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Economic
Review
Federal Reserve Bank
of San Francisco
1994
Number 1
Mark E. Levonian
Bank Capital Standards for Foreign Exchange
and Other Market Risks
Andrew K. Rose
Are Exchange Rates Macroeconomic
Phenomena?
Sun Bae Kim and
Ramon Moreno
Stock Prices and Bank Lending Behavior
in Japan
Table of Contents
Bank Capital Standards for Foreign Exchange and Other Market Risks ................ . . . . 3
Mark E. Levonian
Are Exchange Rates Macroeconomic Phenomena? .......................................... ..
19
Andrew K. Rose
Stock Prices and Bank Lending Behavior in Japan........... ........................ .
Sun Bae Kim and Ramon Moreno
31
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Bank Capital Standards for Foreign Exchange
and Other Market Risks
I.
Mark E. Levonian
Research Officer, Federal Reserve Bank of San Francisco. I
am grateful to Jennifer Soller for research assistance and to
Gary Johnsen for data. Conversations with Beverly Hirtle
and Elizabeth Laderman helped clarify the paper.
INTRODUCTION
This paper investigates the extension of risk-based capital
standards to cover market-related risks. In 1988, the Basle
Committee on Banking Supervision (the Basle Committee) published standards for capital adequacy, establishing
a system in which minimum capital requirements for
banking firms are sensitive to differences in risk.! The riskbased capital standards specified in the Basle Accord came
into full force at the end of 1992, and have been adopted by
many countries. When the standards were issued, the Basle
Committee acknowledged that the resulting assignments
of minimum capital primarily reflected an assessment of
credit risk, or the risk oflosses due to counterparty default.
Consideration of other types of risk was left to national
regulatory authorities or to future deliberations ofthe Basle
The Basle Committee on Banking Supervision has proposed methods for incorporating consideration of market
risks-exchange rate, interest rate, and equity price risks
-into risk-based capital standards for banks. This paper
shows that the separate and seemingly different proposed
approaches to the three sources ofrisk are consistent with
one another, reflecting a single unifying theme. That theme
is the measurement of risk through a weighting of two
different measures ofportfolio size, the gross position and
the net position. A simple theoretical model demonstrates
that such an approach can be viewed as a simple (specifically, an affine) approximation to a portfolio variance
calculation based on the full variance-covariance matrix
ofmarket returns, and thus provides a reasonable basisfor
a practical approach to capital standards. An empirical
test of one part of the framework, the proposal for exchange rate risk, shows that the approximation may be
very accurate: the proposed Basle approach captures over
95 percent ofthe variation in foreign exchange risk across
a sample of banks from the Twelfth Federal Reserve
District.
Committee and its subgroups.
In April 1993, the Basle Committee sought comments
on a consultative paper describing proposals for incorporating additional types of risk into the original framework (Basle Committee, 1993). "Market risks" are those
due to unexpected changes in financial market prices that
are unrelated to the creditworthiness of particular borrowers or counterparties; the Basle proposals cover stock
prices, the prices of foreign currencies as reflected in
exchange rates, and debt prices as reflected in interest
rates. Since market risk is considered distinct from credit
risk, the emphasis is on price fluctuations that reflect
general market movements, rather than those related to
changes in the condition of specific issuers.
This paper develops a conceptual model in which the
new market risk proposals can be understood and analyzed. The underlying, unifying theme of the standards is
emphasized. Building on the conceptual model, the suitability of the proposals is evaluated. For purposes of
illustration, much of the analysis is based on consideration
of foreign exchange rate risk, which in some ways is the
simplest of the three; the paper discusses the parallel
implications for other types of market risk in less detail.
1. The Basle Committee consists of representatives from Belgium,
Canada, France, Germany, Italy, Japan, Luxembourg, the Netherlands,
Sweden, Switzerland, the United Kingdom, and the United States. It
usually meets at the Bank: for International Settlements in Basle,
Switzerland.
4
FRBSF ECONOMIC REVIEW
1994,
NUMBER
1
II.
CONVENTIONAL AND RISK-BASED
CAPITAL STANDARDS
Before turning to market risk, it is helpful to review the
general role of capital standards in bank supervision. Risk
is an unavoidable element of the business of banking, and
banks must take risks to be economically useful in the
financial system. Managers of well-run banks are aware of
the risks they face, and take steps to manage those risks to
maximize the net value of their banks. However, certain
features of the banking system-most notably the imperfectly priced government support of banks through deposit
insurance and other elements of the federal "safety net,"
and the externalities associated with bank failures-lead
to a tendency toward excessive risk. Levels of risk are
"excessive" to the extent that the probability of bank
failure resulting from the private, unregulated decisions of
bank managers exceeds the level of failure that maximizes
social welfare. To deal with this tendency toward excessive
risk, central authorities in most countries impose some
type of oversight on the banking system in speciallicensing, regulation, and ongoing supervision.
Standards for capital adequacy are an aspect of bank
regulation common to most countries. These capital standards establish minimums for bank capital. The term
"capital" is used in many ways in economics and finance,
but in the context of bank capital adequacy it is the portion
of a bank's financing that can absorb losses that would
otherwise cause the bank to fail and impose an external
cost on the economy. Generally this means equity, although
regulators consider certain types of debt to be capital in
some circumstances.
Minimum capital requirements help ensure the solvency
of regulated institutions, but the only capital standard that
can guarantee solvency is a requirement of complete
equity financing. Such a standard is impossible with
depository institutions by definition, so regulators instead set capital standards to reduce the probability of
insolvency to some acceptable level. The acceptable level
depends on regulators' tolerance for risk, which in tum
may reflect judgments regarding the potential welfare costs
of insolvency balanced against the costs imposed by the
regulations.
The probability that a bank will become insolvent depends on the level of its capital and the variance or standard
deviation of changes in that capital. The conventional
approach to capital adequacy sets minimum capital relative to the assets of the bank, with a floor placed under
allowable capital-asset ratios. Under certain assumptions,
such an asset-based standard is equivalent to requiring
capital to exceed a multiple of the standard deviation of
changes in capital. Specifically, if all bank assets have the
same variance, and provided liabilities contribute trivially
if at all to total risk, then the standard deviation of changes
in capital can be expressed as (J"AA, where (JA is the
standard deviation of a bank's return on assets. In that case,
a minimum capital ratio of "f(JA can set the probability of
insolvency at the acceptable level, with the coverage ratio 'Y
determined by regulators. If (J"A is about 2 percent (a
typical empirical finding) and regulators aim to cover two
standard deviations (that is, r = 2), then the minimum
capital ratio should be 4 percent. 2
In contrast to conventional asset-based leverage constraints, the risk-based capital standards established under
the 1988 Basle Accord set minimum capital relative to a
weighted sum of the bank's assets. 3 Levonian and Kendall
(1993) show within a simplified model of the Basle Accord
that the credit risk standards can be viewed as an extension
of simple leverage standards; the Accord relaxes the assumption that all asset types have a common variance,
making (JA a weighted average of the volatilities of the
different asset types. However, the Basle Accord retains
the assumption that liabilities are irrelevant, and the risk
weights largely reflect only credit risk.
m. MARKET RISKS IN THEORY
Neither the conventional nor the credit-risk-based approaches to capital standards can be stretched to cover
market risks. Credit risks generally run in one direction:
The bank gains if the credit standing of a counterparty
improves, and loses if credit quality deteriorates. On the
2. An asset-based standard ignores differences in bank profitability,
implicitly assuming that the expected change in capital is zero. In
practice, regulators aim to err on the side of conservatism, and are
reluctant to presume that banks will achieve a positive rate of return.
Bank supervision may incorporate profitability more subtly, perhaps in
the enforcement of capital standards; for example, supervisors might
exert less pressure on a profitable bank with low capital than on an
unprofitable bank in the same position.
3. The Basle framework applies to assets and off-balance-sheet items.
The notional value of a bank's off-balance-sheet exposures are converted into "credit equivalent" amounts through a set of conversion
factors intended to reflect the amounts actually at risk for the bank; onbalance-sheet assets are combined with the converted off-balance-sheet
amounts and classified into one of several categories according to the
credit risk associated with the underlying counterparties. Amounts in
each risk category are then multiplied by a risk weighting factor (higher
for riskier categories) and the weighted amounts are summed. The
resulting total risk-weighted assets forms the basis for the capital
adequacy calculation; minimum ratios of various types of capital to
risk-weighted assets are established in the Basle Accord. For further
description of the standards established under the Basle Accord, see
Bhala (1989).
LEVONIAN / BANK CAPITAL STANDARDS
other hand, increases in market prices can cause either
gains or losses for a bank, because exposure to these prices
can be either long or short. 4 Liabilities create short positions; for example, a deposit denominated in a foreign
currency creates short foreign exchange exposure for the
issuing bank. Since such positions may contribute substantially (either positively or negatively) to total portfolio risk,
liabilities cannot be ignored, and a simple asset-based
calculation cannot correctly capture the potential for losses
due to market risk.
With risky positions both long and short, the variance of
changes in capital requires a matrix presentation. Suppose
there are N market variables-stock prices, interest rates,
or exchange rates-that might affect the solvency ofbanks .
Let I represent the variance-covariance matrix of percentage changes in the prices of these instruments; thus I is
N x N, with the variance of each instrument on the diagonal, and the covariance between each pair off the diagonal.
Let D represent a vector of the bank's net dollar positions in
the instruments, withN components. Then the bank's portfolio variance-that is, the variance of the change in total
portfolio value-is given by (J"~=D'ID.
It is tempting to regard this matrix-based portfolio
calculation as the solution to the market risk problem.
Regulators could set minimum capital at some multiple 'Y
of the portfolio standard deviation (J"p' at a level deemed
adequate for protection against bank failures. Such standards would accurately reflect differences in risk across
banks and over time.
However, practical considerations may require standards
for market risk to meet additional criteria. Foremost among
these is simplicity; the more complicated the regulation,
the greater the expense, for several reasons. Complex
standards are more difficult to draft, and once written are
more difficult to explain to regulated banks, to supervisory
staff, and to others. Complicated standards often are
information intensive, increasing the reporting burden
imposed on banks and raising the costs of data collection
and analysis for regulators. Banks and regulators also may
find it more difficult to monitor compliance. Moreover, to
the extent that more complicated methods rely on sophisticated computational techniques, or on unobservable values
that must be estimated or subjectively determined, enforcement costs are likely to climb.
4. Positions are defined as "long" if a rise in price increases the value of
the portfolio; this might occur if the bank actually holds the currency,
bond, or stock, or has contracts to receive delivery of those items at
some future date at a prespecified price. Conversely, "short" positions
lose value when price rises; shorts generally result from commitments to
make future delivery.
5
One aspect of simplicity is that elementary functional
forms are desirable. Linear forms are among the simplest,
and therefore are preferred. Regulators also may want any
new capital standards to have the general form of the old
standards, under which minimum capital is set as a ratio to
some measure of value such as total assets or risk-weighted
assets. Requiring that a market risk standard be expressed
similarly places even greater constraints on the functional
form than does the requirement that it be linear. The history
of the Basle Committee's work suggests that these considerations were important. Of course, simplicity cannot be
the only goal in establishing a capital standard; the standard also must be accurate, with risk measured fairly
precisely. An optimal policy balances these concerns,
trading off simplicity for precision. A degree of imprecision may be acceptable when the cost of implementing
more precise but more complex regulatory regimes is
considered.
Viewed within the context of this tradeoff, the matrixbased portfolio variance calculation is precise but is unlikely to be simple enough. The policy challenge is to
develop a precise measure of market-related risks-with
precision measured relative to portfolio variance-that is
sufficiently simple, preferably one that results in a dollar
figure against which a typical minimum capital ratio can
be applied. To meet this challenge, the Basle Committee
began by examining existing approaches in use by bank
supervisors around the world. Of the various market risks,
foreign exchange is the one for which regulators have
developed the best quantitative measures of exposure. The
next section discusses the range of existing practice examined by the Basle Committee.
IV
FOREIGN EXCHANGE MARKET RISK
IN PRACTICE
In many countries, banks are required to calculate their
overall currency positions at given points in time; regulators use the resulting "aggregate open position" for each
bank as a measure of exchange rate risk. Implicitly, regulators assume that foreign exchange risk depends positively
on the size of this open position, analogous to the assumption in conventional capital standards that portfolio risk is
proportional to total assets. Such calculations are based on
the vector of positions D, and do not explicitly use the
matrix I. Since portfolio variance depends on both D and
I, it is reasonable to think that these open position calculations might be related to risk, but with a loose and
imperfect linkage.
Each of the various aggregation approaches in common
use begins by constructing a hypothetical portfolio of
6
FRBSF ECONOMIC REVIEW
1994,
NUMBER
1
foreign currency positions for each bank, or a foreign
exchange "book," with risk identical to the bank as a
whole. For some banks this mirrors the way exposure
actually is managed: Each business unit within the bank
hedges away any currency risk it generates through internal
transactions with the bank's foreign exchange trading
desk. However, the same principle applies whether or not
this is actually done. With all of the relevant risk collapsed
into a single actual or hypothetical book, the problem
becomes one of computing the total exposure arising from
this foreign exchange portfolio. Long and short positions
generally are netted within any single currency, but national practices differ in important ways with regard to the
degree of netting of long and short positions across currencies. Three alternative approaches for netting across currencies to obtain a measure of aggregate open position are
in common use by bank supervisors in major countries.
To illustrate the three alternatives, simple schematic
diagrams of two foreign exchange books are presented in
Figure 1. The relative dimensions of the rectangles reflect
the relative values of the long (L) and short (5) positions,
and the net portfolio position (T), all in terms of the
domestic currency. In Portfolio I the aggregate value of
long positions exceeds the aggregate value of short positions, and the foreign exchange book is a net asset for the
bank; in Portfolio II the short positions are worth more than
the longs, and the book is a net liability. What is a valid
measure of exposure to exchange rate changes for these
portfolios?
One intuitively appealing measure of potential loss is the
net position, which is simply equal to T in Figure 1. This
reflects the net investment of the bank in the foreign
exchange book at a point in time, or the cost of acquiring or
divesting the portfolio on the current market. The net
position has been used by some regulators as the measure
of foreign exchange exposure, most notably in Japan; it will
be referred to here as Net Aggregate Position (NAP). NAP
also can be computed as the absolute value of the sum of all
foreign currency positions, counting shorts as negative
values.
However, suppose the long exposure is in Canadian dollars and the short exposure is in German marks. If the
dollar exchange rates for these two currencies move in
opposite directions, the bank's total loss could far exceed
T; for example, the net position might change from positive
to negative. Consequently, some regulators have chosen to
assess exposure by taking the total of the two areas Land 5;
this measure has been used in Germany and other countries. This will be referred to as Gross Aggregate Position
(GAP). GAP is calculated as the sum of the values of all
long positions, plus the absolute value of all short positions; that is, it is the sum of all foreign currencies counting
shorts as positive POSItIons. Thus, the gross measure
is GAP=L+5, whereas the net measure is NAP=T=
IL - 51. From the definitions, it is evident that GAP;;:::NAP,
and GAP = NAP only if L=O or 5=0.
FIGURE 1
Two
TYPICAL FOREIG:t~ EXCHAt~GE BOOKS
PORTFOLIO I: NET LONG
Short
(S)
Long
(L)
Net
(1)
I
!
I
I
I
I
I
I
I
I
~------------------~----------------~
IL-S I
NAP
GAP
L+S
BAP
L
T
PORTFOLIO II: NET SHORT
Short
(S)
Long
(L)
I
I
II
Net
(1)
I
I
I
IL
.1.1.-
NAP
IS-L I
GAP
S
BAP
S
+L
....1
T
LEVONIAN / BANK CAPITAL STANDARDS
A third practical gauge of foreign exchange exposure,
generally attributed to bank regulators in the U.K. but
adopted by other countries as well, is the larger of the
absolute values of shorts and longs. This "Hank of England" Aggregate Position, or HAP, is therefore max[L,S].
As the larger of Land S, HAP is always the "length" of the
T-account balance sheet, the total value of one side; in
Portfolio I, this would be L, whereas in Portfolio II it would
be S. An alternative definition of BAP that is sometimes
used is "the sum of short positions in all currencies,
including the home currency." The equivalence of the two
definitions is clear from Figure 1. The rectangular area T
gives the net position in the domestic currency, which in
Portfolio I can be viewed as additional short exposure: If
the domestic currency rises in value against other currencies, the value of the book declines. Hence in Portfolio I the
short position including the home currency is the total area
of rectangles S and T together, which is of course equal to
L, the larger of Land S. Similarly, in Portfolio II the
domestic currency position effectively is a long position, so
the aggregate short position is simply S; this again is
equivalent to taking the larger of Land S.
Each measure-NAP, GAP, and HAP-was considered
and tested by the Hasle Committee; in the end, the Committee favored HAP. The Hasle Committee perceived HAP
to be a compromise between the "conservative" GAP and
the "liberal" NAP. In fact, it is a compromise in a very
significant sense: HAP is the simple average of GAP and
NAP. To see this, first note that:
(1)
GAP = L
+S
NAP = IL -
sl
= max[L,S]
+
min[L,S]
= max[L,S] - min[L,S]
Then HAP can be written as:
(2)
HAP = max[L,S]
Yz (max[L,S]
=
+
max[L,S])
Y2 (max[L,S] + min[L,S]
+ max[L,S]
- min[L,S])
7
The other measures are easily seen to be special cases:
GAP ifwg = 1 and wn=O
(4)
WAP = NAPifwg =Oandwn =l
HAP if W g = Y2 and W n = Yz
Turning from risk measurement to the construction of
capital standards, a capital requirement for foreign exchange risk could be based on WAP. A minimum ratio c of
capital to aggregate foreign exchange position could be
established, with position measured by HAP or any other
variant of WAP. This is precisely the Hasle Committee's
proposal: banks would be required to have enough capital
(above that required to cover other types of risk) to cover
8 percent of HAP.6 As indicated in Section II, to be
adequate this minimum capital should correspond to "Wp ,
where (Tp is the standard deviation of changes in capital (in
this case flowing entirely from the foreign exchange portfolio) and 'Y is regulators' desired coverage ratio.
V. EQUITY AND INTEREST RATE
RISK PROPOSALS
The recent Hasle release also covers equity price risk and
interest rate risk. The equity proposal applies to banks'
holdings of common equity shares, as well as options,
futures, warrants, and other instruments whose value depends on share prices or the level of stock market indexes.
The interest rate proposal applies to traded debt securities
and derivatives; as a result, it only incorporates a portion of
total interest rate risk, ignoring major components such as
loans and deposits. 7 This section provides an overview of
both proposals. As with foreign exchange, these two proposals tum out to be versions of WAP.
One notable difference between these two proposals and
the foreign exchange proposal is that they substitute completely for the old treatment; that is, traded debt and equity
instruments would no longer be covered by the original
Y2 (GAP + NAP)
An equivalent restatement is that HAP always yields a
result halfway between the gross and net exposures. Thus
HAP is indeed a "compromise" measure. 5
NAP, GAP, and HAP can be viewed as variants of a more
general measure of portfolio position. Define "weighted
aggregate position" (WAP) as the weighted sum of gross
and net aggregate positions:
(3)
WAP = wgGAP
+ wnNAP
5. The relation BAP=Yz(GAP+NAP) is also evident from Figure 1.
Since GAP + NAP is equal tothesumofL, S, andT, itis twice the value
of either side of the balance sheet separately; BAP is always equal to the
total value of one side of the balance sheet, and hence is always exactly
half of the sum of the other two measures.
6. The Basle Committee also has suggested a possible alternative, under
which banks would simulate the response of their portfolios to typical
exchange rate fluctuations.
7. A separate proposal from the Basle Committee describes a framework for collecting information on interest rate exposure for all of the
assets and liabilities of the bank, both on- and off-balance-sheet. That
framework is for information only; there is no explicit risk calculation or
capital charge, although the Committee expects that the information
may be used as the foundation for future capital standards covering the
bank as a whole.
8
FRBSF ECONOMIC
REVIEW
1994,
NUMBER
1
The equity proposal covers risk due to changes in stock
duration weights are used to convert each time band to a
corresponding interest rate sensitivity. In addition, each
position is multiplied by a risk weight that combines an
interest rate volatility (standard deviation) and a factor for
the number of standard deviations of capital coverage desired by regulators; in terms ofthe discussion in Section II
above, the risk weights correspond to "to'.
Banks report long or short positions in each of the 13
prices. Some banks have direct holdings of equity shares or
bands, \vhich are grouped into three "zones" correspond-
equity-linked instruments. In some countries this could be
quite important, depending on the extent of bank powers.
Also, the new standards apply on a consolidated basis; in
countries (such as the United States) where banks are
affiliated with brokerage or investment banking units, the
equity risk standards may be important.
As in the foreign exchange proposal, banks convert
options and futures into spot equivalents, and then consolidate all exposures into a single hypothetical portfolio. The
result in the foreign exchange case was a set of long and
short positions in individual currencies; for the equity case,
the positions are in the shares of different issuers or in stock
market indexes. Positions may be long or short in each
equity, with short exposure arising from short sales or from
short positions in derivative instruments.
The proposal uses the long and short positions to compute gross and net aggregate positions, GAP and NAP.
Gross and net positions are then weighted and summed to
set minimum capital. This obviously is a weighted aggregate position calculation of the form discussed above. The
weights proposed by the Basle Committee are 1.0 and 1.0,
unless the portfolio is well diversified, in which case the
weights are 1.0 on NAP and 0.5 on GAP. The resulting
aggregate position is multiplied by a minimum capital ratio of 8 percent. The Basle draft combines the capital ratio
with the weights; for example, the weights for the diversified portfolio case are expressed as 8 percent of net and
4 percent of gross. The Basle document refers to the
composite weight on GAP as "x" and the weight on NAP
as "y, " and calls this "the x plus y approach." It clearly is
equivalent to WAP.
ing to short-term, medium-term, and long-term. Table 1
illustrates the structure of the basic maturity ladder. Exposures are netted in stages, first within maturity bands,
then across bands within each of the three maturity zones,
and then finally across the zones. At each stage, a certain
amount of the netting is "disallowed," using various
"disallowance factors." An aggregate position results.
Since individual positions have been premultiplied by risk
weights corresponding to "tIT, the result after the netting
process is not multiplied by a capital ratio (such as 8 percent); it already corresponds to a dollar amount of capital.
The way the disallowances are computed turns the
netting process into a WAP calculation. Consider one stage
of the netting, say, between time bands within a single
zone. In each band the bank may have either a long or a
short position. (For example, there would be a maximum of
risk-based capital framework. Capital required under the
foreign exchange market risk proposal would be in addition to any capital required to meet the existing credit risk
standards.
Equity Price Risk
Interest Rate Risk
The traded debt securities proposal is much more complicated, and has some features that do not fit neady within the
WAP framework. As with the other market risks, a hypothetical portfolio is constructed: Whereas in the foreign
exchange case the positions were in individual currencies,
and in equities the positions corresponded to different
issuers or indexes, in the debt proposal banks report net
positions in different maturities or repricing periods. Derivative instruments are converted to spot equivalents, and
TABLE 1
MATURITY LADDER FOR INTEREST RATE RISK
TIME BAND
MATURITY RANGE
ZONE
0-1 month
2
1-3 months
3
3-6 months
4
6-12 months
5
1-2 years
6
2-3 years
7
3-4 years
8
4-5 years
9
5-7 years
10
7-10 years
11
10-15 years
12
15-20 years
13
over 20 years
Zone 1
(Short Tenn)
}
Zone 2
(Medium Tenn)
Zone 3
(Long Tenn)
9
LEVONIAN I BANK CAPITAL STANDARDS
six long or short positions in Zone 3.) These band exposures are netted, generating a NAP for that zone. The
disallowance factor is a number 0 (between 0.10 and 1.50,
differing by zone and band) to be multiplied by the smaller
of the total long and total short positions; the resulting
dollar-value disallowance is added to NAP from the zone to
compute a position for that zone. Formally, the calculation
is NAP + omin[L,S].
It may not be obvious that this is a WAP calculation.
Note from the pair of equations in (1) that GAP - NAP =
2min[L,S]. Then the computed position is:
(5) NAP
+
omin[L,S] = NAP
=
+ ~ (GAP -
NAP)
~ GAP + (1 - ~ )NAP
Equation (5) shows that the netting process with disallowances does yield WAP. The amount of the disallowance is related to the weighting: a larger disallowance
factor gives relatively more weight to gross versus net.
Note that 8 = 0 corresponds to NAP, 8 = I corresponds to
BAP, and 8 = 2 corresponds to GAP.
Thus, the equity and interest rate risk proposals reflect
the same underlying theme as the foreign exchange proposal: The use of WAP to weight gross and net aggregate
positions, yielding a dollar exposure against which a
minimum capital ratio can be applied. Since all three use
versions of WAP, WAP is the key to understanding and
analyzing the market risk proposals. The next section
returns to the example of exchange rate risk to examine
whether WAP is likely to be a good measure of market risk.
positions could just as easily be interpreted as debt or
equity positions.
Consider a U. S. bank managing a portfolio of N foreign
currencies. Assume that the portfolio consists of n short
currency positions, and therefore N - n long currencies.
The value of each currency is measured in units of the
domestic currency (the U.S. dollar) as numeraire; thus,
there are N + 1 total currencies in the model. The dollar
value of currency i in the portfolio is di Prices of the foreign currencies fluctuate randomly from
period to period due to changes in supply and demand,
perhaps with some anticipated trend. Assume that the
unanticipated rate of change in each of the N exchange
rates is distributed with variance (I2, and that all crosscurrency correlations are equal to p. If D is the N x 1 vector of positions and ""i. is the N x N variance-covariance
matrix of the rates of change in exchange rates-with
diagonal elements equal to (I2 and off-diagonal elements
equal to p(I2-then the variance of changes in the value of
the foreign exchange portfolio is given by:
N
(6) (I~ = D'""i.D = ;~, (I2df
~-.I.
WAP is a simple, practical measure of portfolio position,
linearly combining elements of the position vector D. WAP
has the distinct advantages of readiness of comprehension
and ease of application, as do its variants, such as the Basle
Committee's foreign exchange selection BAP. Moreover,
WAP could serve as the foundation for a proportional
standard, with minimum capital set at some ratio c relative
to WAP. But since WAP bears little obvious resemblance to
the portfolio variance (I~ = D'""i.D discussed in Section III,
its precision-that is, its ability to accurately reflect interbank differences in risk-may seem questionable. This
section presents a simplified model of a portfolio showing
that GAP and NAP, the components ofWAP, are clearly related to the portfolio variance calculated from the variancecovariance matrix; this result has implications for the likely
precision of WAP in general. Foreign exchange risk is
again used as a convenient example, although the currency
N
J-"
(I2 p di dj
•
''''
To simplify the problem further, assume that each position
is of equal absolute dollar value. 8 Long positions have
positive value di = d>O and total dollar value (N - n)d,
whereas short positions are effectively liabilities and hence
have di=-d<O and negative total value -nd. Then the
variance can be written: 9
(7)
(I~
= (I 2d 2N(1- p) + (I 2d 2(N - 2n)2p .
Defining a "portfolio composition factor" Pas:
(8)
VI. WAP IN A SIMPLIFIED PORTFOLIO
N-[
+ 2 1--'"
;~, ;-~,
P = Yd 2N(1-p)
+ d 2(N-2n)2 p ,
the portfolio variance can be written simply as:
(9)
(I~
= (I2P2.
An attractive interpretation of this expression for (I~ is
that foreign exchange risk in a bank's portfolio can be
viewed as the product of two components. One component
is exchange rate volatility arising from the external environment of the foreign exchange markets, in this model
represented by (I2. This variance is multiplied by the
second component, the square of the portfolio composition
factor P, which reflects the size and composition of the
individual bank's foreign exchange book. Since the exchange rate environment does not vary across banks within
8. Alternatively, (Ii could be pennitted to vary across currencies and d i
assumed proportional to 1/ (Ii (that is, smaller positions in more volatile
currencies).
9. Details of this step are given in the Appendix.
10
FRBSF ECONOMIC
REVIEW
1994,
NUMBER
1
a given financial system, the value of 0"2 affects the level of
risk in the system but not how risk varies across banks;
differences in risk across banks must stem from differences
in portfolio composition.
P is related algebraically to the simpler aggregate position measures used by bank supervisors around the world.
In the N foreign currency model, GAP = Nd. With n short
positions and N-n long, NAP = IN - 2n Id. Substituting
into equation (8) above yiehk
(10)
p2
=
GAp2 (1 ~p)
+
NAp2 p .
Thus p2 is a weighted sum of squares of GAP and NAP,
with the weights depending on cross-currency correlations
of exchange rates for any given number of currencies.
In view of this relationship, consider the WAP measures-GAP, NAP and BAP-that have been used in the
past to measure risk. A precise standard would set minimum capital at 'YO"p' which is equal to 'YO"P from equation
(9). If WAP happened to be proportional to P, then minimum capital could be set as a ratio to WAP, with 'Y and 0"
incorporated into the capital ratio. Such a standard would
be precise, in the sense that it would measure risk correctly
for any combination of NAP and GAP, and at the same
time would be simple. Is any variant of WAP proportional
toP?
Several special cases are interesting. Equation (10)
implies that P = NAP if p = 1, an intuitive result: If changes
in exchange rates are perfectly correlated, then the foreign
currencies are effectively interchangeable, and can be
treated as a single currency. Long and short positions
within a single currency of course should be netted. As a
result, NAP, which nets longs and shorts across the entire
book, treats the exposures correctly. With p = 1, a minimum capital ratio c = 'YO" applied to NAP is simple, proportional, and precise. (This result is independent of the
particular form of the model.)
If exchange rate changes are uncorrelated (p = 0), then
equation (10) implies P = GAP/VFi. In that case, a capital
standard for foreign exchange risk could be based on GAP
as the measure of exposure, with the minimum capital ratio
c = 'Y0"1VFi. The special case of NAP = 0 also is interesting; NAP is zero if a bank runs a "balanced book," with no
net position in the domestic currency. GAP again is precisely proportional to portfolio risk: equation (10) shows
that P = GAPY (1- p)1N. The appropriate minimum capital ratio would be c = 'YO"Y (1- p)1N.
Nevertheless, it is clear from (10) that in general a WAP
standard cannot be perfectly precise, because WAP depends linearly on GAP and NAP while P depends on the
square root of their weighted sum of squares. If a standard
based on a weighted root sum of squares of gross and net
exposure were regarded as sufficiently simple, p. itself
could yield a very precise capital standard. However, such
a standard may be regarded as unacceptably complex.
Given that the simpler WAP is imprecise,it still may be
"close enough" to P to be acceptable.
Equation (10) describes P as a function of net and gross
exposure; in three dimensions, P is a portion of anasymmetric cone. In contrast, WAP is affine;lO it is a plane in
three dimensions. The task of devising a capital standard
based on WAP can be viewed as one of choosing the
weights to make the WAP plane approximate the P cone
fairly closely for all n and d, given the number of currencies
N and the correlation coefficient p. As discussed above,
WAP can fit P perfectly only under polar conditions, with
p = 0 or p = 1. In the general case, WAP can only be made
"close" to P; the fit of the capital standard is tailored by adjusting the relative weights on net and gross exposures, W n
and wg • The best weighting will depend in part onN and p.
VII.
OPTIMIZING THE WAP WEIGHTS
The preceding section suggested that WAP might be a good
risk measure, balancing simplicity and precision: simple
because it builds on current practice and is a linear combination of exposures, and precise because a correct choice
of the relative weights on gross and net could make WAP
approximate the theoretically correct portfolio composition factor. The Basle Committee's foreign exchange proposal incorporates a specific weighting, BAP, in which the
weights on NAP and GAP are both liz. Are these the best
choices? More generally, how should the weights be
chosen?
Returning to the simple portfolio model with a .fixed
number N of foreign currencies and a variance-covariance
matrix~, assume that bank portfolios differ only in scale.
That is, assume that all banks have the same currency mix
(reflected in uniform values of n, or equivalently in uniform ratios of NAP to GAP), but may have positions of
different sizes (d differs). Let A be the common NAPI GAP
ratio; A reflects the degree of portfolio imbalance, with
A = 0 for a balanced portfolio, and A = 1 if exposure is all
long or all short. 11 All bank currency portfolios thus lie
along a single ray with slope A in the NAP-GAP plane,
10. An affine function is the multidimensional equivalent of a linear
function; a function/is affine if/(x)=Ax+b. where x is a vector of
variables, b is a vector of constants, and A is a fixed matrix of constants.
In three dimensions, an affine function is a plane.
11. This assumption might not be too unrealistic; banks would have the
same, or nearly the same, net currency positions if they all used similar
portfolio optimization algorithms to manage exposure.
LEVONIAN I BANK CAPITAL STANDARDS
although as exchange rates change randomly over time d is
likely to vary.
Ifwnand Wg are chosen to make WAP tangentto P along
the ray defined by NAP/GAP=d, then WAP will be
locally precise, in the sense that WAP will equal P for any
portfolio scale d selected by individual banks. Moreover,
WAP will track changes in risk precisely for local variation
in d, since tangency equates the partial derivatives ofWAP
and.lD with respect to a; first order changes in measured
risk would be the same as first order changes in actual
portfolio risk.
Formally, since d = IN- 2n liN it is possible to rewrite
WAPand P (from equations (3) and (8» as functions of d
and d, given Nand p:
(11)
(13)
ap
aWAP
ad
ad
ap
and
ad
=
aWAP
ad
The relevant partial derivatives are:
(14a)
(1 ~p)
:: = N (
+ pd2
yl2,
(14b)
(14c)
aWAP
----ax-
(14d)
Equating (14a) to (14c) and (14b) to (14d) as in (13) allows
solution for the optimal weights
and
(15)
w;
= pd
Values of the optimal weights can be computed from
equations (15) for realistic values of N, p, and the ratio d.
What are reasonable choices of parameters? If N is interpreted as the number of major currencies, then p might be
interpreted as the average correlation coefficient. The vast
bulk of currency exposure for U.S. banks is concentrated
in six major foreign currencies-German mark, Japanese
yen, British pound, Swiss franc, Canadian dollar, and
}.\...ustralian dollar-suggesting lv = 6. The average- correlation between biweekly changes in dollar exchange rates of
these six currencies (measured over non-overlapping twoyear intervals from 1981 through 1992 as described in
Section VIII below) ranges from .38 to .56, with a mean of
and
.47. Table 2A presents illustrative calculations of
based on these parameter values. Besides the six major
foreign currencies, U.S. banks tend to have moderate
exposures in other currencies such as the Italian lira,
French franc and Dutch guilder; to consider the implications of differences in the number of currency positions,
Table 2B presents optimal weights for N = 9.
Even for a given combination of the parameters Nand p,
the accuracy of the WAP approximation varies depending
on the NAP/GAP ratio d. Thus, in practice the choice of
weights for WAP should depend on the range of net and
gross positions that regulators aim to fit most closely. For
example, other elements of bank supervision may lead
most banks to run foreign exchange books that are balanced
ornearly balanced, so thatthe typical NAP (and d) is small.
In that case, the choice of weights likely would be made
from the left-most column of Table 2A or of Table 2B.
There are two ways these weights could be used for
capital regulation. Consider the case of N = 6, p = .47, and
NAP/GAP= .33. Under one approach, banks would compute their open foreign exchange positions as 42 percent of
their net exposure plus 24 percent of their gross exposure,
and might be required to have capital equal to at least 4.4
percent of this sum. 12 This is how the Basle foreign
exchange proposal uses WAP in its BAP incarnation. A
second approach would combine the capital ratio with the
weights
and
a composite capital charge would be
made against the net position, and an additional charge
would be made against the gross position. In this example,
banks would be required to have at least enough capital to
cover 1.8 percent of net exposure (4.4 percent of 0.42) and
1.0 percent of gross exposure. This composite approach
w;
wi
w;;,
= Ndw n
w; wi:
((1 ~P) + pd2} 112
11
wi;
and
w*g =
(1-p)
N
(1- p)
( ~
+ pd2
)-112
.
12. The standard deviation of two-week rates of change over the entire
1981-1992 period for the six major foreign currencies was 1.46 percent.
Three standard deviations of coverage ('Y = 3) would imply a capital
ratio of about 4.4 percent to be applied against the aggregate open
position.
12
1994,
FRBSF ECONOMIC REVIEW
NUMBER
1
TABLE2A
OPTIMAL WAP WEIGHTS WITH
N= 6
NAP/GAP= .67
NAP/GAP= 1
NAP/GAP= .33
NAP/GAP=O
p
wg
Wn
wg
Wn
wg
wn
wg
wn
.38
.15
.55
.20
.49
.27
.33
.32
0
.47
.12
.63
.16
.57
.24
.42
.30
0
.56
.09
.70
.13
.66
.20
.51
.27
0
TABLE 2B
OPTIMAL WAP WEIGHTS WITH
N= 9
NAP/GAP= .78
NAP/GAP= .56
NAP/GAP= .33
NAP/GAP= .11
P
.38
.13
.54
.16
.49
.21
.38
.25
.16
.47
.10
.62
.13
.58
.18
.47
.23
.21
.56
.08
.70
.10
.66
.15
.56
.21
.26
would correspond to the treatment in the Basle Committee's equity price risk proposal, the "x plus y" approach.
From (15), the ratio of the WAP weights from the
optimal approximation is:
(16)
w*n
w*g
pNJl
I-p
This ratio depends positively on p, N, and Jl. If exchange
rates are highly correlated, then changes in the value oflong
positions tend to be offset by changes in the value of
short positions; net exposure becomes most relevant, and
the optimal w~ is high relative to wi. With a larger number
of foreign currencies, N, diversification eliminates more
portfolio risk for any given gross size of the portfolio, and
wi is reduced relative to w~. Finally, as Jl goes to zero
and portfolios become more balanced (NAP goes to zero),
then risk comes to depend mainly on GAP, and the optimal
wi becomes large relative to w~.
The Basle Committee's foreign exchange proposal places
equal weights on gross and net. 13 Figure 2 shows combina-
13. The Basle weights are 0.5 and 0.5, but to evaluate WAP's ability to
track risk across banks and over time only the relative weights matter,
not their absolute levels. Since WAP is multiplied by a minimum capital
ratio to set a standard for capital adequacy, the weights can be scaled up
or down proportionally, with the capital ratio scaled in the opposite
tions of Jl and p for which the ratio in equation (16) is equal
to one (and the Basle weighting is optimal) for various N.
The graph implies that with p in the range of .35 to .55, the
Basle proposal may be optimal provided bank portfolios
are reasonably balanced (with NAP no greater than about
30 percent of GAP). The Basle proposal would be optimal
for lower values of p if long and short currency positions
within portfolios tend to be unbalanced. 14
Capital standards based on WAP are fairly clever. They
appear to depend only on the dollar size of positions, and
are simple in form; they also appear to ignore correlations
between different exchange rates. However, information
from the variance-covariance matrix is incorporated in the
choice of weights for gross and net exposures: the covariance determines the relative weights, and the variance
scales the weights proportionally.
direction for the appropriate degree of coverage. For example, weights
of W n = .8 and W g = .4 with a minimum capital ratio of 4 percent have
exactly the precision and coverage ofwn =.4, wg = .2, and an 8 percent
standard.
14. These results suggest that the Basle proposal may weight gross
exposure too heavily. However, other risks related to settlement and
delivery may be relatively high in transactions involving currency
exchange. Those risks plausibly depend on gross exposure; if so,
additional capital related to GAP may be warranted.
LEVONIAN / BANK CAPITAL STANDARDS
FIGURE 2
PARAMETER COMBINATIONS THAT MAKE
EQUALLY WEIGHTED WAP OPTIMAL
P
1.00 ]
0.90
0.80
0.70
0.50
0.40
0.30
0.20
--. --
0.10
-'-
N=6
N=9
N=l1
0.00 +-,--.---,---r---.-.-.---.-,--,-,--.---,---r---.--,
0.05
0.20
0.35
0.50
0.65
0.80
NAP/GAP
vrn.
A TEST OF THE BASLE FOREIGN
EXCHANGE MEASURE
The analysis in the preceding section suggests that BAP
might be expected to work reasonably well in some cases.
However, the model used in that analysis makes highly
stylized assumptions regarding exchange rate processes
and foreign exchange portfolio structures. In practice,
banks do not all have the same ratio of NAP to GAP, and
may not even be tightly distributed around any particular
ratio. Thus, rather than a WAP plane that is tangent along a
single ray, the optimal policy might be a plane that leads to
small differences between WAP and P for combinations of
NAP and GAP over some range of d ratios, perhaps one
minimizing the integral of the squared difference. In addition, relaxation of other simplifying assumptions (such as
the special structure of the I matrix) may mean that in
practice the surface mapping NAP-GAP combinations into
(J"p is less regular in form than the P cone described above.
Thus, actual bank portfolios probably are scattered around
on an irregular surface above the NAP-GAP plane, and the
practical question is whether a WAP approximation can be
constructed to fit these points acceptably well. Requiring
that the result be expressed as a conventional-looking
capital ratio applied to WAP adds an additional constraint,
that the plane should go through the origin, so that risk is
13
measured at zero (and no capital is required) if both NAP
and GAP are zero.
Considering these real-world wrinkles, the relevant question is an empirical one: Can WAP be made approximately
proportional to the actual (J"p ?15 More specifically, the Basle
Committee has proposed BAP, the equally weighted variant
of WAP, to gauge exchange rate risk. This section uses a
regression approach to evaluate BAP empirically as an
affine approximation (see footnote 10) to actual foreign
exchange portfolio risk, using data on exchange rates and on
banks' foreign exchange positions.
The data on banks' foreign currency positions come
from the FFIEC 035 report, a confidential survey of
currency exposure conducted by federal banking regulators. The format of the collected data corresponds closely
to the theoretical specification of the position vector D
above. For the FFIEC 035 report, all of a bank's exposures
in any single currency-including those arising from
loans, deposits, securities and other sources denominated
in foreign currency, both spot and forward-are collapsed
into a single hypothetical position, either long or short. The
only divergence from the theoretical model is that the
positions are denominated in units of foreign currency; for
this analysis, they were converted to U.S. dollars using the
exchange rate prevailing as of the reporting date.
Currency positions were taken from the December reports for 1990,1991, and 1992, for all banks in the Twelfth
Federal Reserve District. Virtually all of the exposure was
in the six major foreign currencies, so only these are
considered in the analysis. One notable feature of the
FFIEC 035 data is that relatively few banks file the report,
reflecting the fact that many banks have immaterial foreign
exchange exposure; in the Twelfth District, only 15 banks
reported foreign exchange exposures for 12/90,9 banks for
12/91, and 8 banks for 12/92. Thus, foreign exchange risk
may not be a widespread concern, although it may be large
for some individual banks. The six individual major currency positions were calculated for each bank, and BAP
was computed from these positions.
Portfolio variances for each bank also were calculated
from the vector of positions, based on variance-covariance
matrices of percentage changes in exchange rates. The
FFIEC 035 positions were considered to be typical portfolios that banks could hold at any time, and applied to I
matrices estimated for specific dates to compute the portfolio variances as they would have been if the portfolios had
15. The theoretical analysis in Section VI investigated the relationship
between WAPand P. Under the assumptions of that model, WAP=P
implied <TWAP = <TP' so an analysis of the first condition encompassed
the second as well.
14
FRBSF ECONOMIC REVIEW
1994,
NUMBER
1
been held at those dates. 16 For the matrix estimations, the
1981-1992 period was divided into six two-year subperiods. Two-year subperiods were deemed to be a reasonable
compromise: I is more likely to be stable over shorter
periods, but an estimation period that is too short produces
estimates with unacceptably wide confidence intervals. A
series of non-overlapping two-week percentage changes in
exchange rates was constructed from actual dollar ex-
conditions are satisfied, then BAP is a simple, proportional, and relatively precise measure of foreign exchange
portfolio risk. For estimation, the exchange rate standard
deviation IT is replaced with the average standard deviation, averaged across the major foreign currencies for
each subperiod. Denoting the variance-covariance matrix
for subperiod t as It, the average volatility is computed as
the square root of the average variance for each subperiod,
change rates \vithin each subperiod for each of the six
nr
iT - '\ /tra"e(~ \/h ~",tt;... n-" """"tal C't" ...r1"rrl than ra
V.l. Vt~ V u
'"' '~tl' v. UVl.L.1J..l5 u. ""u.yu. .1. cn,u..l1uaJ.u \.u,",u .1\......
major foreign currencies. (The two-week convention, initiated by the Basle Committee in testing the proposal, is
based on considerations of how rapidly bank portfolio
losses due to exchange rate changes can be recognized
and acted upon by banks or regulators.) Six variancecovariance matrices (one for each subperiod) were estimated from the percentage changes in exchange rates.
Portfolio standard deviations were estimated as ITp =
[D'ID]lI2, where each of the observed currency portfolios
is characterized by a dollar position vector D. Combining
32 bank portfolios with matrices from six subperiods
yielded a data set with 192 observed pairs of (ITp\t and
BAPit , one for each bank i in period t.
A rough nonparametric test of the strength of the relationship between BAP and ITp can be constructed from the
rank correlation of the two variables. At a minimum, BAP
or any other proposed measure of portfolio risk should
yield higher values for higher risk portfolios and lower
values for lower risk portfolios. Calculation of the Spearman rank correlation coefficient indicates that BAP and ITp
are highly rank correlated: The coefficient for the entire
sample is 0.991, significantly greater than zero at virtually
any confidence level.
The high rank correlation is encouraging, but BAP
should pass more rigorous tests if it is to be the foundation
for a simple yet precise capital standard. In particular, BAP
should be roughly proportional to the theoretical portfolio
composition factor P, that is P= f3BAP. The portfolio standard deviation ITp then would be approximately equal to
ITf3BAP, from equation (9). Thus, in a regression of the
form:
quires an estimate of 0', but this average volatility is
constant across banks, and in practice developing a representative estimate should not be hard. A coverage ratio of "y
would be achieved by setting a minimum capital ratio of
C="YO'f3.
Two types of heteroskedasticity are likely in estimating
(17). One is related to the scale of bank portfolios: the error
variance is likely to be higher for larger portfolios. A
simple correction for scale-related heteroskedasticity is to
divide through by BAP before estimating, creating a
transformed equation with errors that are no longer proportional to BAP. The second type relates to the subperiods
used to estimate the matrices of exchange rate variances
and covariances: In theory, the ability of BAP to match P
depends on p for a given number of currencies, and
exchange rate correlation coefficients vary across the twoyear subperiods. This second source of heteroskedasticity
is handled through weighted least squares estimation,
allowing the variance of the regression residuals to vary
across subperiods.
With the correction for scale-related heteroskedasticity,
the equation to be estimated is:
(17)
(ITp)it =
U
+
ITf3BAP it
+
Eit
,
goodness-of-fit should be high and the coefficient f3 should
be measured with little error; for BAP to be proportional to
ITp' the coefficient u should equal zero. In addition, it may
be desirable for f3 to be stable across subperiods. If those
16. The obvious drawback to this approach is that banks' decisions
regarding foreign exchange exposures may depend in part on the
variance-covariance matrix of exchange rates. The empirical importance of this problem is left as an issue for future testing.
(18)
B(ITAPp)it
it
= u
-AI
B Pit
+ O'tf3 +
uit ,
where i is an index for the portfolio, t indexes the sample
subperiod, and uit = Ei/BAPit . Estimation results are
shown in the first column of Table 3, with standard errors
reported in parentheses below each coefficient. R2 is the
usual goodness'-of-fit statistic corrected for degrees of
freedom, and the sum of squared residuals is reported as
SSR.J7
The results show that most of the conditions for use of
BAP as the basis for a capital standard are satisfied
(intertemporal stability is addressed separately below).
The estimate of u is insignificantly different from zero and
17. The same regression was run without division by BAP, yielding
coefficient estimates that were qualitatively similar to those reported in
the table. Inspection of the residuals from both regressions indicated that
scale-related heteroskedasticity was in fact an issue in the untransformed regression, and that dividing each observation by BAP largely
eliminated the problem.
LEVONIAN / BANK CAPITAL STANDARDS
TABLE
3
TABLE
ESTIMATION OF EQUATION
(18)
(2)
0.01
(0.01)
13
R2
(CTp ) it
BAP.
It
No RESTRICTIONS
13 RESTRICTED
U RESTRICTED
U 81 - 82
0.03
(0.02)
0.04
(0.02)
0.01
(0.01)
0.89
(0.01)
U 83- 84
0.00
(0.01)
-0.01
(0.01)
0.01
(0.01)
0.970
0.971
U 85- 86
0.00
(0.02)
-0.01
(0.02)
0.01
(0.01)
U 87- 88
0.02
(0.01)
0.03
(0.01)
0.01
(0.01)
U 89-90
0.03
(0.02)
0.04
(0.01)
0.01
(0.01)
U 91 - 92
-0.02
(0.02)
-0.01
(0.02)
0.01
(0.01)
1381-82
0.94
(0.04)
0.88
(0.01)
0.96
(0.04)
1383-84
0.83
(0.03)
0.88
(0.01)
0.82
(0.03)
1385-86
0.82
(0.03)
0.88
(0.01)
0.81
(0.02)
1387-88
0.92
(0.03)
0.88
(0.01)
0.93
(0.03)
1389-90
0.94
(0.04)
0.88
(0.01)
0.95
(0.03)
1391-92
0.91
(0.04)
0.88
(0.01)
0.89
(0.04)
0.961
0.970
0.959
14.94
the standard error of 13 is relatively small, so CTp can
be assumed proportional to BAP with relative impunity
(given 0'). The fit of the regression as measured by the
adjustedR2 is high, perhaps remarkably so considering the
simplicity of the BAP approach for measuring market risk.
The second column presents the results with the intercept
restricted to zero to illustrate the relatively minor effect on
13 of forcing CTD to be proportional to BAP.
In equation"(18) and Table 3, the slope and the intercept
of the relationship between BAP and the portfolio variance
are restricted to be the same in each of the sample subperiods. These restrictions on the coefficients must be
relaxed if the stability of 13 is to be evaluated. An alternative regression is:
(19)
(19)
0.88
(0.01)
14.70
SSR
4
ESTIMATION OF EQUATION
(1)
15
_ ~
_1_
- t~I at BAP.
It
~ _
+ t~I CT t l3t +
U it
In this form, restrictions on the coefficients at and I3t can
be tested with standard F tests.
Table 4 shows the estimation results for equation (19). In
the first column, both intercept and slope are allowed to
differ for each subperiod. (In effect these are six separate
regressions, one for each period, since the error variances
also differ across subperiods.) None of the intercepts is
significantly different from zero at the 5 percent level. The
slope coefficients range from 0.82 for the 1985-1986
period to 0.94 for the 1981-1982 period. In the second
column of the table, 13 is restricted to be the same for all
subperiods. The restricted coefficient estimate is 0.88; in
this form, a is significantly different from zero for the
1981-1982 and 1989-1990 subperiods. An F test of the 13
restrictions yields a test statistic of 2.91, with 5 and 180
degrees of freedom; this value lies between the 95th
percentile of the F distribution (2.26) and the 99th percentile (3.12). Thus, although 13 is not truly stable, it is not
terribly unstable. Additional testing reveals that the ]983-
R2
SSR
12.66
13.69
13.22
1984 and 1985-1986 periods are statistically different
from the other subperiods; an F test fails to reject the
hypothesis that 13 takes one value (0.82) for 1983-1986,
and a second value (0.93) for the remainder of the sample.
The fact that even the statistically different coefficients for
the 1983-1986 period are in the rough vicinity of the
other estimates suggests that the Basle approach may be
workable.
The third column of Table 4 shows the effects of
restricting the intercept across subperiods. As would be
expected from the first column of the table, an F test does
16
FRBSF ECONOMIC REVIEW
1994,
NUMBER
1
IX. SOME COMMENTS
ON THE OrHER MARKET RISKS
not reject this restriction. The restricted intercept is not
significantly different from zero, making a BAP-based
proportional capital standard feasible. The primary conclusion from the regressions is that BAP is approximately
proportional to P. The F tests imply that the factor of proportionality f3 is fairly stable over time, and that the value
of P is typically about 80 to 95 percent of BAP.
One concern in moving from equation (19) to the con-
A similarly detailed analysis of the equity and traded debt
(or interest rate) components of the Basle Committee's
market risk proposals is beyond the scope of this paper, and
is deferred for future research. However, a few observations can be made about particular aspects of these other
struction of practical capital standards is that ~ is the factor
drafts.
of proportionality between P and BAP, whereas the ratio of
up to BAP at time t is actuallya t f3r Thus, evidence that f3t
is fairly stable might be of limited relevance, since the
combination at f3t may not be. Additional regressions were
run with at set equal to 1.0 in both (18) and (19), a
restriction which effectively forces the coefficient f3 to
incorporate the effects of exchange rate volatility u, and
therefore permits direct tests of the stability of at f3t. The
results were not materially different from Tables 3 and 4,
and so are not reported; goodness-of-fit was comparable,
the intercepts were still insignificant, and the stability
results for the slope coefficient were the same. As would be
expected, the values of the f3 coefficients were higher,
reflecting the fact that they include a a factor that averages
1.46 over the entire sample period.
Using the restricted estimate of f3 = 0.88, the portfolio
standard deviation is (J"p=0.88aBAP. Based on the average 0', capital equal to 1.28 percent (88 percent of 1.46) of
the typical bank's BAP is sufficient to cover one standard
deviation of changes in the value of the bank's aggregate
foreign currency portfolio. If three standard deviations of
coverage is considered desirable (a level which would
cover all but 0.13 percent of the probable losses under
a normal distribution), then the minimum capital ratio
should be 3.85 percent of BAP. The Basle Committee has
proposed applying an 8 percent ratio to BAP. Even taking
the highest estimate of f3 from Table 4 (0.96 from the 19811982 subperiod with a restricted) and the highest O't(1.86
percent for 1985-1986), three standard deviations of coverage would correspond to a 5.36 percent capital ratio.
Under these extreme assumptions, 8 percent capital provides about 4.5 standard deviations of coverage. Thus,
while BAP appears to be a reasonably precise measure of
risk, the proposed level of capital coverage appears to be
very conservative. Such an apparently excessive degree of
coverage might be justified as compensating for errors in
the BAP approximation. Alternatively, regulators may
want to allow for non-normality in the statistical distribution of exchange rate changes; stochastic processes may incorporate discrete random jumps, or distributions may be
leptokurtic (fat-tailed).
As noted in Section V, the Basle proposal for equity
price risk gives gross exposure less weight in diversified
portfolios than in undiversified portfolios. The analysis in
Section VII indicates that this difference in weighting may
be appropriate: For WAP to approximate P, NAP should
get more weight relative to GAP when the number of
positions is large. (Recall from (16) that w~/w; increases
with N.) The equity proposal also gives GAP less relative
weight than it is given in the foreign exchange proposal.
Such a difference in weights is appropriate if the number of
different issues in a diversified portfolio of equities is
larger than the number. of currencies in a typical bank
currency portfolio, a reasonable assumption. Finally, calculations of return variances for the 30 stocks in the Dow
Jones Industrial Average indicate that stock returns tend to
be more volatile than exchange rate changes. Thus the
higher coverage levels implicit in the equity proposal may
be desirable (the composite capital weights on GAP and
NAP are 4 percent and 8 percent respectively for diversified portfolios, and 8 and 8 for undiversified portfolios,
compared to 4 percent and 4 percent for foreign exchange).
The traded-debt-instruments proposal also seems at
least superficially in accord with the conceptual model. As
discussed in Section V, the netting/disallowance process in
the proposal effectively applies WAP in stages. WAP is a
simple measure of portfolio risk for any portfolio, including sub-portfolios of, for example, Zone 2 (medium-term)
securities. Thus, this proposal can be construed as an
attempt to compute simple but accurate measures of position for various sub-portfolios, then combine these in a
building-block approach to obtain a measure of total
interest rate risk for the debt portfolio. In practice, the
traded-debt framework may provide a better measure ofrisk
than either the foreign exchange or the equity market
risk components; both of those proposals use a single pair
of weights on gross and net exposures for all portfolios,
whereas the debt proposal in effect permits some flexibility
in the NAP/GAP weighting. Allowing the weights to vary
somewhat according to the composition of a bank's debt
portfolio could provide superior results. Another desirable
feature of the proposal is that differing volatilities of
maturity bands are recognized directly, through the premultiplication by risk weights; in contrast, the foreign ex-
LEVONIAN / BANK CAPITAL STANDARDS
change proposal does not account for the fact that some
exchange rates tend to vary more than others.
As equation (5) shows, the weights on gross and net
in the interest rate risk proposal are determined by the
disallowance factors; higher disallowance factors give relatively more weight to GAP versus NAP. Section VII
indicates that an emphasis on GAP is desirable if the
correlations between instruments in a portfolio (or subportfolio) are low. The Basle Conunittee's proposed disallowance factors are lowest within maturity bands, somewhat
higher across bands within a single zone, and higher still
across zones, with the highest disallowance factor (1.5)
applying to netting between the short-term and long-term
zones. These differences appear to correspond to the
empirically observed pattern of correlations between interest rate changes across the term structure. Thus, the
general pattern of disallowances seems roughly appropriate, although a more confident conclusion would require
careful analysis of the entire proposal. 18
Future research should consider applying regression
analysis to both the equity and interest rate proposals, as
was done in this paper for empirical analysis of the foreign
exchange proposal. One difficulty is that data on bank
positions with respect to these other market risks are
inferior to the FFIEC 035 currency data. Central banks in
various countries have done some confidential analyses of
this type.
X.
CONCLUSION
The recent proposals from the Basle Committee for incorporating market risks into risk-based capital standards are
coherent and sensible, embodying a unified underlying
theme: The minimum adequate level of bank capital is
computed as a ratio of capital to risk exposure, with
exposure measured as a weighted sum of gross and net
positions from a hypothetical composite portfolio for each
18. Federal banking regulators in the United States have proposed a
somewhat different approach to measuring interest rate risk for capital
adequacy. The U. S. proposal is similar to the Basle proposal in the construction of a hypothetical portfolio broken into time bands, and the use
of risk weights based on potential changes in the value of debt
instruments when rates change. However, the U.S. proposal makes no
use of "disallowance factors," implicitly setting 8 to zero. As demonstrated above, 8 = 0 makes WAP equivalent to NAP, with no weight on
gross exposure; this is in effect the approach taken by U.S. regulators,
with long exposures in any time band netted against short exposures in
any other band. As also shown above, NAP is the correct measure if
p= 1, that is, if rates in all time bands are perfectly correlated. The Basle
approach using disallowances can be viewed as a simple way to
incorporate the fact that correlations across the yield curve are not
perfect.
17
bank. The conceptual model developed in this paper suggests that this approach can produce capital standards that
are reasonably accurate, and at the same time are simple
enough to be practical. A weighting of gross and net
exposures (the WAP approach) can be viewed as an affine
approximation (the equivalent of linear in several dimensions) to the true portfolio variance, and hence can link
capital standards fairly tightly to portfolio risk in order
to prevent 'failure probabilities from reaching excessive
levels. A system based on a weighted root sum of squares
of gross and net would be more precise, but also more
complex.
Empirical testing of the foreign exchange proposal was
based on exchange rate data for the six major non-U.S.
currencies from 1981-1992 and a recent sampling of actual
U.S. bank currency positions. The results indicate that the
measurement framework proposed by the Basle Committee
tracks foreign exchange rate risk remarkably well, capturing over 95 percent of the total variation in foreign exchange risk across the sample of banks. However, the level
of coverage implicit in the 8 percent capital ratio may be
somewhat high.
Conclusions regarding the equity price risk and interest
rate risk proposals are tentative, since a detailed empirical
analysis was not conducted in this paper. However, an
initial reading of the other two market risk proposals
against the background of the conceptual model suggests
that they incorporate a number of appealing features.
Unfortunately, neither the common thread running
through the market risk proposals nor the desirable properties of the WAP approach have been articulated clearly in
the consultative documents released for public comment.
The equity risk proposal is the only one of the three that
explicitly describes the capital charge as a weighting of
gross and net exposures, and that presentation is muddied
by a discussion of "general risk" and "specific risk" that
has little to do with the analytical merits of WAP. The
interest rate risk proposal, as described above, uses a
system of netting with "disallowances" to accomplish the
weighting, which obscures the fact that the proposal is
fundamentally a WAP calculation. The foreign exchange
draft does point out that the proposal reflects the assumption of "some, but not perfect, correlation between the
movements of different exchange rates" (Basle Committee, 1993, p.39). However, the aggregate foreign exchange
position calculation is described as "the sum of the short
positions or the sum of the long positions, whichever is the
greater" (ibid, p.38); as shown in Section IV, this is
equivalent to equally weighted WAP, but the equivalence
may not be obvious.
The Basle Committee is international, and the proposed
standards are to apply internationally. This paper evaluates
18
FRBSF ECONOMIC REVIEW 1994, NUMBER 1
the proposals solely from a U.S. perspective; results for
other countries might differ. Parallel analyses have been,
and continue to be, pursued at other central banks around
the world. Obviously, the final form of the market risk
standards will be the result of international negotiation and
agreement, and agreement will depend on how well the
proposals meet the needs of the many countries involved.
The Basle Committee also has suggested that the standards
could be applied to other types of financial firms, such as
securities houses and insurance companies, if regulators in
those industries agree. Introducing an interindustry dimension adds to the challenge of reaching a consensus, and
complicates any complete analysis of the market risk
proposals.
As a final note, throughout the Basle documents (and
this paper) each of the many types of risk-including
credit risk, exchange rate risk, equity price risk, and
interest rate risk-is considered and treated separately
from the others. Such a presumption of separability may
not be realistic in view of the likely interactions among
these various sources of risk. Ideally, capital regulations
should consider all types of risk simultaneously in a unified
framework. However, breaking the capital adequacy problem into more manageable pieces may be the only practical
approach, and separability may be a workable approximation. The possible damage done by this assumption should
be the subject of future research.
The second term involves the double summation of
products of positions in all pairs of foreign currencies. The
total number of pairings in a set of N objects is N(N -1)/2,
so this is the total number of didj terms. These terms fall
into three groups:
= d2
Both currencies long: d.d.
I J
= d2
Both currencies short: d.d.
I J
= -d2
One long, one short: d.d.
I J
If the positions were either all long or all short, then the
terms in the double summation would sum to d 2N(N -' 1)/2.
However, by assumption there are n short positions and
N - n long positions. The number of pairings of x objects
with y objects is xy; hence the number of short-long pairs is
n(N - n). It follows that the number of didj = dZ pairs is not
the maximum number N(N -1)/2, but rather N(N -1)/2 n(N - n). In addition, of course, each of the n(N - n) positions with opposing signs contributes didj = -dZ to the sum.
Hence:
N-l
(A2)
I
i= 1
IN
j=i+l
d.d. = d 2 (N(N-1)
.
- n(N-n) )
I
J
2
- dZn(N-n).
Substituting this into the expression for the portfolio variance in (AI) gives:
(A3)
(J;
= (J2d 2N + (J2d 2(N(N -1)
-
4n(N - n»)p
= (J2d 2N + (J2d 2(N - 2n)Z - N»)p
=
(J2d 2N (1- p)
ApPENDIX
as asserted in the text.
This appendix describes one of a number of ways to
demonstrate the transition from equation (6) to equation
(7) in the text. The variance of a portfolio of N currencies
with equal variance and correlation, slightly modified from
(6), is:
REFERENCES
N
(AI)
(J2
P
=
(J2
N-l
N
I d7 + 2(J2p i=l
I j=i+l
I d·d· .
i=l
I
I
J
The crux is evaluation of the summation terms. Note that
by assumption each of the d i is either d (for long positions)
or -d (for shorts). Clearly d'f = d 2 for either type of position, so the first summation is simply d 2N.
+ (J2d 2(N -
2n)2 p
Basle Committee. 1993. The Supervisory Treatment of Market Risks:
Consultative Proposal by the Basle Committee on Banking Supervision (April). Basle, Switzerland, April.
Bhala, Raj. 1989. Perspectives on Risk-Based Capital: A Guide to the
New Risk-Based Capital Adequacy Rules. Bank Administration
Institute.
Levonian, Mark, and Sarah Kendall. 1993. "A Contingent Claim
Analysis of Risk-Based Capital Standards for Banks." Research
Discussion Paper #9302. Reserve Bank of Australia.
Are Exchange Rates Macroeconomic Phenomena?
I.
Andrew K. Rose
Associate Professor, University of California, Berkeley;
Faculty Research Fellow, NBER; Research Fellow, CEPR;
and Visiting Scholar, Federal Reserve Bank of San Francisco. Part of this work was completed while visiting the
Economic Research Department at the Federal Reserve
Bank of SanFrancisco. I have benefited from the comments
of Tim Cogley, Elizabeth Laderman, Adrian Throop, and
Carl Walsh, and discussions with Reuven Glick, Ken Kasa,
and my co-author in related work, Robert Flood.
This paper argues that macroeconomic variables are
relatively unimportant determinants of exchange rates.
The argument hinges on the fact that bilateral exchange
rate volatility differs widely across pairs of countries, but
macroeconomic volatility is much more similar across
countries, at least at short- and medium-termfrequencies.
For instance, the French Franc! German Deutschemark
exchange rate has dramatically lower volatility than the
Canadian dollar/German Deutschemark rate, although
France and Canada have approximately equal macroeconomic volatility vis-it-vis Germany.
INTRODUCTION
Most economists think that macroeconomic phenomena
drive exchange rates. For instance, many economists believe that the 1992-1993 European Currency Crisis was the
result (at least in part) of the Bundesbank's tight monetary
policy, itself a response to the inflationary pressures generated by German unification. For another instance, the
appreciation of the U.S. dollar in the early 1980s is frequently attributed to either Reagan's loose fiscal policy or
Vo1cker's tight monetary policy, or both. Finally, most
economists who model the exchange rate either theoretically or empirically, use macroeconomic models.
In this paper, I argue that macroeconomic phenomena
are not especially important forces in driving exchange
rates; there must be other things which are at least as
important which also determine exchange rates, at least at
short- and medium-term frequencies. While it is undeniable that macroeconomic forces are sometimes important,
in this paper I seek to show that many shocks that drive
exchange rates are not macroeconomic in nature. 1
My argument is quite simple. Suppose that we treat
Germany as the domestic country. Exchange rates of
various OECD countries have significantly different exchange rate regimes vis-a-vis Germany. In particular, the
countries that participate in the Exchange Rate Mechanism
(ERM) of the European Monetary System (EMS), like
Belgium, France, and the Netherlands, have relatively fixed
exchange rates with Germany. On the other hand, a number
of other countries, like Canada, Japan, and the United
States have exchange rates which float relatively freely visa-vis Germany. Thus exchange rate volatility differs significantly by partner country. However, this is not true of
macroeconomic variables. Most OECD countries have
quite similar macroeconomic volatility: Germany's macroeconomic volatility vis-a-vis the ERM countries is not
significantly different from Germany's macroeconomic
volatility vis-a-vis the floating-rate countries. This fact has
implicitly been noticed before in, e.g., Baxter and Stockman (1989). Flood and Rose (1993) use a similar logic, but
compare individual countries over time rather than different countries across the same interval of time.
1. Sometimes of overwhelming importance, for instance, during hyperinflations.
20
FRBSF ECONOMIC
REVIEW
1994,
NUMBER
1
Most countries manage their exchange rates in some
way. But if macroeconomic variables do not account for
much exchange rate volatility, then adjusting macroeconomic policies probably will not change the stability of
exchange rates much. Thus the purpose of this paper is to
understand the determinants of exchange rates better, and
thereby allow policymakers to devise more effective tools
to manage exchange rates. I am also interested in whether
there appears to be an identifiable tradeoff between macroeconomic stability and exchange rate volatility.
The next section lays out the theoretical analysis; the
data are then presented in Section III. The actual empirical
results are presented in Section IV, which is followed by a
brief conclusion.
II.
THEORY
The theoretical model I use is the simplest possible macroeconomic model of the exchange rate; it is a monetary
model with flexible prices. I choose this model for two
reasons. First, it is frequently used by economists. Second,
it is also extremely simple to manipulate and understand.
However, I will show explicitly that the lessons one can
learn from the simple moneta..)' model generalize in a very
natural way to a much broader class of macroeconomic
models of the exchange rate. Thus one should think of the
monetary model as a paradigm rather than as a literal
description of reality.
I assume that domestic residents are allowed to hold
three assets: domestic money, domestic bonds, and foreign
bonds. Money is held to finance domestic (consumption)
transactions; money demand depends negatively on the
domestic interest rate, and positively on output. I assume
for simplicity that the money demand function is linear in
natural logarithms (except for the interest rate). The equation that describes equilibrium in the domestic money
market is thus:
(1)
where mt denotes the (natural logarithm of the) stock of
money at time t, p denotes the price level, y denotes real
income, i denotes the (level of the) nominal interest rate,
and E denotes a shock to money demand. It is important to
note that the equation is explicitly stochastic. Indeed, I
need not assume that E is observable or particularly "wellbehaved"; it need not have a mean of zero, nor be either
independent or identically distributed over time, so long as
it is stationary. It is worth noting explicitly that ex is
modeled as a structural parameter (as is 13).
For simplicity, I assume that there is a comparable
equation for the foreign country, and that domestic and
foreign elasticities are equal:
(1')
m*t - p*
y * - OLi*t
t = Q.I-'t
+
E*t '
where an asterisk denotes a foreign variable. Subtracting
(1') from (1) and rearranging yields:
(2)
(P - P*)t = ex(i - i*\ + (m - m*)t - f3(y - Y*)t
- (E-E*\.
I next assume that goods prices are perfectly flexible in
both countries. While admittedly unrealistic, this turns out
to be a useful simplifying assumption; nothing of substance
hinges on this postulate in the argument that follows. I will
discuss informally the impact of loosening this assumption
later on; Flood and Rose (1993) deal with this matter more
rigorously.
I also assume that there are no large barriers to international trade, either natural (e.g., transportation costs or
differences in natural preferences) or artificial (e. g., tariffs
or other barriers to trade). That is, I assume that purchasing
power parity holds, at least up to a disturbance term:
(3)
(P - P*)t = et
+
vt '
where e denotes the domestic price of a unit of foreign
exchange, and v is a stationa..ry disturbance from purchasing power parity, assumed to be "small" in a sense that
will be defined more precisely below.
Substituting this equation into (2), it is trivial to solve for
the exchange rate:
et
= ex(i-i*)t + (m-m*\ - f3(y-Y*)t - (E-E*)t -
Vt
or
(4)
e t - ex(i-i*)t = (m-m*)t - f3(Y-Y*)t
- (E-E*)t - v t •
It is important to note that this equation is structural, and
does not rely on important exogeneity assumptions (e. g. ,
about the nature of the output, the exchange rate regime, or
the sources of E shocks). (The reason for combining exchange and interest rates on the left-hand side of (4) will be
rationalized explicitly below.)
Domestic and foreign bonds are assumed to be perfect
substitutes vis-a-vis risk, liquidity, tax treatment, and so
forth. It will sometimes be convenient to assume that
agents are risk-neutral and have rational expectations so
that uncovered interest parity (VIP) holds:
(5)
(i - i*)t
= Eldet)ldt ,
where Eldet)ldt is the expected rate of change of the
exchange rate. However, none of the analysis I present
relies on VIP. Below, I discuss the impact of allowing for
deviations from VIP, which are well-known to be important empirically.
By substituting (5) into (4), the "flexible-price monetary
model" can be written:
ROSEl ARE EXCHANGE RATES MACROECONOMIC PHENOMENA?
(6)
et - aE/det)ldt =
it == (m-m*)t
- f3(Y-Y*)t
- (E-E*)t - v t '
where it denotes the "fundamental determinant" of the
exchange rate. 2
The objective of this paper is to investigate the fundamental determinants of exchange rates. I consider two different approaches to measuring fundamentals empirically.
In the flexible-price model, fundamentals are traditionally defined as: .
(7)
TF t == (m-m*)t - f3(y-Y*)t - (E-E*)t·
Fundamentals in the monetary model of exchange rates
with flexible prices are typically defined as TF (although
sometimes the E terms are set to zero); hence I call this
measure "traditional fundamentals," denoted TF. This
variable can be measured with data on money, income,
shocks to monetary equilibrium, and the parameter f3.
TF differs from the right-hand side of (6) by v. Thus
traditional fundamentals are equal to the right-hand side of
(6) under the assumption that deviations to purchasing
power parity are identically zero. Under the more realistic
assumption that such shocks are negligible in the sense that
their conditional volatility is low compared to the conditional volatility of TF, the latter differs from the right-hand
side by the measurement error v.
Traditional fundamentals represent the right-hand side
of equation (4). However, the left-hand side can also be
measured directly. Thus, a different measure of fundamentals is:
(8)
VF t == et - aU - i*)t.
VF denotes "virtual fundamentals."
It was not necessary to make the assumption of uncovered interest parity in deriving (8). However, if UIP
holds, then virtual fundamentals can be used as an empiric~l measure of "fundamentals" f in the context of any
sIngle-factor exchange rate model, as is apparent in (6).
Thus the hypothesis of UIP explains the functional form of
virtual (and traditional) fundamentals, but is not a requisite
component of the analysis.
Virtual fundamentals and the exchange rate will be
high~y correlated if either a is small or the volatility of
the Interest differential is low (or both). Virtual (like
traditional) fundamentals are observable; one only needs
data on exchange rates, interest rates, and a choice of the
a parameter. Virtual fundamentals, in contrast to traditional fundamentals, use highwfrequency asset-market data
2. In many empirical exercises, the E shocks are assumed to be zero
E,(de,)ldt is measured, and then various moments of the exchange rat~
are c.ompared with those of fundamentals and E,(de,)1dt; Meese (1990)
proVIdes references. Here, I eschew explicit measurement of E,(de,)ldt.
21
(rather than coarser-frequency macroeconomic data). Howthe two sets of fundamentals should behave similarly
if the model describes reality "well."
If equation (4) holds exactly, then (7) and (8) are two
different ways of measuring the same latent variable,
namely, exchange rate fundamentals f More gel1erally, if
the monetary model with flexible prices describes the actual
data well, virtual and traditional fundamentals should have
similar characteristics. Conversely, if virtual and traditional fundamentals are strikingly different, then this fact
is strong evidence against the underlying model. Both
virtual and traditional fundamentals are model-based, use
r~w economic data, and rely solely on the structural equation (4).
Much of the analysis that follows hinges on comparing
characteristics of VF and TF. A particularly interesting
characteristic to compare is conditional volatility; I use the
standard deviation of the first difference of TF and VF. This
statistic is a good choice for a few reasons. First, it is intrinsically interesting to policymakers concerned with exchange rate volatility. Second, as Meese (1990) shows,
conditional volatility has proven to be difficult to explain
with current exchange rate models. Third, it allows me to
avoid various statistical issues associated with the potential
nonstationarity of fundamentals. Finally, conditional volatility varies in an interesting and systematic way across
countries with different exchange rate regimes and different ~easures of fundamentals. In particular, the volatility
of Virtual fundamentals differs systematically across curre~cies; unsurprisingly, fixed exchange rates have systematically lower conditional exchange rate volatility than
more ~~xible rates. However, the conditional volatility
of traditIOnal fundamentals is, broadly speaking, similar
across countries.
It is important to note in passing that my use of the term
"fundamental" should not be taken to mean "exogenous,"
and I will certainly not assume that fundamentals are
exogenous in the empirical work which follows. (This
should be clear, since the empirical results of the paper
s.tem from comparing measurements of both sides of equation (4), a structural equation.) The logic of the monetary
model indicates that if the exchange rate is fixed perfectly,
the money supply is endogenous; traditional fundamentals
could only conceivably be exogenous for a country with
perfectly freely floating exchange rates. Since most exchange rates are managed in some way, it would be wholly
unreasonable (in the context of this theoretical model) to
claim that fundamentals are exogenous. It is also unnecessary for me to assume that the exchange rate regime itself is
exogenous.
~ver,
22
ill.
FRBSF ECONOMIC REVIEW
1994,
NUMBER
1
THE DATA SET
My empirical work focuses on bilateral German Deutschemark exchange rates from 1960 through 1992 inclusive. I
choose this sample because I am interested in comparing
exchange rates and their fundamental determinants during
a recent and interesting period; this period also happens to
be one with a relatively high level of capital mobility. The
fact that the sample includes regimes of both fixed and
floating rates will also turn to be advantageous. Germany
is chosen to be the home country since the Deutschemark is
an important currency which has been the core of the fixedrate ERM (and earlier of the "Snake"), while simultaneously floating against currencies like the yen and the U.S.
dollar.
The data set is quarterly, and was extracted from the
IMF's International Financial Statistics CD-ROM; it has
been checked and corrected for transcription and rebasing
errors. Since Germany is considered to be the domestic
country, exchange rates are measured as the Deutschemark
(DM) price of one unit of foreign exchange. The consumer
price index is used to measure prices; short-term money
market rates are used for interest rates (except in the cases
of Canada, Sweden, and the U.K., where Treasury bill
interest rates are used so as to maximize sample availability). All the series are transformed by natural logarithms, except for interest rates; the latter are annualized
and measured as nominal rates divided by 100 so that e.g.,
an interest rate of 8 percent is used as .08. I consider eight
industrial countries (above and beyond Germany): Belgium (which maintains a currency union with Luxembourg), Canada, France, Japan, the Netherlands, Sweden,
the United Kingdom, and the United States. 3
Time series graphs of the raw exchange rate data (not
transformed by logarithms) are presented in Figure 1. I note
that the nominal exchange rates are obviously quite stable
during the Bretton Woods era. However, volatility during
the period after the collapse of Bretton Woods in 1973 is
currency-specific; ERM currencies are observably less
turbulent than more freely floating currencies such as the
dollar and the yen, at least vis-a-vis the DM.
I~ EMPIRICAL RESULTS
In this part of the paper, I construct both virtual and traditional fundamentals for eight different countries, throughout using Germany as the base country. I then compare
3. My STATA 3.0 programs and data set are available upon receipt of
one formated high-density 3.5" diskette along with a self-addressed
stamped envelope.
the different proxies for fundamentals. One key conclusion emerges; the volatility of virtual fundamentals differs
widely across countries, but the volatility of traditional
fundamentals does not. Throughout, I attempt to show that
this key result is relatively insensitive, for instance, with
respect to reasonable perturbations in the parameters, or to
the exact form of the structural equations such as the asset
market equilibrium condition.
I begin by considering virtual fundamentals.
Virtual Fundamentals
Virtual fundamentals are the left-hand side of equation (4),
and are defined as VFt=[e t - a(i - i*)tl. Given that exchange rates and interest rates are observable, the construction of virtual fundamentals requires only one piece of
nonobservable information, namely, a.
The literature indicates that a, the interest semielasticity of money demand, is likely to be a small number
(see, e.g., the discussion in Flood et al. (1991». I believe
that a value of a = O. 1 is reasonable, and that a = I is excessively high. While I believe that a = 0.5 is implausibly
high, I pick it as the default value so as to make the case
under adverse conditions (lower, more realistic, values of
a will typically strengthen the argument of the paper, since
VF trivially converges to e as a shrinks). However, it turns
out that the main results do not really depend on a that
much; even a values of substantially greater than unity
deliver the main point. This robustness will be demonstrated directly with sensitivity analysis. 4
Figure 2 is a series of time series plots of the levels of
virtual fundamentals for all eight countries, using the
default value of a =.5 and the entire sample period.
(Analogues for my preferred value a = 0.1 lead to similar
conclusions.) As in Figure 1, the scales of Figure 2 vary by
country. Clearly, the plots are related and similar to those of
the level of the exchange rate presented in Figure 1. Thus,
the series are all relatively stable during the Bretton Woods
era of fixed exchange rates and more volatile after 1973 for
countries that float freely against the DM. However, ERM
4. I have attempted to estimate ex directly. I derive the estimating
equation by using VIP and taking first-differences: Jle,= exJl(i - i*),
+ TJ" where the fundamental process is given byIt = It-I + TJ, and TJ is a
well-behaved disturbance term (white noise if It is a random walk).
To estimate this equation, I use IV, using three lags of both Jle and
Jl(i - i*) as instrumental variables. The results are poor in the sense that
& is usually imprecisely estimated, usually with a negative point
estimate. (While I doubt that the instrumental variables are highly
correlated with the regressor, OLS delivers similar results.) I have also
tried to estimate ex directly through various money demand equations
with similarly poor results; ex typically turns out to be small and
insignificant, often negative.
ROSEl ARE EXCHANGE RATES MACROECONOMIC PHENOMENA?
FIGURE 1
DM PRICE OF FOREIGN EXCHANGE
5
.09
.B~
.OB
.07
.5
.05
.4
.05
1950.1
.2
1
1992.4
1.: ~.
'~
1950.1
1992.4
1992.4
1960.1
1992.<1
France
Canada
Belgium
.9
1960.1
:~~; ~~
.01
.008
.006 1,--~~-~-~
1950.1
1992.4
Sweden
Japan
Holland
.2 1,-------~
1960.2
1992.4
15
01,--~-_~-~
1950.1
1992.4
1
1960.1
UK
1992.4
USA
Scales vary by country
FIGURE 2
VIRTUAL
DM FUNDAMENTALS
o
-2.4
-.5~
-1
~
o
1,--~~-~-~
1960.1
.~ ~
~
1992.4
=::~y
UK
-.5
-1
-4.8
-5 1,--~~-~-~
1960.1
1992.4
o
1..,--~~-~-~
1950.1
- 1. 5 '-r--------~
1950.2
1992.4
Sweden
Japan
1992.4
o
-4.6
Holland
1960.1
- 1. 5 1,--~-~~-~
1960.1
1992.4
France
Canada
Belgium
-.1
1960.1
1992.4
1992.4
USA
Alpha=.5: Scales vary by country
23
24
FRBSF ECONOMIC
REVIEW
1994,
NUMBER
1
participants have more stable virtual fundamentals; for
instance, Holland, which has pursued a policy of pegging
rigorously to the DM, has a very stable virtual fundamental. That is, the graphs show a striking phenomenon which
is central to this paper, namely that the volatility ofvirtual
fundamentals is much higher for floating currencies than
for currencies that arefixed. This result does not depend on
the exact choice of a.
Traditional Fundamentals
I now consider the right-hand side of equation (4), Le.,
traditional fundamentals, defined to be: TFt==[(m - m*)t13(Y -Y*)t - (e - e *)tl.
At first glance, it appears to be difficult to produce
empirical measures of traditional fundamentals. While
money and income are readily observable, one needs an
estimate of 13, the income elasticity of money demand.
Money demand functions are notoriously unstable and
unreliable, making 13 a difficult parameter to estimate with
any sense of reliability. For the same reason, the e terms,
which represent shocks to money demand, are an additional source of difficulty in measuring traditional fundamentals precisely.
Nevertheless, it turns out that for simple money demand
functions, the only additional information that is actually
required to build traditional fundamentals is a measure of
prices. This can be seen by considering a linear regression
of the differential form ofthe money demand function (i.e.,
the difference between domestic and foreign money demand functions, (1) - (I')):
(9)
(m - m*\ - (p - P*)t =
=
>
13(Y - y*\ + (e-e*)t
a(i - i*)t
(e. - e*)t == [em - m*)t - (P - p*)tl
A
- [13(Y - Y*)t
- &(i - i*)tl·
Recall
(7)
TF t == (m - m*\ -
= > Tit
=
13(Y - Y*)t -
(e - e*)t
(m-m*)t - ~(y-Y*)t
- {[em - m*)t - (P - p*)tl
- [~(y-y*\ - &(i-i*)tH
(10)
=
> Tit
= (P - P*)t - &(i - i*)t .
It might be objected that a simple static (differential)
money demand function such as (9) is likely to fit the data
extremely poorly. While this point is surely true, my
interest in (9) is peripheral, since I am most interested in
the conditional innovations of the traditional fundamentals. Including extra lagged terms in (9), which would
improve the fit of the money demand model, will not
change the conditional volatility of traditional fundamentals. Thus the levels ofTF are less interesting to me than its
first difference.
Time series plots of the levels of TF are presented in
Figure 3; again the scales are country-specific. There are
some differences across countries in TF volatility, and also
differences for a given country between periods of fixed
and floating rates. However, these differences tend to be
relatively small and subtle. Thus, in contrast with virtual
fundamentals, the' volatility of traditional fundamentals
does not vary dramatically across countries. This conclusion also does not depend on the exact value of a chosen.
Comparing Alternative Measures
of Fundamentals
I now compare virtual and traditional fundamentals for the
flexible-price monetary model.
While Figures 2 and 3 can be used to compare virtual
and traditional fundamentals informally, they are somewhat unhelpful in a number of respects. First, the scales on
the "small multiple" graphics vary by country. Second,
they do not emphasize the object of greatest interest,
namely, the conditional innovations in fundamentals. This
is especially important, given the issue of dynamic specification of the money-demand function which was discussed
in the previous subsection. Finally, the distinctive properties of VF and TF can be easily emphasized by a close
examination of an interesting subsample, namely, the period since the first quarter of 1979. This sample corresponds to the effective lifetime of the European Monetary
System (EMS).
Figures 4 and 5 are analogues to Figures 2 and 3 in that
they are respectively time series plots of virtual and traditional fundamentals for the eight countries. However,
Figures 4 and 5 have three different features from Figures 2
and 3: (1) scales are comparable across countries within a
figure (though still not across figures); (2) the sample is
restricted to the period since the beginning of the EMS; and
(3) the first differences (rather than the levels) are plotted.
If fundamentals follow a random walk, then the firstdifference is also the innovation. 5 Incorporating these
features makes it much easier to compare traditional and
virtual fundamentals.
5. The hypothesis that both virtual fundamentals and traditional fundamentals contain a unit root cannot typically be rejected at conventional
significance levels. However, some mean reversion undoubtedly exists,
especially at lower frequencies. This issue is addressed more closely by
Mark (1992) and Chinn and Meese (1993).
ROSEl ARE EXCHANGE RATES MACROECONOMIC PHENOMENA?
FIGURE 3
TRADITIONAL
DM FUNDAMENTALS
.6
:~
1960.1
'4~
.2
o
-.2
1960.1
1992.4
1992.4
:~
1960.1
Canada
Belgium
.~~
1960.1
France
::~
.2
o
-.2
1992.4
"S--::--,-.,-~~-,...",--=-=-~
1960.1
Holland
1992.4
1992.4
,Japan
1
.5
o
-.T9':c6~0"".2 ::-----19-9-2-.~4
Sweden
:~
-.r
9'='6--::-0-.1~-~-1""'9"--9=-2=-.~4
-.2 ':r:--~~-~:-:-~
1960.1
1992.4
UK
USA
Alpha=.5: Scales vary by country
FIGURE 4
CHANGE IN VIRTUAL
DM FUNDAMENTALS
.2
.2
.1
o~
-.1
-.2
1...,-------,--~
1979.1
1992.4
_.~ ,vv
-.2
~,.....----
1....,-------~
1979.1
1992.4
.~
1992.4
'v
~
A. Jvv.M A/'-, !A I
"I vV' \j"'J
yv
,Japan
I
fJ'\. IN
VV
v
\
1....,-------~
1979.1
UK
1992.-'1
-·19:':;7T;:.9=-.1;--------,-,19:::-:9:::-:2::-.'4
.~~
'-r-------~
1979.1
.1
o
-.1
-'1 9'=7T;:.9-.1;-----1,...,9::-:9::-:2=-.~4
Sweden
-.1
-.2
o~
-.1
France
.2
.~ ~t!\ MrvJ\
.1
.2
- . ~ 9'=7:r=9=-.1.,-----1,...,9::-:9::-:2=-.~4
Holland
.2
-.2
1...,-------~
1979.1
-.1
-.1
-.1
.AflA,
r \IV' W\AJ
vv
.2
.1
-.2
l.n'I\t\h
Canada
Belgium
.2
o
.1
.2
1992.4
USA
Alpha=.5: EMS PerlOd
25
26
FRBSF ECONOMIC
REVIEW
1994,
NUMBER
1
FIGURE 5
CHANGE IN TRADITIONAL
DM FUNDAMENTALS
.04
.04
.0Ll
.O~ AAL .
.O~
.02
nAflr\/\M
_.02vV~'VIf'NVvvvv .
-.OLl
1979.1
1992.4
-.02
..A
II.
r-AA/\
,-.JJlf\
Vy'f"V"
rJ
V~
-.04 ':::o------~
197'9.1
1992.4
Canada
Belgium
France
.0Ll
.04
.O~~
.O~~
-.02
.04
~~
1992.4
-.04 "'--r----~-~
1979.1
1992.LI
Japan
Holland
'O~~
-.02
-.02
- .0Ll ..'=:----,--1979.1
o
-.02
-.04
1979.1
1992.4
Sweden
.04
.0Ll
_::~ \WrA~nrMM~f!
r
-OLI
IV
1979.1
UK
I'
1992.4
-:~~
-.04 '::r:---------:c--,-----~
1979.1
1992.<1
USA
Alpha=.5: EMS PerIod
A number of points emerge from Figures 4 and 5. First,
Figure 4 clearly shows that the volatility of virtual fundamentals differs systematically and strongly by country. The
three ERM members (Belgium, France, and especially
Holland) have very stable virtual fundamentals. They stand
in sharp contrast to countries with floating exchange rates
like Japan and the United States. The differences in conditional volatility are statistically as well as economically
significant. The actual sample standard deviation estimates
of the first differences of virtual (and traditional) fundamentals are tabulated for three different values of a in
Table 1. The statistics verify that the hypothesis of different
levels of volatility can be confirmed at any reasonable level
of statistical confidence.
Second, by way of contrast with Figure 4, the time series
evidence in Figure 5, which portrays the first differences in
traditional fundamentals, is not radically different across
country. The actual sample statistics (again tabulated in
Table I for three different values of a) confirm the presence
of nontrivial differences in conditional volatility. However,
the TF standard deviations are of the same order of
magnitude for all eight countries considered, in contrast
with the wild differences in VF volatility.
This point is perhaps easier to see in Figure 6, which is a
graphical representation of some of the information pre-
sented in Table 1. The height of the bars measures the
sample standard deviation of the first difference of fundamentals; two different values of a (.1 and 1.) are used for
both traditional and virtual fundamentals. Figure 6 also
emphasizes another interesting point; the typical measure
of TF volatility is much lower than most comparable
measures of VF volatility, (though there are obviously
important differences across countries).
Perhaps the most striking presentation of the evidence is
Figure 7, a simple scatterplot of TF volatility (on the
ordinate) against VF volatility. The benchmark value of
a = 0.5 is used; the sample standard deviations for the
EMS period are marked by the country name (the Canadian and U.S. observations overlap at the extreme righthand side of the graph).
To summarize, there is overwhelming evidence that the
volatility of virtual fundamentals for floating currencies is
significantly higher than that for fixed currencies. However, this is by no means clear for traditional macroeconomic fundamentals; for reasonable parameter values,
there is no substantial difference in volatility across countries with different exchange rate regimes.
ROSE /
ARE EXCHANGE RATES
MACROECONOMIC PHENOMENA?
27
TABLE 1
FUNDAMENTAL VOLATILITY DURING
EMS
(SAMPLE STANDARD DEVIATIONS OF FIRST-DIFFERENCE)
e
Alpha
Belgium
Canada
France
Holland
Japan
Sweden
UK
US
.013
.055
.014
.005
.048
.035
.045
.056
.1
.006
.007
.010
.006
.007
.010
.012
.007
TF
.5
.008
.009
.010
.007
.008
.012
.014
.009
1
.012
.014
.012
.009
.011
.019
.017
.015
.1
.013
.055
.014
.005
.048
.036
.044
.056
VF
.5
.013
.056
.014
.006
.048
.037
.043
.058
1
.014
.057
.016
.008
.047
.040
.042
.060
TF, == [(m-m*), - f3(Y-Y*), - (E -E*),J == [(P - p*), - cx(i-i*),J; VF, == [e, - cx(i - i*),J; Germany is the home country.
FIGURE 6
VOLATILITY OF FUNDAMENTALS
Standard Deviation of First-Difference of Fundamentals
EMS Period: 1979:2-1992:<1
.05
.05
.0Ll
.0Ll
.02
.02
CSelQium France
USA
Japan
UK
Canada Holland Sweden
USA
Tradi tional, Alpha= 1.
Sensitivity Analysis
In this subsection, I show that the most important results of
the empirical analysis are robust in the sense that a variety
of perturbations in my basic methodology lead to the same
conclusions.
Clearly u, the interest semi-elasticity of money demand,
plays a critical role in the paper. The conclusion that VF
volatility varies significantly more than TF volatility is
consistent with a wide range of values for u.
Dealing with deviations from uncovered interest parity
is only slightly more difficult. Under a strict interpretation
of the monetary model, interest rates enter equation (4)
because they affect money demand. Since the empirical
work presented above merely compares measures of both
sides of equation (4), UIP need not be assumed; hence
28
FRBSF ECONOMIC REVIEW 1994,
NUMBER
1
FIGURE 7
TRADITIONAL AGAINST VIRTUAL VOLATILITY
Standard Deviation of First-Difference of Fundamentals
EMS Period: 1979:2-1992:4
.0"1
.......
a
>
Lfl
.......
+-'
.02
UK
Sweden
France
Holland
Japan
Belgium
o
I
o
I
.02
deviations from VIP have no impact on the analysis. 6 This
seems especially reasonable since interest differentials
enter the empirical measures of VF and TF symmetrically.
I have already discussed the impact of lagged terms in
the money demand function; since the analysis relies on the
conditional volatility of fundamentals, the impact of such
dynamics is negligible. Still, this is part of a more general
issue, namely misspecification of the asset market equilibrium condition, i.e., equation (4). The form of misspecification of greatest concern is omitted variable bias;
that is, the fact that important variables that affect monetary equilibrium have potentially been omitted from the
right-hand side of (4), causing the latter term to have insufficiently different conditional volatility across countries.
There are two important points of relevance. First, it was
not assumed that the money demand function worked
perfectly in equation (1); indeed, the equation need not
6. It is possible to interpret the left-hand side of equation (4) more
generally. If one assumes DIP, then virtual fundamentals measure any
single-factor model of the exchange rate. Correspondingly, if DIP holds
up to a (possibly time-varying) risk premium, then virtual fundamentals
measure this factor, plus the risk premium. So long as risk premia do not
vary dramatically by country, such DIP deviations cannot account for the
dramatic variation of VF volatility.
I
.0"1
Alpha=.5
I
.06
even hold particularly well. Nontrivial deviations from
money market equilibrium were incorporated into the E.
terms; it may be recalled that there was no need to assume
that these were particularly well-behaved. Specification
errors in the money demand function can be dealt with in
exactly the same fashion.
However, it turns out that there is no need to bury the
issue by an appeal to the very general nature ofthe E. terms.
Perhaps of greater importance is the fact that explicit
inclusion of extra terms on the right-hand side of equation
(4) will fundamentally change results only if the conditional volatility of these variables varies significantly
across countries.? However, it is exceedingly difficult to
find macroeconomic variables with conditional volatility
that vary across countries as much as that of virtual fundamentals, let alone in the same way. Expressed differently,
almost no macroeconomic variables have conditional volatility that varies by exchange rate regime. For instance,
Figure 8 is an analogue to Figure 6, but instead portrays
country-specific standard deviations of the first difference
of three different macroeconomic variables: the ratio of
7. Implicitly, in a way that is correlated with the country-specific
differences in conditional VF volatility.
ROSE /
ARE EXCHANGE RATES MACROECONOMIC PHENOMENA?
29
FIGURE 8
VOLATILITY COMPARISONS: DIFFERENTIALS VIS-A.-VIS GERMANY
Standard Deviation of First-Difference of Fundamentals
EMS Period: 1979:2-1992:4
., i
f:'J Hscel
f:3
,1
.05
rtI0nl!'tBry
lO0OI
.05
ranee
FIscal Oeilclt/GOP
.,
.,
.05
.05
£::3
ano
Japan
UK
I!!'VO]
ranee
Log 01 Real GOP
the fiscal deficit to nominal GDP; the log of real GDP;
and the log of narrow money (Ml). (All three variables
are displayed in differential form, so that the statistics are
actually the sample standard deviation of, e.g., the first
difference of the difference between the logs of German
and domestic money. Also, the Swedish fiscal and Canadian real output data are missing.) Compared with the
log of the exchange rate (which is also presented in Figure 8 and has dramatically different volatility by country),
macroeconomic variables are just too similar to explain
country-specific VF volatility. For this reason, it is not
necessary to interpret the empirical work strictly within the
confines of the monetary model with flexible prices, since
plausible extensions that incorporate extra macroeconomic
variables are unlikely to change the key conclusion of
the paper. For instance, Flood and Rose (1993) replace the
assumption of purchasing power parity with a sticky-price
analogue (consisting of aggregate demand and Phillipscurves relationships) and show that extra terms must then
be included in traditional fundamentals. However, inclusion of such terms leads to identical conclusions.
Succinctly, exchange rate volatility varies dramatically
by country; macroeconomic volatility does not. For this
reason it is hard to imagine that macroeconomic factors are
very important determinants of exchange rates.
Ho
Log oi Money Supply
Ho
ana
Japan
Swecen
UK
U A
Log of Exchange Rate
V.
CONCLUSION
Expensive institutions such as the International Monetary
Fund and the European Monetary System have been developed to combat exchange rate volatility; the latter is
manifestly perceived by governments as being costly. Most
developing and many developed countries in the world
manage their exchange rates in some way, at least in part to
reduce exchange rate volatility. These policy actions appear to have been at least partially successful; conditional
exchange rate volatility varies strongly and systematically
across countries. However, macroeconomic volatility does
not vary nearly as dramatically. This brute stylized fact
leads me to two policy conclusions and one puzzle.
First, countries concerned with "excessively high" exchange rate volatility should not look to macroeconomic
conditions, at least not exclusively. This follows from the
core conjecture of th~paper, namely, that macroeconomic
factors are not very important determinants of exchange
rates. Empirically, this hypothesis finds a great deal of
support in the data.
The second conclusion is that exchange rate stability
need not come at the cost of macroeconomic instability.
30
FRBSF ECONOMIC REVIEW 1994, NUMBER 1
This should be obvious simply from Figure 8; countries
(like France and the U. K.) that are apparently quite similar
in terms of macroeconomic volatility vis-a.-vis Germany
have dramatically different levels of exchange rate instability. Expressed alternatively, countries that have reduced their level of exchange rate volatility (such as
Holland) do not appear to have paid a price in terms of
macroeconomic volatility. If there are costs to reduced
exchange rate volatility, they do not appear to be macroeconomic. This line of reasoning strengthens the case for
fixed exchange rates, since low exchange rate volatility is
manifestly a policy objective for many countries.
The remaining puzzle is, of course, "what can explain
exchange rate volatility?" Unfortunately, there does not
currently appear to be a good answer to this question. The
empirical analysis has been shown to be relatively insensitive to a number of perturbations; it is hard to imagine that
any set of macroeconomic variables has the characteristics
necessary to explain exchange rate volatility. I am driven
to the conclusion that much exchange rate volatility may
be caused by microeconomic phenomena, such as noise
traders and excessive speculation. However, this is just an
unsubstantiated conjecture, which must be pursued further
in future research. In the meanwhile, the determinants of
exchange rate volatility remain an enigma.
For at least a decade it has been known that models of
exchange rates work poorly in floating exchange rate
regimes. This has led most economists to conclude that
there may be an important variable (or set of variables)
omitted from standard models. For instance, Meese (1990,
p. 132) states: "It remains an enigma why the current
exchange rate regime has engendered a time-series data
base where macroeconomic variables and exchange rates
appear to be independent of one another. One possible
explanation is that economists have not yet discovered the
appropriate set of fundamentals . . ." To date, relatively
little progress has been made in identifying such variables.
This paper has argued that the omitted (set of) variable(s)
have an important identifiable characteristic, namely conditional volatility which is specific to the exchange rate
regime. I am unaware of macroeconomic variables which
have these characteristics.
REFERENCES
Baxter, Marianne, and Alan C. Stockman. 1989. "Business Cycles and
the Exchange-Rate System." Journal ofMonetary Economics 23,
pp. 377-400.
Chinn, Menzie D., and Richard A. Meese. 1993. "Banking on Currency Forecasts." Working Paper No. 264. University of California
at Santa Cruz.
Flood, Robert A., and Andrew K. Rose. 1993. "Fixing Exchange
Rates." Discussion Paper No. 163. London School of Economics,
FMG.
_ _ _ _ _ _ _ _ , and Donald 1. Mathieson. 1991. "An Empirical Exploration of Exchange-Rate Target Zones." CarnegieRochester Series on Public Policy 35, pp. 7-66.
Mark, Nelson C. 1992. "Exchange Rates and Fundamentals." Mimeo.
Ohio State Univ.
Meese, Richard A. 1990. "Currency Fluctuations in the Post-Bretton
Woods Era." Journal of Economic Perspectives 4, pp. 117-131.
Stock Prices and Bank Lending Behavior in Japan
I.
Sun Bae Kim and Ramon Moreno
Economists, Federal Reserve Bank of San Francisco. The
authors would like to thank, without otherwise implicating, Elizabeth Laderman, Chan Huh, and Bharat Trehan
for helpful comments. Research assistance by Dung Anh
Nhan and Jacob Pozharny is gratefully acknowledged.
This study attempts to shed light on whether stock price
movements have contributed to recentfluctuations in bank
lending in Japan by examining the historical relationship
between stockprices and bank lending in that country. It is
found that prior to the mid-1980s the relationship between
stock prices and bank lending was weak, but subsequently
strengthened considerably. This coincided with a change
in the regulatory environment that encouraged banking
institutions to pay more attention to their capitalpositions.
Since the late 1980s, fluctuations in stock prices appear to
have made important contributions to fluctuations in bank
lending in Japan.
INTRODUCTION
Japan has experienced unusually sluggish growth in bank
lending in recent years. Following double-digit growth in
the second half of the 1980s, bank lending slackened
markedly as the Japanese economy entered the current economic downswing. Nominal loan growth averaged 3.6 percent annually between February 1991 (when the Economic
Planning Agency's coincident index of business conditions
peaked) and May 1993. In contrast, in the three previous
recessions Japan experienced since 1977, loan growth averaged nearly 11 percent. 1
While the reasons for sluggish credit and money growth
are not yet fully understood, the timing is suggestive: the
credit slowdown followed a steep decline in the Nikkei
stock price index, which more tha..'1 halved in value since
reaching its peak at the end of 1989. 2 Indeed, the impact of
such a steep asset price deflation on the Japanese financial
system and on the real economy recently has been the
subject of serious debate. To shed some light on this
question, this article examines the historical relationship
between movements in the stock price and bank lending in
Japan, and explores whether stock price fluctuations appear to have contributed to explaining recent sluggish loan
growth.
Changes in stock prices may influence bank lending
through two channels. First, stock price fluctuations may
affect loan demand by signaling changes in future economic activity. For example, the decline in the stock price
after 1989 may reflect contractionary influences that lower
loan demand, such as the decline in corporate capital
spending triggered by the slump in final demand, poor
1. In real terms, loan growth fell to 1.2 percent over the same period,
compared to 7.2 percent in the preceding 3 recessions. Note that loan
growth was sluggish even though economic activity picked up for a time
in the first half of 1993. The growth in broad monetary aggregate has
also been sluggish. After expanding at an average annual rate of 11 percent in the late 1980s, nominal M2 + CDs growth slowed to 3.7 percent
in 1991 and to 0.6 percent in 1992. Money growth actually turned
negative during the second half of 1992.
2. After closing at ¥38,915 on the last trading day of 1989, the Nikkei
225 Stock Average bottomed out at ¥14,309 in August 1992. The index
subsequently traded in the ¥18,000-¥20,000 range up to the time this
paper was being completed (November 1993).
32
FRBSF ECONOMIC REVIEW
1994,
NUMBER
1
corporate earnings, and excess capacity. 3 Loan demand in
the recent downturn may have been weakened further by
the need to roll over large amounts of equity-linked bonds
that Japanese firms issued in the late 1980s and by sharp
declines in land prices.
Second, stock price fluctuations may affect loan supply
by affecting the capital position of banks. This second
channel is potentially of greater importance in Japan than,
say, in the U.S., because Japanese banks traditionally have
taken significant positions in the equity as well as debt of
the same firm. 4 Under these conditions, a Japanese bank
may be willing to lend more when Japanese stock prices are
high or rising, and conversely, to lend less when stock
prices are falling, since the bank can use capital gains on
stocks to cushion itself from adverse shocks to assets.
Analysis of these demand and supply factors is complicated in part because it is likely that up to the early to
mid-1980s, Japan's regulatory regime tended to dampen
the relationship between stock prices and lending. Up to
that time bank credit was heavily influenced by Bank of
Japan (BOJ) credit guidelines (or "window guidance"),
which limited the ability of banks to adjust lending in
response to market conditions or their capital positions.
Banks in any case had little incentive to pay attention to
their capital positions. One reason is that the government is
likely to have cushioned banks from adverse shocks that
might be related to government-sanctioned credit. Another
reason is that Japanese banks were not subject to explicit
capital adequacy requirements until the 1980s. Under these
conditions, stock prices would be expected to have little
influence on bank lending.
Two developments in the 1980s are likely to have
strengthened the link between stock prices and lending
in Japan. First, the Bank of Japan deemphasized credit
guidelines and gave Japanese banks more leeway in making loan decisions. The primary role of BOJ lending has
been increasingly geared to very short-term adjustments
in the financial market rather than to serve as a means
to (implicitly) guarantee liquidity in the banking system
(Suzuki 1987).
3. See for example the report by the Institute of Fiscal and Monetary
Policy, Japanese Ministry of Finance (1993) and the Bank of Japan
(1992).
4. Until 1987 the legal limit on corporate equity holding by financial institutions was set at 10 percent of outstanding shares of any single firm.
Since then, the limit was lowered to 5 percent. In 1991, close to 45 percent of the total number of corporate shares outstanding was held by financial institutions; about half of this share is estimated to be held by
banks. In the U.S., where the Glass-Steagall Act strictly separates
commercial and investment banking, corporate shareholding by banks
is virtually nil.
Second, there was growing international concern in the
early 1980s about weak capital positions of banking institutions (Cooke 1984). In particular, partly as a result of
the adoption of more stringent capital guidelines in the
U.S. in 1981 and 1983, Japanese banks that were expanding
their international operations in the 1980s faced pressure to
strengthen their capital positions, so as to ensure that the
Japanese banks faced foreign banks on an even competitive
footing. 5 The concern \vith ha..rmonizing capital adequacy
requirements eventually resulted in the drafting of riskadjusted capital standards in Basle in December 1987.
These were formally adopted by Japan and other industrial
countries in July 1988.
Under the Basle Accord, by 1993 Japanese banks were
to achieve risk-adjusted capital-to-asset ratios of8 percent,
in two tiers. Banks are allowed to count up to 45 percent of
unrealized gains on equity holdings as Tier II capital. Under these rules, it is possible that during the stock market
boom of the second half of the 1980s, rising stock prices
fueled lending to a greater extent than if banks could not
hold corporate shares. The subsequent decline in stock
prices may have put the capital of some Japanese banks
near the regulatory floor, thus constraining their loan
supply. One indicator that this effect may have been
important is the strong contraction in hidden reserves (reflecting unrealized capital gains) of city, long-term credit,
and trust banks, from a combined total of ¥ 55.4 trillion in
March 1989 to ¥14.6 trillion in September 1992 (Japanese
Ministry of Finance 1993).
The possibility appears to be widely recognized that the
Basle capital standards may have strengthened the link
between fluctuations in Japanese stock prices and the
supply of Japanese bank lending in the 19808. For example,
the Japanese Ministry of Finance (1993) points out that as a
result of the Basle standard, broad fluctuations in asset
prices "could have a destabilizing influence on the balance
between fund supply and demand," and that (in the wake
of asset price declines) the Basle standard "could be
making it difficult to expand quantitative lending levels...." Similarly, the Bank of Japan (1992), cites "the
possible negative influence of BIS capital requirements in
the event of any further slide in stock prices" on bank loan
decisions. Since Japanese stock prices began declining, the
financial press has also focused a great deal of attention on
how such declines would affect the ability of banks to meet
their capital requirements under the Basle Accord and the
implications for bank lending behavior. 6
5. See Kareken (1984).
6. From time to time the financial press offers estimates of the approximate level of the Nikkei stock price at which the Basle constraints
KIM AND MORENO / JAPAN:
To examine the relationship between the stock price and
bank lending in Japan, we estimate a small vector autoregression model of the Japanese economy using monthly
data covering two samples: 1970.1-1983.12 and 1984.11992.12. To anticipate the main findings of this paper, we
find that in the first period innovations in stock prices are
followed by positive, but very small increases in bank
lending. In contrast, innovations in the stock price are
followed by relatively large increases in ba.'lk lending in the
second period. In line with this, stock price changes playa
negligible role in explaining fluctuations in bank lending in
the first period, and a much more important role in the
second period. In particular, stock price increases appear
to have contributed to unexpectedly rapid increases in
lending in the late 1980s and to unexpectedly slow growth
in lending in the early 1990s.
These findings are consistent with the shift in the regulatory environment in the 1980s. Prior to the 1980s, banks
attached relatively little importance to the amount of
capital held and government credit guidelines may have
limited their ability to adjust lending fully in response to
shocks to their capital position. Other things equal, this
would have loosened the linkage between stock price and
lending. Growing concern about capital adequacy, eventually formalized in the Basle Accord, changed the rules of
the game, inducing Japanese banks to pay more attention to
their capital position. The unexpectedly steep decline in
stock prices appears to have made this new regulatory
constraint binding, or at least of concern, for the Japanese
banks during the current economic downturn. However,
because of the wide variety of contractionary influences
affecting the Japanese economy, we cannot rule out sluggish demand as a contributor to the marked decline in loan
growth.
This paper is organized as follows. In Section II, we
briefly discuss the possible link between stock price movements and bank lending. We then examine regulatory and
institutional factors in Japan that have affected this linkage
and propose some hypotheses. Section III implements the
empirical analysis, followed by concluding remarks in
Section IV.
become binding. These estimates were particularly prevalent in 1992,
when the Nikkei hit a trough. More recently, an article expresses
concern about recent stock price declines in Japan, which are seen as
" . . . beginning to crimp Japanese banks' ability to lend to business."
(Wall Street Journal, November 16, 1993, p. 1). Nikkei stock price
fluctuations are also believed to have affected the international operations of Japanese banks. See Terrell (1993).
STOCK PRICES AND BANK LENDING
33
II.
THE LINK BETWEEN STOCK PRICE
FLUCTUATIONS AND BANK LENDING
As the mechanism by which fluctuations in stock prices
may affect loan demand is relatively straightforward, we
will focus here on clarifying the possible link between
stock price fluctuations and bank loan supply. To discuss
such a link, it is necessary first to examine the relationship
between bank capital and the supply of bank loans. 7
To serve as a benchmark, the discussion initially abstracts from the role of regulation. We later relax this
assumption and examine how the regulatory and other
institutional environments in Japanese banking may have
strengthened or weakened this capital to loan relationship.
Bank Capital and Lending
The bulk ofassets that intermediaries hold consists ofloans,
each of which pays off only if the borrower's investment
project succeeds. The deposits that banks collect, by contrast, are noncontingent liabilities with a fixed amount of
promised payment, regardless of the outcome of the pro-
jects that the bank finances. An unexpected drop in the value
of its assets, due to, say, borrowers' investment projects
going awry, may thus force the bank into insolvency.
Banks can cushion themselves against such an adverse
shock by maintaining equity capital. Bernanke and Gertler
(1987) present a model where banks ".voluntarily" adjust
their capital-to-asset ratios to control default risk. Their
model assumes that depositors have imperfect information
on the quality of a bank's assets, which precludes the possibility of a payoff to depositors contingent on the return to
the bank's investments. In such a setting, an incentivecompatible contract is for the bank to issue a noncontingent
liability and collateralize it with bank equity capital. Ceteris paribus, a greater amount of capital allows banks to
issue more deposits and to finance riskier investment projects. A similar equilibrium can arise if financial distress or
insolvency is costly to the bank. For example, banks may
hold capital because managers value their reputations,
which would be lost in the event of bank default.
The supply of capital facing banks is not likely to be
perfectly elastic, however. There is a limit, at least in the
short run, to the extent to which capital can be accumulated through retained earnings. Capital market imperfections such as "lemons" or agency problems will also
constrain banks' ability to raise capital through new equity
7. Our discussion abstracts from the demand side of the loan market.
For example, to the extent stock prices reflect expectations on future
corporate perfonnance or economic conditions in general, a decline in
stock price will be associated with a decline in loan demand.
34
FRBSF ECONOMIC REVIEW 1994,
NUMBER
1
issues. 8 Given the imperfectly elastic equity capital then, a
bank's loan supply can be constrained by its capital position. For example, a bank with a low capital-to-assets
ratio-due either to large loan losses or rapid growth in
deposits and loans in the past-may be forced to improve
its capital position by reducing the growth in assets, and
one way to achieve this is to decrease loan growth.
undertake more risk at the expense of depositors. The
incentive problem is exacerbated if banks have access to an
underpriced deposit insurance. 10
Until the second half of the 1980s, Japanese banks were
not subject to explicit capital-asset ratio requirements.
Article 5 of the Banking Law (1981) stipulates a minimum
bank capitalization of ¥1 billion for banks. 11 Although no
liquid asset-to-deposit ratio is imposed· by law, the Minis-
Stock Price Movements
and the Supply ofBank Loans
try of Financepiovided adirtinistrative guidance that in the
Up to this point, we have focused on the ratio of book value
capital to assets as an indicator of bank default risk.
However, the capacity of a bank to absorb adverse shocks
may vary significantly according to its off-balance sheet
characteristics; that is, the market value of the bank's
capital should also be a relevant factor determining bank
risk and hence its loan supply behavior.
To see why, suppose that in addition to risky loans, the
asset side of the bank's balance sheet also includes corporate shares, as is the case in Japan. Changes in the market
value of the bank's shareholding clearly will have a bearing
on its default risk. For example, a bank with substantial
unrealized capital gains on its stockholdings will be able
to write off larger amounts of loan losses by selling
the securities and realizing the gains. By implication,
loan supply will be relatively less constrained by book
capital position for banks with sufficiently large "hidden
reserves."
Conversely, a significant decline in stock prices will
expose the bank to a greater amount of default risk than
would be suggested by book capital position alone. Other
things equal, therefore, we would expect a positive relationship between stock prices and bank lending. 9
Regulatory and Institutional Factors
While theory suggests that capital position should affect
bank loan behavior, the relationship also may be affected
by regulation. A generally accepted view in the U.S. is that
regulation tightens the linkage between bank capital position and lending (Keeley 1988, Bernanke and Lown 1991,
Furlong 1992, Peek and Rosengren 1993). Some view the
tightening of linkage through regulation as necessary because banks, as leveraged enterprises, have an incentive to
first half of the 1980s limited the average ratio of lending to
deposit to below 80 percent, and maintained bank liquidity
ratios above 30 percent. Banks also faced a maximum
lending limit to one borrower: 20 percent of capital and
reserves for city banks and 30 percent for long-term credit
and trust banks. However, none of these provisions, legal
or informal, directed Japanese banks to maintain some
minimum ratio of capital to assets (Hendrie 1986).
In fact, throughout most of the postwar period, the
regulatory and institutional environment in Japan appears
to have worked to loosen rather than tighten the linkage
between banks' capital position and lending. First, the
Japanese financial system sought to minimize defaultrisks
of financial institutions by limiting competition. Under the
so-called "convoy system" governing banking regulation,
the authorities sought to reduce "destructive competition"
and create a stable business environment for banks. To this
end, the domestic financial market was isolated from
foreign competition, and strict controls were applied to
deposit rates, new entry into banking, and separation of
long-term versus short-term finance. 12 Under the convoy
system, all incumbent city banks grew at about the same
pace, earning substantial rents from interest rate spreads
and, tellingly, no financial institution was allowed to fail
throughout the entire postwar period. The implicit socialization of risk is likely to have diluted individual banks'
incentive to control risk and contributed to the low capitalto-asset ratios observed throughout most of the postwar
period.
Second, lending by the BOJ provided a substitute to
bank equity capital as a cushion against shocks to asset
value. In fact, one defining characteristic of the postwar
Japanese financial system is "overloan," which denotes a
chronic tendency of commercial banks to extend more
credit, either by lending or by purchase of securities, than
they acquired from deposits or own capital, with the gap
8. Asquith and Mullins (1986) show, for example, that a finn's stock
price decreases upon announcement of new equity issue, suggesting that
the market discounts a lemons premium.
10. See Furlong, (1992) for further discussion.
9.· For purposes of this discussion, it is assumed that stock price changes
are sufficiently persistent that they may be treated as pennanent.
12. See for example Suzuki (1987) and Aoki, Patrick, and Sheard
(1993).
11. Federation of Bankers Associations of Japan (1989).
KIM
filled primarily by relying on borrowing from the BOJ. As
noted by Suzuki (1987, p. 24) "the policies of allowing
over-loan ... reduced the banks' consciousness of their
own funding position; that is, there was a diminution of
self-reliance by banks because they were not forced to
adjust total credit granted so long as reserves were available from the Bank of Japan. . . ." Third, the dependence
of commercial banks on BOJ credit provided leverage for
the monetary authority to influence the quantity and allocation of loans by banks under the system of window guidance. By constraining banks' lending decisions, window
guidance would have further weakened the link between
bank capital and lending.
Finally, close supervision and prudential control by the
regulatory authorities provided an effective substitute for
bank capital regulation as a means to control the moral
hazard problem in banking discussed earlier. For example,
in the course of conducting window guidance, the BOJ
closely monitored on a daily basis individual banks' operations and fund positions. 13 The Ministry of Finance (MOF)
also played an instrumental role as monitor, especially in
situations when a bank was judged to be mismanaged and
needed drastic organization and asset restructuring. Typically, banks undergoing restructuring would be forced to
accept a retired high-ranking MOF bureaucrat as an executive or even as president. Close monitoring of individual
banks was possible to a greater extent in Japan than would
have been possible in the US. because of the relatively
smaller number of financial institutions. 14
Under the convoy system, Japanese banks pursued a
strategy of aggressively expanding deposits and lending,
paying little heed to capital position (Goldsmith 1983,
Suzuki 1987). For example, throughout most of the rapid
growth period (roughly from the early 1950s to. the early
1970s), the own capital-to-assetratio averaged a little over
5 percent,15 Excluding various reserves, bank capital has
averaged well under 1 percent of total assets since the early
1970s. These ratios are low by international standards. For
example, the average ratio of primary book capital to asset
in the US. was a little under 6.7 percent in the first half of
the 1980s (Keeley 1988). They are also low by Japan's own
historical standard: In the prewar period, bank own capital
AND MORENO / JAPAN: STOCK PRICES AND BANK LENDING
35
was about 20 percent of total liabilities and total capital was
15 percent of liabilities16 (Suzuki 1987, p. 193).
The regulatory environment affecting bank capital and
lending changed in the early 1980s in light of international
concern about the weaker capital positions of, banking
institutions (Cooke, 1984). A particularly significantdevelopment was the concern expressed by US. regulators
about the low capital ratios of Japanese banks expanding in
the U.S. market. For exalnple, in December 1983, the
Federal Reserve Board approved Fuji Bank's application to
acquire a nonbank subsidiary of a bank holding corporation (Walter E. Heller International Corporation) in the
US. However, in its order, the Board observed that Fuji's
reported capital ratio was much less than the 5 percent ratio
that applied to US. banks. The Board also raised "the
general question of whether the capital standards applicable to domestic bank holding companies should also
be applied to foreign banking organizations making ac~
quisitions in the United States ..." (see Kareken 1984,
p.43-46).
The concern with harmonizing capital adequacy requirements eventually resulted in the drafting of riskadjusted capital standards in Basle in December 1987.
These standards were formally adopted in July 1988. The
Basle capital adequacy standard requires that international
banks achieve an overall risk-adjusted capital-asset ratio
equal to at least 8 percent. 17 The Accord provides a role for
both book as well as market value capital. Specifically,·at
least half of the overall 8 percent ratio must consist ofTier I
capital, which includes shareholders' equity and retained
earnings. The balance can be met by Tier II capital, which
can include subordinated debt, preferred shares, and hidden reserves, that is, unrealized gains on.stockholding. To·
allow for its relatively risky nature, banks are allowed
to count only up to 45 percent ofunrealized gains as hidden
reserves.
14. For instance, strict entry restrictions limited the number of city
banks to a maximum 13 since 1953.
16. To be sure, the book value capital to asset ratio would understate the
market value capital to asset ratio to the extent that stock prices have
been appreciating throughout most of the postwar period. However, this
effect is likely to have been significant only towards the second half of
the 1980s, when the regulatory environment had already shifted towards
more stringent capital standards. According to a recent BOJ study
(Shinagawa, 1993), hidden reserves represented over 2Yz times the value
of banks' own capital when the Nikkei stock index reached its peak in
the fall of 1989.
15. Own capital of a bank includes capital, legal reserves (capital
reserves and profit reserves), surplus accounts (voluntary reserves and
undistributed profits), and provisions for payment (reserve for loan loss,
retirement pension payment, etc.).
17. The initial plan for the risk-based capital standards was proposed in
1986 and the Accord itself was reached among the Group ofTen
countries in July 1988. The deadline for Japanese banks was March 31,
1993.
13. See Moreno and Kim (1993) for further details on window guidance
and related procedures.
36
FRBSF ECONOMIC REVIEW
1994, NUMBER 1
Questions for Empirical Analysis
Our review of the institutional features of the Japanese
financial system and the process of regulatory change
poses the following questions for empirical analysis.
First, does Japanese bank lending increase in response to
an increase in the stock price, as predicted by either view of
the relationship between stock price and lending (that stock
price changes affect loan demand or loan supply)? This
question will be addressed by examining the dynamic
response of bank lending to innovations in the stock price.
Second, how significant is the effect of stock prices on
bank lending and has this relationship changed over time?
To address these questions, we proceed in three steps:
(i) we examine the magnitude of impulse responses to unit
shocks in the stock price; (ii) we assess the predictive
ability of stock prices for bank lending according to exclusion restrictions and variance decompositions; (iii) we
compare the magnitude of the response of bank lending to
stock prices and the ability of stock prices to predict
lending (according to exclusion restrictions and variance
decompositions) over the sample periods 1970.1-1983.12
and 1984.1-1993.5.
Third, have fluctuations in Nikkei been important in
explaining specific recent episodes of loan expansion or
contraction? This question will be addressed by performing a historical decomposition of the forecast error in
lending that allows us to determine the sources of loan
fluctuations over the two samples.
ID.
EMPIRICAL ANALYSIS
The Model and Estimation
To address the empirical questions, we estimate a VAR
model for Japan that includes macroeconomic variables that
may be expected to affect lending as well as the Nikkei. The
model may be expressed compactly as follows:
A(L)Zt = ut
where A(L) is a matrix of polynomials in the lag operator, Zt
= [it Yt Pt it St]' in which it = bank loans, Yt = industrial
production, Pt = consumer price index, it = call money
rate, and St = Nikkei stock average, and Ut is a vector
of residuals that may be contemporaneously correlated.
While the primary focus of this paper is the relationship
between the Nikkei stock price and bank lending, the inclusion of industrial production, the consumer price index
and the call money rate is meant to control for cyclical
factors that might affect bank lending.
To identifY orthogonalized innovations in each of the
variables and the dynamic responses to such innovations
we factor the variance-covariance matrix of the VAR using
the Choleski decomposition to obtain the moving average
representation:
Zt
= A(L)-l BB-1 ut =
C(L)E t
where the variables in Zt are entered in the order described
earlier, Et , = [Elf EZt E3t E4t ESt] and E1t to ESt respectively
refer to orthogonalized innovations in bank loans, output,
.....1
•
C'lJ... .............. +0......... ;_... ~ ...
n_rl s.. _nolr --: el"
goouS
pnces,
~l1Vll..-",vl1l1 lULvl\.l13l. la"\.113 allU
LlJ\".J.\.. pJ.H. 13.
This ordering assumes that lending is contemporaneously
unaffected by all the other variables in the system, whereas
the stock price is affected by all these variables.
To estimate the model, data were collected for Japan
over the period 1970.1-1993.5, which spans the years after
Japan's "high growth period." Data and sources are described in the Appendix. The model was estimated over
two subsamples, 1970.1-1983.12 and 1984.1-1993.5. As
there is no reason to expect that any effect stock prices have
on loan demand changed over the full period, the sample
was broken to attempt to see how the changes in Japan's
regulatory environment may have affected the relationship
between stock prices and lending. While the choice of a
date to break the sample is to some extent arbitrary, an
effort was made to pick a date when Japanese banks
became aware that capital adequacy was assuming priority
in the minds of regulators, which would tend to strengthen
the links between stock price changes and total lending.
Plausible dates include 1984.1, the month after the Federal
Reserve Board openly expressed concern about the capital
adequacy of foreign banks in its approval of a Fuji Bank
acquisition in the U. S., 1987.12, when the Basle riskadjusted capital standards agreement was drafted, and
1988.7, when the standards were officially adopted. The
date 1984.1 was selected, as it allows enough degrees of
freedom to strengthen confidence in the results.
Unit root tests provide mixed evidence that the data in
the model are non-stationary over the period 1970.11993.5. 18 To account for such possible non-stationarity,
the VAR model was estimated using the first difference
of the logs of the variables (with the exception of the call
money rate, where the first difference was used). Lag
lengths were set at 9 in the first subsample and 7 in the
second subsample. At these lag lengths, the null hypothesis of residual white noise could not be rejected according
to the Q statistic.
'OC'l ...
.... ",+.OC'
18. Tests for unit roots are performed over the full period 1970.1-1993.5
because they attempt to identify long-run properties of the data that are
not well captured by the smaller subsamples. The Phillips-Perron test (16
lags) fails to reject the unit root null for all the series in levels. However,
the Augmented Dickey-Fuller test (12 lags) rejects the unit root null
for the call money rate at 1% and for industrial production at 5%.
KIM
Dynamic Responses to Shocks
To assess the qualitative responses to shocks, Figure 1
reports the dynamic responses to innovations in the Nikkei
stock price over the two subsamples. As expected, the
response of loans to innovations in the stock price is
positive.
Figure 1reveals that two features distinguish the response
of loans to Nikkei innovations over the two subsamples.
First, the magnitude of the response of loans to Nikkei
innovations is much smaller in the first period than in
the second. Second, the response of loans is temporary
in the first period and permanent in the second. The
smaller response in the first sample is consistent with the
interpretation offered earlier, namely, that the ability of
banks to obtain funding from the BOJ reduced the importance of capital constraints on lending behavior. The transitory nature of the response in the first period suggests that
window guidance may have effectively constrained lending
decisions.
To conserve space, other impulse responses are not
illustrated here. However, to facilitate interpretation of the
historical decomposition later on, it is v/orth surruY}1arizing
some of the responses of lending to innovations in other
variables in the second sample period, when stock price
effects are important. In this period, lending rises permanently in response to its own innovations as well as to
AND MORENO I JAPAN: STOCK PRICES AND BANK LENDING
37
innovations in the Nikkei stock price. Lending falls permanently in response to innovations in the call money rate,
industrial production, and the CPI.
The qualitative responses of lending to innovations in
the Nikkei stock price, lending, or the call money rate do
not clarify whether such responses reflect change-s in loan
demand or loan supply. It is also apparent that the countercyclical response of lending to macroeconomic activity
(industrial production and Cpr) is inconsistent with a
change in loan demand. However, it may reflect changes in
loan supply that in turn reflect monetary policy. This last
interpretation is supported (or at least not contradicted)
by the fact that interest rates also rise (temporarily)
in response to innovations in industrial production and
the CPJ.l9
19. In isolation, the rise in interest rate in response to innovations in
industrial production and the cpr may be interpreted as reflecting
increased demand. Together with a contraction in loan demand, however, it suggests that a countercyclical policy response has taken place. It
is worth stressing, however, that innovations in interest rates or in
aggregates such as lending cannot necessarily be interpreted as innovations in monetary policy over this period. See Moreno and Kim (1993).
FIGUREl
RESPONSE OF LENDING TO INNOVATIONS IN THE STOCK PRICE
LOG
0.018
1970.1 - 1983.12
1984.1 - 1993.5
0.014
0.010
0.006
0.002
8
12
16
20
24
28
32
36
-0.002 -1----.---r---r----,.-,.--,-r---r-;--,
4 8 12 16 20 24 28 32 36
38
FRBSF ECONOMIC REVIEW
1994,
NUMBER
1
1
Exclusion Restrictions
and Variance Decompositions
TABLE
The importance of the various innovations in influencing
lending will be apparent from the tests of predictive ability
and the historical decomposition. 20 Table 1 reports the
marginal significance levels of tests of exclusion restrictions on the lagged variables of the VAR model for the loan
equation and the decomposition of the variance of the
forecast error of lending at various forecast horizons. As
can be seen, according to the exclusion restrictions, the
Nikkei is a poor predictor oflending in the first subsample,
1970.1-1983.12, and a good predictor in the second subsample 1984.1-1993.5. In the second sample, the hypothesis that lagged changes in the Nikkei stock price do not
affect bank lending is rejected at the 1percent level. This is
consistent with our findings that the response of lending to
innovations of the stock price was small and temporary in
the first subsample, and larger and more persistent in the
second sUbsample.
A similar impression is conveyed by the variance decompositions. According to Table 1, at a two-year horizon,
innovations in the stock price accounted for about 1percent
of the variance of the forecast error of lending in the first
sample period, and 28 percent in the second sample. The
success of the stock price as a predictor of loan behavior is
remarkable, because in a four-variable VAR model that
excludes stock prices, lending is predicted largely by its
own lags. Thus, it appears that stock prices have had an
important effect on loan behavior since the mid-1980s.
The VAR methodology used here does not allow us to
determine whether stock prices affect loan supply or loan
demand. However, the stock price exerts an influence on
bank lending after a significant change in the regulatory
regime that placed greater emphasis on the capital position
of banks. This suggests that the effect of changes in the
stock price on Japanese bank lending at least partly reflects
the impact on loan supply. The view that loan supply effects
may have been important is supported by the large magnitude of fluctuations in hidden reserves associated with
fluctuations in stock prices. At the same time, the fact that
stock prices do not predict lending prior to the mid-1980s
suggests that any effects of stock prices on loan demand
have historically been weak. 2I
EQUATIONS AND VARIANCE DECOMPOSITION OF THE
20. The responses of other variables to the stock price suggest that
innovations in the stock price reflect pennanent supply shocks. The
nominal interest rate, industrial production and the stock price rise
pennanently in response to a stock price innovation. The response of the
CPI is small and erratic, initially falling, and then tending to rise.
21. We also ran a similar model for the U.S., where banks do not hold
equity capital and hence any stock price effects would be through loan
TESTS OF EXCLUSION RESTRICTIONS FOR LoAN
FORECAST ERROR IN LENDING
EXCLUSION
RESTRICTIONS
LENDING
INT. RATE
OUTPUT
CPI
NIKKEI
VARIANCE
DECOMPosrrION
70.1-83.12 84.1-93.5
70.1-83.12 84.1-93.5
Horizons (months)
12 24 36
12 24 36
4.0xlO- 8
0.5
0.1
0.7
0.4
91 84 80
1 2 1
4 12 17
0 0 1
4 1 0
6.9 X 10- 8
0.5
4.2x 10-3
2.2x 10-2
9.2X 10-7
57
0
27
11
25
49
1
11
10
28
44
2
15
10
29
NOTE: Totals may not sum to 100 because of rounding.
The Nikkei's Contribution during Episodes
of Loan Expansion and Contraction
To assess the Nikkei's contribution to loan behavior, we use
the estimated coefficients to compute the forecast error in
lending at a two-year horizon. A large forecast error means
that lending was unexpectedly large or small, given the
information available at the time the forecast was being
made. A historical decomposition can be performed (using
the coefficients of the moving average representation ofthe
model) to determine the contribution of (orthogonalized)
innovations in each of the components of the model to this
forecast error. One advantage of this approach is that it
controls for factors other than the Nikkei that may account
for sluggish loan growth, including output.
Figures 2 and 3 report historical decompositions for the
first and second subsamples respectively. (Note that some
observations are lost in setting a 24-month forecast horizon.) Inspection of the figures indicates that in the first
sample, a number of episodes involved relatively large
"surprises" (forecast errors) in lending-positive errors
around the time of the first oil shock and in 1982; and
negative errors in 1975,1977, and 1981. These episodes are
largely attributable to unexpected innovations in lending.
The exception is 1977, when unusually sluggish loan
growth occurred in response to innovations in output. The
Nikkei appeared to make some contribution to the large
positive forecast errors in lending in the early 1970s and the
subsequent contraction, but this contribution was very
small in relative terms.
demand. We found that the stock price has little or no influence on bank
lending. The U.S. evidence therefore suggests that the effects of the
stock price on loan demand are unimportant.
KIM AND MORENO / JAPAN: STOCK PRICES AND BANK LENDING
FIGURE 2
HISTORICAL DECOMPOSITION OF THE FORECAST ERROR IN LENDING
(SAMPLE
1970.1-1983.12)
PORTION CAUSED BY: OUTPUT
FORECAST ERROR (24-MONTHS)
0. 16 1
0.161
0.08
0.08
0.00
0.00
-0.08
-0.08
-0.16
-0.16
72 73 74 75 76 77 78 79 80 81 82 83
72 73 74 75 76 77 78 79 80 81 82 83
PORTION CAUSED BY: CPI
PORTION CAUSED BY: LENDING
0.16
0.16
0.08
0.08
0.00
0.00
-0.08
-0.08
-0.16
-0.16
72 73 74 75 76 77 78 79 80 81 82 83
72 73 74 75 76 77 78 79 80 81 82 83
PORTION CAUSED BY: INTEREST
PORTION CAUSED BY: NIKKEI
0.16
0.16
0.08
0.08
0.00
0.00
-0.08
-0.08
-0.16
-0.16
72 73 74 75 76 77 78 79 80 81 82 83
72 73 74 75 76 77 78 79 80 81 82 83
39
40
FRBSF ECONOMIC REVIEW 1994,
NUMBER
1
FIGURE 3
HISTORICAL DECOMPOSITION OF THE FORECAST ERROR IN LENDING
(SAMPLE
1984.1-1993.12)
FORECAST ERROR (24-MONTHS)
0. 08
PORTION CAUSED BY: OUTPUT
1
0. 08 1
0.04
0.04
0.00
0.00
-0.04
-0.04
-0.08
-0.08
86
87
88
89
90
91
92
93
86
87
PORTION CAUSED BY: LENDING
88
89
90
91
92
93
92
93
92
93
PORTION CAUSED BY: CPI
0.08
0.08
0.04
0.04
0.00
0.00
-0.04
-0.04
-0.08
-0.08
86
87
88
89
90
91
92
93
86
87
PORTION CAUSED BY: INTEREST
88
89
90
91
PORTION CAUSED BY: NIKKEI
0.08
0.08
0.04
0.04
0.00
0.00
-0.04
-0.04
-0.08
-0.08
86
87
88
89
90
91
92
93
86
87
88
89
90
91
KIM AND MORENO / JAPAN:
The second historical decomposition is of more immediate interest, as it helps shed light on the factors that have
affected recent loan behavior in Japan. We observe positive
forecast errors (unusually robust lending) in 1986-1987
and 1990, and negative forecast errors (unusually weak
lending) in 1988-1989 and 1991-1992.
Rapid loan growth in 1986 and 1987, and slower loan
growth in 1988 and 1989 are in part attributable to fluctuations in output. As discussed previously, the response of
lending to output fluctuations is negative in the second
sample, so these loan movements may reflect the effects of
countercyclical monetary policy. In particular, this historical decomposition is consistent with statements by the
Japanese Ministry of Finance (1993, p. 6) that monetary
conditions eased between 1986 and 1987. However, the
historical decomposition suggests monetary tightening began in 1988, whereas policy actions that might reflect
tightening (such as increases in the official discount rate)
only became apparent in 1989 or 1990. Thus, some care
needs to be taken in interpreting the responses of lending to
output as entirely reflecting countercyclical policy.
Starting in 1989, a larger portion of the forecast error in
lending is due to its own innovations. Innovations in the
Nikkei account for little of robust lending in 1986-1987,
but they make a distinct positive contribution in 19891990. Innovations in the Nikkei have contractionary effects
in 1988-1989, and 1991-1992. In particular, the recent
episode of sluggish growth in lending appears to be largely
associated with negative innovations in lending and in the
Nikkei stock price.
IV.
CONCLUSIONS
The preceding empirical analysis allows us to shed some
light on certain characteristics of the relationship between the Nikkei stock price and bank lending in Japan.
First, the response of Japanese bank lending to an increase
in the stock price is positive in the two sample periods
(1970.1-1983.12 and 1984.1-1993.5) examined in this
paper. This result is intuitive and is consistent with the
stock price affecting loan demand or loan supply.
Second, there has been a change in the historical relationship between stock prices and bank .lending. This
relationship was weak until about the mid-1980s, but
became quite significant subsequently.
Third, recent fluctuations in the Nikkei stock price
appear to have contributed significantly to fluctuations in
bank lending in Japan. In particular, the Nikkei stock price
appears to have played an important role in accounting for
the recent sluggish growth in lending in Japan.
While the techniques used in this paper do not allow us
directly to isolate the effects of the stock price on loan
SroCK PRICES AND BANK LENDING
41
demand and loan supply, the stock price appears to exert an
influence on Japanese bank lending following a significant
change in the regulatory regime that placed greater emphasis on the capital position of banks. This suggests that
the effect of changes in the stock price on Japanese bank
lending at least partly reflect their impact on loan supply.
At the same time, the weak relationship between stock
prices and lending prior to the mid-1980s suggests that any
effects of stock prices on loan dema.lld have historically
been weak. However, Japan's recent cyclical downturn is
quite unusual, so we cannot rule out the possibility that the
stock price has affected loan demand without further
analysis.
Future research in two directions may shed further light
on the relationship between stock prices and lending and
the factors that underlie such a relationship: (i) developing structural models that distinguish explicitly between
the loan demand and loan supply effects of stock prices;
(ii) isolating the role of other asset prices, notably land
prices, in influencing bank lending.
42
FRBSF ECONOMIC
REVIEW
1994,
NUMBER
1
ApPENDIX
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@FedFRASER