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FEDERAL RESERVE BANK
OF SAN FRANCISCO

ECONOMIC
REVIEW

SUMMER

1877

Reactions to Uncertainty

Introd uctio n and Sum m ary

II.

Savings, M oney Demand and the
InfSation/Unem ploym ent T radeoff

Joseph B isignano

III. Risk Prem iums in international Securities Markets:
The Canadian-U.S. Experience
Kenneth Froewiss

The Federal Reserve Bank of San Francisco’s Economic Review is published quarterly by
the Bank’s Research, Public Information and Bank Relations Department under the supervision
of Michael W. Keran, Vice President. The publication is edited by William Burke, with the
assistance of Karen Rusk (editorial) and William Rosenthal (graphics).
For copies of this and other Federal Reserve publications, write or phone the Public
Information Section, Federal Reserve Bank of San Francisco, P.O. Box 7702, San Francisco,
California 94120. Phone (415) 544-2184.

No one has a crystal ball to read the future,
and not surprisingly, we wake up each day to
learn that our expectations had not been quite
accurate. Uncertainty thus is an all-pervading
fact in our economic as in our personal lives.
(Frank Knight, for instance, defined profit and
loss in terms of the unforeseeable discrepancies
created by uncertainty.) Examples abound of the
economy's response to unforeseen events, and
this issue of the Economic Review presents two
such studies, based upon our experiences in a
decade dominated by increasing risk and uncertainty. The first article analyzes the perverse
effect of an unanticipated rise in inflation upon
general economic activity. The second article
then analyzes the effect of unanticipated risks in
international securities markets.
Joseph Bisignano, in a contribution to the
growing literature on "rational expectations,"
considers the role that unexpected price changes
play in determining the behavior of the economy
in an environment of rapid inflation. He compares the differing impact of anticipated and
unanticipated inflation on various economic
variables, with the objective of providing a better
understanding of the trade-off between unemployment and inflation.
Considering the supply side of the economy,
Bisignano refers to the studies which show that
suppliers have more accurate price information
available for their own products (output and
labor) than they do for all products in the
aggregate. Suppliers interpret a rise in the price
of their output as an increase in their "relative
prices," so that they tend to increase both output
and labor supply in the short-run. This supplyside response is consistent with the standard
Phillips-curve relationship of increased inflation
leading to a short-run decline in unemployment.
But this argument is incomplete, in Bisignano's
view, because it ignores the fact that economic
agents have a demand response as well as a

supply response to unanticipated inflation. By
considering the demand side, we will see that the
increased saving response to surprise inflation
may offset any positive supply response to these
same inflation surprises.
In demand theory, an absolute price changefor example, a proportionate rise in the prices of
all goods and incomes-should in principle leave
the demand for any particular good unchanged.
However, unexpected changes in inflation increase the difficulties of households in making
decisions about changes in relative prices. An
unexpected inflation leads consumers to perceive
higher relative prices for the goods they buy,
increasing the variability in the absolute price

level. As a result, households would tend to
reduce their consumption by choosing to save
more. Increased variability in the absolute price
level leads consumers to perceive increased variability in their real income, which uncertainty in
turn leads them to increase their saving rate.
Bisignano next points out that unanticipated
inflation also affects the money market. For a
given nominal money stock, a rise in prices
decreases the real (supply) stock of money balances. However, the surprise tax on real money
balances induces an ex post decline in the real
demand for money, which partially offsets the
contractionary effect of the decline in the real
money stock. The resultant of the two conflicting
effects of unanticipated inflation should be a
decrease in the demand for real money balances.
The empirical evidence analyzed by
Bisignano-with supply effects positive and demand effects negative-suggests that a rise in
unanticipated inflation could lower the rate of
growth of economic activity and raise the unemployment rate. "In other words, the private
sector's response to an increase in unanticipated
inflation in many cases involves an actual worsening of the unemployment situation." Meanwhile, he notes, anticipated inflation tends to
4

have no long-run impact on savings behavior or
the unemployment rate.
Some important policy implications follow
from this apparent lack of any beneficial tradeoff. "The evidence appears to support the argument that monetary policy can best stabilize the
economy by stabilizing or reducing the rate of
inflation. Greater instability in the rate of inflation creates the conditions for greater instability
in aggregate demand and employment."
In a second article, Kenneth Froewiss considers the reactions to uncertainty of investors who
purchase foreign securities. Specifically, he analyzes the role played by two types of riskunanticipated movements in exchange rates and
in interest rates-in determining yield spreads
between countries. Comparing yield spreads
between Canadian and U.S. long-term bonds,
Froewiss notes the traditional view-that
spreads merely reflect expected exchange-rate
movements-assumes that investors ignore risk.
But in those cases when investors are averse to
risk, the yield spreads also reflect adjustments for
the combined effects of interest-rate risk and
exchange-rate risk.

Froewiss asks: "Why would an investor simultaneously hold both domestic and foreign long
bonds when their expected yields (adjusted for
anticipated exchange-rate changes) are not
equal?" An explanation lies in the concept of
"portfolio balance." By holding a diversified
portfolio which includes both domestic and
foreign bonds, an investor is generally able to
reduce the fluctuations in his total earnings. A
risk-averse investor will therefore find it worthwhile to hold some portion of his wealth in the
form of the bond with the lower expected yield,
in order to reap the gains from diversification.
Empirical evidence based on the behavior of
Canadian-U.S. interest-rate differentials supports the hypothesis that investors are riskaverse. Froewiss thus questions the traditional
view that yield spreads between countries provide a good measure of the market's expectations
about future exchange-rate movements. "At the
very least, these yield spreads may give a false
impression about the size of expected movements. At worst, if the risk premium is large
enough, they may even give a wrong signal
regarding the sign of such movements."

Joseph Bisignano·
words, the private sector's response to an increase in unanticipated inflation in many cases
involves an actual short-run worsening of the
unemployment situation. Anticipated inflation,
meanwhile, tends to have no long-run impact on
savings behavior, money demand, or the unemployment rate.
Our results for the effect of anticipated inflation on the unemployment rate are consistent
with the "rational expectations" literature, that
price expectations are formed by utilizing knowledge of the structure of the economic system and
of the behavior of policymakers. However, our
finding of a possible perverse short-run trade-off
between unemployment and unanticipated inflation is at variance with previous empirical work
in this area.

In recent years the rapid rise in the rate of
inflation has caused economists to consider what
role price expectations play in determining the
behavior of the private economy, especially in
regard to savings behavior and the demand for
money.l Both of these questions are analyzed in
this paper. In addition, the question of the effect
of unanticipated (as opposed to anticipated)
inflation on such variables is considered in relation to the presumed "trade-off' between unemployment and inflation.
This paper argues that the rise in unanticipated inflation in recent years has tended to increase
the personal saving rate and to decrease the
demand for real money balances. The net effect
of these offsetting actions has been a decrease in
the rate of growth of economic activity and an
increase in the unemployment rate. In other

I. Prices and the SaVing Rate
Our saving-rate analysis is based on the argument that aggregate demand is influenced by
errors in price forecasts. Surprises with respect to
the rate of inflation cause the demand side of the
economy to retrench on real spending in favor of
increased saving.
One of the most basic propositions of demand
theory is that consumer demand is dependent on
"relative prices" (e.g., the price of good A
"relative" to the price of good B). An absolute
price change-for example, a proportionate rise
in the prices of all goods and incomes-should in
principle leave the demand for any particular
good unchanged. However, unexpected changes
in inflation create increased difficulties for
households in making decisions about relative
prices. Indeed, consumers may interpret a sudden increase in inflation as a worsening in their

relative prices-the price of their labor versus the
prices of various goods. When consumers perceive relative prices worsening because of unexpected variability in the absolute price level
(unanticipated inflation), they tend to change
their consumption decisions by choosing t6 save
more today. That is, increased variability in the
absolute price level leads consumers to perceive
increased variability in their real income, which
uncertainty in turn leads them to increase their
saving rate. This argument, it should be noted,
assumes that individuals require greater price
stability if they are to maintain a stable relationship of saving to income. The greater the inflation instability, the greater will be the instability
in the personal saving rate.
This argument is the demand counterpart to
what is observed on the supply side of the
economy. In the latter case, it is assumed that
suppliers have more accurate price information
available for their own products (output and

*Assistant

Vice President and Assistant Director of Research, Federal Reserve Bank of San Francisco. Jackie Kau
provided research assistance for this article.

labor) than they do for all products in the
aggregate. Suppliers interpret a rise in the price
of their output as an increase in their "relative
prices," so that they tend to increase both output
and labor supply in the short-run. In this sense,
workers are "fooled" in the short-run, when they
see their nominal wages rising, but "smarten up"
in the long-run, when they realize that the rise in
nominal wages was simply the result of a rise in
the aggregate price level. This "rational expectations" argument, developed by Lucas and Sargent and Wallace,2 assumes that economic
agents have a supply response to unanticipated
inflation, but not a demand response. In this
view, a surprise increase in the rate of inflation
can result in a short-run rise in aggregate output.
Nonetheless, ignoring the effects of unanticipated or "surprise" inflation on the demand side
of the economy ignores the important intertemporal decision consumers make regarding
the proportion saved out of current income. We
argue that the increased saving response to
surprise inflation may offset any positive supply
response to these same inflation surprises.
Thus, unanticipated inflation can increase the
perceived variability of real income-even when
expected real income remains unchanged-and
can thereby result in a rise in the saving rate. This
argument, adapted from the work of Jacques
Dreze and Franco Modigliani,3 can be developed
as follows. Assume that we have an individual
who plans for two periods into the future. In the
first period, he knows his income with certainty,
and presumably he also knows the rate of interest
at which he can invest any first-period income
that is not consumed. In the second period, this
individual's consumption will be equal to his
investment returns plus his second-period income. Algebraically, C2 = (Yl - c 1) (l + r) + Y2
where y denotes income, c consumption, r the
rate of interest and numerical subscripts denote
time periods. Saving in period one is equal to (Yl
- c 1)·
Let us assume, however, that this individual
does not know with certainty the real

purchasing-power value of the next period's
income, specifically because of a rise in uncertainty with respect to the rate of inflation. In this
situation, the individual's real income in the next
period may be either higher or lower in real terms
than had been anticipated before the introduction of inflation uncertainty. The question thus
arises-will· he maintain the same level of consumption which he would have done in the
absence of any uncertainty with respect to the
value of the next period's income? Ifthe individual is a "risk averter"-that is, if he prefers less
rather than more variability in the range of
possible uncertain events-he would decrease his
consumption in period one in the face of uncertainty with respect to period two's real income.
At the same time, an increase in anticipated
inflation should have little, if any, impact on
aggregate saving behavior. In this case, current
spending decisions incorporate the gains (for
some) and the losses (for others) of the current
anticipated rate of inflation. Anticipated inflation has little effect on real spending decisions, to
the extent that relative prices are unaffected by
any such change. Unanticipated inflation, however, tends to create the impression that relative
prices have changed, and thereby generates decisions to alter spending patterns. 4
To summarize, a rise in unanticipated inflation should increase the saving rate, while a rise
in anticipated inflation should have no signifi~
cant effect on this rate. If unanticipated inflation
fails to affect money demand or the supply of real
output, the rise in the saving rate would tend to
decrease aggregate demand and increase the
unemployment rate. There may, however, be an
offsetting effect of unanticipated inflation on the
monetary side of the economy. A decrease in the
demand for real money balances, i.e., an excess
nominal money supply, would tend to stimulate
aggregate demand, and could offset the decline
in aggregate demand resulting from an increased
saving rate. Before considering these possibly
offsetting forces, we turn to a discussion of
money demand and price expectations.

II. Prices and Money Demand
In the traditional textbook formulation, the
demand for money is dependent on a measure of
aggregate transactions-for example, income
(y)-and some measure of the opportunity cost
of holding money-typically a short-term interest rate (r). This state of the "desired" real
demand for money (m
can be expressed as

*
mt

rate of inflation, r captures expected price inflation over the remaining maturity of the financial
asset to which it is related. The assumption in (3)
is that the nominal market rate of interest fully
incorporates the implicit anticipated rate of inflation.
If we assume that a one-percent rise in anticipated inflation results in a one-percent rise in the
desired nominal demand for money-our priceelasticity assumption-there is no reason to add
any further estimate of anticipated inflation to
the demand for money. However, an argument
can be made for including the remaining "unanticipated" (forecast error) component of inflation in the equation. A rise in the price level
requires a rise in nominal money balances to
finance a given volume of real transactions, but it
also entails a tax on real (price-deflated) money
balances. Interest-rate effects capture the negative impact of anticipated inflation. However,
after the fact-after actually observing the rate
of inflation-individuals and businesses may
attempt to economize further on real cash balances in response to the surprise excise tax
imposed by unanticipated inflation. That is, an
increase in the variance of the "tax" rate (unanticipated inflation) causes individuals to reduce
the tax base (their holdings of real money balances).
An unanticipated rise in prices thus creates
two partially offsetting effects in the money
market. First, for a given nominal money stock,
a rise in prices decreases the real (supply) stock of
money balances. Secondly, the surprise tax on
real money balances induces an expost decline in
the real demand for money, which partially
offsets the contractionary effect of the decline in
the real money stock. On balance, a rise in
unanticipated inflation should decrease the demand for real money balances, in contrast to a
rise in anticipated inflation, which should have
no statistically significant effect on real money
demand aside from the effect captured in interest
rates.

= 0'0 +0'1 Yt + 0'2 r t
(1)
where subscripts refer to time periods. Since m*
is defined in "real" terms, multiplying it by the
actual price level yields a "nominal" demand for
money, or M t = m; x Pt. In models of shortterm demand for money balances, when the
period of analysis is less than a year, it is common
to assume that individuals reduce the gap between desired and actual money balances by
some constant fraction, A , where A is positive
but less than unity. This "partial adjustment"
hypothesis may be stated as
M t -:- M t - 1 = A(M; - M t _ I)
(2)
On the basis of this hypothesis, consider how
prices and inflation expectations influence the
demand for money. First, a one-percent rise in
the observed price level may result in a onepercent rise in the desired nominal demand for
money, under an assumption of "unitary price
elasticity." Secondly, price expectations are already embedded in the desired demand for
money, equation (1), to the extent that the
interest rate incorporates this price expectation.
That is, price expectations are already adequately reflected in the desired demand for money,
under the assumption that the nominal rate of
interest, r, is composed of both a "real rate of
interest," defined as the lending rate in the
absence of price inflation or deflation, and an
"anticipated rate of inflation" defined over the
life of the respective financial asset. Hence in the
"Fisher equation,"
a
r t = r* + TT t
(3)
where r = the nominal market rate of interest, r*
the real rate of interest, and TT a the anticipated

III. Measuring Anticipated Inflation
In order to conduct statistical tests regarding
money demand and saving behavior, we must
derive a measure of anticipated inflation. As a
first approximation, the Fisher equation, with an
additive random-error term, may represent the
relationship between the nominal rate of interest
and the anticipated rate of inflation.

Table I

Comparison of Inflation Forecasts:
Annual Rates of Change
(1954 first half to 1976 first half)

r rt

Livingston
Forecast

+ 51T ~ + EO t 0 2 0
(4)
t =
Equation (4) is similar to equation (3) except that
the real rate of interest is not assumed constant
and the nominal rate is also influenced by a
random error term, EO t, which is uncorrelated
.
*
WIt h rt an d rr a .
t
To obtain an estimate of rr ~ , the antIcIpated
rate of inflation, we compare the nominal rate of
interest-measured by Standard and Poor's
high-grade long-term bond yield-and the real
rate of interest, measured by Standard and
Poor's dividend-price ratio. Subtracting, we obtain:
* ~ a
I\a
rt - r t = u1T t + EO t = 1T t
(5)
In view of the inclusion of the measurement
error, EO t, our estimate of anticipated inflation,
~ ~,is at best a crude approximation. N onetheless, we may subtract this estimate of the anticipated rate of inflation from the observed rate of
inflation, measured by the consumer-price index, to obtain a rough estimate of the "unanticipated rate of inflation."5
As a check, we compared our series with the
eight-month inflation forecasts, and forecast
errors, obtained by John A. Carlson on the basis
of the semi-annual survey of price forecasts
conducted by Joseph Livingston of the Philadelphia Inquirer. 6 (The Livingston forecast survey is
conducted two months before the close of each
half year.) The Livingston surveys provide semiannual forecasts, so we averaged our quarterly
average values to obtain similar semi-annual
figures. Estimates for the anticipated rate of
inflation can then be compared for the Livingston method and what we will call the "Crude
Fisher Method" (Table 1).

Crude
Fisher
Forecast

2.09%
1.95%
Mean
Standard Deviation
1.97
1.90
0.98
Coefficient of Variation
0.94
Correlation
0.85
The two approaches yield similar results,
although the Fisher method contains a measurement error, which can be large (Chart 1). Thus,
generally speaking, data obtained from financial
markets can yield imputed inflation forecasts
similar to those obtained from pure survey
techniques. Fama's finding 7 that short-term interest yields accurately reflect very short-term
inflation expectations may be true for longerterm corporate securities as well. In addition, it is
interesting that a long-term bond incorporates,
according to the Fisher measure, an anticipated
rate of inflation similar to a survey rate with orily
an eight-month horizon. This suggests that
short- and long-run inflation forecasts were not
significantly different except for the 1974-75
period. Given these qualifications, the "Crude
Fisher" measure seems to provide a reasonable
method for estimating the unanticipated rate of
inflation.
A further test was obtained by regressing the
Livingston forecast (LF) on the contemporaneous Fisher forecast (FF), for the period 1954H 1
to 1971H2.
LF = 0.54 + 0.63 FF
(6)
(2.1) (5.8)

=0.88 SER =0.40 DF =36
D.W. = 1.91 RHO =0.61
RHO =estimated first-order serial correlation coeffiR2

cient;

R2 = adjusted R2, DF = degrees of freedom;
D.W. = Durbin-Watson statistic, and SER = standard

coefficient, 0.61. As indicated in Chart 1, inclusion of post-1971 data provided a poorer statistical fit, because the "Fisher approach imputed a
high inflation rate over the 1972-1973 period-

error of the regression; t-statistics in parentheses.

Equation (6) reveals a high correlation between
the two series, after quasi-first-differencing the
two series by the estimated serial correlation

Chart 1

ANTiCIPATED RATE OF iNFLATION'"
Percent

Percent

"Crude Fisher"
Anticipated Rate

\. Livingston
Anticipated Rate

OI---I--~~';;;;=-----------------------10

-1

*Annual change in consumer-price index

the period of price controls-but a lower rate
over the late 1974-1975 period-the post-control
period.
Next, both approaches yielded very similar
rates of unanticipated inflation, or forecast errors (Table II). The Livingston forecast yielded a
lower average rate of unanticipated inflation
over the period as a whole, but the "Crude
Fisher" procedure performed marginally better
until the recent experience with price controls.

The high correlation and the similar average
values should not be surprising, since both measures were obtained by subtracting the observed
CPI rate of inflation from the anticipated inflation series.
It should be noted that the unanticipated
inflation variable may actually be a proxy for
another aspect of inflation-the variance of the
expected inflation rate (Chart 2). The chart plots
the unanticipated inflation rate against the variance in price expectations around the expected
mean change in prices, developed from Survey
Research Center data. 8 The fact that two survey
measures of inflation, Livingston and SRC,
parallel the movement of our financial-market
determined measure of unanticipated inflation
supports the use of the latter variable in our
analyses of both personal saving and money
demand.
At this point we have developed arguments
regarding how unanticipated inflation affects
saving behavior and money demand, and have
obtained a proxy measure for unanticipated
inflation. We now turn to the statistical testing of
saving behavior and money demand.

Table II
Comparison Rates of Unanticipated Inflation:
Annual Rates of Change
(1954 first half to 1976 first half)
Livingston Crude Fisher
Forecast
Forecast
Mean
Standard
Deviation
Coefficient of
Variation
Correlation

1.27%
1.52

1.37%
2.05

1.20

1.50

0.86

IV. Testing the SaVing Rate Hypothesis
saving rate (PS) is closed each quarter by a
constant fraction,/3, as seen in equation (8).
Equation (7) is intentionally parsimonious.
We argue that short-term variations in the saving
rate around its trend value result from variables
proxying for uncertainty in employment, income
and inflation.
The estimated equation for the personalsaving rate is
PSt = 0.60 + .717
PSt-l + .201 UR t +
(1.3) (10.7)
(2.8)
15.93(yT /yh + .031 Al t + .083 UIt
_
(3.7)
(.8)
(2.7)
(9)

The basic formulation of the saving-rate hypothesis for empirical estimation can be stated as
(7)
PS* = f(UR, yT /y, UI)
+

PSt-PSt 1 =/3(PS*t- PS t-l)

0</3< 1
(8)

Equation (7) states that the desired personal
saving rate (PS*) is positively influenced by
employment uncertainty as measured by the
unemployment rate (UR), positively related to
the ratio of transitory (windfall) to observed
income (y T / y), and positively influenced by the
unanticipated rate of inflation (UI). The implicit
assumptions are that most transitory income is
saved and that anticipated inflation (AI) does
not influence the saving decision. We may hypothesize that if the anticipated inflation variable is included in the estimated equation, its
coefficient should be statistically insignificant.
Also, we may hypothesize that the gap between
the desired personal saving rate and the actual

R2 =.655
SER = .63
DF = 79
D.W. = 1.86
RHO = -.25
Sample Period: 1955.1-1976.3
t - statistics appear below the coefficients.

The ratio of "transitory income" (observed less
permanent income) to observed income was
measured by real per capita disposable personal
income. Transitory income was obtained by first
estimating "permanent income" as an adaptive
II

1970's, when unanticipated inflation was significantly above its average value of the 1960's, the
private sector adjusted its saving rate much more
rapidly, completing this adjustment fully within
one quarter. For example, the coefficient on the
lagged saving rate was found to be near zero
when equation (9) was estimated for the 1966-76
period.
Further testing of the inflation-saving hypothesis involves estimating the equation for the
level of real per capita personal saving. The
saving rate could, for example, rise because
income has fallen, while the level of saving
remains unchanged, so it is necessary to determine whether unanticipated inflation has any
effect when income is held constant. As detailed

trend. 9 Equation (9) supports the argument that
a rise in unanticipated inflation increases the
saving rate while anticipated inflation has no
statistically significant effect. The t-statistic on
the unanticipated inflation variable is 2.7, which
is statistically significant at the .995 significance
level. In addition, both the unemployment rate
and the transitory/observed income ratio are
positive, as expected, and statistically significant.
To obtain the estimated "adjustment coefficientl1," we simply subtract the estimated coefficient on the lagged personal-saving rate from
unity. This implies that approximately 30 percent of the gap between the desired and actual
saving rate is removed each quarter. During the

Chart 2

UNANTICIPATED INFLATION AND VARIANCE
OF EXPECTED PRICE CHANGES
Percent

Percent

Variance of
Expected Price ...
,6-Change

6
5

3
10

2
1

0 1-----4-----,,,..,,...------1-------------+.--1---10
-1

-2

-10

1970

1971

1972

1973

1974

1975

1976

Table III
Personal Saving Rate and Inflation

in Appendix I, unanticipated inflation affects
the level of saving in much the same way as it
affects the saving rate.
The rise in unanticipated inflation, from an
average 0.6 percent in the 1960's to 2.0 percent in
the 1970's, apparently helped to account for the
1.3-percentage point rise in the personal saving
rate between these two periods. (Table III and
Chart 3).

1960.1-1976.4
1960.1-1969.4 1970.1-1976.4

Personal Saving
Rate
Mean
Standard
Deviation
Rate of Inflation
(CPI)
Mean
Standard
Deviation
Unanticipated
Inflation
Mean
Standard
Deviation

5.9%
0.96

7.2%
0.9

2.4
1.8

6.3

2.8

0.6

2.0

1.1

3.1
Chart 3

PERSONAL SAVINGS BEHAVIOR IN THE 19705
Percent

10.
Unanticipated
Inflation

Percent

01-!.-.:.-+-A---\----,H~-------__t__r__t--16

2
1970

1971

1972

1973

1974

V. Money Demand and Price Expectations
pothesize that anticipated infla.tion should be
statistically insignificant but unanticipated inflation should be significant and negative. The
estimated equation, in linear form, is given
below. All dollar variables are in real per capita
terms, with the consumer-price index used as the
deflator.
Ml t =20.62+.013yf +.038y +.954Ml t
(.6) (1.8)
(2.5)
(34.5)
-2.22 CPR t -1.833 VI t - .077 AI t
(.1)
(3.9)
(4.8)

Many analysts have argued recently that the
demand for money has declined because of
structural changes in the economy. 10 While this
phenomenon may reflect certain regulatory
changes and financial innovations, we argue that
it is also due to the rise in unanticipated inflation.
Because the holding of real money balances
involves a cost, roughly measured by the observed rate of inflation, and because this cost is
not known without error, it would appear that
real money balances may respond to that anticipational error, as measured by the rate of
unanticipated inflation. Any decline in money
demand due to unanticipated inflation could
have a potentially stimulative effect on the economy, which could offset the contractionary impact exerted by a rise in the saving rate.
To test the appropriateness of unanticipated
inflation in the real money-demand equation, we
first estimated a partial-adjustment equation for
real M I per capita balances. Desired real money
demand is defined as dependent on both "permanent" (trend) real disposable personal income
(y p), "transitory" (observed less permanent) real
disposable personal income (y T), a short-term
interest rate, defined as the commercial paper
rate (CPR), unanticipated inflation (VI) and
anticipated inflation (AI). As before, we hy-

(10)

=.987
D.W. =1.82

=3.60
RHO = .45

SER

DF = 71

Sample period: 1955.1-1974.4

In this equation, unanticipated inf1ation (VI)
has a statistically significant negative impact on
real per capita M 1 balances with a respectable tstatistic of 4.8. Also, the anticipated inflation
(AI) variable is statistically insignificant, with a
t-statistic of only 0.1 11 As detailed in Appendix
2, the same result with respect to the effect of
unanticipated inflation is found when household
(rather than total) real money balances are used
to estimate the relation.

VI. Implications for Economic Activity
We have argued in this paper that a rise in
unanticipated inflation will increase the personal
saving rate and decrease the real demand for
money. Given those effects, unanticipated inflation could lead to a decline in real output and a
rise in the unemployment rate. This conclusion is
not theoretically certain, however, because the
effects cited are partially offsetting. That is, a rise
in unanticipated inflation tends to increase the
saving rate, which is contractionary, but also
tends to reduce the demand for money, which is
expansionary. Depending on the magnitude of
these offsetting forces, we may find the unemployment rate either rising or falling.
This argument is an addition to the arguments
of Lucas, Sargent and Wallace, who suggest that

apositive supply response to unanticipated inflation, in the short-run, will decrease the unemployment rate. They implicitly assume that the
demand side of the economy is not subject to the
same misconceptions about relative prices as is
the supply side. Thus, in their models a rise in
unanticipated inflation can exert only a beneficial effect on the unemployment rate. Our argument is closer to that of Robert Barra's. In his
study, Barro contends that a "surprise" regarding the rate of inflation can also affect the
demand side of the economy, creating the possibility of either a beneficial or perverse short-run
trade-off between unemployment and unanticipated inflation. 12
Our analysis assumes that the real rate of

interest, the given level of real money balances
will be held only at a higher level of income. The
IS curve represents the equilibrium between
investment and saving. This curve slopes
downward, because a lower real rate of interest
(with its stimulus to investment) will equilibrate
saving and investment only if income increases to
generate the necessary saving.
Assume now that prices unexpectedly rise.
This price rise will increase the level of saving,
which, for a given level of income, can equal
investment only if the real rate falls to encourage
investment. Hence, the IS curve shifts down and
to the left with respect to the money market. The
unexpected rise in prices will first decrease the
level of the real money supply, shifting the LM
curve to the left, say to LMI-perhaps shifting
enough to retain the old real rate of interest rOo If
real money demand declines at the same time, the
LM curve will make a partially offsetting move
to the right, between points F and G. That new

interest can be more variable in the short-run, as
a result of short-term shifts in saving behavior
andreal money demand. Errors in price forecasts
increase the actual (ex post) variability in the real
rate, and this variability is greater the greater the
variance in inflation (Chart 4). The chart shows
the real rate on 6-month Treasury bills, obtained
by subtracting June and December 6-month
Livingston inflation forecasts (made two months
previous) from the market yield on 6-month
bills.
Determination of the real rate can be shown in
a graphical analysis (Chart 5), which illustrates
the effects of unanticipated inflation on aggregate demand. "Normal full capacity utilization"
is assumed to generate a real income level of yO,
associated with which is a "natural rate of unemployment," u o. The LM curve represents the
equilibrium between the supply and demand for
real money balances. The LM curve slopes
upward, because with a rise in the real rate of

Chart 4

UNEMPLOYMENT RATE AND EX ANTE REAL TREASURY BILL RATE •
Percent

9
Unemployment ...
Rate
.........
Percent

1959

Chart 5

pl()yment rate ()n lagged values of itself, and on
the rates ofanticipated and unanticipated inflation. Under our basic hyp()thesis, the coefficient
on the anticipated inflation should be near zero
and insignificant, while the coefficient on the
unanticipated inflation variable should be significant. The sign of the coefficient on the latter
variable will determine whether a rise in unanticipated inflation tends, in the aggregate, to raise
or to l()wer the unemployment rate. The estimated equation is

REAL INTEREST RATE and REAL INCOME

Real
Interest Rate

Unt = .044 + 1.873 Unt_l
(.3) (19.5)
+ .368 Unt-3

(3.8)
t.....-----':-----'::-------Real Income
yl

R2 = .954

D.W.

equilibrium level-where there is equality of real
saving and real investment and equality of real
money demand and supply-results in a lower
real income level (higher unemployment rate)
and a lower real rate of interest. Hence, a surprise
increase in the rate of inflation can result in
higher nominal rates of interest but lower real
rates ofinterest and a higher unemployment rate.
This would also imply an inverse relationship
between the unemployment rate and the real rate
of interest over the business cycle. This inverse
relationship has been especially evident since
about 1969, when a fall in the real rate of interest
was associated with a rapid rise in the unemployment rate (Chart 4). In particular, the drastic fall
in the real rate after 1972 was associated with a
proportionately large rise in the unemployment
rate.
If unanticipated inflation has a significant
impact on the demand side of the economy, the
unemployment rate and real output should be
statistically related to that variable. To test these
propositions, we next present two alternative
tests of the hypothesis that a rise in unanticipated
inflation has had a negative effect on unemployment, while anticipated employment has had no
effect on aggregate output and unemployment.
The first test involves the unemployment rate,
following a procedure developed by Thomas
Sargent, and the second test employs real output. 13
The first statistical test regresses the unem-

=2.01

(7.3)

+ .046 UI t + .004 AI t
(.2)
(11)
(3.6)

SER::: .285

RHO

- 1.259 Un t _2

=80

=-.20

Sample Period: 1955.1-1976.4

This equation supports the hypothesis that
anticipated inflation (AI) has no statistically
significant effect on the unemployment rate. It
also supports the argument that a rise in unanticipated inflation (UI) will increase the unemployment rate, at least to some small extent. In other
words, an adverse effect through the demand
side of the economy has, in the past 20 years,
been greater than the positive effect through the
supply side. On balance, a rise in unanticipated
inflation has resulted in an increase in the unemployment rate.
We observe in equation (I 1) that the quantitative impact of unanticipated inflation on the
unemployment rate is small. This is due to the
fact that unanticipated inflation gives rise to
offsetting influences on the demand and supply
sides of the economy, which can be reversed
given a different set of circumstances. The important point is that unanticipated inflation's
effect on the unemployment rate can be positive
or negative. The theoretical argument does not
yield a definitive answer, so that empirical estimation must settle the issue.
In a further test, the dependent variable employed was "residual real GNP" (RRGNP),
which may be defined as the difference between
the observed level of real GNP and its trend
value.'4 Because residual real GNP is trendless,
we used no lagged values, but instead regressed it
16

on a constant term, anticipated and unanticipated inflation. The estimated equation is
RRGNP t = 1.52 - 1.793 UI t + .500 AI t
(1.0)
(1.0) (4.4)

R2 = .171

SER

=8.49

D.W. = 2.35
Sample Period = 1955.1-1976.4

DF = 85

below, indicates that a rise in unanticipated
inflation of one percentage point decreased real
GNP by almost $2 billion.
RRGNP t=

(12)

5.81
(.2)

1.953 UI t + 2.354 AI t
(2.0)
(.3)

R,2 = .197 SER = 12.13
D.W. = 2.53

In this equation, a rise in anticipated inflation
has no significant effect on real GNP, while a rise
in unanticipated inflation decreases real GNP
from its trend value. The coefficient on the latter
variable is 4.4, easily passing conventional significance tests. The overall fit ofequation (12) is not
very large, but this is not surprising since the
dependent variable is a sequence of variations in
the level of real GNP.
Sub-sample results indicate the lack of any
"trade-off" during the 1950's between real GNP
and either variety of inflation. During the 1960's,
a perverse trade-off developed, with output
decreasing with a rise in unanticipated inflation,
and this trade-off worsened during the 1970's.
The estimated equation for the 1970's, given

DF = 25

Sample Period

(13)

= 1970.1-1976.4

The equations reported above were reexamined in a variety of ways, utilizing Sargent's
test procedures,ls to determine whether a beneficial trade-off between unemployment and inflation could be discovered. In no case were such
results obtained. Indeed, during the period considered, there was an adverse relation between
inflation and unemployment. The indicated neutrality of the anticipated rate of inflation in
relation to real output and employment is entirely consistent with the results obtained in our
analysis of the saving rate and the demand for
money. Anticipated inflation appears to have
had no statistically significant effect on either
real output or unemployment.

VII. Conclusion
In his recent Nobel Lecture, Professor Milton
Friedman argued that the increased variability of
inflation decreases the efficiency of the price
system in coordinating economic activity. 16
Prices are means of conveying information on
the relative scarcity of goods. However, individuals must extract information about "relative
prices" from observations on "absolute prices."
The greater the variability in absolute prices, the
greater the difficulty in abstracting the informational content regarding relative prices from
absolute price-level information. Friedman's
argument is relevant to the decisions consumers
must make with regard to saving and holding of
real money balances. Errors in price forecasts in
recent years, as evidenced either in the Livingston survey data or our measure of unanticipated
inflation, have tended to raise the saving rate and
to decrease the demand for real money balances.
The difficulty of extracting the "signal" from
information on absolute prices has increased
consumers' uncertainty regarding the value of
both their future income and their future wealth.

This increased uncertainty in turn has led to a
significant rise in the saving rate, and thereby
contributed to the severity of the worst postwar
recession. The result has been a concurrent rise in
inflation and unemployment, contrary to what
we would expect from the received wisdom of the
1960's. The evidence considered in this paper
forces us to cast a skeptical eye not only on any
long-term trade-off between unemployment and
anticipated inflation, but also on any short-term
trade-off between unemployment and unanticipated inflation. Economic theory posits an
ambiguous relation between unemployment and
unanticipated inflation. If supply considerations
dominate, the trade-off will be beneficial; if
demand considerations dominate, the trade-off
will be adverse. Our evidence suggests that the
trade-off has been adverse during the last 20
years.
The policy implications of our paper which
follow from this apparent lack of any beneficial
trade-off support the argument that monetary
policy can best stabilize the economy by stabiliz17

conditions for greater instability
demand and employment.

ing (or reducing) the rate of inflation. Greater
instability in the rate of inflation creates the

aggregate

Appendix 1
The level of real personal saving is hypothesized to be dependent on permanent real disposable personal income, y P, transitory real disposable personal income, yT, unanticipated
inflation, anticipated inflation, and the unemployment rate. All dollar magnitudes were deflated by the consumer-price index.
We also introduce into the analysis the effect
of real per capita money balances, MI. In line
with the "real balance effect," emphasized in the
work of A. C. Pigou, Lloyd Metzler and Robert
Mundell, we argue that a fall in real money
balances should lead to a rise in real saving. Also.
we introduce the 3-month Treasury bill rate,
TBR, as an additional explanatory variable. The
bill rate serves as a proxy for the real rate of
interest. Thus, a rise in the nominal interest rate,
with the anticipated rate of inflation held constant, would imply a rise in the real rate of
interest.
Although additional variables have been
added to explain the level of personal saving, the
overall results are not significantly changed if the
interest rate and money balances are dropped
from consideration. These additional variables
are added to determine whether our previous
conclusions with respect to anticipated and unanticipated inflation continue to hold up when
the theoretical model is expanded.
The general form of the equation for the level
of personal savings, S, appears below. The signs
below the variables indicate the expected signs
on the estimated coefficients.
S = S(yP, y T, TBR, VI, AI, UR, Ml)
+, +,
+,
+, 0, +,

All dollar variables are in real per capita terms.
We drop the partial-adjustment hypothesis because this hypothesis does not appear reasonable
for the entire sample period. Also, the elimination of the lagged dependent variable improves
our statistical results if the equation errors prove
serially dependent. The estimated equation is
S = 716.1 + .029 y +.68y +2.89TBR t
(2.5)
(.6)
(8.8)
(.9)
(15)
+2.68 VI t +10.08 AI t
(2.1)
(1.67)
+ 7.99 UR t - .78 Ml
(2.2)
(3.0)

R2 = .902

D.W.

=2.38

SER = 15.16
RHO

= 77

=.90

Sample period = 1955.1-1976.3

The equation indicates that personal savingeven in level form- is influenced by independent
effects arising, first, from the level of real money
balances, and second, from surprises in inflation,
measured by our proxy for unanticipated inflation. Again we see that anticipated inflation does
not have a statistically significant effect at conventional significance levels. The real interest
rate is positive, as expected, but not significant.
We also note that the most significant impact on
real personal saving arises from changes in
transitory income. The estimated equation implies that 68 percent of an increase in transitory
(windfall) income will be saved. These results
support the argument that an unanticipated
increase in prices will cause the aggregate level of
real saving to rise, due to a decline in real wealth
and to an increased desire for precautionary
saving.

(14)

Appendix 2
To further test the appropriateness of inclusion of unanticipated inflation, we incorporated
Federal Reserve flow-of-funds data in the real

money-demand equations. The new series included "demand deposit and currency" holdings
of the household sector M I H , deflated by
18

MIH t =7.6 + .035 Yt P + .050Yt T + .873 MIHt-l
(.1) (2.7)
(4.3)
(17.6)

consumer prices and by total "households," AI
giving us a "permanent real per household disposable personal income" variable. A2 The difference between observed real personal income
and the computed "permanent" component was
defined as "transitory" income. Here again,
una.nticipated inflation was statistically significant and anticipated inflation insignificant.
However, the inclusion of the anticipatedinflation variable tended to bias downward the
adjustment coefficient. The estimated equation,
without the inclusion of the anticipated-inflation
variable, is reported below. The commercialbank passbook saving rate (PSR) is used as the
interest-rate variable, because it is the best measure of the household sector's opportunity cost of
holding money balances.

- 32.55 PSR t
(2.8)

R2 = .921
D.W.

=2.00

- 3.58 UIt
(3.3)

SER = 24.6

(16)

DF = 79

RHO = -.31

Sample Period: 1955.1-1976.3

For the household sector as for the more general
case, unanticipated inflation exerts a statistically
significant negative impact on real cash balances.
For the household sector also, the quarterly
adjustment speed again is rather low, but it is
also much more realistic than in the general case,
at 13 percent per quarter.

FOOTNOTES
when the expected rate of inflation is held with certainty
(inflation is always perfectly anticipated) will the nominal bond
yield perfectly incorporate the expected rate of inflation (i.e., =
1). On the question of bond-equity yield spreads in reiation to
the variability of inflation, see M. J. Gordon and P. J. Halpern,
"Bond Share Yield Spreads Under Uncertain Inflation," American Economic Review (September 1976). Gordon and Halpern
argue that the real rate of return on bonds is an increasing
function of the variability of the inflation rate.
6. Carlson's study, together with the Livingston forecasts, are
found in "A Study of Price Forecasts," Annals of Economic and
Social Measurement (Winter 1977). Note that the reported "6month forecasts" found in Table 1 for the CPI are, in fact, 8month forecasts. The reasons are noted in Carlson's text.
7. See Eugene F. Fama. "Short-Term Interest Rates as Predictors of Inflation," American Economic Review (June 1975), and
Fama's book, Foundations of Finance, New York: Basic Books
(1976).
8. I am grateful to Mr. Richard T. Curtin, Director of Surveys of
Consumer Attitudes, Survey Research Center, University of
Michigan, for supplying me with these series. For a discussion
of how the "expected price change" survey is conducted, see F.
Thomas Juster and Lester D. Taylor, "Towards a Theory of
Saving Behavior," American Economic Review (May 1975).
9. Real per capita permanent disposable income (deflated by
the CPI) was estimated along the lines suggested in Michael
Darby, "The Allocation of Transitory Income Among Consumers' Assets," American Economic Review (December 1972).
10. "How Velocity Can Fool the Money Watchers," Business
Week, May 30, 1977.
11. The one unrealistic result was the implied quarterly adjustment speed of .05 per quarter, which was especially evident as
the sample period was extended, and which declined even
further with the addition of the anticipated-inflation variable.
12. Robert J. Barro, "Rational Expectations and the Role of
Monetary Policy," Journal of Monetary Economics (January
1976).
13. The Sargent test was first presented in his article, "Rational
Expectations, the Real Rate of Interest, and the Natural Rate of
Unemployment" Brookings Papers on Economic Activity (2:

1. For some recent examples, see F. Thomas Juster and Paul
Wachtel, "Inflation and the Consumer," Brookings Papers on
Economic Activity (1 :1972), and Stephen M. Goldfeld,' "The
Demand for Money Revisited," Brookings Papers on Economic
Activity (3:1973), pp. 607-613.
2. Robert E. Lucas, Jr., "Some International EVidence on
Output-Inflation Trade-Offs," American Economic Review
(June 1973), and Thomas J. Sargent and Neil Wallace, "'Rational Expectations,' the Optimal Monetary Instrument, and the
Qptimal Money Supply Rule," Journal of Political Economy
(2:1975).
3. Jacques H. Dreze and Franco Modigliani, "Consumption
Decisions Under Uncertainty," Journal of Economic Theory
(1972). For a simple graphical illustration that increased income uncertainty will increase saving, see their Appendix D.
4. The inflation-saving hypothesis has been tested by Lester D.
Taylor, using data from the "Consumer Anticipations Survey,"
and by Juster and Wachtel. Our arguments are similar to theirs,
but we utilize different measures of anticipated inflation and
obtain different results from our statistical tests. Lester D.
Taylor, "Price Expectations and Households' Demand for Financial Assets," Explorations In Economic Research (Fall
1974). Thomas Juster and Paul Wachtel, "A Note on Inflation
and the Saving Rate," Brookings Papers on Economic Activity
(3:1972).
5. Another argument as to why the spread between the bond
rate and the dividend yield provides a reasonable approximation to the expected rate of inflation concerns the assumption
that the variability of inflation is positively related to the rate of
inflation. If we assume that the return on equities includes an
inflation premium but that the real return on equities is statistically independent of the inflation rate, then as the variability of
the inflation rate (and the rate of inflation itself) rises, the real
yield on bonds must rise relative to the real yield on stocks in
order to induce individuals to hold the existing supply of these
assets. Equivalently, the spread between the nominal yield on
bonds and the real returns on equities (dividend yield) must
widen with the rise in the expected rate of inflation. Thus the
"expected rate of inflation" we are measuring in the text also
includes a premium for inflation variability. Only in the case

alternative procedure was employed, in which the unemployment, CPI inflation and real GNP series were all first estimated
by Box-Jenkins time-series models. The residuals from the
unemployment ARIMA model and the real GNP model (both
level and rate of growth) were cross-correlated with the CPI
inflation residuals (both ievel and rate of growth). The chisquare test proposed by Larry Haugh was then employed to see
if there was any "causality" between unemployment, real GNP
and price inflation. In no case was any significant relationship
revealed. For the test procedure employed in these analyses,
see Lairy D. Haugh, "Checking the Independence of Two
Covariance-Stationary Time Series: A Univariate Residual
Cross-Correlation Approach," Journal of the American Statistical Association (June 1976). The results of these analyses are
available upon request. The Haugh and related tests are discussed in C. W. J. Granger and Paul Newbold, Forecasling
Economic Time Series. New York: Academic Press (1977).
16. Milton Friedman, "Nobel Lecture: Inflation and Unemployment," Journal of Political Economy (3, 1977).

1973). Additional anaylsesoftests ofthe natural-rate hypothesis
can be found in Thomas J. Sargent, "Testing for Neutrality and
Rationality," in Studies in Monetary Economics, No.3, Federai
Reserve Balik of Minneapolis (June 1976).
14. To obtain these "real GNP residuals," we estimated a BoxJenkins ARIMA model for the period 1950.1 to 1976.IVand used
the white noise residuals as the dependent variable for the
regression reported in the text. The ARIMA model estimated
was a (1, 1,0) model in the levels of real GNP. That is, our model
was
(1-<P1 B) AZ t=8 0 +at
where AZt is the change in real GNP.
The estimated coefficients and their t-statistics are:

q, 1 = .466 and 8 0 = 3.78; Residual Standard Error = 8.83
(5.3)

(3.5)

The chi-square value for the test of the "white noise" of the
residuals was 27.3, with 25 degrees of freedom. Thecritical chisquare value at the 95-percent significance level is 37.6. Hence
the "residual real GNP series" is white noise.
15. Thomas J. Sargent, "Testing for Neutrality and Rationality," op. cit. Because the results obtained here are so dependent
on our estimates of anticipated and unanticipated inflation, an

Al. The number of households is available only annually. To
obtain a quarterly series we interpolated using the population
series as a related variable.
A2. See footnote (9) for the reference on estimating permanent income. In both the per capita and household estimation of
real disposable personal income, the quarterly adjustment
coefficient was set equal to 0.1.

I
Kenneth Froewiss*

hedge against inflation in countries where his
firm purchases raw materials. This way of looking at exchange risk is analogous to the "preferred habitat" theory of the domestic term
structure~in which some investors view long
bonds as less risky than short ones2~and serves
as a useful complement to the view adopted here.
Since the concept of risk is central to this
article, Section I examines just what is meant by
the term. It introduces the notion of "risk aversion" in the simple case in which the only risk is
that of unanticipated exchange-rate movements.
Section II then proceeds to the case.in which
interest-rate risk is present as well. It discusses in
qualitative terms what patterns of international
yield relationships might obtain if investors are
assumed to be averse to risk. Section III presents
a formal model of the effect of risk aversion on
international yield spreads. The model is used to
derive an expression relating interest rates in two
countries to (a) the expected change in the
exchange rate between the currencies of the two
countries and (b) an adjustment for risk. The
latter term is seen to be a simple international
analogue of the measure of risk developed in the
literature on domestic securities markets. 3 This
section is more technical than the others and may
be skipped by those readers not interested in the
mathematical formulation of the argument.
Section IV tests the model against the evidence
provided by the pattern of interest rate differentials between government bonds in Canada and
the U.S. in the period from mid-1971 through
1975. The data appear to support the hypothesis
that these yield differences can be partly explained as adjustments for risk. Section V briefly
summarizes the principal conclusions and their
implications.

An investor who purchases foreign securities
exposes himself to a variety of risks. For example, unanticipated movements in exchange rates
may adversely affect the returns on his investment. Or the sudden imposition of exchange
controls may prevent the repatriation of interest
and dividends. There is also the possibility that
interest rates may rise, causing a capital loss if the
security has to be sold prior to maturity. (This
type of risk is common to domestic securities as
well.) And, of course, a borrower~whether a
corporation or a country~may default.
This article analyzes the role which two of
these categories of risk~unanticipated movements in exchange rates and in interest rates~
play in the determination of yield spreads between countries. An understanding of this issue
helps to explain why international yield differentials may be poor guides to the market's beliefs
about future exchange-rate movements. Furthermore, the article shows how the interaction
of exchange-rate risk and interest-rate risk may
at times make foreign assets appear less risky to
an investor than domestic ones.
The fact that foreign assets are not necessarily
more risky has also been emphasized by Donald
Heckerman. 1 He reaches that conclusion
through a consideration of the risk of changes in
the terms-of-trade to an individual whose consumption is heavily weighted towards imports.
For example, the treasurer of a multinational
corporation may find foreign assets the better
*Economist, Federal Reserve Bank of San Francisco. The
author wishes to thank Ladan Amir-Aslani for her careful
research assistance for this article. The article is based on a
portion of the author's Harvard doctoral dissertation, which
was written under the direction of Richard E. Caves and
Benjamin M. Friedman.

I. The Nature of Exchange Risk
Perhaps the easiest way to approach the problem of risk in general and of exchange risk in
particular is to consider the choice faced by an
individual as he decides whether to purchase a
domestic bond or a foreign bond. To keep the
example simple, it will be assumed that both
bonds mature in one year, and that the individual
intends to hold whichever one he purchases until
maturity. These assumptions imply that the
investor knows for certain the nominal returns
on both bonds. 4 He must then ask himself: What
are the chances that any difference in the nominal yields will be more than offset by changes in
the exchange rate?
He knows, of course, the current (spot) exchange rate at which he could purchase the
currency needed to buy the foreign bond. What
he does not know is what the spot exchange rate
will be a year in the future. 5 However, he no
doubt has some beliefs about the likelihood of
alternative values of the exchange-rate obtaining. It is convenient to think of these views as
constituting a "subjective probability distribution;" i.e., with each possible future value of the
exchange rate, the investor associates a number
representing the probability that that rate will be
the actual one. The expected value of the distribution then represents his "best guess" as to what
rate will prevail in a year.
To make this example more concrete, imagine
that a V.S. investor could get a 7-percent return
on a domestic bond and 9 percent on a Canadian
bond of comparable quality. If he expects the
Canadian dollar to depreciate vis-a-vis the V.S.
dollar by less than 1.835 percent at the very
worst, his expected net gain would be greater on
the Canadian bond than on the American one.
To see why, suppose that the current spot exchange rate were unity. Then a U.S. investor
could convert $100 into C$100, buy a Canadian
bond, and have C$109 at the end of a year. If the
Canadian dollar had depreciated by 1.835 percent in the interim, each Canadian dollar would
than exchange for only $0.98165. The investor's
C$109 would be worth just $107, the amount
which he could have obtained by purchasing the
V.S. security instead.
In general, if F is the current spot exchange
rate (expressed as the U.S. dollar price of a unit

of foreign currency), E(F) the expected value of
the future spot rate, R the domestic yield, and R *
the foreign yield, then the U.S. investor will
expect a net gain from choosing the foreign
security whenever
(1)
I + R < (E(F)jF) . (1 + R*).
The left-hand side of expression (1) represents
the value in one year of a V.S. dollar invested in
the U.S. security. The right-hand side shows the
value in one year of a U.S. dollar which was first
converted into (1 j F) units of foreign currency
and then invested in the foreign security, the
proceeds from which investment were then converted back to U.S. dollars at the expected future
spot exchange rate, E(F). It should be noted that
if the foreign currency were expected to appreciate, then E(F) > F, and it would be possible to
have R * less than R and yet for the U.S. investor
to still expect a net gain from buying the foreign
security as opposed to the domestic one.
Of course, the investor's expectations about
the exchange rate might turn out to be wrong.lf,
in the above example, he had bought the Canadian bond on the basis of an expected I-percent
depreciation of the Canadian dollar and it had in
fact depreciated by 3 percent, his net return on
the foreign investment would be less than the
amount which he could have earned domestically. Economists reserve the term "exchange risk"
for the possibility of such deviations from expected movements in the value of a currency.
Some individuals may be willing to make their
investment decisions on the basis of expected
returns alone, without regard for the risk of
unfulfilled expectations. Such individuals are
said to be "risk-neutral." In the above example, a
risk-neutral investor would opt for the Canadian
bond as long as his expectation of the rate of
depreciation of the Canadian dollar were less
than 1.835 percent. Other individuals, while also
expecting a depreciation of under 1.835 percent,
might only buy the Canadian bond if its return
were higher than 9 percent. These individuals are
said to be "risk-averse."
In a world dominated by risk-neutral investors, equilibrium in international bond markets
would require that yield differentials in favor of
any country be exactly offset by an expected

depreciation of that country's currency. Any
other configuration of interest rates and exchange rates (both actual and expected) would
leave at least some investors with inducements to
change the composition of their portfolios. For
consider again the above example, in which there
exists a 2-percent yield differential in favor of
Canada. If the expected depreciation of the
Canadian dollar were less than 1.835 percent,
risk-neutral American investors would have an
incentive to sell their holdings of U.S. bonds and
to buy Canadian bonds. These actions would
tend to raise U.S. yields and to depress Canadian
ones, thereby reducing the differential in favor of
Canada. Canadian investors would similarly
switch from U.S. to Canadian bonds. This process would continue until the yield spread just
offset the expected rate of depreciation of the
Canadian dollar, i.e., until6
I + R = (E(F)/F)· (I + R*).

back toward the relationship given in (2).
However, if Canada were a net international
debtor, the movement would not be complete.
For then Canadian holdings of U.S. bonds
would be less than U.S. holdings of Canadian
bonds. As Canadians proceeded to switch to their
own bonds, a situation would be reached in
which Canadians held only the obligations of
their own country while some U.S. investors stili
held Canadian securities. Again, the risk-averse
U.S. investors would only be willing to hold the
Canadian bonds if the premium attached to them
in the form of a higher yield exceeded the amount
necessary to just offset the expected depreciation
of the Canadian dollar. But now there would be
no further possibility of riskless arbitrage on the
part of the Canadians. In order to take advantage of the international yield spread, they would
have to borrow U.S. dollars to buy more Canadian bonds. If they, too, were risk-averse, they
would not expose themselves to an uncovered
U.S.-dollar liability unless the gain from doing
so, i.e., the yield spread, were greater than the
expected appreciation of the U.S. dollar. In
other words, it would be possible for the Canadians as well as for the Americans to be in equilibrium with the interest rate differential between the
two countries larger than that given by (2).
Several observations should be made regarding this conclusion. If it were only to hold for the
case in which investors in one country specialized
completely in their own bonds, it would not be
very interesting. However, the same conclusion
holds for the more general case-in which investors in both countries hold internationally diversified portfolios-once the menu of available
assets is expanded to include bonds which are
subject to interest-rate risk as well as exchangerate risk. Moreover, nothing in the discussion so
far limits the applicability of these results to a
world of floating exchange rates. Even if exchange rates were officiaUy "pegged," as under
the Bretton Woods system, investors would
reasonably attach positive probabilities to the
prospect of different rates obtaining in the future. Finally, since there is ample evidence from
the domestic term-structure literature that investors tend to be risk-averse,7 it seems worthwhile
to pursue further the implications of risk aversion for international yield spreads. That is the
subject of the next two sections.

(2)

Could a different equilibrium relationship
hold in a world of risk-averse investors? In this
simple example in which there is no interest-rate
risk, the answer is "Yes" only when one of the
countries is a net international debtor. In that
case, the yield on the bonds of the debtor nation
will have to incorporate a risk premium in order
to induce investors in the creditor nation to hold
such bonds.
In order to see why, recall that a risk-averse
investor, by definition, is content to give up some
expected yield as the necessary price of reducing
his exposure to risk. Thus, a U.S. investor, for
example, faced with a yield spread in favor of
Canada which exceeds the expected rate of
depreciation of the Canadian dollar, might not
feel any incentive to switch from U.S. securities
to Canadian ones. But although there might not
be any market forces emanating from the U.S. to
drive the yield differential back into conformity
with (2), the actions of Canadian investors might
achieve the same results. For in their eyes, it is the
U.S. bonds only which are risky. Given the
circumstances just described, a Canadian investor could get a certain return on his own country's security which exceeds the expected return
on the U.S. security. Clearly, he would have an
incentive to sell his U.S. bonds and buy Canadian ones, whether he were risk-neutral or riskaverse. Once again, yield spreads would move
23

II. International Yield Spreads in a
Risk-Averse World
less variability than will the earnings of either of
them individually. Therefore, when an investor
assesses the value of a potential addition to his
portfolio, he places particular attention on the

In order to highlight the concept of exchange
risk, the only investment choice considered so far
has been the choice between a domestic bond and
a foreign bond whose nominal returns in their
respective currencies are kno",'n with certainty.

covariance between the returns on the new asset

In the real world, of course, the typical investor
can also hold domestic assets whose nominal
returns are uncertain. For example, one might
purchase a long-term bond with the knowledge
that it might have to be sold prior to maturity.
Once the range of asset choice is extended to
include in each country a domestic bond subject
to interest-rate risk, the question of how risk
affects international yield spreads becomes more
complex.
Each investor can hold one asset which is free
from both interest-rate and exchange-rate risk.
For simplicity, this asset may be thought of as a
short-term bond issued by the government of the
investor's own country. He may also hold one
asset subject only to interest-rate risk, which will
be considered here as a long-term bond of his
own government. A third asset-the foreign
government short-term bond-is subject only to
exchange risk, and a fourth-the foreign government long-term bond-is subject to both types of
risk. One safe and three risky assets are therefore
available to all investors, but the risk attributes
of any given asset depend on the nationality of
the investor appraising it.
The decision faced by a risk-averse investor
who must allocate his funds among one safe and
several risky assets has been extensively analyzed
in terms of the portfolio-balance theory pioneered by Markowitz8 and Tobin. 9 That theory
focuses on the way in which an investor, through
diversification, can reduce the fluctuations in the
earnings of his portfolio as a whole. In other
words, "Don't put all your eggs in one basket."
In order for diversification to have this benefit,
it is necessary that the returns on the various
assets held be less than perfectly correlated. If the
returns on different assets move together, there is
no advantage to diversification. However, if the
returns on one asset tend to be high when those
on another are low, and vice versa, the earnings
of a portfolio consisting of both of them will have

and the returns on those which he already holds.
The lower that covariance, the greater is the
reduction in risk gained from purchasing the new
asset. It follows that even a risk-averse investor
will generally find it to his advantage to include
in his portfolio some assets which, when viewed
individually, appear very risky.
Herbert Grubel has extended these ideas to an
international setting. 10 He points out that diversification into foreign assets can also reduce the
overall risk (i.e., variability of earnings) of a
portfolio even though it involves purchasing
assets subject to exchange risk. Of course, the
investor must now "translate" the returns on the
foreign assets into his own currency. Even so, if
business cycles are out of phase in different
countries, a portfolio consisting of assets of
several countries might generate more stable
earnings than a portfolio consisting only of
domestic assets.
Grubel is primarily interested in showing the
potential welfare gains from international diversification and in explaining observed patterns of
capital flows. However, it is possible to use his
idea of international portfolio balance to see how
yield spreads between countries in a risk-averse
world could be different from those under riskneutrality. Consider again a situation in which
the yield spread-in this case, on long bonds-in
favor of Canada more than compensated for an
expected depreciation of the Canadian dollar. As
before, it is clear that such a situation could
represent an equilibrium position from the point
of view of U.S. investors. But, once more, the
question arises whether it could represent an
equilibrium from the point of view of Canadians.
Would not Canadians have an incentive to sell
their U.S. long bonds and to buy Canadian long
bonds until the spread were equal to the expected
change in the exchange rate?
Not necessarily, because the Canadian long
bond is not a riskless asset from a Canadian

perspective. Although it is free from exchange
risk, it is still subject to interest-rate risk. There is
no reason to presume a priori that it is less risky
(to the Canadians) than the U.S. long bond. Hit
is not, risk-averse Canadian investors, like their
U.S. counterparts, would be willing to hold U.S.
long bonds despite the higher expected yield on
the Canadian securities.
There is a fundamental difference, then, between the example considered in Section I, in
which the only risk was exchange risk, and that
considered here, in which interest-rate risk is
present as well. Investors in either country might
find the combined risks on the foreign long-term
bond to be less than the interest-rate risk on the

domestic long bond. In that situation, they
would demand a premium on their domestic long
bond rather than on the foreign long bond.
To recapitulate, once account is taken of both
kinds of risk, it is possible to explain how
international yield spreads under risk aversion
can differ from those under risk neutrality without any appeal to the net debtor status of a
particular country. However, it would be desirable to be more precise than that. In particular, it
would be desirable to develop a relationship
equivalent to equation (2) for the case of riskaverse investors. To do so, it is necessary to
develop a formal model of international bond
markets.

III. A Model of International Bond Markets
In recent years, several authors have developed elaborate models of international securities
markets. I I However, the flavor of their results
can be adequately captured by a much simpler
model which we have developed based on the
work of Michael Porter. I2 Porter considers the
case of a country whose international lendings
and borrowings'are too small to have any impact
on the level of yields prevailing in the world
capital market. The yields in the world market
are taken as given and are not explained within
the model. What the model explains are the
spreads-positive or negative-between those
yields and the ones in the "small" country.
This model will be the starting point for the
empirical work in Section IV, in which Canada
will be viewed as a small country and the U.S. as
the world market. In 1976, the total value of new
Canadian bond issues sold abroad by all
entities-corporate and governmentamounted to less than three percent of net funds
raised in the U.S. Moreover, 1976 was a year of
unusually heavy borrowing by Canadians. During the first half of the 1970's, Canadian bond
issues sold abroad typically amounted to only
about one percent of net funds raised in the
U.S.I3 Therefore, the simplifying assumption of
the model-that the small country does not have
an appreciable effect on yields in the world
market-appears to be a reasonable one in the
context of this study.
As in the previous discussion, investors are

assumed to have four assets to choose from:
short and long bonds issued by both the small
country and the "rest-of-the-world" (which will
be referred to as Canada and the U.S., respectively). The stock of bonds outstanding is taken
as exogenous. Each investor knows with certainty the spot exchange rate and the one-period
nominal yields on both short securities; i.e., the
"period" of the analysis just matches the maturity of the shorts. He does not know for certain the
value of the exchange rate at the end of the
period nor the one-period nominal yields on the
longs, but his subjective probability distributions
for these variables can be completely summarized by their means and variances. With that
information, he sets out to allocate his funds
among the available assets so as to maximize the
expected utility of his end-of-period wealth,
expressed in terms of his domestic currency. 14
The maximization problem is straightforward, and the details are set forth in a technical
appendix which is available upon request. The
resulting conditions for a maximum can be
simplified in the case of the average U.S. investor
by recognizing that, in equilibrium, Canadian
bonds must account for only a negligible fraction
of the value of his portfolio. Otherwise, Canadian lending and borrowing decisions would influence U.S. yields, in violation of the small country
assumption. If the shares of Canadian bonds in
the typical U.S. portfolio are actually set at zero
as an approximation to the condition for an
25

where the subscript j refers to the risky asset in
question, S to the safe asset, and M to a market
basket of risky assets. In the risk premium term
in (3), Rj is replaced by the total return to a U.S.
investor on the risky foreign long. In place of
R M there appears R L, which is the domestic
market basket in this simplified model.
There are intuitive explanations for the presence of the various components of the risk
premium in (3). The higher the expected yield on
the U.S. long relative to the yield on the safe
asset-the U.S. short-the higher must be the
total return expected on the Canadian ·long
before a risk-averse U.S. investor will purchase
it. Thus, [E(R L) - R S] enters the premium term
with a positive sign. The greater the covariance
between the yields on the U.S. long and on the
Canadian long (adju;sted for expected exchange
rate changes), the smaller are the gains from
diversification provided by the latter. Again, the
total return of the Canadian long must be higher
to compensate, so A enters positively. Its total
vield must similarlv be higher, the smaller the
~ariance of the retu~n on the U.S. long, for then
the risk of a capital loss on the U.S. long is
smaller. The variance of R L therefore enters
negatively.
The preceding discussion looked at the components of the risk premium from the point of
view of a U.S. investor, who would demand such
a premium as a condition for holding Canadian
bonds. But, as was argued in Section II, a riskaverse Canadian investor would generally not
want to sell all of his U.S. longs in order to buy
Canadian longs whenever the yield on the latter
was higher than the level consistent with equation (2). Both longs are risky assets to him, and
the relative desirability of each would depend on
the same kind of factors which entered the
calculations of the U.S. investor.
The fact that the concerns of investors in both
countries are really quite similar suggests that, a
priori, one should not expect a positive premium
to be always included in the yield on the long
bond of the small country. U.S. investors could
reasonably decide that the combined exchangerate risk and interest-rate risk of the Canadian
security is less than the interest-rate risk of the
U.S. long. In fact, the "premium" in equation (3)
could clearly be negative as well as positive, for

expected-utility maximum for U.S. investors.' it
is possible to derive expressions for CanadIan
yields.
.
The result which is of most interest here IS:
'"
'"
[E(R L) - R S] . A
E[(l + R* ) (l +dF)] = I + R S +
'"
L
var(RL)
where A = cov[(l + Ie
-

), (l + R! ) (I

+dF)].
(3)

Rs is the known one-period yield on the U.S.
short, and R L the one-period yield on the U.S.
long. Since R L is a random variable at the start
of the period, it is written with a tilde. RS and
Rt are the corresponding Canadian yields. The
symbol LlF stands for the percentage chan~e in
the spot exchange rate during the next penod.
Equation (3) relates the total expected yield ~n
the Canadian long, adjusted for any change III
the exchange rate, to the yield on the U.S. short,
plus a term which may be thought of as cons~itu~
ing a risk premium. The reason for interpretmg It
as a risk premium is simple: were it to be zero,
equation (3) would reduce to (2), the equilibrium
condition under risk neutrality.
Since (3) was derived solely from the conditions for a maximum for U.S. investors, the
small-country assumption might seem to imply
that Canadian yields are determined in the U.S.
However, it would be incorrect to make that
inference. For (3) is merely a statement about the
expected product of the Canadian long yield and
the rate of change in the exchange rate. It says
nothing about the determination of either ~f
those magnitudes individually. For example, It
does not rule out the possibility that Canada
could arbitrarily peg the yield on its long bonds.
But equation (3) does say that such an acti~n
would determine the expected rate of change III
the exchange rate, given values for the yield on
the U.S. short and for the risk premium. I5
The risk premium term will look familiar to
anyone acquainted with the work done on domestic financial markets by Lintner and
Sharpe. I6 Their "capital asset pricing model"
indicates that the expected yield on a risky asset
will, in equilibrium, equal the yield on the safe
asset plus a premium of the form:
[E(RM) - RS]' cov (Rj, RM)
var (RM)

the foreign currency was expected to depreciate.
In the case of risk-aversion, no such inference
about expected exchange-rate changes can be
made from an observation of yield differentials
alone. A yield differential in favor of a foreign
country would be compatible with an expected
appreciation of the foreign currency, provided
that the risk premium associated with that country's bonds were great enough. The likelihood of
such an occurrence depends on the quantitative
significance of the risk premiums, which is the
subject of the next section.

the two terms in the numerator could individually be ofeither sign. It is really better thought ofas
an "adjustment" for risk. But the word "premium" is well-established and will be maintained
here, with the understanding that it need not be
positive.
The incorporation of risk premiums (positive
or negative) into the yields of internationally
traded assets can create a fundamental difference
in the interpretation of international yield
spreads, depending on the risk characteristics of
investors. In a risk-neutral world, the foreign
yield could exceed the domestic one only when

IV. Empirical Tests of the Model
whether the effect of exchange risk on interestrate differentials had in fact differed under the
two regimes. Conceptually, the model outlined
in the technical appendix is applicable to both
fixed and flexible rates. However, the problem of
finding adequate proxies for expectations and
risk under fixed rates has so far prevented its use
outside of a period of flexible rates.
The behavior of yield spreads between the two
countries, under both types of exchange-rate
systems, is summarized in Table I and in Chart I.

In real-world financial markets, of course,
there are many factors influencing interest-rate
spreads other than expectations of exchangerate movements and adjustments for interestrate and exchange-rate risk. Differences among
national tax systems and government controls
on capital flows are two which come immediately
to mind. Some of these problems are avoided in
the present case by choosing Canada and the
U.S. for the empirical part of this study. Observation of model relationships is facilitated by the
high degree of integration of the U.S. and Canadian capital markets, and by the relative absence
of official interference in financial transactions
between the two countries. Also, by limiting
observations to yields on government bonds, we
avoid distortions caused by default risk. Because
of difficulties in obtaining comparably-defined
data series for the two countries, yields on bonds
maturing in three-to-five years were used for
their long-term interest rates. The market yield
on three-month Treasury bills was used for the
U.S. short rate. l ?
The period analyzed was from June 1971
through December 1975, during all of which time
the Canadian dollar was allowed to float. Canada had actually dropped its fixed exchange rate
in mid-1970, but, as is explained below, a year's
worth of observations was used up in the formation of a proxy for the risk premium. It would
have been desirable to have included a period of
fixed exchange rates in the study, to determine

Table 1
Summary Statistics for Canadian-U.S.
Yield Differentials on 3-5-Year Bonds
2

5.609
1.097

0.747
0.319

0.957

7.048
l.lOO

0.148
0.490

0.904

4
Correlation
U.S. Canadian Yield Spread, Coefficient
Yields Yields Canadian-U.S. Cols. 1 & 2

JUly 1962December
1969
4.862
Mean
1.079
Standard
deviation
June 1971December
1975
Mean
6.900
Standard
0.889
deviation

periods when U.S. balance of payments programs were applied to Canada, the predominant
pressures on the Canadian dollar [from 1962 to
1970] were up, not down."18 Given the expectation of a revalued Canadian dollar, the model of
risk neutrality would predict lower, not higher,
Canadian yields in relation to U.S. yields.
These observations suggest the importance of
risk premiums in Canadian-U.S. interest differentials, but econometric tests are necessary to see
whether those premiums are really statistically
significant. Consider again the basic model,
which is rewritten here with the left-hand side
expanded:
[1 + E(RV] [1 + E(D.F)] +cov(R:t ,~F)= 1+ R S

Perhaps the most obvious relationship is the
close parallel movement of yields on Canadian
and U.S. medium-term bonds under both types
of exchange-rate regimes. The correlation is
higher for the fixed-rate period than for the
period of float, but not strikingly so.
The comparison also shows that the average
spread in the 1960's exceeded that of the flexiblerate period of the 1970's. This pattern of yield
spreads does not accord with the simple view that
foreign lending is riskier under flexible rates than
under fixed rates, and that U.S. lenders, who are
assumed to determine the spread, therefore demand higher yields to compensate for the greater
risk resulting from flexible rates. The fact that
average spreads were positive during the fixedrate period also casts doubts on the model of risk
neutrality, since, "with the exception of brief

[E(R: U -RS] . A
var(R L)

Chart 1

CANADIAN-U.S. BOND RATES
Percent

Percent

Panel 2

1971-1975

Panel 1
1962-1969

Canadian bonds »(3-5 year maturity)

Canadian bonds
(3-5 year maturity)

...

6
""U.S. bonds
(3-5 year maturity)

1..--_.l..-_..I.-_.....L...._-1..._--1.._--'-_--I._---' ~_i..--_.l.--_....1.-_-1..._--l.._---'

1962

1963

1964

1965

1966

1967

1968

1969

1971

1972

1973

1974

1975

1916

premium, the only presumption we could make
about this coefficient was that it should be
positive and significant. Similarly, although no
constant term appears in the theoretical equation, one was included in the regressions to pick
up those effects not covered by the model, such
as differential tax policies in the two countries.
For the expectations assumption of no
exchange-rate change, the results of a leastsquares estimation were:

Before one can run a regression on that equation,
the unobservable expectation and risk variables
have to be replaced with observable magnitudes.
For the expected yields on the long bonds, we
made the usual assumption that expected yields
equal current-market yields.J9 For the components of the risk premium, we proxied the unobserved variances and co-variances with twelvemonth moving sample variances and
covariances. This procedure is also a standard
one, although the choice of twelve months for the
size of the sample was somewhat arbitrary.2o
It was also necessary to find a suitable proxy
for exchange-rate expectations-a crucial problem, since the use of an inadequate expectations
proxy could seriously bias the tests for the
significance of the risk premium. Rather than
trying to find "the" correct proxy, we decided to
run regressions with two different expectations
variables in order to gauge the strength of any
results involving the risk premium.
Under the first alternative, we assumed that
investors expect no change in the exchange rate.
They may have a wide variance concerning their
expectations, but their "best guess" is that the
rate will be the same in the future as now. 21
Under the second alternative, we assumed that
investors expect some "normal" level of the
exchange rate to prevail in the long-run. Whenever the current rate deviates from this level, they
expect that future rates will move back to it. This
assumption is supported by the fact that the
Canadian-U.S. exchange rate could statistically
be described as "stationary" during the sample
period, showing a tendency to fluctuate around a
mean level of$1.003. 22 This value was used as the
expected future spot rate in the second set of
estimations.
The tests of the model were based on regressions of the form:
[1 + E(R

t)] [1 + E(LlF)] + cov(Rt,

Constant 0.0034 (2.9)
Risk Premium 0.57 (9.1)
R2 0.61
D.W.0.44

(Note: Numbers in parentheses are t-statistics.)
Although the t-statistics are quite large, the
very low Durbin-Watson statistic indicates that
the t-values may be biased upwards. The low
D. W. value indicates either positive autocorrelation in the error-term of the equation or the
inclusion of a distributed lag in the correct
specification of the equation. On the basis of a
test suggested by Griliches, it was concluded that
autocorrelation was the better explanation. 23
Accordingly, the equation was re-estimated using the Cochrane-Orcutt correction for autocorrelation. The results were:
Constant 0.0051 (1.5)
Risk Premium 0.42 (4.5)
p 0.81 (9.9)
R2 0.85
D.W.1.8

The risk premium appeared to be highly significant and had the correct sign. But, of course, the
validity of any inferences based on the equation
are conditional on the assumption that
exchange-rate expectations are adequately captured by the proxy used for them. It was therefore important to see how robust these results
would be under an alternative expectations assumption.
When the equation was re-estimated with the
second expectations proxy-the exchange rate
reverting to its mean-the Durbin-Watson statistic was again very low, 0.21. Application ofthe
Cochrane-Orcutt procedure did not cure the
problem. After some experimentation with alternative distributed lags, it was found that the

LlF)-

(l + RS) = a + b . (Risk Premium) + u.

The left-hand variable is the amount by which
the expected total return on a Canadian bond to
a U.S. investor exceeds the return on the U.S.
safe asset. The model would predict a coefficient
on the risk premium of + 1. However, since the
model itself was based on highly restrictive
assumptions, and since a proxy was used for the
29

[1/(1 0.81)] (0.29) = 1.5, which is much larger
than the coefficient under the first expectations
assumption.

best specification was a simple Koyck lag, corrected for autocorrelation.
Constant -0.011 (-2.8)
Risk Premium 0.29 (2.7)
Dependent Lagged One 0.81 (12.0)
p 0.26 (1.9)
R2 0.91

The fact that the risk premium is significant in
both sets of regressions suggests that CanadianU.S. yield spreads do incorporate adjustments
for risk, caused by interest-rate and exchangerate variability. But without a more rigorous
approach to modeling exchange-rate expectations, the magnitude of those adjustments is
difficult to gauge.

D.W. 24 2.03

The risk premium is still significant at the 5percent level and still has the correct sign. However, the steady-state value of its coefficient is

V. Summary and Conclusions
investor is generally able to reduce the fluctuations in his total earnings. A risk-averse investor
will therefore find it worthwhile to hold some
portion of his wealth in the form of the bond with
the lower expected yield, in order to reap the
gains from diversification.
Empirical evidence based on the behavior of
Canadian-U.S. interest-rate differentials supports the hypothesis that investors are riskaverse. As a result, yield spreads between countries may be a poor guide to the market's
expectations about future exchange rate movements. At the very least, those yield spreads may
give a false impression about the size of expected
movements. At worst, ifthe risk premium is large
enough, they may even give a wrong signal
regarding the sign of such movements.

The major theme of this article has been the
difference in international yield spreads on longterm bonds when investors are averse to risk, as
opposed to when they ignore risk. In the latter
case, yield spreads merely reflect expected
exchange-rate movements. In the former, they
also reflect adjustments for the combined effects
of interest-rate risk and exchange-rate risk.
Why would an investor simultaneously hold
both domestic and foreign long bonds when their
expected yields (adjusted for anticipated
exchange-rate changes) are not equal? The explanation can be found in the concept of "portfolio balance." Both bonds are subject to
interest-rate risk; the foreign bond is subject to
exchange-rate risk as well. By holding a diversified portfolio which includes both of them, an

FOOTNOTES

1. Donald Heckerman, "On the Effects of Exchange Risk,"
Journal of International Economics (September 1973). pp. 379387.
2. Franco Modigliani and Richard C. Sutch, "Innovations in
Interest Rate Policy," American Economic Review (May 1966).
pp. 178-197.
3. See, for example, the survey article by Michael C. Jensen,
"Capital Markets: Theory and Evidence," Bell Journal of Economics and Management Science (Autumn 1972). pp. 357-398.
4. Other sources of risk, such as default risk, have been implicitly assumed away in this example in order to highlight the
effect of exchange risk. Furthermore, the complications introduced by differences in national tax policies are not considered. For a recent discussion of the potential impact of such
differences, see Maurice D. Levi, "Taxation and 'Abnormal'
International Capital Flows," Journal of Political Economy
(June 1977), pp. 635-646.
5. The investor could, of course, sell forward the anticipated
foreign exchange receipts. But for most currencies, organized

forward markets do not exist for maturities as long as a year.
Throughout Section I, it is assumed that investors are concerned with the value of their wealth as expressed in terms of
their own currencies. Some of the implications of relaxing this
assumption are discussed in Section III.
6. The adjustment mechanism need not work entirely through
changes in the yields. As funds are shifted from the U.S. to
Canada, F will increase, helping to restore equality (2). But E(F)
may then change in response to the change in F, further
complicating matters. A priori, all that can be said is that some
or all of the four quantities, R, R", F, and E(F) will change until
(2) is satisfied.
7. For a summary discussion of recent work on domestic termstructure, see Rose McElhattan, "The Term Structure of Interest Rates and Inflation Uncertainty," Economic Review, Federal
Reserve Bank of San Francisco (December 1975). pp. 27-35.
8. Harry Markowitz, Portfolio Selection (New York: Wiley,
1959).

9. James Tobin, "Liquidity Preference as Behavior Toward
Risk," Review of Economic Studies (February 1958), pp. 65-86.
10. Herbert Grubel, "Internationally Diversified Portfolios:
Welfare Gains and Capital Flows," American Economic Review
(December 1968), pp. 1299-1314.
11. Bruno H. Solnik, European Capital Markets (Lexington,
Massachusetts: D.C. Heath and Company, 1973); Frederick
Grauer, Robert Litzenberger, and Richard Stehle, "Sharing
Rules and Equilibrium in an International Capital Market under
Uncertainty," Journal 01 Financial Economics (June 1976), pp.
233-256.
12. Michael G. Porter, "A Theoretical and Empirical Framework
for Analyzing the Term Structure of Exchange Rate Expectations," International Monetary Fund Staff Papers (November
1971), pp. 613-642.
13. Sources: Bank 01 Canada Review and Federal Reserve
Bulletin.
14. The conditions under which it would be optimal for an
investor to have a time horizon of only one period into the future
are detailed in the author's, An Analysis 01 International Yield
Curve Differentials (unpublished Ph.D. thesis, Harvard University, 1977), pp. 38-40.
15. An even stronger version of the small-country assumption
appears in Robert Mundell's article, "Capital Mobility and
Stabilization Policy under Fixed and Flexible Exchange Rates,"
Canadian Journal 01 Economics and Political Science (November 1963), pp. 475-485. There, he assumes that the expected
change in the exchange rate is zero, so that the small-country
yield is determined abroad. It is worth noting that, in assessing
the realism of the small-country simplification, he states that "It
should have a high degree of relevance in a country like Canada
whose financial markets are dominated to a great degree by the
vast New York market." (p. 475.).

16. The basic references to these and other authors may be
found in the survey article by Jensen cited in fn. 3.
17. These series all appear in various issues of the Federal
Reserve Bulletin and of the Bank of Canada Review. The latter
publication was the source of the exchange rate series, which
consists of monthly averages of daily noon rates.
18. Paul Wonnacott, The Floating Canadian Dollar (Washington, D.C.: American Enterprise Institute, 1972), p. 39.
19. See the discussion of FW. Sharpe, "Reply," Journal of
Business (April 1968), p. 235.
20. It would be wrong to use as a risk proxy just a moving
variance of the exchange rate, despite the intuitive appeal of
such a construct as a measure of the risk on foreign assets. To
do so would ignore the role of interest-rate risk. Furthermore, it
would miss the fundamental notion of portfolio-balance theory:
that covariances among yields are the key factors in gauging
risk. Finally, a moving variance is always positive, while the
"premium" can be positive or negative.
21. Empirical support for this expectations assumption, based
on its forecasting ability, may be found in Ian H. Giddy and
Gunter Dufey, "The Random Behavior of Flexible Exchange
Rates: Implications for Forecasting," Journal of International
Business Studies (Spring 1975), pp. 1-32.
22. A time-series analysis of the Canadian-U.S. exchange rate
is contained in the author's dissertation, cited in fn. 14.
23. Zvi Griliches, "Distributed Lags: A Survey," Econometrica
(January 1967), pp. 33-34.
24. When one of the regressors is a lagged-dependent variable,
the proper test for autocorrelation is based on the h-statistic.
See Potluri Rao and Roger Miller, Applied Econometrics (Belmont, California: Wadsworth, 1971), p. 123. In this instance,
however, the h-test merely confirms the impression given by
the OW. statistic, that autocorrelation is no longer present.

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