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The Federal Reserve Bank of San Francisco’s Economic Review is published quarterly
by the Bank’s Research and Public Information Department under the supervision of
Michael W. Keran, Vice President. The publication is edited by William Burke, with the
assistance of Karen Rusk (editorial) and Janis Wilson (graphics). Subscribers to the
Economic Review may also be interested in receiving this Bank’s Publications List or
weekly Business and Financial Letter. For copies of these and other Federal Reserve
publications, contact the Public Information Section, Federal Reserve Bank of San Fran
cisco, P.O. Box 7702, San Francisco, California 94120. Phone (415) 544-2184.

"Financiers live in a world of illusion," said
George Bernard Shaw, and never has this been
truer than in the past decade, when everything
has had to be viewed through the prism of inflation. But financiers also deal with the very real
world of the marketplace, and the resulting conflicts between reality and inflationary illusions
have led to serious distortions in various segments of the market and in broad monetary relationships. The 1970's thus have developed
into a decade of financial uncertainty, unlike
any decade since the 1930's.
The four papers in this issue discuss the responses to increased uncertainty occurring in
four separate financial markets-the mortgage
market, the debt market, the equity market, and
tlle money market. The responses may differ in
each case-for example, an institutional response in the mortgage market and a market
response in the debt market-but all represent
aspects of a general attempt to compensate for
uncertainty in financial markets.
George Kaufman examines some of the structural changes brought about by inflationary uncertainty in the imperfectly functioning mortgage market. He compares the conventional
fixed interest rate mortgage (FRM) with an
alternative mortgage plan containing a variable
rate (VRM), and shows how the latter has developed as a response to the uncertainty facing
lenders and borrowers of long-term mortgage
credit.
The industry, faced with an inflationary environment, has created the VRM in order to
reduce the financial pressures on mortgagelending intermediaries, to increase the flow of
funds through the mortgage market, and to
stimulate the purchase of additional housing.
Kaufman describes how the VRM breaks the

link between long maturity and high risk associated with uncertainty regarding future interest
rates-two characteristics which the traditional
FRM mortgage contract combines. By decoupling the current interest charge from the future
interest rate, the risks surrounding future interest cost are transferred-all or in part-from
the lender to the borrower. With lenders feeling
a lower risk they will be more willing to undertake mortgage financing. The lowered risk
should also mean that a VRM will have a lower
expected cost to the borrower over the life of
the mortgage than an equivalent FRM.
In Kaufman's view, "The VRM is a complex
instrument, much more complex than first analysis would suggest, and there is good evidence
that it is not yet fully understood by any of the
parties concerned-borrowers, lenders or regulators." The recent experience of seven California financial institutions suggests that the
VRM can operate successfully, but only under
certain specific conditions. "The California experience to date suggests that it may not be easy
to realize the full potential of this mortgage
instrument."
Joseph Bisignano, in a second paper, analyzes
the bond market's response to the uncertainty
created by unanticipated inflation. The market
has experienced not only a dramatic rise in
yields on long-term debt securities, but also a
change in the spreads between different grades
of corporate and municipal bonds, and in the
spreads between yields on prime-grade corporates and yields on long-term Government
securities. This raises the question whether the
market has been "efficient" in establishing yield
differentials of this type.
Bisignano's response is that the market has
been efficient in removing any systematic profits

thought the virtues of high leverage ratios. There
have been no increases in leverage in recent
years, following a period of steady rise toward
more risky financing in the late 1960's. Recent
emphasis on cash flow suggests a return to a
lower mixture of debt to equity finance. To the
extent that external financing is required in the
future, it is likely to be met with greater stock
market financing and less reliance on bonds and
and on bank borrowing.
Rose McElhattan's paper considers the puzzling overforecast of money growth which economists' money demand relationships have produced since mid-1974, thus demonstrating how
a useful money-market equation can go astray
in an era of uncertainty. She points out that
forecast money growth was about twice as great
as actual money growth for the first year of the
current recovery-a finding which throws doubt
on the ability of standard models of the U.S.
economy to forecast GNP. But after examining
the GNP forecast errors developed in a large
quarterly econometric model, she concludes
that the current relation between money and
income has remained similar to its past behavior.
McElhattan examines several alternative explanations for this situation, the most persuasive one being that the public's demand for
money has not really changed. In other words,
the observed errors may be the fault of the misspecification of the equation used to predict the
public's actual demand for money. But although
this provides a plausible explanation of the
equation's erratic behavior, a good portion of
the overforecast remains unexplained. Uncertainty appears to be at the root of the problem.
In the real economy, for example, the recent
business decline-the steepest of the past generation-was much worse than expected, and
thus generated enough uncertainty to destabilize
traditional money-demand relationships.

available by arbitraging across different grades
of securities-for example, between Aaa and
Baa bonds-but that it has not been efficient
in establishing the differential between primegrade corporates and long-term Government
bonds. "The difficulty in determining this
spread appears to be related to the unprecedented rise in unanticipated inflation experienced since the late 1960's." Unanticipated inflation has caused the market to demand much
greater premiums for prime corporates over
Governments than the underlying risk would
have justified. Long-term Governments apparently have lost some of their role as a "safe
asset" in long-term portfolios, and this has impaired the market's ability to determine the
appropriate spread between the two types of
bonds.
Herbert Runyon analyzes the shifting relationships of debt and equity in corporate balance sheets, under the spur of inflation and increased uncertainty. These changes, he says,
can be viewed as a matter of corporate treasurers trying to find the best mix of equity and
debt in response to the uncertainty of the past
decade.
Manufacturing corporations financed themselves rather conservatively until about the mid1960's, but then began to expand the debt in
their balance sheets in an attempt to increase
the rate of return on equity shares. For a while
they were successful, widening the spread between the return on equity and the return on
assets. "This was altogether in tune with the
temper of the Sixties, when performance was
the name of the game and the bottom line took
precedence." But then a day of reckoning came
in the 1970's, when highly leveraged firms became increasingly exposed to higher market interest rates and to cyclical fluctuations in corporate earnings.
Corporate treasurers seem now to have re-

George G. Kaufman*

Housing has been one of the most volatile
and, over the last ten years, most troubled of
industries. The causes of housing's problems
are varied and complex, but one of them deserves special mention-the imperfect functioning of the mortgage market. Because most new
residential housing acquisition is financed by
mortgage debt, conditions in the mortgage market are important to the housing industry. This
paper examines one special aspect of the mortgage market, the mortgage instrument. It considers, first, whether the characteristics of the
conventional fixed interest rate mortgage
(FRM) may have both limited and destabilized
the supply of mortgage funds and, second,
whether an alternative mortgage plan containing
a variable rate may increase and smooth the

supply without reducing demand.'
In this paper, we analyze the implications of
variable rate mortgages (VRMs) for both
lenders and borrowers. We pay particular emphasis to the experiences resulting from the use
of VRMs by six large savings and loan associations and one large· bank in California which
have been offering these mortgages since 1975.'
The California experience is the most widespread use of VRMs in the country, and thus
should provide useful insights for other areas.
Because many VRM characteristics are stipulated by law, we examine the implications of
these constraints and recommend specific
changes in those features which appear to reduce the efficiency of the instrument.

FRM and VRM: Theoretical Issues
Most mortgage funds are supplied by private
financial institutions. At year-end 1975, savings
and loan associations had extended 51 percent
of all residential mortgages outstanding, commercial banks 17 percent, mutual savings banks
10 percent, and life insurance companies 4 percent. Government supported agencies extended
13 percent and other private lenders 5 percent.
Although they are the largest lenders of mortgage loans, thrift institutions (savings and loan
associations and mutual savings banks) and
commercial banks have complained of the relative lack of profitability of mortgage lending,

and have at times appealed to the Federal
government for assistance. In response, the government has introduced a host of mortgage subsidy programs and has limited the costs of
depository mortgage-lending institutions by imposing ceilings on the rates they may pay on
savings and time deposits. The latter restriction,
popularly referred to as Regulation Q, not only
limits cost increases for the bulk of the funds
available to depository institutions, but also provides thrift institutions with a slight deposit rate
edge over commercial banks as a means of encouraging savings flows into the thrifts. Evidence suggests, however, that these restrictions
have not improved the operation of the mortgage market. At times market rates of interest
have risen sharply above the Q ceilings, and

"George G. Kaufman, Professor of Finance at the University of Oregon, was Visiting Scholar at the Federal
Reserve Bank of San Francisco during Winter 1976. His
paper is a shortened version of a study which is available
from the Bank's Research Department. Research assistance provided by Donna Luke.

funds have been redirected away from institutions not offering competitive rates. This has
exacerbated the volatility of mortgage flows.
The growing evidence of the unsatisfactory performance of these government programs has
stimulated a search for other ways of assisting
mortgage lending institutions which would have
fewer side effects on the mortgage market.

Figure 1

Log l1+il

Maturity and interest-rate intermediation

Because residential dwellings are both bigticket items and long-lived assets, they are
financed primarily by long-term mortgage loans
collateralized by the dwelling purchased. Many
of the institutions extending such loans raise
their funds by selling securities in the form of
deposits with considerably shorter maturities, so
that they engage in maturity intermediation. In
addition, to the extent that the mortgages have
a fixed rate of interest over their life, while rates
on deposits may vary through time, the institutions also engage in interest-rate intermediation.
Although these two activities in the past have
been identical, they do not necessarily have to
be so. In fact, the VRM represents a device for
separating the two types of intermediation.
Economic theory tells us that the relationship
between a long-term rate and a short-term rate
on securities which are similar in all respects but
term to maturity is determined largely by the
expected course of short-term rates during the
remaining life of the longer-term security. If
we assume a world of perfect certainty in which
the values of all future short-term interest rates
are known, the long-term rate is a geometric
average of the current short-term rate and future
short-term rates on out to the maturity of the
long-term security. This implies that, if a depository mortgage-lending institution is to break
even, abstracting from costs of operations other
than interest rates, the rate it charges on a fixed
rate mortgage should be the geometric average
of the current deposit rate and the deposit rates
it expects to pay until the mortgage matures.
This relationship is illustrated in Figure 1.
Time is measured on the horizontal axis and
interest rates on the vertical axis. 3 Consider a
loan starting in period P and maturing in period

Q. Assume that there is no prepayment provi~
sion, and that the current deposit rate at P is A
and that deposit rates are expected to rise
steadily through the period C in Q. Again,
abstracting from operating costs and a competitive return on capital, the appropriate fixed rate
on the loan would be B. At the rate B, the
expected total return on the loan would equal
the expected total of deposits over the life of
the loan, so that the institution would break
even on its intermediation operations. The dollar gain in the triangle ABO would be exactly
equal to the loss in the triangle OCD.
Although the intermediary breaks even over
the life of the mortgage, in any arbitrary shorter
period, e.g., one year, it may be incurring either
a profit or a loss. In our example, with deposit
rates expected to increase, the loan rate will be
above the initial deposit rate, so that the intermediary will be generating a profit. Through
time, as deposit rates increase, the profit becomes progressively smaller unti~ at Z the deposit rate is equal to the loan rate. Thereafter,
the deposit rate rises above the loan rate and
the institution experiences progressively larger
losses. Thus the appropriate accounting period
for evaluating the performance of the intermediary is the life of the loan and not any
shorter period.
Under some circumstances the losses may
precede the gains, with the loss and gain triangles reversed. In such a case, short-term
loans from another financial institution or from

a government agency may be needed to ease the
institution's resulting liquidity problem. It
should be noted, however, that the problem is
one of liquidity and not of solvency.
Our analysis demonstrates that in a world of
certainty the return on any successive combination of shorter term investments summing to the
maturity of the mortgage loan will be the same
as for the mortgage loan itself. This is true because the long-term rate is an average of any
combination of composite shorter-term rates
and the latter, in turn, are averages of their
composite shorter-term rates. Thus, the return
on a 1a-period loan is equal to that of two comparable five-period loans-and the latter return,
in turn, is equal to that of 1a comparable oneperiod loans. In a world of certainty, long-term
maturity and long-term interest-rate intermediation are just as advantageous as similar shorterterm intermediation.
Figure 1 also shows that, if the loan rate
changes in synchronization with the deposit rate,
the gain and loss periods are eliminated and the

institution breaks even at all times. In this instance, the institution engages only in maturity
intermediation without interest-rate intermediation.
Effect of uncertainty
We can now remove the assumption of perfect certainty so that future rates are only expected rates. If the intermediary's deposit rate
expectations are realized, the analysis is unaltered. The institution breaks even on its fixed
rate mortgage lending but experiences subperiods of gains and losses. If expectations are
not realized, then it no longer breaks even. If
deposit rates rise slower than anticipated, say
along line AF in Figure 1, the gain triangle will
be enlarged and the loss triangle reduced. The
institution earns greater profits than expected.
Conversely, if deposit rates rise faster than anticipated, say, along line AE, the loss triangle
will be greater than the gain triangle. The institution will generate lasting losses and experience a solvency problem. Because it is lasting,

a solvency problem requires a different solution
than a short-term liquidity problem.
When an intermediary extends a long-term
loan at a fixed interest rate, it accepts the risk
that the underlying expected short-term interest
rates may not be realized. Although this may
result in gains or losses, many market participants are risk averse and assign greater weight
to an extra dollar loss than to an extra dollar
gain. A fixed rate mortgage contains two components for the borrower: (1) a long-term financing commitment and (2) insurance against
loss from higher than expected short-term interest rates. Like any insurance seller, the lender
will charge a premium for the interest rate insurance. The premium would be related to the
expected loss, or the probability of losses from
greater than expected interest rate increases
multiplied by the magnitude of the associated
loss. This premium is added to the long-term
rate obtained by averaging the relevant expected
short-term rates. If this is done and deposit
rates are realized, the gain triangle will exceed
the loss triangle. In Figure 2 the solid line AC
is now the expected path of short-term rates,
and the dotted lines above and below AC represent the degree of uncertainty about that path.
The rate BB I is purely expectational, based on
expected future short-term rates. This is the
standard explanation of the mortgage interest
rate without risk. BD is the insurance premium
payable by the borrower and is proportional to
the amount of risk. With the total market interest rate at PB I there is neither a profit to the
intermediary nor a net loss to the fixed rate
mortgage borrower, because the cost of providing insurance for the former and the cost of
purchasing insurance for the latter are the
same. If short rates turned out below expectations, long rates would fall and the borrower
would wish to refinance. With no prepayment
penalty an underpriced premium would imply
that realized losses exceeded expected losses,
and the intermediary would incur net losses on
its lending.
The analysis also indicates that the profitability of fixed rate mortgage lending is dependent only upon whether expected future interest

Figure 2
Log (1+j)

/~
// I

/ / /
6 '1 - - -

- - :) - /
/

"//-

°1

rate changes are realized, and not on the shape
of the yield curve. Financial intermediaries
can operate as profitably under descending or
flat, as under "normal" ascending yield curves.
Thrift institutions, in fact, expanded as rapidly
as commercial banks between 1905 and 1930,
though the yield curve was downward sloping
throughout almost all of that period. Except
where the yield curve is flat, realization of expected interest rates shifts the yield curve, and

consequently, the level of profitability reflects
the extent to which changes in the yield curve
are greater or less than those consistent with
the realization of expected rates. Fixed rate
mortgage lending can be profitable to intermediaries even if short-term rates rise more
than long-term rates, provided that the increases
do not exceed expectations.
Implications of VRM
Variable rate mortgages are long-term mortgage contracts in which the interest rate changes
at prearranged periods, in sympathy with
changes in some designated market interest rate
that is referred to as the standard index.. 4 Unlike
a series of consecutive short-term loans, a VRM
avoids the transactions costs that accompany a
new mortgage note. As Figure 1 indicates, a
VRM would simplify the operations of the intermediary by eliminating or greatly reducing
interest rate intermediation. Under the assumptions that VRM interest rates 1) change concurrently with deposit rates and 2) are translated into changes in the dollar amount (rather
than in the number) of monthly payments, the
institution's interest receipts and payments are

short-term interest rates increased more than
expected, the VRM would be costlier to the
borrower than the FRM, while if short-term interest rates increased less thiln expected, the
VRM would be cheaper.
A compromise between an FRM and a full
VRM would involve a risk-sharing arrangement
between the lender and borrower. 5 This could
be accomplished by placing a symmetrical maximum interest rate band on either side of the
rate on a new mortgage. Within the band, the
borrower assumes the risk; outside the band, the
lender assumes the risk. The wider the band, the
greater the risk assumed by the borrower. The
two polar cases are represented by an infinitely
wide band, which is a pure VRM, and an infinitesimally narrow band, which is a pure FRM.

perfectly synchronized and no interest rate risk
arises.
What happens to the interest rate risk? If
there are no constraints on VRM interest rate
changes, all the risk is shifted to the borrower.
The latter knows the amount of the first monthly
payment and the length of the mortgage, but
not the amount of the subsequent payments or
of the total payments. In contrast, on a fixed
rate mortgage he would know the amount of all
payments and the length of the payments. If
interest rates over the life of the mortgage
changed in line with market expectations, the
borrower would pay the same average rate on
the VRM as on the FRM (less the FRM interest
rate insurance premium), although the time pattern of the payments would be different. If

The California Experience
Six large state chartered savings and loan
cial banks offering VRMs also use this S&L cost
associations in California began offering VRMs
of funds index. However, the index presents
in early or mid-1975. Five of these associations
three problems, two economic and one political.
rank in the top ten in the country. (Their examFirst, when individual lenders are forced to
use an all-lender index, those institutions in
ple was followed at year end by the Wells Fargo
National Bank, the eleventh largest commercial
capital-short areas may be discouraged from
bank in the nation.) These six savings and loan
bidding more aggressively for deposits by offerassociations together extended some $1.7 miling higher interest rates, knowing as they do
lion of VRMs between April and December
that the rates on their outstanding mortgages
1975-about two-thirds of the total mortgages
will not be increased correspondingly. Because
they made in this period. Although this experia lender's decisions on the deposit rates it pays
ence is too brief to develop meaningful concluwill not greatly affect the index value, some
sions, some tentative impressions can be exindividual institutions could bid less aggressively
pressed. On the whole, the VRM is a much
for funds by offering lower rates and still benefit
more complex instrument than either lenders or
from higher mortgage rates. This reduces comregulators generally realize. As a result, regulapetition among individual lenders.
tions and pricing practices could limit the value
Secondly, the index is published semi-anof the instrument to both lenders and borrowers.
nually with a lag of two to eight months, and
In addition, difficulties could arise under seven
thus does not reflect current market rates. If
different headings, as described below.
market dates decline in any period, the drop will
not be reflected in the index until later. Yet to
Standard index
be competitive with FRM lenders, VRM lenders
must lower their rates in the current period. In
Regulations of the California Savings and
the absence of a decline in the standard index,
Loan Commissioner tie the rate on VRMs to a
they can remain competitive only by reducing
standard index, defined as the last published
the differential between the market rate and the
weighted average cost of savings, borrowings,
standard index. This spread, which remains
and Federal Home Loan Bank advances to California member associations of the Federal
constant over the life of the mortgage, is deHome Loan Bank of San Francisco. Commersigned to compensate the intermediary for the

eosts and risks of operations, which remain
unchanged. A lower spread than necessary to
cover the costs would, of course, lead to unprofitable operations over the life of the mortgage. It would appear at first that lower than
required spreads when the standard index lags
a decline in market rates would be offset by
higher than required spreads when the index
lags an increase in market rates. But because of
the combined impact of prepayment provisions
and limits on maximum interest rate changes,
borrowers are encouraged to switch from higher
spread mortgages to lower spread mortgages,
reducing the profitability of lending institutions.
A more appropriate solution would be the use
of an up-to-date index, such as a two-month
moving average of the cost of funds for individual institutions.
Lastly, a political problem arises because the
cost of funds index is greatly affected by Regulation Q. Major increases have occurred in the
cost of funds index in past periods when Regulation Q ceilings were increased. Because increases in Reg Q ceilings would lead to increases
in rates on all outstanding VRM mortgages, and
not only on new mortgages, it is reasonable to
predict that all homeowners would exert significant political pressure to maintain-or even
reduce-Reg Q ceilings as market rates rose.
If financial intermediaries could not offer competitive deposit rates, depositors would transfer
their funds away from these institutions into
private capital markets, depriving the mortgage
market of funds.

risk on the lender, increasing the rate that he
is likely to charge on each new loan. Also, because borrowers are allowed to prepay without
penalty within 90 days of any announced increase in loan rates, they have an incentive to
shift into new VRMs during any later period of
declining market rates in order to take advantage of lower maximum VRM rates.
Secondly, the maximum limit is based upon
the initial VRM rate rather than upon the rate
on a comparable FRM extended at the same
time. This feature benefits VRM borrowers
who obtain their mortgages when deposit or
short-term rates are high, because they can not
only ride the rates down, but can also convert
to new VRMs with lower maximum interest
rate limits. On the other hand, lenders are unable to recoup these losses from those borrowers
who obtain their mortgages when rates are low
and assume only limited upside risk. As a result, lenders must charge a higher interest rate
in order to be compensated for the added risk.
Limits on the maximum interest rate change'
also cause new VRMs to differ from comparable
outstanding VRMs, either in the loan rate or in
the maximum permissible loan rate. These differences, in tum, may encourage lenders and
borrowers to shift from old to new mortgages,
and thereby encourage the use of prepayment
and assumption restrictions to compensate
either party for potential losses from such transfers.
Prepayment fees
Prepayment fees on mortgages have frequently been a problem for lenders. If the prepayment penalty fees are nonexistent or too low,
in periods of low interest rates the lender will
experience losses from expected income and become reluctant to engage in additional lending
under the same conditions. Casual inspection
suggests that prepayment penalties generally
have not been very severe on fixed rate mortgages, so that borrowers have been able to refinance into lower rate mortgages in periods of
declining rates. On the other hand, borrowers
were locked into lower rates during periods of
rising market rates. This situation has helped

Maximum interest rate limit
A limit on the maximum VRM interest rate
change causes the risk of unexpected interest
rate changes to be shared between lender and
borrower. Two difficulties exist with the current
California regulations regarding this limit. First,
they make possible asymmetrical rate changes
for the affected savings and loan associations.
The rate cannot be increased more than 21/2
percentage points above the initial rate, but
there is no limit on the amount it can decline as
the standard index falls below the initial rate.
This regulation places a greater share of the

terest rates are above the initial rate (rather
than the lender when interest rates are below
the initial rate) .
Because of these general similarities, loan
assumption provisions may be analyzed best
relative to prepay1l1entprovisions. If there are
no .prepayment penalties to compensate the
lender when interest rates dedine, equity suggests that assumption should be restricted so as
not to compensate the borrower when interest
rates increase. (Although the burden of higher
rates falls. directly on the buyer, the new mortgage rate affects the price at which property can
be sold and thus indirectly affects the seller.)
On the other hand, if sufficient prepayment
penalties are permitted to compensate the lender
for any loss he may experience, restrictions on
assumption would not appear to be warranted.
Unlike prepayment penalties, only part of th@
assumption penalties-the part made up of the
higher rate on the new mortgage-accrues to
the lender. The remainder is absorbed in the
process of obtaining a new promissory note,
in the form of search loss, title insurance costs,
recording costs, and legal costs. Thus, the effective assumption costs to the borrower are
greater than the benefits to the lender.
As in the case of prepayment provisions, if
there were no restrictions on VRM maximum
interest rate changes, there would be no need
for assumption restrictions. The rate on a new
mortgage would be the same as on the old
mortgage. However, as already noted, restrictions on interest rate changes may at times not
make the two mortgages equivalent, so that
either the borrower or the lender can find some
advantage at such times in choosing between a
new and an old mortgage. As a result, some
VRM lenders have imposed assumption restricttions similar to those on FRMs, even though
unrestricted assumption has often been cited as
an advantage of VRMs.
Because only part of the benefit from restricted assumption goes to the lender, it would
help both sides if these restrictions were modified. One alternative is to reset the maximum
interest rate band each time the property were
sold. (This could be done without having to

make FRMs unfavorable instruments for lenders.
If there were no limits on changes in VRM
rates, old VRMs would yield the same rate as
new VRMs of the same credit quality-and thus
there would be no advantage to borrowers to
refinance at lower rates, no loss to lenders, and
no need for prepayment fees. However, rates
are generally not free to fluctuate without limit.
If the maximum interest rate limits are either
asymmetrical or centered around the initial
VRM rate rather than the comparable FRM
rate, it may be advantageous for the borrower
to refinance into a new VRM when interest rates
decline sufficiently. This, of course, would be
disadvantageous to the lender, so that he would
be likely, if permitted by law, to impose prepayment penalties on VRMs when market rates fell
below initial rates. At other times, there would
be no loss to the lender, so that he would be
likely to permit prepayment without charge.
The California code permits prepayment of
VRMs without penalty anytime within 90 days
of an announced increase in loan rates. Thus,
if rates had been falling for a period, borrowers
would be able to refinance into new, lower rate
VRMs after the first announcement of an increase. This provision should be changed to
permit prepayment without charge at any time
the loan rate is at or above the initial rate. At
other times, when the loan rate is below the
initial rate, prepayment penalties should be
permitted.
Loan assumptions
Most conventional FRMs have "due on sale"
clauses, which permit the lender to demand repayment of the outstanding balance (plus prepayment fees) at the time the mortgaged property is sold. This feature permits the lender to
extend a new mortgage at a higher loan rate if
market rates have risen since the initial mortgage contract. Restrictions on the assumption
of an existing mortgage by the property buyer
are analogous to unrestricted prepayment, with
two differences: the option to terminate the loan
rests with the lender rather than the borrower,
and the injured party is the borrower when in-

write a new promissory note.) The band on the
existing mortgage would then be equivalent to
that on a comparable new VRM. The necessary
legal changes could be achieved with only a
minor change in the California code.

rate. increases, could help lenders without creating any undue problems for borrowers.

Complexity of mortgage contract
Because a VRM is a complex instrument, the
VRMcontract or promissory note is also complex--much more so than an FRM contract.
Like theFRM note, the VRM note must specify
the initial •interest rate, the amount of the
monthly payments, and the length of the mortgage. But in addition, the VRM note must also
stipulate the conditions under which the interest
rate can change, the methods by which an interest rate change may be implemented, the options
available to either side for implementing rate
changes, the maximum and minimum limits on
interest rate changes, the frequency of possible
rate changes, and the maximum limits on the
total interest rate change over the life of the
mortgage. VRM prepayment provisions are
also more complicated, since they can shift with
the relationship of the current market rate with
the initial rate. Lastly, the legal provisions
applicable to VRMs are numerous, complex,
and subject to frequent changes.
Asa result, it is easy for errors to appear in
the promissory note. An analysis of the notes
used by the seven major users of VRMs in midJanuary, 1976, revealed that many contained
errors of nonconformity with the state laws and
regulations then in effect. The largest number
of errors pertained to the alternative procedures
by which loan rate changes could be implemented. Such errors are not binding on the
borrower, but they do reduce the amount of
information provided and thereby lower the
borrower's ability to evaluate the contract.
In addition, almost all of the promissory notes
omitted information that was materially relevant
to the ability of the borrower to understand the
provisions and the value of the standard index
at the time the loan was originated. Because of
the complexities of the instrument, lenders and
borrowers alike should benefit from the development of a model VRM contract. This would
be of considerable use to lenders in preparing
their own promissory notes and to borrowers in
becoming knowledgable about the information
that is material to them.

Implementation of rate changes
Changes in loan rates may be implemented
either .• as changes in the dollar amount of
monthly paYl1lents or as changes in the number
of unchanged monthly payments. Because deposit rate changes are reflected only in changes
in the amount of interest payments, discrepancies between the time of inflows and outflows
are reduced if loan rate changes are implemented in the same fashion, making interest
receipts match interest payments. However,
VRM loan rates can increase sharply, increasing
monthly payments sharply, while most borrowers' incomes increase only slowly. As a result,
borrowers may occasionally experience payments difficulties.
To ease the burden of such rate changes,
lenders frequently permit increases in loan rates
to be implemented, at the option of the borrower, as increases in the number of monthly
payments rather than in the dollar amount. This
eliminates interest rate risk, but because cash
inflows and outflows are not snychronized,
liquidity problems may still arise. The lender
may need to meet deposit rate payments before
receiving his loan rate payments. Thus, whenever a lender increases the length of a mortgage
in response to loan rate increases, he should
reserve the right to shorten the length again to
the original maturity in the event rates decline.
California regulations permit VRM rate increases to be translated into increases in the
number of monthly payments, provided that the
remaining life of the mortgage does not exceed
40 years. Although this is reasonable for a
mortgage with 20 or more years left to maturity,
it appears to be an unnecessarily long extension
for shorter mortgages. If rates increased over
time, some mortgages might never be completely
repaid. A change in the regulations, permitting
mortgage maturities to be lengthened by no
more than, say, 10 years in response to loan
12

Consumer protection
The intrinsic complexity of the VRM makes
it more important to protect borrowers against
errors resulting from incorrect or omitted material information. One source of error unique
to VRMs arises from the computation of the
change in monthly payments resulting from
changing loan rates.
Interest rates on almost all new residential
mortgages of any type are denominated in multiplesofO.25 percent, e.g. 91;4 percent. Borrowerscan check the monthly payments. that are
consistent with this rate and the .loan maturity
by using a standard mortgage payments table.
(Computations of these amounts without the
assistance of a calculator or computer is not
recommended.) However, as interest rates
change, the loan rate on outstanding VRMS can
be in multiples smaller than 0.25 percent. Interest rate fractions in these smaller multiples
are not included in standard mortgage tables.
Thus there is no easy way for a borrower to
check the monthly payment stipulated by the
lender and obtained through the use of a computer. To remove doubts about the accuracy of
such figures, all VRM lenders should make
available at their offices a monthly mortgage
payments table, perhaps in computer printout
form, for all interest 'rate fractions and maturities in which their mortgages are outstanding.
California law requires lenders to provide
borrowers with at least 30 days' written notice
before the effective date of a change in VRM
loan rates. When the economy is stable, with
only small changes in market interest rates, there
may be no changes in VRM loan rates for extended periods of time. But some borrowers
may forget that these rates can actually change,
and be both surprised and upset when an increase in monthly payments finally occurs.
Lenders would be well advised to send borrowers a brief notice on every mortgage anniversary,
possibly describing interest rate developments
in the mortgage market since the last notice and
reminding them that their loan rates could
change if market rates change sufficiently. At
least one smaller California savings and loan
association, which has used VRMs for some

years, has found such a program successful in
defusing borrower animosity to rate increases.
Evaluation of VRM
The mortgage industry has developed the
VR.Mas an alternative and/or supplement to
the FRM in order to reduce the financial pressures on mortgage-lending financial intennediaries, to increase the flow of funds through the
mortgage market, and to stimulate the purchase
of additional housing. Hence, the usefulness of
the VRM as a mortgage instrument can be
evaluated by examining its actual and potential
impacts on the mortgage and housing markets.
This, in turn, requires a determination of the
advantages and disadvantages of VRMs, relative to FRMs, for mortgage borrowers and lenders. These advantages and disadvantages can
be set forth in tabular form, based in part on
theoretical considerations, and in part on our
observation of California's limited experience
with this instrument.
Mortgage Borrowers
Advantages
1. Possible gain from lower than currently
expected interest rates over the life of the
mortgage.
2. Possible gain from lower prepayment
fees. 6
3. Possible gain from more liberal assumption provisions. G
4. Greater availability in periods of great interest rate uncertainty.
Disadvantages
1. Possible loss from higher than expected
short-term interest rates and need to predict interest rates.
2. Possible risk of financial strain if mortgage rate increases sharply but family in-come remains unchanged.
3. Greater complexity of mortgage contract.
4. Difficulty of ascertaining accuracy of
changes in monthly payments as a result
of changes in standard index.
Mortgage Lenders
Advantages
1. Reduced solvency problem from risk of
13

higher than expected cost of funds through
shifting of part or all of risk to borrower.
2. Reduced liquidity problem through increased synchronization of interest payments and receipts, whenever changes in
loan rates are translated into corresponding changes in dollar amount of monthly
payments.

Housing Market

Advantages

Possiple greater demand for new and improved housing from greater availability
of mortgage funds.
2. Possible smoother demand for new and
improved housing over cycle from
smoother flow of mortgage funds.
3. Possiple greater demand for new and improved housing from increased ability of
ll.Omeowners to sell, as a result of more
liberal prepayment and assumption provisions.

Disadvantages
1. Difficulty in pricing of new VRMs and
potential inability to compete for new
mortgages in periods of declining rates because of standard index lagging behind
market rate changes.
2. Reduction in potential gains from lower
than expected cost of funds.
3. Elimination of potential profit from sale of
"interest rate insurance."
4. Lack of synchronization of monthly payments and receipts, and possible liquidity
problems, whenever changes in standard
index are translated into changes in number of monthly payments.
5. Necessity of educating borrowers in complexities of mortgage contract, and possible borrower animosity whenever rates
are raised on outstanding mortgages.
6. Difficulty in designing features of mortgage contract and simple promissory note.

Disadvantages

1. Possible reduced housing demand from
reduced demand for mortgages.
2. Possible reduced housing demand from
(a) increased disintermediation if free
movement of standard index is restricted;
and (b) mispricing of mortgage if standard index is not sufficiently current.
Conclusion

The VRM is a complex instrument, much
more complex than first analysis would suggest,
and there is good evidence that it is not yet fully
understood by any of the parties concernedborrowers, lenders, or regulators. The potential
success or harm of the VRM is heavily dependent upon the regulations and practices defining
its .characteristics. The California experience
highlights a number of requirements that must
be met for the VRM to operate successfully:
1) the need to select an appropriate standardindex;
2) the need for thrift institutions io understand fully the complexities of maturity
and term structure intermediation;
3) the need to offset political pressures for
greater government interference with interest rates;
4) the need to determine loan rate changes
in the light of the desired degree of risk
sharing and the implications for prepayment and assumption provisions;
5) the need to "educate" borrowers;

Mortgage Market
Advantages
1. Possible increase in supply of funds from
lenders.
2. Possible smoother supply of funds over
the cycle.
3. Protection of solvency of thrift institutions, provided that new contracts are
priced correctly.

Disadvantages
1. Possible decrease in demand for funds by
borrowers because of greater risk.
2. Possible pressure on government from
mortgagors to prevent increases in standard index, particularly through use of
Regulation Q to hold down cost of funds
and thus level of index.

initial contract and subsequent changes in
interest rates.
Inappropriate decisions in any of these areas
could. greatly reduce the potential contribution
of· VRMs. The California experience to date
suggests that it may not be easy to realize the
full potential of this mortgage instrument.

6) the need to design the promissory note to
provide complete, accurate, and understandable disclosure of all material information;
7) the need to provide proper protection to
borrowers; and
8) the need for careful marketing of both the

APPENDIX
How a VRM Works
The VRM is a long term mortgage contract in
which the loan rate may change periodically, concurrently with changes in some predetermined market rate of interest, referred to as the standard
index. The provisions governing the relationship
between the loan rate and the standard index are
stipulated in the promissory note and, in part, are
established by state statute or regulation. These
provisions generally include the fixed differential
between the standard index and the loan rate, the
frequency at which the loan rate may be changed,
the amount by which the loan rate may be changed
(at any single time and over the life of the note),
and the method by which changes in the loan rate
are translated into changes in the monthly payments (and at whose option). In California, many
of these provisions are stipulated either in the State
Civil Code or regulations of the Savings and Loan
Commissioner.
The operation of a VRM may be illustrated with
a hypothetical example developed in Table A-I.
The standard index is the actual current value of
the average cost of funds of insured savings and
loan associations in the San Francisco Federal
Home Loan Bank District. l The loan rate is assumed to be 11/2 percentage points (150 basis
points) above the standard index, to compensate
the lender for all costs of operation and provide
him with a competitive return. Changes in the loan
rate are subject to the following restrictions:

3. Number of changes: no more than one per
six month period.
4. Overall limit: 250 basis points from the rate
on a comparable fixed rate mortgage extended on the same date.
The carryover (or cumulative) provision requires
the computation of two numbers:
Total loan rate carryover (TC) = UC l + /':, SI
Unused loan rate carryover (UC) = UC l +
/':, SI-P /':, =TC-P 6
where:
SI = change in standard index
P 6 = permissible change in loan rate
UC. l = unused carryover in previous period
A $20,000, 30-year VRM is assumed to be extended on January 1, 1967, at 6.85 percent, based
on a standard index of 5.35 percent. (A comparable FRM is assumed to cost 7 percent.) In the
second semiannual period, the standard index declines by 32 basis points. As a result, the loan rate
is reduced by the maximum 25 basis points to 6.60
percent. The l'emaining 7 basis points are included
in the unused carryover and aI'e applied to the
change in the next period. By the end of the first
half of 1975, the standard index had climbed to
6.41 percent, or 106 basis points over its initial
value. The loan rate had increased by 105 basis
points to 7.90 percent. In the 16 semiannual periods following the origination of the mortgage, the
standard index had declined five times and increased 11 times, while the loan rate had declined
twice and increased seven times.
The montWy payments, as the table shows, are
$131.06 in the first six months when the interest
rate is at the initial 6.85 percent level. The payments then decline to $127.77 in the next six month
period when the loan rate declines to 6.60 percent.
(This assumes that all changes in the loan rate are
translated into changes in the dollar amount of
monthly payments.) In the first six months of
1975, the last semiannual period shown, the monthly mortgage payments have increased to $143.24.

1. Limit per change:
maximum = 25 basis points
minimum = 10 basis poirits
2. Carryover: changes in the standard index
greater than 25 basis points or less than 10
basis points are carried over to the next and,
if necessary, subsequent periods and added to
the change in the index at that- time.
1 This

rate is not published until some months after the
close of the respective semiannual period. Nevertheless,
we assume here that it is available at the beginning of the
period, in order to have a current index that permits
lenders to price their new mortgages at the current market loan rate without changing the rate differential.

The unpaid balance at the end of this period is
$17,754.10.
In contrast, aFRM extended on January 1, 1967
at a 7-percent fixed rate would call for constant
monthly payments of $133.20. At the end of the
period, the unpaid balance would be $17,703.20,
only $50 less than on the VRM. Of course, if interest rates had increased faster, the .difference
would have been greater, but the initial rate on the
FRM may also have been higher.

3. The interest rate on the vertical axis is scaled in terms
of the logarithm of 1 plus the interest rate, to reflect reinvestment of the interest on both the mortgage and the
deposit, as is required by the definition of compound
interest.
4. The operation of a typical VRM is shown in Appendix
(A).
5. The risk could also be. shared or aSSUmed totally by the
Federal government as a third party. For such suggestions
see . George •G.Kaufman, "The. Case for Mortgage Rate
Insurance," Journal of Money, Credit, and Banking, November 1975, and James L. Pierce, "A Program to Protect
Mortgage Lenders Against Rate Increases," in Financial
Institutions and the Nation's Economy (FINE), Committee
on Banking and Currency, U.S. House of Representatives,
November 1975.
6. Prepayment and assumption provisions depend on the
magnitude of the maximum interest rate band and degree
of risk sharing. The larger the spread, the more liberal the
provisions are.

FOOTNOTES

1. For a discussion of alternative changes in mortgage
plans, see D. Lessard and F. MOdigliani, New Mortgage
Designs for Stable Housing in an Inflationary Environment
(Boston: Federal Reserve Bank of Boston, 1975).
2. Another large commercial bank began offering VRMs
after the conclusion of the study.

TABLE A"l
Monthly Payments and Unpaid Balance
Variable and Fixed Rate Mortgagest

1967-1975
Variable Rate Mortgage*
Period
(Semi·Annuai)

Standard
Index

loan
Rate

1/1/67
1967.1
1967.2
1968.1
1968.2
1969.1
1969.2
1970.1
1970.2
1971.1
1971.2
1972.1
1972.2
1973.1
1973.2
1974.1
1974.2
1975.1

5.35
5.03
5.08
5.10
5.17
5.27
5.58
5.67
5.64
5.57
5.55
5.56
5.60
5.83
6.14
6.44
6.41

6.85
6.60
6.60
6.60
6.60
6.75
7.00
7.15
7.15
7.15
7.05
7.05
7.05
7.30
7.55
7.80
7.90

Fixed Rate Mortgage:j:

Monthly
Unpaid
Payments
Balance @
(dollars)

131.06
127.77
127.77
127.77
127.77
129.65
132.78
134.65
134.65
134.65
133.45
133.45
133.45
136.35
139.23
142.10
143.24

t$20,OOO, 30-year mortgage extended January 1, 1967.
6.85 percent.
tLoan rate = 7 percent.
@At end of semi-annual period.

*Initial loan rate

20,000.
19,897.
19,785.
19,670.
19,551.
19,428.
19,304.
19,181.
19,057.
18,928.
18,795.
18,655.
18,510.
18,359.
18,209.
18,059.
17,908.
17,754.

Monthly
Unpaid
Payments
Balance @
(dollars)

133.20
133.20
133.20
133.20
133.20
133.20
133.20
133.20
133.20
133.20
133.20
133.20
133.20
133.20
133.20
133.20
133.20

20,000.
19,899.
19,794.
19,686.
19,575.
19,459.
19,339.
19,215.
19,086.
18,953.
18,815.
18,672.
18,524.
18,371.
18,213.
18,049.
17,879.
17,703.

Joseph Bisignano*

modern finance theory concerns the extent to
which the price of a security "reflects" the "information" the "market" has available to it. An
efficient market is one in which the price always
incorporates all of the information available to
the market. 1 It is obvious that this concept of
efficiency is a loose one and needs to be more
rigorously stated in order to make it operational.
(See Appendix I for a technical treatment of the
concept of market efficiency.) There is, however, a more intuitive corollary to this notion of
capital market efficiency. If a market is efficient
it should not be possible for participants to exploit the available information to make abovenormal profits on the basis of some "trading
rule." More precisely, an efficient market is one
in which the history of the price of the security,
other than the current price, provides no useful
information for knowing what the expected
value of tomorrow's (or next year's) price will
be. All the information is "fully reflected" in
the current price. This notion of efficiency leads
to the equation of an efficient market with a concept of a "fair game," in which there is an equal
expectation of gain or loss-or in which the
expectation is for a zero gain.
Tests of the efficient market hypothesis are
implicitly "joint tests," that is, they are both a
test of the hypothesis that the market is efficient
and a· test of a particular hypothesis regarding
how investors' expected returns on the security
are formed to establish equilibrium in the market for the security. This complication creates
some ambiguity in deriving implications regarding the efficiency of markets. If the hypothesis
is rejected, it may imply either (1) that the
market is efficient and that the theory of the
formation of the expected return is in error or

The recent period of inflation resulted in a
dramatic rise in yields on long-term debt securities. The rise in yields was accompanied by a
change in the spreads between different grades
of corporate and municipal bonds, and in the
spreads between yields on prime-grade corporates and yields on long-term U.S. Government
securities. In this paper we investigate the question of whether the bond markets were "efficient" in establishing yield differentials between
different grades of bonds and between prime
corporate and long-term Government bonds. In
addition, we consider to what extent "inefficiencies" were related to the recent period of inflation, more specifically, related to the unanticipated portion of the recent inflation.
Our analysis suggests that while the market
was efficient in removing any systematic profits
available by arbitraging across different grades
of securities (for example, between Aaa and
Baa bonds), the market was not efficient in
establishing the differential between prime grade
corporates and long-term Government bonds.
The significant rise in unanticipated inflation
caused the market to demand much greater premiums for prime corporates over Governments
than the underlying risk would have justified.
Long-term Governments appear to have lost at
least in part their role as a "safe asset" in longterm portfolios, and this has impaired the market's ability to determine the appropriate spread
of prime corporates over long-term Governments.
Defining capital market "efficiency"
The concept of capital-market efficiency in
"'Assistant Vice President and Economist, Federal Reserve
Bank of San Francisco. Jackie Kau provided research
assistance for this article.

Chart 1
Corporate Bond Yield and Yield Spreads

of securities in the same market (e.g., Aaa vs.
Baa corporates) .
12
10

0
Basis
points
400

Difference
(Baa-Aaa>

400

300

200

100

Measuring risk spreads
A glance at the postwar data indicates that
the Baa-Aaa "quality differential" was very
stable for the corporate sector and fairly stable
for the municipal market, except for the last few
years. The Baa and Aaa market yields and their
spreads are shown in Charts 1 and 2, while the
numerical averages, standard deviations, and
coefficients of variation (standard deviation
divided by the mean) are shown in Tables 1
and 2.
Between the 1950's and the 1960's, corporate
bond yields rose significantly but the average
Baa-Aaa corporate yield spread and its variation
remained almost unchanged, averaging about
65 basis points, with a standard deviation of 16
basis points. This quality yield differential remained stable even though both Baa and Aaa
corporate rates rose by about 170 basis points
during the 1960's. Assuming an efficient marChart 2
Municipal Bond Yield and Yield Spreads

0
1919

1925

1935

1945

1955

1965

Percent

(2) the reverse, that the expected return model
is correct but the market is inefficient.
Our interest in the efficient markets hypothesis first centers on the question of whether the
yield spread between various "grades" of rated
bonds adequately incorporates all the market
information which reflects substantive differences in the quality of the securities. To test
this hypothesis, we assume at the start that the
underlying quality differential between Aaa and
Baa bonds remained constant in the corporate
and municipal markets in the period since 1950.
Thus, our test of the efficiency of these markets
is made "conditional" on this assumption. Interpretation of our statistical results should recall this conditionality. Simply stated, our argument is that if bond markets are operating efficiently, it should not be possible to gain arbitrage profits systematically between different
security markets (e.g., corporate vs. Governments), and similarly, it should not be possible
to arbitrage systematically between risk classes

r .

Basis
points.

Difference
(Baa-Aaa>

,oo~
50~

100

I
o
1975

Table 1

ket, we can interpret this stability as indicating
an unchanged quality differential over this
period.
Market yields on municipals rose about 100
basis points during the 1960's, while the BaaAaa yield differential narrowed appreciably,
from 95 to 61 basis points, but with greater
relative variability. These data would indicate,
assuming an efficient market and constant quality of rating services, that the average quality of
Baa issues may have improved significantly,
relative to Aaa municipals, over this. period.
The evidence concerning the quality differential between Aaa and Baa bonds gives rise to a
question of market efficiency. Did the markets
in the 1950-69 period utilize information in an
efficient manner, such that knowledge of past
movements in the Baa-Aaa differential provided
little or no help in predicting each subsequent
monthly change in the differential? To answer
this question, we should consider the auto-correlations of the Baa-Aaa market yield spread
over that period, assuming constancy in the underlying Baa-Aaa quality differential.
Table 3 shows the autocorrelations for twelve
lagged periods, although 50 autocorrelations
were estimated. 2 The test statistics indicate that
there was very little serial dependence in the
changes in the Baa-Aaa yield spread during the
1950-69 period. The autocorrelations were all
quite low, and only the first-order autocorrelation in the corporate bond spreads was statistically significant. This latter result is not unexpected, however. As Holbrook Working has
shown, the monthly averaging of daily random
increments will often produce a first-period
autocorrelation of +0.25. 3

Corporate Yields and Yield Spreads

1919-1975
(percent)
Average
Market Yield
Period

Aaa

1919-1929
1930-1939
1940-1949
1950-1959
1960-1969
1970-1975 III

3.89
2.71
3.30
5.00
7.90

Baa

6.72
6.32
3.73
3.93
5.65
8.97

J.ll

Yield Spread: Baa-Aaa
Standard Coefficient
Mean Deviation of Variation

0.51
0.98
0.46
0.16
0.16
0.29

1.61
2.43
1.02
0.63
0.65
1.06

0.31
0.40
0.45
0.25
0.24
0.27

Table 2
Municipal Yields and Yield Spreads

1950-1975
(percent)
Average
Market Yield

Yield Spread: Baa·Aaa
Standard Coefficient
Mean Deviation of Variation

Period

Aaa

Baa

1950-1959
1960-1969
1970-1975

2.34
3.59
5.61

3.29
0.95
4.20
0.61
6.31 I 0.70

------_._~

0.13
0.16
0.25

0.13
0.27
0.35

Since the remaining autocorrelations were all
small and statistically insignificant, we can conclude that past changes in the Baa-Aaa spread
-for both the corporate and municipal markets
-were of no use in predicting the change in the
spread. This can be interpreted, loosely, as saying that people cannot profitably arbitrage between different grades of securities in the same
market.
Decomposition of risk exposure

The notion of risk is a relative one. The BaaAaa spread represents only the marginal risknot the total risk-that a Baa bond holder

Table 3
Estimated Autocorrelations for the Change
in the Baa·Aaa Yield Spread

1950-1969
Lag: (months)

Corporate Bonds
Municipal Bonds

0.20*
0.07
0.07 -0.08

3
0.06
-0.13

4
0.01
-0.08

-0.05
-0.10

"Coefficient is more than twice its standard error.
Box-Pierce Q-statistic: Municipals 50.95; Corporates 40.49
Critical:X' 95 % value: 67.5

-0.06 -0.04
0.00 -0.04

8
-0.02
0.12

0.02
0.12

-0.04
-0.03

0.07
-0.06

0.00
-0.12

Table 4 indicates that, between the 1940's
and the 1950's, the total risk differential between a Baa corporate bond and a long-term
government security declined from 128 basis
points to 94 basis points. Most of this decline
was due to a 29 b.p. decline in the "Baa quality
premium," compared to only a 6 b.p. decline in
the average Aaa risk premium over the "safe
asset," U.S. Government securities. During the
1960's there was only a modest change in these
spreads. However, the 1970-75 period witnessed a dramatic swing in these premiums, with
the total risk differential growing from 114 to
262 basis points. But in this case, most of the
higher differential (104 b.p.) was due to an
increase in the Aaa risk premium over long-term
governments, while only 44 basis points was
due to the increased risk of holding a Baa corporate security. The recent rise in the risk
structure of interest rates thus seems to reflect
the perceived greater risk of corporate securities
generally, rather than the greater riskiness of
less than premium rated corporate securities.
After the mid-1960's, quite atypically for the
postwar period, the risk premium between Aaa
corporates and long-term Governments began
to increase greatly and with much more variability (Chart 3). Indeed, in early 1968, this
risk premium exceeded the Baa-Aaa quality
differential for the first time in the postwar
period. This shift may be best understood in
terms of an increased public demand for greater
risk premiums on corporate securities. As
Edward S. Shaw has emphasized in a previous

assumes by not holding a prime grade bond. A
Baa bond holder's total risk can only be measured with reference to the most default-free
long-term debt instrument, a government bond.
To capture this total risk, we divide the differential between the market yield on a Baa bond
and that on a . long-term U.S. Government
security into two components-the spread between a Baa and Aaa, and the spread between
a Aaa and a long-term U.S. Government.
(Table 4) The sum of these two components
we have defined as the "total risk differential,"
on the grounds that this can only be defined
with respect to a "safe" long-term asset, in terms
of default risk .and marketability.
Given this definition of "total risk differential," the Baa-Aaa differential can be regarded
as equivalent to a Baa default premium only if
the two assets are alike in every other respect
(marketability, price variability, and so on).
Although the total risk differential may reflect
other institutional factors, such as liquidity and
call protection, we assume that it is dominated
by default considerations. The differential between the Aaa corporate bond and the longterm U.S. Government bond-the premium
over the safe asset-can then be thought of as
the additional risk one assumes by purchasing
the highest quality corporate long-term debt.
Let us refer to the Baa-Aaa spread as the "Baa
quality premium." The decomposition of the
"total risk differential" provides some interesting insights into the risk one assumes with a
Baa corporate security.

Table 4
Decomposition of Risk Exposure
Corporate Bonds
(basis points)
Baa-Aaa
"Baa Quality Premiums"

Periods

1941 ~ 1949
1950-1959
1960-1975
1969
1960
1970 - 1975

Means

92
63
81
64

108

Standard Coefficient
Deviations of Variation

37
16
31
16
31

040
.25
.38
.25
.28

Aaa-U.S. Gov't
"Aaa Risk Premium"

Means

37
31
89
50
154

Standard Coefficient
Deviations of Variation
~

13
7
57
25
30

.35
.23
.64
.51
.19

Baa-U.S. Gov't
"Total Risk Differentia'"

Means

128
94
169
114
262

Standard Coefficient
Deviations of Variation

44
21
84
37
55

.34
.23
.49
.33
.21

article in this Review,4 price inflation can play
havoc with so-called "safe assets"-i.e., assets
which have real yields with small unanticipated
variance. The existence of safe assets normally
permits risk-averse individuals to increase their
expected returns by forming portfolios of safe
and risky assets. In Shaw's words, "accumulation of safe assets is complementary with accumulation of productive and risky assets, reducing the supply price of savings to riskier
uses."5 However, the gradual erosion of U.S.
Government securities as safe assets during the
late 1960's and 1970's, due to a rise in unanticipated inflation, led investors to demand
greater premiums for purchasing corporate securities rather than Governments.
The hitherto strong correlation between different types of bond rates also disappeared during the 1970's. Long-term Governments and
Aaa corporates were very strongly correlated
in the two preceding decades, with a simple correlation of 0.98, but this correlation fell to a
modest 0.34 in the 1970-75 period. A simiiar
but less dramatic fall occurred in the municipal

bond market. In the 1970's Aaa corporate bond
holders demanded three times' the 50-basis
point premium that these securities commanded
over long-term Governments during the 1960's.
There are a number of possible explanations for
this phenomenon, but the very rapid (and atypical) rise in unanticipated inflation may be cruciaL The rate of unanticipated inflation reached
8 percent in 1974, and this increased uncertainty was reflected in the premium demanded
on corporate securities.
The risk premium between Aaa corporates
and long-term Governments went from an average of 50 basis points in the 1960's to 154 basis
points in the first half of the 1970's. In contrast,
the Baa-Aaa corporate spread increased by only
44 basis points between these periods. Thus,
the capital markets in recent years have been
demanding greater interest yields on Baa corporate securities, more because of the loss of the
safe asset than because of the increased inherent risk of Baa bonds.
Our previous results concerning the 1950-69
constancy of the Aaa-Baa risk differential, sug-

Chart 3
Corporate Bond Yield Differentials
Percent
4

Total risk differential
(Baa- U.S. gov't.>

2
premium (Baa-Aaa)

o
'41

'45

'50

'55

'60

'65

'70

'75

Chart 4
Unanticipated Inflation and Aaa Corporate Risk Premium

gested that the capital markets operated efficiently in incorporating available information in
the differential, so that knowledge of past
changes in the Baa-Aaa spread was of little
more use than knowledge of the most recent
change. Was the market equally efficient in removing the potential for arbitrage profits between U.S. Governments and Aaa corporates?
The autocorrelations for the change in the AaaU.S. Government spread have a substantial
amount of statistical significance, and the chisquare statistic rejects the hypothesis of random
fluctuations in the monthly change in this series
(Table 5). Similar results were evident for the
municipal-bond market. This evidence supports the argument that the loss of the safe asset
during the late 1960's and 1970's led to inefficient capital markets.
For most periods, the capital markets efficiently used available information in determining the Baa-Aaa corporate and municipal bond
spreads. Some evidence suggests, however, that
the market had difficulty properly determining
the premium between Aaa bonds and long-term
Governments. As we stated earlier, autocorrelation results provide only tentative information
on capital-market efficiency, because they are
really a joint test of the hypotheses that the market is efficient and that the true underlying risk
premium between the two securities is constant.
Significant autocorrelations may indicate that
either or both of these hypotheses are false, so
that we are unable, with these simple statistics,
to distinguish which of them is rejected. 6 However, our evidence indicates (at least conditionally) that the capital market properly assessed
default-risk differentials between Aaa and Baa

r .. ",,~~:::~~~

B_a.-,is points

200

150

100

bonds but was inefficient in capturing the risk
differential between Aaa bonds and long-term
Governments. This supports Shaw's suggestion
that the rise of "dirty inflation" (i.e., unanticipated inflation) helped distort relative financial
prices in recent years.
A rough estimate of unanticipated inflation
may be obtained by the following procedure.
Following a definition developed by Irving
Fisher, we may calculate the anticipated portion
of price inflation by subtracting an estimate of
the real rate of interest from the nominal (market) rate of interest-specifically, by subtracting Standard and Poor's composite dividend
yield from S&P's high grade bond yield. Then
we can obtain a rough estimate of "unanticipated inflation"7 by subtracting this estimated
"anticipated rate of inflation" from the observed
inflation rate calculated from the Consumer
Price Index.

TableS
Estimated Autocorrelations of the Change in the
Aaa-Iong-term U.S. Government Yield Spread

1950-1969
Lag (months)

Aaa-U.S. Gov't

-0.17* -0.27*

3
0.06

-0.02

5
0.00

*Coefficient is more than twice its standard error.
Box-Pierce Q-statistic: 117.6
Critical):' 95% value: 67.5

0.16* -0.10

8
-0.16*

0.15* -0.05

-0.05

0.12

kets, deserves to be considered as an important
cost of the recent U.S. inflation.

Table 6
Aaa Corporate Risk Premium and
Unanticipated Inflation

Conclusion

1960-1975
Period

1960-1964
1965-1969
1970-1975

Aaa corporateLong-term U.S. Gov't.
Bond Spread

Unanticipated
Inflation

(basis points)

(annual
rate of change)

0.06
1.23
2.32

65
154

The period of tranquil stability in bond markets experienced during the 1950's and early
1960's was replaced by an entirely different
situation after 1965. Yield spreads increased
between different grades of bonds in both the
corporate and municipal market, as did their
variability. While the bond markets apparently
were efficient in incorporating available information in the spread between Aaa and Baa securities, this was not the case for the market's
determination of the appropriate spread between Aaa corporates and long-term U.S. Government bonds. The difficulty in determining
this spread appears to be related to the unprecedented rise in unanticipated inflation experienced since the late 1960's.
It should be emphasized that the conclusions
of this paper are strongly conditional on the
assumption of long-term constancy of the underlying risks between different grades of rated
securities-a somewhat questionable assumption in light of the severity of the recent recession and inflation. Further work needs to be
done on an alternative hypothesis, namely, that
capital markets were efficient throughout the
post-war period in assessing risk differentials,
but that the underlying risk differentials widened
significantly because of substantive and pervasive changes in the economic environment. This
Bank's Research Department is continuing an
extensive study of the impact of these changes
on the capital market's perception of financial
risks.

Table 6 provides estimates of unanticipated
inflation for the 1960-75 period, together with
the spread between the Aaa corporate bond rate
and the long-term U.S. Government bond rate.
The Aaa corporate risk premium increased from
35 basis points between 1960 and 1964, when
the average rate of unanticipated inflation was
only 0.06 percent, to 154 basis points between
1970 and 1975, when unanticipated inflation
grew to over 2 percent annually.
Chart 4 shows that the Aaa corporate risk
premium over long-term U.S. governments remained quite stable during the early 1960's, but
then rose rapidly when the rate of unanticipated
inflation began to climb after 1965. However,
the two series did not always move together.
The fall in unanticipated inflation between 1970
and 1972 failed to show up in the Aaa corporate
risk premium until 1973. But then, as unanticipated inflation increased, the Aaa corporate
risk premium responded as expected by rising
rapidly. From the third quarter of 1973 to the
fourth quarter of 1974 the Aaa risk premium
rose by 104 basis points, reflecting the ll-percent increase in unanticipated inflation which
began in 1972.
The unprecedented demand for risk premiums on high-rated corporate bonds is yet another example of the so-called "rush for quality"
seen in both short-term and long-term debt
markets in recent years. Unanticipated inflation
is but one ingredient in the premium demanded
by the holders of private debt instruments.
Nonetheless, the distortion in financial markets
caused by unanticipated inflation, here described in terms of the efficiency of capital mar-

FOOTNOTES
1 The most thorough review of efficient markets theory
i; Eugene F. Fama, "Efficient Capital Market.s: A Review
of Theory and Empirical Work," Journal of Finance (May
1970).
2. See G. E. P. Box and G. M. Jenkins, Time Series Analysis: Forecasting and Control, Hold~n-D.ay, San Fra~ci~co
(1970), for a discussion of the estlmatlOn and statistIcal
tests conducted in the text.
3. Holbrook Working, "Note of the Correlation of First
Differences of Averages in a Random Chain," Econometrica
(October 1960).
4. Edward S. Shaw, "Inflation, Finance and Capital Markets," Economic Review, Federal Reserve Bank of San
Francisco (December 1975).
5. Ibid. p. 7.
6. With regard to the joint hypothesis nature of efficient

market tests see Eugene F. Fama, "Short-term Interest
Rates as Predictors of Inflation," American Economic Review (June 1975).
7. For a further discussion of unanticipated inflation, see
Joseph Bisignano, "The Effect of Inflation on Savings Behavior," Federal Reserve Bank of San Francisco, Economic
Review (December 1975).

8. See, for example, Burton G. Malkiel, A Random Walk
Down Wall Street, W. W. Norton and Company, Inc., New
York (1973).
9. For an insightful clarification of Fama's concept of
market efficiency, see Stephen F. LeRoy, "Efficient Capital
Markets: Comment," Journal of Finance, March 1976, and
Fama's reply.

APPENDIX I
The Concept of Efficient Markets
One form of an efficient market (the so-called
"weak form"), in which the "information" is
only the history of the price itself, can be stated
quite simply as:

price change, given the information available,
Zt, is equal to zero,

E(P t+j IPt'P t - 1 ,P t - 2 , · · · ) = E(P t +j IP t ) (1)

While the above concepts of market efficiency
may appear somewhat esoteric, they are important concepts for enhancing our general understanding of financial markets. Equation (1),
for example, states that in an efficient market
the current price is an unbiased estimate of the
future price. It also implies that successive
changes in the price of the security ought to be
uncorrelated, that is, statistically unrelated. Indeed, a wealth of information on stock-market
prices indicates that the equity market is efficient
under these definitions. In recent years, a
number of non - technical publications have
stressed this notion that prices in the stock market follow a "random walk;" that is, successive
price changes are independent. 8 Although this
concept is not formally equivalent to the statement that the stock market is an efficient market, it says something very similar. The general
point is the same-the market incorporates
price information in such a manner that one
'cannot exploit this information in a systematic
fashion to make a profit. 9

(4)

Equation (1) states that the mathematical expectations (denoted by E) of the price (P) to
prevail j periods hence, P t+ j, given our knowledge of the current price and the previous
history of this price, is precisely equal to the
expected value of the price j periods hence given
only the knowledge of the current price. In
other words, knowledge of past prices is irrelevant. Alternative definitions of market efficiency
differ primarily by extending the range of information upon which the expectation of the
future price in (1) is made conditional. In
addition, a more concrete notion of market
efficiency would suggest that the probability
density function of the future security price,
given the market's set of information, is equal to
the true density function of the future price
given the available information.
The efficient market theory, however, says
more than (1). Let us define the information
available to the market at time t as Zt. Then, if
the market is efficient,
E(P* t+j

IZ t )

=P t

Data Sources
Yield data for Aaa and Baa corporate bonds
and the long-term U.S. Government bonds were
obtained from the Federal Reserve Bulletin.
Banking and Monetary Statistics, and the Supplement to Banking and Monetary Statistics
(M:()lley Rates and Security Markets). All are
Federal Reserve publications.
Data on municipal yields were obtained from
Moody's Municipal and Government Manual.

(2)

where the * denotes that the future price is a
random variable; that is, not known with certainty. If we define the change in the future
price from time t, we have
LlP*

. :: p* . - P
t+J
t+J
t

(3)

From (2) and (3) it is clear that the expected
24

Herbert Runyon':'

balance sheets have been transformed since the
mid-1950's, with corporations making extensive
use of the debt markets to modify the composition of their capital base, despite the rising cost
of such funds. On the surface, this situation
might seem difficult to explain. However; a
more thorough examination suggests that there
are sound economic explanations of the changes
occurring in corporate balance sheets over the
past 20 years. Both the shift to debt of earlier
years and the recent corporate response to rising inflation can be viewed as a matter of corporate treasurers trying to find the best mix
of equity and debt in response to changing
conditions.
Our examination of this subject gives rise to
three basic questions. First, has a shift actually
occurred in the composition of corporate capital
structures? Second, how vulnerable have leveraged corporations become to the inflation of the
1970's and to the longer-term changes in the tax
structure? Finally, to what extent did the necessity for selling equity into a rather unfavorable
market spring from the need to lessen the exposure of leveraged corporations?

The renascence of the stock market has been
one of the more newsworthy aspects of the
1975-76 economic recovery. This spring, after
a suitable period of suspense, the closely
watched Dow Jones Industrial Average broke
through the four-digit barrier which had not
been broached since the January 1973 peak.
Stock prices surged ahead on a rising volume of
transactions. The recovery of economic activity
promised a higher stream of future profits, and
the price/earnings ratio-a barometer of the
state of investor expectations-made at least a
partial recovery from its 1974 trough.
Another important development has been the
upswing in the issuance of new equity shares,
amidst the hospitable environment created by
rising prices and heightened investor expectations. Corporations have attempted to maximize the amount of new capital at their command without unduly diluting the earnings of
shares already outstanding. Small firms, with a
limited ability to raise new capital, have gone
"public" and sold shares of ownership to investors. In 1975, nearly 25 percent of total
long-term financing raised in the capital markets
was secured in the equities markets. Yet, despite the recent increase, equity financing in the
last two decades has remained a relatively minor
source of new corporate financing, generally
averaging about 10 percent of the funds raised
in the financial markets.
In fact, over the past two decades, corporations have frequently been forced to go to market with new shares at unfavorable times. This
reflects the fact that equity is only part of the
capital structure of corporations. Corporate

Changes in the corporate capital structure
follow a clearly discernible sequence. An increase in corporate debt, relative to equity, results in higher leverage. The higher leverage
has a two-fold effect; it leads first to an increase
in profits available to stockholders, but at the
same time, it increases the risks inherent in a
greater dependence upon debt financing. The
resulting increase in risk may lead corporate
treasurers to sell more equity relative to debt,
leading to a decline in the leverage of the corporate capital structure. In essence, this is just

*Research Officer, Federal Reserve Bank of San Francisco.

Equation 1 only holds in a situation where
there is no direct income tax, and must be modified to be applicable to the U.S. Where corporate-bond interest payments are deductible
from corporate income, we have the following:

what has happened over the past 20 years, as
this paper shows by its analysis of the changes
in capital structure and their impact on the capitalmarket.
Factors affecting return to equity

(2)

In a pioneering work, Franco Modigliani and
Merton Miller demonstrated that, under certain
conditions, the market value of a corporationoutstanding equity plus debt-is independent of
its capital structure. 1 Given this premise, the
introduction of debt into the capital structure
of a firm increases the expected rate of return
on a share of stock by an amount equal to the
spread between the expected rate of return and
the interest rate on bonds times the debt to
equity ratio (i.e., leverage).
(1)

7r t =

(X -rD (1

where: X = total income, including the return
to debt generated by the firm
t = corporate income-tax rate
n = net income available for common stockholders
rD = cost of debt service (interest rate times
outstanding debt)
Equations (1) and (2) contain all three of the
elements which have contributed to the change
in corporate balance-sheets over the past two
decades.
The first element is leverage, or the ratio of
debt to equity. If the return on a firm's total
assets consistently exceeds the market rate of
interest, the firm has an incentive to borrow in
the market, thus increasing the return to equity.
The second factor is the corporate tax rate and
the deductibility of bond interest. To the extent
that bond interest payments are a deductible
business expense, the government assumes a
part of the risk of borrowing to increase investment. Government risk sharing does not decrease total risk taking in the economy; this will
normally increase in response to corporate taxes
as companies move to a riskier but higher-yield
leverage position in order to get back part of
the income government has taxed away.3
The last element in the picture is the interest
rate. The high market rates at which corporations have had to borrow in recent years have
made debt a relatively less attractive source of
new funds, and have reduced the prospects of
increasing the returns to equity through raising
the leverage of the capital structure.

J2.
E

where: i = expected rate of return on the equity
to the firm.
P = internal rate of return for the firm.
(Firms have differing risk characteristics and
appropriate P's will thus vary from firm to
firm.)
r rate of interest payable on the firm's outstanding bonds.
D=value of the firm's outstanding debt.
E = value of the firm's outstanding stock.
This formula says that the return on equity, i,
depends upon the internal rate of return plus the
spread between P and the market rate of interest and the capital structure of the firm (D/E,
the ratio of outstanding debt to equity). If the
risk associated with the stream of income is low,
the firm can increase its expected rate of return
by issuing debt. The price that the firm must
pay is the increased risk on its return, because
the reduced share of equity in total capital must
bear all of the risk inherent in the profits stream.
For the individual corporation, investment will
be expanded as long as P exceeds the market
rate of interest. The limiting case for all firms
is i=r. At this point, the expected return on
assets (i) is equal to the market rate of interest
(r), and firms will cease borrowing.
2

Benefits of leverage
The role of leverage in the composition of
corporate capital structures has been argued for
years, and cannot yet be said to be resolved to
anyone's complete satisfaction. At one end of
the spectrum, Modigliani and Miller argue that
26

fluctuated for several years, and then stabilized
near 44 percent throughout the 1969-75 period. 7 The stability maintained during the 195769 period, and again during the 1969-75 period,
strongly suggests that corporations desired the
particular capital structure existing during each
of those periods.
The purpose of increasing leverage is to increase the return to common stockholders. By
introducing relatively more debt into the capital
structure and increasing the debt!equity ratio,
corporate treasurers seek to increase the return
on total assets to improve their return to equity.
Chart 2 describes the relation between the
spread in the return to equity and the return on
assets for the two periods of relatively stable
leverage. Although there is a certain amount of

Chart 1
Capital Structure of Manufacturing Corporations

D/E ratio

0.5

0.4

0.3

0.2

0.1

Chart 2
Leverage and Earnings

+New series

Ol-J--I.--'--'--'--'--'---'--L-'--I.-'--'--'-...L-.L-l-.I-..l
'57

'60

'70

8,Or

Relative return to equity

'75

the average cost of capital is completely independent of the degree of leverage. 4 Ezra
Solomon expresses the more traditional view,
wherein increased leverage affects market value
because total earnings rise relative to the increased use of debt capital, causing lower costs. 5
However, all agree that, although leverage may
be safely increased within a certain range, further increases will adversely affect equity earnings. 6
Whatever their reasoning, corporation treasurers began to alter the debt-equity mix of their
capital portfolios in the mid 1960's (Chart 1).
The relative costs of alternative sources of capital funds was an incidental but by no means
negligible consideration in the determination of
the capital structure, but the ultimate objective
of the shift was to expand the share of earnings
accruing to the firm's common-stock holders.
The experience of the 1957-65 period illustrates in vivid detail the advantages of debt
financing to increase the leverage of the corporate capital structure. Within rather narrow
limits, the debt!equity ratio (i.e., leverage) of a
selected group of corporations remained near
25 percent throughout the 1957-64 period,

(%)

7.0

6.0

5.0

...•
...
....
..

4.0

3,0

-:••

1957-64
2.0
Quarterly Observations

0'L-,,/

0.2

0.3

0.4

Debt/Equity ratio

"Spread between return on equity and return on assets.

0.5

overlap in the yield spread in the two sets of
observations, this could be expected in view of
the highly cyclical nature of the return to equity.
The change in the composition of the. corporate capital structure that took place between
1957-64 and 1969-75 res~lted ina distinct upward shift in the return to shareholders. With
a greater proportion of debt included in the capital base, the spread rose from a range of about
21h to 5 percent to a rangeof 4 to 71h percent.
This finding supports the first premise of this
paper; viz., corporate treasurers changed the
composition of the corporate capital structure
in a successful effort to improve the earnings of
common stockholders.

their leverage positions by changing the proportion of equity and debt funds in· response to a
given capital need. But as all corporate treasurers know, other financing sources are also
important. Indeed, internal sources of fundsalso known as cash flow-are the mainstay of
corporate capital funds for investment. In the
main, these consist of undistributed profits
after taxes (i.e., retained earnings) and capitalconsumption allowances (i.e., depreciation).
Depreciation simply provides funds for the replacement of existing capital as it wears out or
becomes obsolete; therefore, depreciation does
not provide for net capital expansion.
From 1957 through 1964, internally generated funds supplied most of the nation's capitalexpenditure requirements. However, the situa-

Sources of corporate funds
Corporations thus can be seen as altering

Table 1
Sources of Nonfinancial Corporate Financing
1957-1975
($ billion)
Gross
Internal
Funds

Retained
Earnings

Net Funds
Raised in
Financial Markets'"

Internal Funds
as Percent of
Capital Expenditures

1957
1958
1959
1960

30.6
29.5
35.0
34.4

10.6
7.3
11.6
9.0

11.9
11.7
20.1
12.8

89.1
109.6
95.7
89.3

1961
1962
1963
1964
1965

35.6
41.8
43.9
50.5
56.6

9.0
11.1
12.0
16.5
21.3

18.8
17.2
21.6
22.2
34.8

98.3
95.9
97.2
98.1
91.0

1966
1967
1968
1969
1970

61.2
61.5
61.7
60.7
59.5

23.0
19.0
17.5
13.6
8.3

36.3
32.5
51.9
57.4
44.1

80.1
86.1
82.4
72.6
70.7

1971
1972
1973
1974
1975

68.0
78.7
84.6
81.5
103.9

13.3
20.7
31.0
33.5
27.7

52.4
69.3
91.6
101.8
40.1

78.0
76.9
69.9
64.7
108.1

*Includes equity sales
Source: Federal Reserve Board of Governors

in the general context of the usual market for
commodities, a high or rising price should elicit
a greater volume of the good in question. However, financial markets are not quite the same
as the markets for shoes and ships and sealing
wax. Common stocks gain their value from expectations of the future stream of earnings that
may accrue from ownership in the corporation.
If expectations are favorable for a corporation's
future earning power, this will be reflected in
the market price of its shares.
The relative desirability of a corporation's
shares may be gauged by comparing its price/
earnings ratio with that of other firms. This
ratio, known as the "multiple," embodies the
stock's current market price and the firm's current earnings. The value of the stock to the
rational investor is the discounted value of the
stream of future earnings that the stock is expected to generate. But to paraphrase Keynes,
the actual price is likely to be closer to the expectations generated by what the "rational" investor perceives to be the expectations of other
rational investors.

tion changed markedly by 1970, when funds
raised in the financial markets were more than
five times the amount of new equity generated
by retained earnings. This situation reflected a
sharp fall-off in retained earnings, which came
about because of both the Viet Nam tax increase
and the post-1966 profits decline. In the first
period of observations (1957-64), retained
earnings averaged nearly two-thirds of the average net volume of funds rai~ed externally in the
financial markets. In contrast, in the period
1969-75, the situation was dramatically reversed and retained earnings amounted to only
one-quarter of externally-generated funds.
Questions arise also about internally generated funds as a source of equity. Although retained earnings may remain in the corporation's
possession, this only means that stockholders
are content to settle for the prospect of future
capital gains as opposed to present income in
the form of paid-out dividends. Retained earnings are a highly erratic source of investment
funds, subject as they are to unexpected movements in both gross earnings and corporate taxes
(Chart 3). In addition, retained earnings are
the buffer between net profits after tax and net
dividends paid, and corporate policymakers traditionally try to stabilize dividend payments,
holding them steady when profits fall off and
increasing them less rapidly when profits are on
the rise.
On the surface, it would appear that retained
earnings are a cheap source of funds to corporate treasurers. However, a number of studies
have shown that the cost of retained earnings,
from the shareholder's point of view, is in the
neighborhood of 10 percent. 8 Retained earnings
are subject to two sets of taxes affecting stockholders-the corporate income tax and the capital gains tax-and IRS data on these tax categories (Statistics of Income for 1972) indicate
the validity of this 10-percent estimate. Also,
transaction costs must be incurred if the stockholder should wish to realize a capital gain by
selling his stock. It

Chart 3
Profits, Retained Earnings and the Corporate Tax Rate
Percent
55
50

45
40
35
Billions
of dollars

r---------------

./ Ratio scale
1

Stock prices and equity sales
If shares of common stock were to be viewed

'57

'60

'63

'66

'69

'72

'75

Another peculiarity of the stock market is
that it is essentially a secondhand market. Stocks
which have traded in the market for some time
are a more-or-less known quantity (i.e., "seasoned") and unlike used cars, may command
a premium over new issues just entering the
market. A prevailing high price/earning ratio
for the market in general would seem to create
a hospitable environment for the sale of new
equity shares. However, precisely the reverse
has been true over much of the past two decades
(Chart 4).
The combined price/earnings ratio of the 500
stocks in the'Standard and Poor's industrial index averaged above 16 throughout the 195870 period, and during most of that time, the
demands upon the equity market were fairly
modest. During 1957-64, nonfinancial corporations were consistent (if small) net sellers of
equity, averaging $2-3 billion per year. In the
mid- and late-1960's they retired outstanding
stock almost as often as they sold it. But then,
in the first half of the 1970's, these corporations

paradoxically became substantial net sellers of
equity, selling new issues in the face of a price/
earnings ratio that averaged about 11 and which
dipped below 7 on occasion (Chart 4). In
other words, corporations were reluctant to sell
equity in a period of relatively high stock prices,
and then turned around and marketed shares in
a period of far less favorable prices.
All of this suggests that market conditions
may be only a sec<imdary factor in the decision
to sell stock. Corporate treasurers stayed on
the sidelines during the long period of rising
stock prices, and then entered the market in the
1970's when it was much less amenable to new
issues. This can be explained in terms' of the
desire of financial managers either to reduce the
degree of leverage or, alternatively, to maintain
a given leverage position but with the substitution of retained-earnings equity for marketraised equity. (The first explanation accords
with a wish to reduce leverage in an increasingly
risky world.) The steadiness of the leverage
ratio in the 1969-75 period noted in Chart 1

Chart 4
Stock Prices and Net Equity Sales for Nonfinancial Corporations
Ratio

Bi Ilion. of dollars

20
)--Price/Earnings ratio ___

........... Net equity sales

-5

LLL.LL.LLLLJ--LL.LL.LLLLJU-l.LL.L.LLLJ-LJ.-LL..L.L.L.LJLLl-LL..L.L.L.LJU-l-'-LLLLLJU-l-'-L..L.L.L..L-L.L..l--'--L--'--'---,--"---L.L..L-'J.-l-I-.L..!1

1957

1960

1963

1966

1969

1972

1975 1976

Taxes, markets and risk assumption

suggests that corporate treasurers now wish only
to maintain their current leverage position.

Several sets of factors influenced the sources
of corporate financing over the past two decades,
the first of these being changes in the corporate
income tax. The average or effective corporate
tax rate varied substantially-from 50 to 37
percent.-because of the institution (and suspension) of the investment tax credit, as well
as changes in depreciation accounting and in
tax-rate structure. These shifts had the direct
effect of increasing or constricting the flow of
retained earnings, depending upon the direction
of the tax rate.
The tax rate thus represents another influence
on the cost of funds raised by credit-market
borrowing. Since interest costs are fully deductible for tax purposes, changes in the corporate
tax rate directly affect the costs of borrowing.
A high tax rate tends to insulate the firm from

Limits of leverage

The higher rate of return on a leveraged capital structure carries with it a greater degree of
risk as the costs of debt service rise relative to
income. This is true in a period of price inflation, and doubly true in a recession when pre-tax
profits fall. Dividend payments upon common
stock may need to be trimmed or eliminated if
the profitability of a firm worsens. But since
interest payments are not postponable without
a threat of default, the leveraged firm in this case
faces more risk than the firm capitalized with
equity. Thus, it should be expected that as firms
come to rely more heavily upon debt as a source
of capital funds, their vulnerability to fluctuations in profits and interest rates would increase
accordingly.
The relationship of changes in the leverage
ratio of manufacturing corporations to their
interest-payment burden is described in Chart
5. 10 Here, as in Chart 2, there is a bifurcation
of observations, with 1957-64 observations
clustering around a debt!equity ratio of 25 percent and 1969 - 75 observations clustering
around a ratio of 44 percent, with the schedule
shifting upward and to the right. During the
latter period, corporations' increased reliance
upon debt in their capital structure increased
their possible exposure, and their high debt/
equity ratio served as an effective ceiling for
leverage. In 1970, when the debt-equity ratio
reached 44 percent, interest costs assumed a
much larger claim upon corporate revenues, and
net equity sales showed a significant increase.
The close clustering of observations around
the low (25 percent) and high (44 percent)
debt!equity ratios helps illustrate the trade-off
between risk and earnings that was implicit in
the shift in corporate leverage between the two
periods studied (Chart 6). In this comparison,
the spread between return on equity and assets
after taxes is used as a measure of equity earnings, and the net interest cover is used as a
surrogate for risk, with a diminishing coverage
corresponding to an increasing degree of risk.

Chart 5
Leverage and Risk
Risk ratio'

1969-75

0.7

0.6

0.5

0.4

0.3

"'
1\
IU:.
.

0.2

'II
.\~

•••

0.1

1957-64

Quarterly Observations

OG11
0.2

I
0.3

0.4

Debt/Equity ratio
'Reciprocal of net interest times profits after tax.

0.5

favored equity financing-chiefly through retained earnings-over credit-market borrowing.
This has been accomplished through a redistribution of the risks related to capital expansion
based upon borrowed funds, Let us say that a
corporation is indifferent to the tax rate when
considering the risk of credit-market borrowing.
If the tax. rate is high and bond interest is deductible, the government essentially underwrites
a part of the firm's interest cost and shoulders
a corresponding part of its risk. As the tax rate
faUs, the corporation's net interest cost rises
and the federal share correspondingly declines.
As long as interest expense is fully deductible
as a cost of doing business, the corporation income tax will have a differential impact upon
equity and debt financing. However, a declining
tax rate tends to favor equity financing, because
it forces the corporation to absorb a proportionately greater part of the total interest cost. As
the debt/equity ratio rises-and the corporation becomes more highly leveraged-the interest burden becomes a much more critical consideration, especially during a period of inflation
and rising market interest rates. It should also
be noted, however, that the costs of capitalwhether equity or debt-both rose in this period
as stock prices fell and the terms of borrowing
grew more onerous. Whether corporations
sought to reduce leverage or to replace the

Chart 6
Change in the Terms of the Earnings-Risk Tradeoff
Relative return on equity (%) •

Debl/EquitF.444

I ~\

7.0

1969-75

(0 \

6.0

Debt/Equity=.250

5.0

4.0

\ Y"

.·.

·.
.·.

3.0

\ '.

\~~--

1957-64
2.0
Quarterly Observations

I
0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Risk ratio
·Spread between return on equity and return on assets

market interest costs, because the government
assumes a share of the borrower's risk to the
extent of the amount of interest deducted. Conversely, a lower tax rate increases the net burden
of interest costs to the corporation-as was
seen in 1974-75, when net interest costs continued to rise in the face of falling market interest rates (Chart 7) .
Corporate borrowers are also affected by inflation, through its impact upon the long-term
interest rate. The long rate was remarkably
constant, around 4V:z percent, in the first half of
the 1960's, when the inflation rate fluctuated
around a base rate of about 1 ~ percent. But
then as inflation increased, long-term interest
rates increased, and corporate net interest costs
also started to rise. Thus, throughout this decade of large net borrowing by corporations, the
actual terms of borrowing were working against
them with respect to the interest burden.
The decline in the effective corporate income
tax over the past two decades has, on the whole,

I \

Percent

Chart 7
Corporate Bond Yields and
Net Interest Cost
1957 - 75

8
6

Net interest cost

'57

'60

'63

'66

'69

'72

'75

increased the exposure of highly leveraged firms
to both higher market interest rates and cyclical
fluctuations in earnings. And these corporations
r~acted to their problems in the manner we have
seen in recent years.
All these changes in corporate financing have
demonstrated in rather dramatic fashion both
the positive and negative aspects of financial
leverage. The events of the past several years
have probably given many painful moments to
corporate treasurers. Given a world of increased
risks, less leverage may be well advised. Still,
the retreat from the high leverage ratios of 1970
could be rather limited. There are still advantages to be realized if the yield on the total capital base exceeds the cost of borrowed funds.
The breadth and complexity of financial markets and the experience and imagination of corporate financial officers have increased apace.
However, corporations in the years ahead will
probably meet their capital requirements in a
more balanced fashion than they have recently,
drawing on both the equity and debt markets as
they keep in mind the main lesson of the 1970's
-leverage can cut both ways.

diminished internal flow of equity, the result was
the same: they sold more equity into the financial markets.
Conclusion
Corporate behavior over the past two decades
with respect to equity sales is readily explainable
in terms of the institutional structure within
which financial markets function. As a group,
manufacturing corporations followed a fairly
conservative capital-financing program from the
mid-1950's through the mid-1960's. At that
point,however, they began to expand the debt
in their balance sheets in an attempt to realize
their full profit-maximization potential on equity
shares. For a while they were successful, widening the spread between the return on equity and
the return on assets. This was altogether in tune
with the temper of the Sixties, when performance was the name of the game and the bottom
line took precedence.
Manufacturing corporations, like other firms,
faced a more difficult situation in the 1970's.
The combination of inflation (with higher interest rates) and declining effective tax rates

FOOTNOTES
The financial information for this group of corporations is
presented in balance-sheet and income-statement form,
with equity and debt shown on the basis of book value
rather than market value. The ratios are presented in the
QFC as equity/debt but are transposed to accord with
the more usual definition of leverage.
8. Martin J. Bailey, "Capital Gains and Income Taxation,"
Taxations of Income from Capital, M. J. Bailey and A. C.
Harberger (Washington, D.C. Brookings Institution, 1969),
pp.11-49.
9. William J. Baumol and Burton G. Malkiel, "The Firms'
Optimal Debt-Equity Combinations and the Cost of Capital," The Quarterly Journal of Economics, November 1967,
pp. 565-566.
10. The ratio of after-tax profits to interest for nonfinancial
corporations is used here as a measure of the relative
burden of debt service. This ratio is quite different from
the usual accounting ratio, which measures before tax
profits plus interest payments divided by interest payment.
Because of data deficiencies, it was not possible to obtain
both gross earnings and interest payments for manufacturing firms. The "times interest" ratios on an after-tax basis
are much lower than on a pre-tax basis. For example, a
times-interest coverage of 1.0 on a pre-tax basis indicates
that the firm is insolvent, since gross earnings are zero.
On an after,tax basis, a ratio of 1.0 is roughly equivalent
to a ratio of 3.0 on a pre-tax basis, assuming a corporate
tax rate of 50 percent, since interest payments and taxes
have been deducted from gross earnings. In order to make
a lower interest cover correspond to higher risk, the reciprocal of after tax times-interest is used, scaled from
0.1 to 1.0.

1. Franco Modigliani and Merton H. Miller, "The Cost of
Capital, Corporation Finance and the Theory of Investment," American Economic Review, June 1968, p. 267, ff.
2. As long as relatively safe investments are available, the
firm will not be pressed by this limit because the proceeds
of a financing can be used to lower the firm's intrinsic risk.
This process-the firm's deliberate mixing-of safe and
risky investments-is logically no different from issuing
"negative" debt. The only limit on this process is that
debt cannot be less than zero, so that a firm with risky
profits cannot, under equation 1, reduce the risk exposure
of its earnings.
3. For a recent discussion of this point, see Richard A.
Musgrave and Peggy B. Musgrave, Public Finance in Theory
and Practice, second edition (New York: McGraw Hill,

1976), p. 307.
4. Modigliani and Miller, "The Cost of Capital, Corporation
Finance and the Theory of Investment," op.cit., pp. 281282.
5. Ezra Solomon, The Theory of Financial Management,
(New York: Columbia University Press, 1963), p. 94.
6. Ibid., Modigliani and Miller, op.cit., p. 275. The location of such a point of leveral$e is proximate rather than
precise. Modigliani and Miller, after testing the effect of
leverage on common stock yields for electric utilities and
oil companies, concluded that the results appeared to support their theoretical construct, but that the empirical evidence was not conclusive. Ibid, pp. 284-287.
7. The debt/equity ratios used in Chart 1 and thereafter
are for manufacturing corporations as reported in the
Federal Trade Commissions' Quarterly Financial Report.

Rose McElhattan*

During the first year of the current economic
recovery (1975.1-1976.1), the nation's gross
national product, in nominal terms, increased
by 13 percent. This rapid rate of economic expansion occurred along with relative ease in
financial markets; interest rates were lower in
the first quarter of 1976 than when the expansion began in 1975. Surprisingly, however, the
growth in the economy and the decline in interest rates have been accomplished with a relatively moderate rate of growth in the money supply.
The actual M , rate of growth was 5.1 percent
from 1975.1 to 1976.J1-about half the rate
which standard money demand models estimate
as necessary to support the observed income
growth and decline in interest rates. This overprediction of money demand constitutes an unusually large forecast error, since standard
money demand functions (which relate the public's demand for money balances to the level of
GNP and interest rates) generally have performed well in estimating the growth in money."
However, beginning with the third quarter of
1974, these equations began overestimating the
public's demand for money by relatively large
and increasing amounts.
The demand for money is an important component in the final relationship between money
and GNP. Changes in money have had fairly
predictable, although not exact, effects over
time on the gross national product. 3 Because
of this relationship, the money stock has become a significant variable in economic analysis. The central bank, in turn, has a degree
of control over the stock of money, making it
an important Federal Reserve policy variable.

The recent large forecast errors in the estimated
demand for money suggest a deterioration in
the ability of policymakers to predict the impact
of changes in money upon economic activity.
This in turn suggests that less emphasis should
be placed upon the money supply as a guide in
the conduct of monetary policy. This paper
attempts to determine how much M, has deteriorated as an indicator of movements in GNP
since the recent appearance of large errors in
money demand.
Utilizing a version of the MPS model (Massachusetts Institute of Technology-University of
Pennsylvania-Social Science Research Council),4 we conclude that there has been no material deterioration in the overall relationship
between money and GNP since mid-1974, relative to what would be expected from past experience. The money supply (M, ) remains as
useful an indicator of overall economic activity
as it has been in the past.
In the next section, we indicate the forecast
errors in the money demand equation included
in the MPS model and, using the familiar LMIS diagram, illustrate the policy question raised
by the recent shifts (Le., forecast errors) in
estimated money demand functions. Following
that, we analyze GNP forecast errors generated
by the MPS model and attempt to interpret recent velocity movements.
Forecast errors in money demand

Since 1974.3, money demand equations have
shown large forecast errors, with forecasted
money holdings by the private sector exceeding
actual money (M , ) balances. A conventional
relation which illustrates the nature of these

"Economist, Federal Reserve Bank of San Francisco.

errors is included in the MPS model. This model
uses two equations to forecast money (M i ) demand-one for the demand for currency and
one for the demand for demand deposits. The
currency equation has performed well since
mid-l 974; the errors are relatively small and
within the range of past experience for this
equation. The demand deposit equation, on the
other hand, has overestimated the public's demand for demand deposits and by relatively
large amounts. This equation (Appendix A) is
the major source of error in the prediction of

formation is available only through 1975.4.
Consequently, we cannot extend the MPS model
estimates beyond the end of last year-but we
are able to estimate a standard-type money demand equation using newly revised NIPA data.
This differs from the MPS model specification
in Appendix A in only a minor way: the discount rate is deleted and the commercial-bank
passbook rate is used instead of the weighted
time-and-savings deposit rate. These minor
changes do not alter the error pattern shown
above.
The demand deposit equation estimated with
the revised NIPA data displays the same problematic errors as the MPS equation, with errors
increasing after 1974.3 and sharply accelerating
in the last half of 1975. However, the magnitude of the errors then appears to stabilize, at

Mi'
In four of the six quarters from 1974.3 to
1975.4, the error in the demand deposit equation was outside the range of past experience
(Chart 1A and B, Table 1).' The largest error
prior to mid-1974 was $4.7 billion in 1972.2.
By 1974.4, however, demand deposits were
over-estimated by $6.7 billion and the error
reached $19.9 billion in 1975.4.
These estimates and the MPS model equations are based upon National Income and
Product Accounts (NIPA) data for which in-

TABLE 1
Quarter

1970.1
.2
.3
.4
1971.1
.2
.3
.4
1972.1
.2
.3
.4
1973.1

M PS Model Demand Deposit Equation
Chart 1A

8;1.$

240

220

Predicted

Y----,
200

//~
./

----'

~Actual

180

.2
.3
.4
1974.1
.2
.3
.4
1975.1
.2
.3
.4

Chart 16

Percent
8.0

Forecast error as percent of actual'

4.0

_4.0

L...L-'-J--'----'~.L--"-____'__l.......l~L--'--L...L_'_.L__L_._.L.._'___.1~.L.L__'.......J

1970

1971

1972

1973

1974

1975

<Forecasl eHoraoua!s Drooir:le<! less actual value divided by aClual

Forecast Error
in billions $

-2.1
-1.8
-2.6
-1.3
1.1
0.3
1.2
3.8
4.1
4.7
2.2
0.4
4.4
0.5
0.3
0.3
-0.6
-0.3
4.2
6.7
5.1
3.5
11.7
19.9

Forecast Error as
Percent of
Actual Level

-1.3
-1.1
-1.5
- .7
.6
.2
.6
2.1
2.2
2.5
1.1
.2
2.2

.2
.1
.1
- .3
- .1
1.9
3.1
2.4
1.6
5.3
9.0

shift downward (LM,). The observed value of
GNP will be Y, (the intersection of IS and LM1 )
rather than the forecasted value, Yo'
H the public's demand for money and the LM
curve continually shift downward by substantial
magnitudes, the model (which provides a forecast based upon IS and the "old" LM function)
\vill underestimate G}~P by increasing amounts'.
It is in this sense that instability (i.e., shifts) in
the money demand equation will lead to insta~
bility in the overall relationship between money
and GNP. The uncertainty surrounding the degree and cause of shifts in the public's demand
for money translates into uncertainty about the
impact which monetary changes will have upon
aggregate economic activity.
However, it is unrealistic to assume that
everything else remains unchanged when LM
fluctuates. The demand functions for goods
and services, such as inventory investment and
consumption, are not exact; in terms of Diagram
1, we expect shifts in the IS function also. A
degree of uncertainty surrounds economic relations in both markets, so that a forecast generally is associated with a probable error range.
This range can be represented in an LM-IS
framework. In Diagram 2, LM 1 and LM 2 represent the range of values within which actual
future values may be observed in this money
market; IS, and IS z incorporate the range for
the goods-and-services market values. As before, the forecast value for GNP is represented
as the solution of the model, Yo' Y 1 and Y z
represent the range within which the actual
value may occur because the model's estimate
may be in error. When we take into consideration the uncertainty surrounding future events,

about $20 billion in each quarter from 1975.4
to 1976.2.
These relatively large forecast errors have led
to· questions regarding the stability of the public's demand for money-and even moreimportantly, to questions regarding the stability in
the relationship between money and income.
Specifically, do forecast errors in the demand
for money indicate a change from pastexperience in the relationship between changes in
money and changes in income? The question
can be illustrated in terms of the familiar LM-IS
diagram.
Large econometric models, such as the MPS
model, can be thought of in terms of their two
major economic markets-that for goods-andservices and that for money.6 The IS function
represents the equilibrium condition in the
goods-and-services market. It provides the
combination of all income levels and interest
rates for which intended saving plus taxes are
equal to investment plus government expenditures. The LM function represents the equilibrium condition in the money market. On the
assumption of a given stock of money, it provides the combination of all income levels and
interest rates for which the demand for money
is equal to this supply. The equilibrium condition in the two markets is stated as a function
of two variables-the rate of interest and the
level of income.
In Diagram 1, the intersection of the LM and
IS curves represents a solution of the model
which provides the forecasted value of GNP, Yo'
H the public wishes to hold smaller money balances at each level of income, the demand for
money and the corresponding LM curve will

Diagram 2

Diagram 1
Interest rate

Interest rate

LM,

IS
Income

Income

the actual value of GNP could occur anywhere
within the range Y,-Y2'
Diagram 2 illustrates that the forecast error
in one equation-for example, the demand for
money-may not throw the estimate of GNP
outside the expected range when changes occur
elsewhere, even when the forecast errors are
very large. In other words, the overall net impact of unpredictable shifts in both the LM and
IS sectors are important in the final determination of GNP. Despite the uncertainty surrounding the public's demand for money balances, we
can determine empirically whether the overall

relationship between money and GNP has
changed from what past experience would lead
us to expect.
Forecast errors in MPS model

The MPS model was designed to capture the
channels through which monetary policy affects
aggregate economic activity, as is described in
a recent article by Albert Ando. a The forecast
errors generated by the model should reveal any
change in the ability of money to track GNP
since large errors first occurred in money demand equations. The model was used to generate ex-post forecasts of GNP one to four quar-

TABLE 2
Nominal GNP Forecast Errors':'
MPS Quarterly Model
No Correction for Serial Correlation
(in billions of dollars)
Quarters Beyond Initial Conditions* *

Forecast of:

1.8
-9.3
-22.5
-20.4
-36.0
-24.1
-17.7
-23.6
-22.0
-16.0
-16.8
-14.1
-17.2
0.6
5.2
3.2
3.4
-26.0
-30.9
-16.5
-17.2
-4.6
-47.4

1970.1
.2
.3
.4
1971.1
.2
.3
.4
1972.1
.2
.3
.4
1973.1
.2
.3
.4
1974.1
.2
.3
.4
1975.1
.2
.3

-8.2
-15.4
-'22.7
-33.2
-30.1
-16.6
-18.2
-16.2
-15.8
-9.7
-14.6
-15.9
-12.7
5.6
3.4
15.3
-10.9
-31.6
-16.8
1.1
6.1
-29.6

-12.3
-11.8
-31.8
-22.5
-21.5
-19.5
-14.6
-6.3
-13.3
-8.5
-15.5
-6.5
-2.5
11.4
18.1
-1.0
-15.1
-6.6
17.2
22.7
-18.4

-6.6
-17.8
-17.6
-10.1
-21.8
-14.9
-5.6
-2.2
-14.6
-10.9
-7.7
3.5
3.5
24.6
1.2
-8.5
-6.5
28.7
40.6
-5.6

* Forecast error
Forecasted minus Actual.
**Quarters beyond initial conditions refers to the number of quarters after the initial conditions quarter on which the
forecast was based. The first initial conditions quarter is 1969.4.

ters ahead from 1970.1 to 1975.3, the last
quarter for which we have a consistent data
bank. 7 Results of these simulations are presented in Table 2. 8
These ex-post forecasts differ from the usual
type _of ex-ante forecasts in several important
respects. First, all values of the exogenous variables are known and are set equal· to their historical values. For the MPS model version we
are using, this means that the forecasts use actual values for the money supply and such variables as federal government expenditures, tax
rates, farm inventories, population measures,
and exports.
Second, in our model simulations, we do not
utilize information available from knowledge of
previous behavioral equation errors. In an actual ex-ante forecast, the pattern of equation
errors is projected forward if the errors appear
systematic. Because this procedure is somewhat
arbitrary, we have not used it here, and in fact
have not used any information about past equation errors. All serial correlation terms have
been removed from the behavioral equations.
Third, we do not utilize the ex-ante forecast
procedure, whereby knowledge of special factors not included in the model specification
would be used to adjust the appropriate equations. For example, a labor strike which is expected in the forecast period would lead to some
adjustment of the labor market equations, which
of course are not structured to capture the impact of such events. This type of information,
when used in an actual ex-ante forecast, can cut
the model's errors substantially.
We do not utilize such model adjustments
(with several exceptions noted below), because
they contain an eiement of arbitrariness. We
are interested in what the model's estimated
structure has to say about the changing ability
of money to predict total income in the recent
period of money-demand overestimation. It is
not our concern here to minimize model errors,
but to observe and compare their size and pattern over time. Nevertheless, we have made several exceptions to take account of certain economic events which have directly affected the
model's basic structure.

First, after the 1971 change in the international payments system, the model's import
equations began to generate very large underestimates of imports. Second, the introduction
of revenue sharing (which the model's stateand-local -government expenditure equations
could only treat as categorical grants) caused
overestimates of state-and=local government ex-

penditures. Third, major errors occurred because of the failure of the model's price equations to pass through price increases generated
outside the domestic economy-such as those
occurring in the wake of the dollar devaluations,
OPEC oil price increases, and world crop shortages.
We adjusted for these factors by adding the
residuals from the estimated behavioral equations into the model equations, using some
judgment in adjusting for price increases. The
adjusted equations for these variables then forecast historical values exactly when all the "righthand" variables were known. In our dynamic
simulations, errors in the adjusted equations result only from misestimates by other equations
as they feed into the "corrected" equations.
Thus the obvious misspecification in the foreign
Nominal GNP
MPS Quarterly Model
Chart 2A

Billions
of dollars
1.600

t,400

1.200

1.000

Percent
1.0

Chart 2B
Forecast error as percent of actual'

-2.0

1970

1971

'Forecasterrorequalspred;C:I(t<jlessactlJal

1972

1973

1974

1975

billion respectively. The four quarter-out forecast errors for 1975.2 and 1975.3 are $40.6
billion and -$5.6 billion. These forecast errors,
with one exception, are within the range of
error which the model has displayed since 1970.
The size and pattern of these errors suggest no
deterioration in the overall money-income relationship as structured in the MPS model. The
one exception is the $40.6-billion overforecast
of 1975.2, which results from the model's failure
to capture the depth of the recent trough approximately one year before it occurred. However, this does not indicate a continuing forecasting failure, since the model was otherwise
able to forecast within the range of past experience for all other forecast quarters since mid1974.
We should emphasize that many of the errors
in third and fourth quarter-out forecasts have
the opposite sign from what the typical money
demand-GNP model would suggest. Normally
we would expect a decline in the demand for
money to lead the model to underforecast GNP,
and not the reverse. This point was demonstrated above in LM-IS Diagram 1. While the
errors we have observed generally are within
the expected historic range, the signs of many of
the forecast errors are not consistent with the
assumption that a downward shift in the money
demand has dominated the money-income relationship.
In brief, no matter how uncertain money demand estimates have been since 1974.3, the
money-income relation-as structured in the
MPS model-does not appear to have gone off
track because of shifts in money demand. In
the one quarter in which the error was outside
past experience, we observed a $40.6 billion
overforecast of GNP. But we would have expected a negative forecast error, an underforecast of GNP, if downward shifts in money demand had dominated the money-income relationship.

and state-and-Iocal government sectors is not
allowed to bias the full model simulation results.
The forecast error for one-quarter out (column 1, Table 2) is shown in Graph 2B as a
percentage of actual GNP. When shown in this
form, the forecast errors remain within the range
of the model's past experience throughout the
period of large money-demand overforecasts.
After declining from 1974.3 to 1975.2; the
error increased in 1975.3 to 3.1 percent of
GNP-understandably so, because quarters following a business-cycle trough are difficult periods to predict. Generally, however, these percentage errors do not reflect any marked deterioration in the money-income relation as structured in the MPS model after mid-1974. From
1974.3 to 1975.2, both the dollar level and the
GNP percentage level of forecast errors are
within the range of past observations (column 1,
Table 2). It is interesting to note that the large
$47.4-billion underforecast of GNP in 1975.3
occurred in the same quarter as the largest error
in the demand-deposit estimate. But as noted
above, this error is within the range of past
model behavior when considered as a percentage of actual GNP.
It may be argued that changes in money have
an impact upon GNP only after some delay, so
that changes in money demand behavior should
have little influence on aggregate demand until
several quarters have passed. Thus, errors in
the money demand equation may not show up
immediately in the GNP forecasting model.
Many studies indicate that between 25 and 40
percent of the response in nominal GNP to a
change in money will occur within four quarters
of a monetary change,9 so we could expect a
significant forecast error in GNP to appear
about 4 quarters after the initial date (1974.3)
of the large money demand errors. In other
words, we should look at least three and four
quarters ahead, in order to allow more time for
a given change in money demand to influence
GNP.
Only a limited number of such forecasts are
available after 1974.3. The third quarter-out
forecast errors for the first three quarters of
1975 are $17.2 billion, $22.7 billion and -$18.4

A look at M1 velocity
A key question is what has happened to the
money-GNP relationship since 1975.3. The M J
velocity series, the ratio of nominal GNP to the

money stock, provides some information regarding this matter. Current erratic movements
in the velocity series could signal instability in
the •complicated economic process by which
changes in money are related to current eco. nOIllicactivity. In Michael Keran's words, "If
we are entering a period of unpredictable movementsinmoney turnover, it means increasingly
unstable relationships between money and income due possibly to an increased instability in
the demand for mol1ey."lO But after looking at
deviations from trend in the velocity data, Keran
concluded that "velocity may not be too far out
of line given the present stage of the business
cycle.... "
The data in Chart 3 portray the typical cyclical pattern in M 1 velocity-growing below the
trend rate in the downswing of a cycle and above
it in the upswing. Recent velocity behavior follows that pattern. The past recession was particularly severe-the steepest decline since the
late 1930's-and this was followed by the
sharpest recovery of post-World War II history,
with a 13-percent gain in nominal GNP from
1975.2 to 1976.2. Velocity mirrored these
sharp GNP movements, growing slowly relative
to trend during the recession and quite rapidly
in the last half of 1975 (at about a 10-percent

annual rate cOIilpared with a3-percent trend
rate). Thus, velocity was close to its long-run
trend value by late 1975, and it has remained
close to trend during the first half of 1976.
Despite . the large shifts in· velocity since
1974.3, the deviations from trend are within the
range of past experience and are actually smaller
than in· Some earlier· periods, such as ·1966-67.
This suggests that a model relating movements
in money to GNP should continue to be successful in its trackingabiIities, as has been demonstratedbya small model developed at the>Federal Reserve Bank of San Francisco. l1 The
model's basic output equation relates· movements in real money balances to real GNP. Its
forecasting errors through 1975.4 indicate an
ability to track GNP within an error range consistent with the equation's past performance.
In brief, the M 1 velocity series is not displaying atypical behavior. This suggests that the
money-income relationship has remained stable
after 1974.3, when increasingly large errors began to appear in money demand equations.
Summary and conclusions

Since mid-1974, economists have been bewiIdered by the large overforecasts of money
growth which their standard money demand re-

Chart 3

M1 Velocity

Ratio

Trend 1950.1 -1976.2 at 2.9 Percent
5.5
5.0

4.5

4.0

3.5

3.0

2.5
1950

1955

1960

1965

1970

19751976

lationships have produced. Forecast money
growth was about twice as great as actual money
growth for the first year of the current recovery.
These large forecasting errors haveled to questions regarding the ability of standard models
of the U.S. economy to forecast GNP.. Econometric models of the U.S. economy link changes
in a monetary aggregate to changes in overall
economic activity. The demand for money is
an important element in the transmission mechanism by which changes in money lead to
changes in income.
In this paper we have focused upon an empirical study of the GNP forecast errors in one
large quarterly econometric model. The forecast
errors in GNP since mid-1974-the start of the
large errors in money demand-were generally
inside the range of forecast errors made by the
model in the past. But since MPS data extend
only through 1975.3, we have utilized the M]
velocity series to gain some indication of the
more recent money-income relationship. The
data suggest that the current relation between
money and income has remained similar to its
past expected behavior. The relationship, while
not exact, has remained consistent, and thus did
not fall apart during the time of unpredictable
shifts in money demand.
Our study suggests two possible interpretations of this finding. First, the MPS model results demonstrate that the money-income relationship may remain on track as a result of the
net impact of errors in both the IS and LM sectors. Although errors in the money demand
equation (and corresponding LM function)
were larger than expected in late 1974, the GNP
forecast errors demonstrate that the uncertainty
in the goods-and-services sector for several
quarters dominated the actual deviation of output from its expected value. The largest GNP
errors in the latter forecast quarters were overestimates of GNP-rather than underestimates,
which would have been consistent with the
errors in money demand.
Whether or not money fails to track GNP will
depend upon the behavior of all economic markets. This has an important policy implication.
One factor in the choice of a monetary policy

instrument is the relative stability of the monetary sector compared· with that of the goodsand-services sector. When there is greater uncertainty • (i.e., unpredictaNe shifts) in the
monetary than in the goods-and-services sector,
there maybe less variation in final output with
an interest-rate policy instrument than with a
monetary aggregate. Accordingly, the unpredictable shifts in money demand since mid-1974
led some observers to advocate an interest rate
policy. This policy, however, is not appropriate
when the major source of unpredictability in
GNP stems from changes in investment behavior, consumption expenditures or any of the
other components of GNP. The MPS simulations suggest that the unpredictable nature of
the real sector may have been the major source
of unpredictable movements in GNP for some
time after mid"1974, and that a monetary aggregate policy was appropriate although the money
demand equation exhibited large overforecasts
of money demand at that time.
This interpretation thus emphasizes the net
impact of sector errors, and assumes that the
estimated money demand function is an accurate representation of the public'S behavior.
However, there is an alternative explanation
for the stability of the money-income relationship-namely, that the public's demand for
money has not· changed. The velocity series
appear consistent with this alternative interpretation. The observed errors may be the fault of
a misspecification of the equation used to predict the public's actual demand for money. The
estimated money demand function simply failed
to capture the money demand relationship accurately, and the errors became pronounced beginning in 1974.3. Similar situations have occurred .before, with large errors occurring in
estimated money demand equations. 12 In previous instances, many analysts argued that forecast errors were the result of an inadequate specification of the demand for money. Their efforts
led to the development of improved equations
which provided a more accurate measurement
of the public's behavior.
Recent work by Enzler, Johnson and Paulus 13
may be interpreted along these lines. These
41

As the research into money demand continues,we may find that institutional factors and
teGhnological innovations will cause significant
changes in the relationship between money
(however defined) and total economic activity
(as.measur~d .by. GNP). However, theevid~ncepresentedinthis paper suggests that much
oUhe recent uncertainty in money demand can
be reduced and that since mid-1974 the ability
of Mlto track movements in GNP has not deteriorated relative to past expected behavior.
The Federal Reserve has found M 1 to be a
useful policy variable, although the achievement
ofa.particular preconceived money stock is not
the objective of monetary policy. Federal Reserve Chairman Arthur Burns, referring to targeted growth rates for monetary aggregates, has
stated before Congress,

authors contend that while the post mid-1974
en:ors in the money demand function are still
relatively large, they can be substantially reduc~d from those shown in Table 1 by respecifying the. income variable and the interest rate in
tb,eMPSequation. They also note that recent
errors may be reduced by $4.5-5.0 billion, by
adjusting demand deposit data to exclude foreign bank and official deposits and to include
NOW accounts (Negotiable Orders of Withdrawal) . Foreign balances are generally held
for purposes. unrelated to domestic economic
activity; NOW accounts, which are still quite
small but growing, are interest bearing accounts
at commercial banks and thrift institutions on
which checks can be drawn.
Work along these lines appears most promising and deserving of further research. Keran,10
for example, is critical of the typical use of the
Treasury bill rate as the appropriate measure of
the.opportunity cost of holding money. He suggests that alternative measures be sought to capture the substantial rise in risk which accompanied the recent era of unprecedented inflation
and recession. In addition, there are many institutional factors and technological innovations
which may reduce the (actual or potential) demand for transaction balances. Several of these
factors, such as changes in compensating balance requirements or in the corporate management of cash balances, have been analyzed by
Ruth Wilson. 14

We at the Federal Reserve have viewed these
growth ranges as useful guides for the conduct
of monetary policy. However, the objective
of monetary policy is not to achieve any preconceived growth rates of monetary or credit
aggregates, but to facilitate expansion of
economic activity and to foster stability in the
general price levelY
The recent errors in forecasting the public's
demand .for money have raised questions as to
whether the money supply can still serve as a
useful guide to monetary policy. The results
presented in this paper suggest that it can do so.

APPENDIX A
The MPS Model Demand Deposit Equation
The demand for Demand Deposits by the
nonbank public is represented in the MPS model
bya standard type of money demand function
which is consistent with the Baumol transaction
demand model. *
In DD

GN~

_ .519 + .280 In DD_ 1

GN~

(-4.1)

(1.6)

-.123 In RS-.339
(-5.1)

(-2.3)

.062 In RTB
(-5.1)

GNP

In~+.078

RDISC
In - S C
RDI
-I

(3.9)

DD is the commercial bank demand deposits measured as the two - month
average surrounding the end of the
quarter.
GNP$ is Gross National Product (GNP) in
current dollars.
GNP is GNP in 1958 dollars.
RTB represents the 90-day Treasury Bill
Rate.
RS is an average offering rate paid on time
and savings deposits at commercial
banks and thrift institutions.

value early in 1974 although the equation was
not re-estimated. The values in parenthesis are
T-statistics. For further discussion of this equation as well as the currency equation, see Franco
Modigliani, Richard Cooper and Robert
Rasche, Central Bank Policy, Interest Rates,
and the Money Supply, Journal of Money,
Credit and Banking, Vol. 2, 1970: 166-218.

RDISC is the Federal Reserve Discount Rate.
GNP is the U.S. population.
N is the highest per capita GNP achieved
in the current or any preceding 19
quarters.
Sample period: 1955.3 - 1972.4.
An iterated instrumental variable estimation
technique was used to estimate the equation together with the bank free reserves equation. The
estimation included GNP per capita; this term
was replaced by the maximum GNP per capita

"See W. J. Baumol, "The Transactions Demand for Cash;
An Inventory Theoretic Approach, Quarterly Journal 0/
Economics, November 1952.

FOOTNOTES
1. M, refers to the narrowly defined money supply which
is equal to currency in the hands of the public and demand
deposits of commercial banks.
2. for a comprehensive review of conventional money demand equations see Stephen Goldfeld, "The Demand for
Money Revisited." Brookings Papers on Economic Activity,
3 (1973): 577-638.
3. for a recent survey of the monetary transmission process which contains a comprehensive bibliography see Roger
W. Spencer, "Channels of Monetary Influence: A Survey,"
federal Reserve Bank of St. Louis Review, November 1974;
8-26. for a recent discussion of the channels of monetary
influence structured in the MPS mOdel, see Albert Ando,
"Some Aspects of Stabilization Policies, the Monetarist
Controversy, and the MPS Model," International Economic
Review, Vol. 15, No.3, October 1974: 541-571.
4. A listing of the MPS econometric model equations is
obtainable from EfA, University of Pennsylvania, Philadelphia, Pennsylvania, and a comprehensive description is
provided by Ando, see footnote 3.
5. The prediction errors in the MPS demand for demand
deposits equation were obtained by setting all the explanatory variables equal to actual values and setting the autocorrelation coefficient equal to zero. The third quarter of
1975 is the last quarter for which we have consistent data
bank: revisions are being made in light of the recently
issued NIA data. Appendix A provides the money demand
equation used in the MPS model.
6. for a text which describes the LM-IS functions, see
Thomas f. Dernburg and Duncan M. McDougall, MacroEconomics, McGraw-Hili Book Co., Inc., New York, 1960.
7. The Board of Governors Staff is re-estimating an enlarged version of the MPS model using the recently revised
NIPAdata.
8. Table 2 is read as follows: The first forecast is based

upon historical data values known through 1969.4 (i.e.,
the first initial conditions quarter is 1969.4). The firstquarter ahead forecast of GNP is a forecast for 1970.1 and
GNP was overforecasted by $1.8 billion. The second-quarter ahead forecast for 1970.2 (still based upon the initial
conditions of 1969.4) is an underforecast of $8.2 billion.
The third- and fourth-quarter ahead forecasts for 1970.3
and 1970.4 are also underforecasts of $12.3 and $6.6
billion. The last simulation reported in the table was
based upon historical data through 1975.2 and we could
simulate only one-quarter ahead; the forecast error for
1975.3 is an underestimate of $47.4 billion.
9. for a discussion which uses an early version of the
MPS model see Franco Modigliani, "Monetary Policy and
Consumption, Consumer Spending and Monetary Policy:
The Linkage," the Federal Reserve Bank of Boston, Conference Series No.5, June 1971.
10. Keran, Michael, "Changing Money Demand?" Business
and Financial letter, Federal Reserve Bank of San Francisco, April 30, 1976.
11. See Larry Butler, "Has the Relation Between Income
and Money Shifted?" unpublished paper, Federal Reserve
Bank of San Francisco.
12. Meigs, James A. "Recent Innovations: Do They Require
a New Framework for Monetary Analysis," Financial Innovations, William Silber editor, LeXington Books, 1975.
13. Enzler, Jared, Johnson, Lewis and Paulus, John;
"Some Problems of Money Demand," Brookings Papers on
Economic Activity, 1976.
14. Wilson, Ruth, "M,'s Institutional factors," Business
and Financial letter, Federal Reserve Bank of San Francisco, March 5, 1976.
15. Statement by Arthur Burns before the Committee on
Banking, Housing and Urban Affairs, U.S. Senate, May 3,
1976.

Full text of Economic Review (Federal Reserve Bank of San Francisco) : Summer 1976

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