enhanced bonds
provide a good example of this effect. These bonds
pay well in normal times, but either part of the principal
or interest is pledged against a tranche of a property
reinsurance contract. Thus, the bonds promise an
average return of 10 percent to 20 percent (depending
on ones view of the chance of hurricanes). However,
the risk of hurricane damage is uncorrelated with anything else, and hence it is perfectly diversifiable.
Therefore, catastrophe bonds are an attractive opportunity. Before the introduction of catastrophe bonds,
there was no easy way for the average investor or
fund to participate in property reinsurance. As more
and more investors and funds hold these securities,
the prices will rise and average returns will fall. Once
the risks are widely shared, every investor (at least
those not located in hurricane-prone areas) will hold
a little bit of the risk and the high average returns will
have vanished.
71
The essential ingredients for this story are that
the risk is narrowly shared; the high average returns
only disappear when the risk is widely shared (it cannot be arbitraged away by a few savvy investors);
and an institutional change (the introduction, packaging, and marketing of catastrophe-linked bonds)
is required before it all can happen.
This story gives a plausible interpretation of many
of the anomalies I document above. Small-cap stocks
were found in about 1979 to provide higher returns
than was justified by their market (β) risk. Yet at that
time, most funds did not invest in such stocks, and individual investors would have had a hard time forming a portfolio of small-cap stocks without losing all
the benefits in the very illiquid markets for these
stocks. The risks were narrowly held. After the popularization of the small-cap effect, many small-cap funds
were started, and it is now easy for investors to hold
such stocks. As the risk has been more widely shared,
the average returns seem to have fallen.
The value effect may be amenable to a similar interpretation. Before about 1990, as I noted earlier, few
funds actually followed the high-return strategy of
buying really distressed stocks or shorting the popular growth stocks. It would be a difficult strategy for
an individual investor to follow, requiring courage and
frequent trading of small illiquid stocks. Now that the
effect is clear, value funds have emerged that really
do follow the strategy, and the average investor can
easily include such an offering in his portfolio. The
risk is becoming widely shared, and its average return
seems to be falling.
Even average returns on the stock market as a
whole (the equity premium) may follow the same story,
since participation has increased a great deal through
the invention of index funds, low-commission brokerages, and tax-sheltered retirement plans.
This story does not mean that the average returns
corresponding to such risks will vanish. They will
decline, however, until the markets have established
an equilibrium, in which every investor has bought as
much of the risk as he likes. In this story, one would
expect a large return as investors discover each strategy and bid prices up to their equilibrium levels. This
may account for some of the success of small and
value stocks observed in the literature, as well as
some of the stunning success of the overall market
in recent years.
Inconsistent advice
Unfortunately, the arguments that a factor will
persist are all inconsistent with aggressive portfolio
advice. If the premium is real, an equilibrium reward
72
for holding risk, then the average investor knows
about it but does not invest because the extra risk exactly counteracts the extra average return. If more
than a minuscule fraction of investors are not already
at their best allocations, then the market has not
reached equilibrium and the premiums will change.
If the risk is irrational, then by the time you and
I know about it, its gone. An expected return corresponding to an irrational risk premium has the strongest portfolio implicationseveryone should do
itbut the shortest lifetime. Thus, this view is also
inconsistent with the widespread usefulness of portfolio advice.
If the average return comes from a behavioral
aversion to risk, it is just as inconsistent with widespread portfolio advice as if were real. We can not all
be less behavioral than average, just as we can not
all be less exposed to a risk than average. The whole
argument for behavioral persistence is that the average
investor would not change his portfolio, just as the
average traveler would not quickly adjust his traveling
behavior to fear the cab ride out to the airport more
than the flight. Thus, the advice must be useless to
the vast majority of investors. If most people, on seeing the strategy, can be persuaded to act differently
and buy, then it is an irrational risk and will disappear.
If it is real or behavioral and will persist, then this
necessarily means that very few people will follow
the portfolio advice.
If the average return comes from a narrowly held
risk, one has to ask what institutional barriers keep
investors from sharing this risk more widely. Simple
portfolio advice may help a bitmost investors still
do not appreciate the risk/return advantages of stocks
overall, small-caps, value stocks, market-timing, and
aggressive liquidity trades. But by and large, a risk
like this needs packaging, securitizing, and marketing
more than advice. Then there will be a period of high
average returns to the early investors, followed by
lower returns, but still commoditization of the product with fees for the intermediaries.
Economic logic
The issue of why the risk gives an average return
premium is also important to decide whether the opportunity is really there. It is not that easy to establish the
average returns of stocks and dynamic portfolio
strategies. There are many statistical anomalies that
vanish quickly out of sample. Figuring out why a
strategy carries a high average return is one of the
best ways to ensure that the high average return is
really there in the first place. Anything that is going
to work has a real economic function. A story such
Economic Perspectives
as I dont care much about recessions; the average
investor does; hence it makes good sense for me to
buy extra amounts of recession sensitive stocks since
I am selling insurance to the others at a premium
makes a strategy much more plausible than the output
of some statistical black box.
Conclusion
Practical application of portfolio theory
How does an investor who is trying patiently to
sort through the bewildering variety of investment
opportunities use all the new portfolio theory? Its
best to follow a step by step procedure, starting with
a little introspection.
1. What is your overall risk tolerance? As before,
you must first figure out to what extent you are willing to trade off volatility for extra average returns, to
determine an appropriate overall allocation to risky
versus risk-free assets. While this question is hard to
answer in the abstract, you only need to know whether
you are more or less risk tolerant than the average investor. (Honestly, noweveryone wants to say they
are a risk taker.) The overall market is about 60 percent
stocks and 40 percent bonds, so average levels of risk
aversion, whatever they are, wind up at this value.
2. What is your horizon? This question is first
of all important for figuring out what is the relevant
risk-free asset. Longer term investors can hold longer
term bonds despite their poor one-year performance,
especially in a low-inflation environment. Second, we
have seen that stocks are somewhat safer for longrun investors.
3. What are your risks? Would you be willing to
trade some average return in order to make sure that
your portfolio does well in particular circumstances?
For example, an investor who owns a small company
would not want his investment portfolio to do poorly
at the same time that his industry suffers a downturn,
that there is a recession, or a credit crunch, or that the
industries he sells to suffer a downturn. Thus, it makes
good sense for him to avoid stocks in the same industry
or downstream industries, or stocks that are particularly sensitive to recessions or credit crunches, or
even to short them if possible. This strategy would
make sense even if these stocks give high average
returns, like the value portfolios. Similarly, he should
avoid high yield bonds that will all do badly in a credit
crunch. If the company will do poorly in response to
increases in interest rates, oil prices or similar events,
and if the company does not hedge these risks, then
the investor should take positions in interest rate sensitive or oil-price sensitive securities to offset those
Federal Reserve Bank of Chicago
risks as well. Were just extending the principles behind
fire and casualty insurance to investment portfolios.
This logic extends beyond the kind of factors
(size, book to market, and so on) that have attracted
academic attention. It applies to any identifiable movement in asset portfolios. For example, industry portfolios are not badly explained by the CAPM, as they all
seem to have about the same average return. Therefore, they do not show up in multifactor models. However, shorting your industry portfolio protects you
against the risks of your occupation. In fact, factors
that do not carry unusual risk premiums are even better opportunities than the priced factors that attract
attention, since you buy insurance at zero premium.
This was always true, even in the CAPM, unpredictable return view. I think that the experience with multifactor models just increases our awareness of how
important this issue is.
4. What are not your risks? Next, figure out what
risks you do not face, but that give rise to an average
return premium in the market because most other investors do face these risks. For example, an investor who
has no other source of income beyond his investment
portfolio does not particularly care about recessions.
Therefore, he should buy extra amounts of recessionsensitive stocks, value stocks, high yield bonds, etc.,
if these strategies carry a credible high average return.
This action works just like selling insurance, in return
for a premium. This is the type of investor for whom
all the portfolio advice is well worked out.
In my opinion, too many investors think they are
in this class. The extra factors and time-varying returns
would not be there (and will quickly disappear in the
future) if lots of people were willing and able to take
them. The presence of multiple factors wakes us up to
the possibility that we, like the average investor, may
be exposed to extra risks, possibly without realizing it.
5. Apply the logic of the multifactor-efficient
frontier. Figure 2 now summarizes the basic advice.
After thinking through which risk factors are good to
hold, and which ones you are already too exposed to;
after thinking through what extra premiums you are
likely to get for taking on extra risks, you can come to
a sensible decision about which risks to take and
which to hedge.
6. Do not forget, the average investor holds the
market. If youre pretty much average, all this thought
will lead you right back to holding the market index.
To rationalize anything but the market portfolio, you
have to be different from the average investor in some
identifiable way. The average investor sees some risk
in value stocks that counteracts their attractive average
returns. Maybe you should too! Right now the average
73
investor is feeling very wealthy and risk-tolerant,
therefore stock prices have risen to unprecedented
levels and expected stock returns look very low. Its
tempting to sell, but perhaps youre feeling pretty
wealthy and risk-tolerant as well.
7. Of course, avoid taxes and snake oil. The marketing of many securities and funds is not particularly clear on the nature of the risks. There is no reliable
extra return without risk. The economic reasoning in
this article should be useful to figure out exactly what
type of risk a specific fund or strategy is exposed to,
and then whether it is appropriate for you. The average actively managed fund still underperforms its style
benchmark, and past performance has almost no information about future performance.
The most important piece in traditional portfolio
advice applies as much as ever: Avoid taxes and
transaction costs. The losses from churning a portfolio and paying needless short-term capital gain, inheritance, and other taxes are larger than any of the
multifactor and predictability effects I have reviewed.
Tax issues are much less fun but more important to
the bottom line.
A big insurance market
It is tempting to think of asset markets like a
racetrack, but they are in reality a big insurance market.
Value funds seem to provide extra returns to their investors by buying distressed stocks on the edge of
bankruptcy. Long-Term Capital Management was, it
seems, providing catastrophe insurance by intermediating liquid assets that investors like into illiquid
assets that were vulnerable to a liquidity crunch.
Who better to provide catastrophe insurance than rich
investors with no other labor income or other risk exposure? Once again, we are reminded that Adam
Smiths invisible hand guides self-interested decisions
to socially useful ends, often in mysterious ways.
However, asset markets could be better insurance
markets. Both new and old portfolio advice implies
that the typical investor should hold a stock position
that is short his company, industry, or other easily
hedgeable kinds of risk. Many managers and some
senior employees must hold long positions in their
own companies, for obvious incentive reasons. But
there is no reason that this applies to union pension
funds, for example. A little marketing and help from
policy should make funds that hedge industry-specific risks to labor income much more attractive vehicles.
APPENDIX
The mean of the portfolio return is
Multifactor portfolio mathematics
This section summarizes algebra in Fama (1996). The
big picture is that we still get a hyperbolic region
since betas are linear functions of portfolio weights
just like means.
The problem is, minimize the variance of a portfolio given a value for the portfolio mean and its beta
on some factor. Let
w "# R
w #
R
w=
;R=
##
!w $ ! R
1
1
2
2
M
M
M
N
"# 1" b
## ; 1 = 1## ; b = b
## 1## b
$ !$ !
N
1, F
2, F
M
N ,F
"#
## .
##
$
E ( R p ) = E ( wR) = wE ( R) = w E .
The last equality just simplifies notation. The beta of
the portfolio on the extra factor is
b p = w b.
The variance of the portfolio return is
var( R p ) = w Vw,
where V is the variance-covariance matrix of returns.
The problem is then
min
w
Then the portfolio return is
R = w R ;
p
the condition that the weights add up to 1 is
1 = 1 w.
74
1
w Vw s. t. w E = m ; w 1 = 1; w b = b p .
2
The Lagrangian is
3
8
1
w Vw - l 0 ( w E - m ) - l 1 ( w 1 - 1) - l 2 w b - b p .
2
The first order conditions with respect to w give
1
6
w = V -1 El 0 + 1l 1 + bl 2 = V -1 Al
Economic Perspectives
where
where
A= E 1 b
s * = max E ( R - R f ) / s ( R - R f )
l = l 0 l1 l 2
denotes the unconditional Sharpe ratio, and
st = max E t ( R - R f ) / s t ( R - R f )
d = m 1 b p .
Plugging this value of w into the constraint
equations
A′ w = δ ,
denotes the conditional Sharpe ratio.
The technique exploits ideas from Gallant, Hansen,
and Tauchen (1990). I exploit Hansen and Jagannathans
(1991) theorem that for any excess return Z and discount factor m such that 0 = E(mZ), we have
AV Aλ = δ
−1
we get
E (Z )
s( Z )
λ = ( A′ V A) δ
−1
−1
w = V −1 A( A′V −1 A)−1δ .
var ( R p ) = w Vw = d ( AV -1 A) -1 d.
max
Or, writing out the sum of the matrix notation,
Var( R ) = m 1 b
p
-1
( A V A)
-1
E (m)
,
m "#
1 #.
! b #$
The variance is a quadratic function of the mean
return and of the desired beta on additional factors.
Thats why we draw cup-shaped frontiers. As with
the mean-variance case, the multifactor efficient frontier is a revolution of a hyperbola. If V is a second
moment matrix, to handle a risk-free rate,
var ( R p ) = d ( A V -1 A) -1 A V -1 SV -1 A( A V -1 A) -1 d,
where Σ now denotes the return variance-covariance
matrix.
Finding the benefits of a market timing
strategy without computing the strategy
I show first that the squared maximum unconditional
Sharpe ratio is the average of the squared conditional
Sharpe ratios when the riskfree rate is constant,
E = s(m*) ,
s E (m*)
where m* solves
m* = arg min s (m) s.t.
{m}
Et (mt +1Zt +1 ) = 0; Et (mt +1 ) = 1/ Rtf .
p
s *2 = E st2 ,
s(m)
and equality is attained for some choice of m. Thus,
the maximal unconditional Sharpe ratio is
The portfolio variance is then
p
Gallant, Hansen, and Tauchen show how to
solve this problem in quite general situations. They
phrase their result as a lower bound on discount
factor volatility but given E(Z)/σ(Z) ≤ σ(m)/E(m), one
can read the maximum slope of the unconditional meanvariance frontier (Sharpe ratio) available from markettiming portfolios. To keep the calculation transparent
and simple, I specialize to the case of a constant and
observed real risk-free rate Rf = 1/Et(m). Then, the
unconditional squared Sharpe ratio is the average
of the conditional squared Sharpe ratios,
s 2 ( m)
E ( m)
2
=
s[ Et (m) 2 ] + E[ s 2t ( m)]
E ( m)
2
=E
s (m) .
E (m)
2
t
2
t
Next, I show that when we forecast stock returns
with a regression such as equation 1, and interest
rates and the conditional variance of the error term
are constant, then the best unconditional Sharpe
ratio is related to the regression R2 by
s* =
s02 + R 2
1 - R2
,
where s0 = E ( R - R f ) / s( R - R f ) denotes the unconditional buy-and-hold Sharpe ratio.
Federal Reserve Bank of Chicago
75
If the conditional Sharpe ratio is generated by
a single asset (the market), and a linear model with
constant error variance,
Z t +1 = EZ + b( xt - Ex ) + e t +1 ,
then,
s (m) = E (Z) = EZ +b( x - Ex) ,
E (m) s (Z) s
2
and
2
2
t
t
t
t
t
e
EZ + b( x − Ex) 2
σ t2 (m)
t
E
= E
σ
Et (m)2
ε
=
( E ( Z )) 2 + b 2σ 2 ( x)
σ ε2
=
( E ( Z ))2
b 2σ 2 ( x)
+
2
2
(1 − R )σ ( Z ) (1 − R 2 )σ 2 ( Z )
=
1
( EZ ) 2
R2
+
2
2
(1 − R ) σ ( Z ) (1 − R 2 )
=
1
(1 − R 2 )
E ( Z ) 2
+ R2 .
σ ( Z )
The last line demonstrates s* = s02 + R 2 / 1- R2 .
To obtain the annualized Sharpe ratios reported in
table 1, I divide by the square root of horizon, since
mean returns roughly scale with horizon and standard deviations roughly scale with the square root
of horizon.
76
Economic Perspectives
NOTES
To be precise, these statements refer to the conditional serial
correlation of returns. It is possible for the conditional serial
correlations to be non-zero, resulting in conditional variances
that increase with horizon faster or slower than linearly, while
the unconditional serial correlation of returns is zero. Conditional distributions drive portfolio decisions.
portfolio. For example, in the simplest case of a one-period
investment problem, consumption equals terminal wealth.
Equation 3 then becomes
This effort falls in a broader inquiry in economics. Once we
recognize that people are unlikely to have much more data
and experience than economists, we have to think about economic models in which people learn about the world they live
in through time, rather than models in which people have so
much history that they have learned all there is to know about
the world. See Sargent (1993) for a review of learning in macroeconomics.
Brandt uses this condition to estimate the portfolio allocation
α. He extends the technique to multiperiod problems and problems in which the allocation decision depends on a forecasting
variable, that is, market-timing problems.
1
2
The standard first-order condition for optimal consumption
and portfolio choice is
3
3)
E[(ct +1 ) -g Z t +1 ] = 0,
where c denotes consumption, Z denotes an excess return, and
γ is a preference parameter. We usually take data on c and Z,
estimate γ, and then test whether the condition actually does
hold across assets. In a portfolio problem, however, we know
the preference parameter γ, but we want to estimate the
E [(aR f + (1 - a ) Rtm+1 ) - g Zt +1 ] = 0.
That is, Campbell and Vicera model investors objectives by
a utility function, max E Ít b t u(ct ) rather than a desire for
wealth at some particular date, max Eu(W T ).
4
I thank Nick Barberis for providing this figure. While it is not
in Barberis (1999), it can be constructed from results given in
that paper.
5
Of course, in theory, institutions, as such, should not have
preferences, as their stockholders or residual claimants can
unwind any portfolio decisions they make. This is the famous
Modigliani-Miller theorem. In practice, institutions often
make portfolio decisions as if they were individuals, and people
purveying portfolio advice will run into many such institutions.
6
REFERENCES
Barberis, Nicholas, 1999, Investing for the long run
when returns are predictable, Journal of Finance,
forthcoming.
Black, Fischer, and Robert Litterman, 1991, Global
asset allocation with equities, bonds, and currencies,
Goldman Sachs Fixed Income Research.
Brandt, Michael W., 1999, Estimating portfolio and
consumption choice: A conditional Euler equations
approach, Journal of Finance, October, forthcoming.
Brennan, Michael J., Eduardo S. Schwartz, and
Roland Lagnado, 1997, Strategic asset allocation,
Journal of Economic Dynamics and Control, Vol. 21,
No. 7, pp. 13771403.
, 1998, Who should buy long term bonds?,
Harvard University, manuscript.
Cochrane, John H., and Argia M. Sbordone, 1988,
Multivariate estimates of the permanent components
in GNP and stock prices, Journal of Economic
Dynamics and Control, Vol. 12, No. 2, pp. 255296.
Cochrane, John H., 1997, Where is the market going? Uncertain facts and novel theories, Economic
Perspectives, Federal Reserve Bank of Chicago, Vol.
21, No. 6, November/December, pp. 337.
, 1994, Permanent and transitory components of GNP and stock prices, Quarterly Journal
of Economics, Vol. 109, February, pp. 241266.
Campbell, John Y., and John H. Cochrane, 1999, By
force of habit: A consumption-based explanation of
aggregate stock market behavior, Journal of Political
Economy, Vol. 107, No. 2, April, pp. 205251.
Daniel, Kent, David Hirshleifer, and Ananidhar
Subrahmanyam, 1998, Investor psychology and
security market under- and overreactions, Journal
of Finance, Vol. 53, No. 6, pp. 18391885.
Campbell, John Y., Andrew W. Lo, and A. Craig
MacKinlay, 1996, The Econometrics of Financial
Markets Princeton, NJ: Princeton University Press.
DeBondt, Werner F. M., and Richard H. Thaler, 1985,
Does the stock market overreact?, Journal of
Finance, Vol. 40, No. 3, pp. 793808
Campbell, John Y. and Luis M. Vicera, 1999, Consumption and portfolio decisions when expected
returns are time varying, Quarterly Journal of
Economics, forthcoming.
Fama, Eugene F., 1996, Multifactor portfolio efficiency and multifactor asset pricing, Journal of Financial
and Quantitative Analysis, Vol. 31, No. 4, December,
pp. 441465.
Federal Reserve Bank of Chicago
77
Fama, Eugene F., and Kenneth R. French, 1993,
Common risk factors in the returns on stocks and
bonds, Journal of Financial Economics, Vol. 33,
No. 1, February, pp. 356.
, 1989, Business conditions and expected
returns on stocks and bonds, Journal of Financial
Economics, Vol. 25, No. 1, pp. 2349.
Gallant, A. Ronald, Lars Peter Hansen, and George
Tauchen, 1990, Using conditional moments of asset
payoffs to infer the volatility of intertemporal marginal
rates of substitution, Journal of Econometrics, Vol.
45, No. 1/2, pp. 141179.
Kandel, Shmuel, and Robert F. Stambaugh, 1996, On
the predictability of stock returns: An asset allocation perspective, Journal of Finance, Vol. 51, No. 2,
June, pp. 385424.
Kim, Tong Suk, and Edward Omberg, 1996, Dynamic
nonmyopic portfolio behavior, Review of Financial
Studies, Vol. 9, No. 1, Winter, pp. 141161.
Markowitz, H., 1952, Portfolio selection, Journal
of Finance, Vol. 7, No. 1, pp. 7791.
Merton, Robert C., 1973, An intertemporal capital
asset pricing model, Econometrica, Vol. 41, No. 5,
pp. 867887.
, 1971, Optimum consumption and portfolio rules in a continuous time model, Journal of
Economic Theory, Vol. 3, No. 4, pp. 373413.
, 1969, Lifetime portfolio selection under
uncertainty: The continuous time case, Review of
Economics and Statistics, Vol. 51, No. 3, August,
pp. 247257.
Samuelson, Paul A., 1969, Lifetime portfolio selection by dynamic stochastic programming, Review
of Economics and Statistics, Vol. 51, No. 3, August,
pp. 239246.
Sargent, Thomas J., 1993, Bounded Rationality in
Macroeconomics, Oxford: Oxford University Press.
Lakonishok, Josef, Andrei Shleifer, and Robert W.
Vishny, 1994, Contrarian investment, extrapolation
and risk, Journal of Finance, Vol. 49, No. 5, December, pp. 15411578.
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