- Email: [email protected]
What explains the risk premium in foreign exchange returns?
Journal of’ International
Money and Finance 1994 13(6) 729-738
What explains the risk premium in foreign exchange returns? TIMOTHY C GOKEY* McKinsey
& Company,
Minneapolis,
MN 55402, USA
We decompose excess returns to holding foreign exchange into components associated with deviations from real interest rate parity and purchasing power parity, respectively. We find that deviations from purchasing power parity account for over 80 percent of the predictable variation in excess returns to holding foreign exchange in the period 1974489 and that deviations from real interest rate parity play a relatively minor role. (JEL
F31, G12, G15). For some time now, there has been a considerable body of evidence showing the existence of predictable components in excess returns to holding foreign exchange.’ The most popular explanation for such components is that non-zero expected returns represent compensation for economic risk. Nevertheless, a substantial amount of empirical research has failed to demonstrate a measure of foreign exchange risk which can account for observed predictable components in foreign exchange or, indeed, which is even priced. At least since Solnik (1974), and particularly since Adler and Dumas (1983), one strong current in literature has been that deviations from purchasing power parity (PPP) are the distinguishing feature of asset pricing in an international context. Yet empirical work seeking to apply asset pricing models to foreign exchange has continued to focus on models which assume purchasing power parity.2 These models imply that the risk premium on foreign exchange is identically equal to real interest rate differentials across countries. The implicit argument in empirical work pursuing this approach is that deviations from PPP are of secondary importance for explaining risk premia on foreign exchange. This point of view was bolstered by the widely cited empirical paper of Korajczyk (1985) who could not reject the hypothesis that real interest rate differentials completely account for risk premia on foreign exchange. While more recent evidence has shown that Korajczyk’s tests lacked power and that deviations from PPP must play some role in pricing foreign exchange, the key question of just how important they really are in explaining predictable returns remains unclear. *This paper is derived from chapter 2 of the author’s doctoral dissertation at Oxford University. I wish to thank Michael Adler, Stephen Bond, Derek Morris, Tim Jenkinson, Stewart Hodges, James Lothian and two anonymous referees for helpful comments. All remaining errors are the author’s responsibility. Financial support from the Rhodes Trust and Harry S Truman Foundation is gratefully acknowledged. 0261.-5606/94/06072910
I$ 1994 Butterworth-Heinemann
Ltd
In this paper we decompose ex ante exchange risk premia into components associated with deviations from real interest rate parity (RIRP) and ex ante purchasing power parity (EPPP), respectively. We find that the latter is of far greater significance than the former, accounting for over 80 percent of the predictable variation in excess returns to holding foreign exchange in the period 1974 to 1989. This finding complements and confirms the work of Levine (1989, 1991) and strongly suggests that an asset pricing model which accounts for deviations from purchasing power parity is required in order to seriously address the issue of pricing of foreign exchange risk. The paper is organized as follows: Section I provides the relevant background; Section II describes the methodology and results and Section III concludes.
I. Background The evidence we review below is based on a simple decomposition of excess returns to holding foreign currency into deviations from purchasing power parity and differences across countries in real interest rates. This well-known decomposition may be stated as follows: E,_,(i/-$+ds,) (1)
= E,_,(r[-r;)
+ E,_,(~s,-~c~+?I[),
Ex ante excess
Real interest
Ex ante
return to
differential
deviation
foreign exchange
from
relative PPP
where rl and i, are the real and nominal interest rates from t - 1 to t, rc, is the rate of inflation from t - 1 to t (all stated in continuously compounded terms), ds, is the change in the log of the exchange rate (domestic currency per unit foreign currency) from t - 1 to r, and superscripts r and d refer to foreign and domestic values3 In (I), the operator E,_ 1 indicates that all values are conditional on information available at time t - 1, but the identity also holds in ex post form. Note that the excess return as defined here is the dollar denominated excess return to holding foreign currency. The decomposition (1) has motivated several empirical investigations. In a widely cited study, Korajczyk (1985) could not reject the hypothesis that expected excess returns to holding foreign exchange are equal to expected real interest differentials. Using more powerful instruments, Levine (1989) does reject the hypothesis that real interest rate differentials fully account for predictable components of returns. Going further, Levine (1991) cannot reject the hypothesis that predictable components in real exchange rates (deviations from PPP) fully account for predictable components in returns, implying that real rate differentials play no role. Although focusing on deviations from EPPP, Huang (1990) also provides evidence which links such deviations to risk premia in forward foreign exchange. Applying a regression methodology analogous to that of Fama (1984), Huang demonstrates that the variability of time-varying deviations from EPPP exceeds the variation in ex ante real interest rate differentials and that the variation in ex ante real interest rate differentials is too low to account for the systematic
Risk premia
in ,fiwign
exchange:
Timo/hy
C Gokq,
UK 30
20
10
0
-10
I
-20
I
I
1978
I
1
I
I
i 982
1980
I
I
1984
I
i 986
I
I
1988
20
10
0
-10
-20
I
I
I
1978
I
1980
I
I
I
1982
I
I
1984
I
1986
I
I
1988
Year FIGURE
Journul
of Intcmational
1. Decomposition
Mane),
and Finance
of ex post exchange
1994 Volume
13 Number
risk premia.
6
731
Germany
30:
_^
I
differentia
Deviation from PPP
1980
1978
1982
1984
1988
1986
Year
Canada
20
10
Exchange
Real
interest
premium
differential
0
-10
-20
I
1978
I
I
1980
I
I
I
I
1984
1982
Year
732
I
I
1986
I
,
1988
I
Ri.yk premix
in forrign
eschange:
Timoth),
C Coke),
failure of EPPP, implying that predictable components in nominal returns and deviations from EPPP must be related. He also uses a latent variable model to show that the forward exchange risk premium and deviations from EPPP move together. Due to the inherent unobservability of the risk premium, Korajczyk, Levine and Huang employ somewhat indirect methods to arrive at their conclusions. Moreover, while it seems that both deviations from EPPP and real interest rate differentials must play some part in explaining risk premia in foreign exchange, the relative importance of the two components remains unclear.
II. Evidence
from a direct decomposition
In order to address these issues, we employ an approach based on direct examination of the decomposition (1). The findings complement previous results discussed above and strongly suggest that deviations from EPPP play the primary role.
ZZ.A. Description qf data We consider spot exchange and eurodeposit rates for nine countries versus the US dollar over the period 1974:l to 1989: 12. The data are obtained from the Foreign E_whange Weekly tape from the Harris Trust and Savings Bank of Chicago, IL. The Harris Bank data are chosen because of its extensive use by previous investigators.4 The underlying data are weekly, and monthly observations are created by sampling the Friday closest to the end of each month. Extensive diagnostics are undertaken and the data are in most cases cross-checked against a second source. Local inflation is based on consumer price indices as reported by the International Monetary Fund’s International Financial Statistics data tape.5 To set the context, Figure 1 displays the decomposition (1) in ex post form. Several previous investigators (e.g. Frankel and MacArthur, 1988) have conducted such examinations. However, their focus and data sets typically provide a snapshot of one time period only. In order to address the issue of time-variation, we examine every possible 36 month sub-period between 1974:l and 1989:12. Figure 1 presents the results for four countries; the others are qualitatively similar. Each observation represents the average ex post outcome for each quantity over the previous 36 months. The important role played by deviations from purchasing power parity is illustrated by their much greater magnitude and time variation compared to real interest rate differentials. The result is very high correlation between deviations from PPP and exchange premia, while real interest rate differentials appear to play a much smaller role. One reason to be cautious about the results in Figure 1 is that a substantial portion of the apparent relation between ex post excess returns and PPP deviations could be due to shared unpredictable components related to changes in the exchange rate. Journal
of Inirrnutionnl
Mane>, und Finance
1994 Volume
I3 Number 6
733
0.892 (0.125)
0.799 (0.080)
0.815 (0.121)
0.051 (0.042)
0.035 (0.025)
0.047 (0.035)
0.093 (0.066)
0.037 (0.024)
0.035 (0.032)
0.083 (0.059)
UK
Germany
Japan
Canada
Belgium
France
Italy
Netherlands
0.120 (0.096) 0.125 (0.115) 0.042 (0.036) 0.119
0.257 (0.092) - 0.006 (0.138) 0.102 (0.209) 0.115
0.660 (0.103)
0.967 (0.130)
0.800 (0.177)
0.827
0.039 (0.027)
0.098 (0.093)
0.058
Switzerland
Average
0.989
0.974 (0.145)
1.206 (0.260)
0.709 (0.182)
0.894 (0.114)
1.203 (0.286)
0.028 (0.028)
1.028 (0.338)
0.153 (0.253)
0.132 (0.163)
0.135 (0.094)
1.028 (0.454)
0.191 (0.248)
0.138 (0.114)
0.830 (0.101)
0.979 (0.108)
0.025 (0.036)
0.166 (0.072)
0.134 (0.137)
0.877 (0.370)
0.254 (0.215)
0.057 (0.130)
0.053 (0.101)
Deviation from PPP
Real rate difference
Interaction effect
variation
by component.
-0.108
-0.016 (0.155)
-0.331 (0.316)
0.171 (0.208)
0.077 (0.122)
-0.337 (0.372)
-0.181 (0.542)
-0.219 (0.641)
0.036
0.030 (0.026)
0.020 (0.014)
0.030 (0.019)
0.018 (0.013)
0.012 (0.009)
0.147 (0.128)
0.034 (0.028)
0.012 (0.010)
- 0.004 (0.115)
0.025 (0.016)
Real rate difference
-0.131 (0.491)
Interaction effect
B. 1974:1-1980:12
of predictable
0.910 (0.100)
0.775 (0.167)
Deviation from PPP
Real rate difference
A. 1974:lL1989:12
TABLE 1. Decomposition
0.838
0.819 (0.087)
0.862 (0.074)
0.845 (0.083)
0.871 (0.069)
0.864 (0.059)
0.776 (0.237)
0.804 (0.096)
0.859 (0.056)
0.842 (0.08 1)
Deviation from PPP
C. 1981:1-1989:12
0.126
0.151 (0.083)
0.118 (0.068)
0.125 (0.078)
0.111 (0.066)
0.124 (0.052)
0.077 (0.270)
0.162 (0.084)
0.129 (0.051)
0.133 (0.074)
Interaction effect
.j-
;
P ,Z-
g
6 2 ;r. 4 2 $5
5’
2.
II.B. Ex ante results To investigate the ex ante (predictable) components in which we are chiefly interested, we examine the variability of fitted values from a linear projection of each quantity onto an instrument set available at time t - 1. This has the effect of purging each series of expectational errors and focusing attention on ex ante components. The instrument set employed here consists of a constant, five of the nine forward premia (lagged one period to avoid problems due to measurement error),6 and the time t - 1 own country inflation differential versus the USA. Using the simple identity Var(a + b) = Var(a) + Var(b) + 2 Cov(a, b), we are able to decompose the total ex ante variation in risk premium into components due to variation in ex ante real interest rate differentials, variation in deviations from EPPP and interaction between the two. We then normalize by the ex ante variation in excess returns so that each component is expressed as a percentage of the total variance and the three components sum to one. The results are presented in Table 1. They provide further support for the qualitative story of Figure 1. Over the full period 1974 to 1989, variation in ex ante real rate differentials accounted for less than 6 percent of the total predictable variation in excess returns on foreign exchange, while deviations from EPPP accounted for over 80 percent. Sub-period results, also reported in Table 1, confirm these findings. For 1974480, deviations from RIRP explain about 12 percent of predictable variation in excess returns; for 1981-89, they account for less than 4 percent. The robustness of the findings in Table 1 is investigated in two ways. First, a small Monte Carlo experiment, described in the Appendix, is conducted to assess the potential impact of sampling error in the linear projection equations. Resulting standard errors are reported in parentheses in Table 1. The implication that deviations from PPP account for the major proportion of predictable variation and that deviations from RIRP play a much smaller role is strongly confirmed in all cases.’ As a final check, the analysis of Table 1 is repeated with an alternative instrument set consisting of a constant, the own forward premium, exchange rate change, and inflation differential (all lagged one period). The results are qualitatively similar to those reported here.8
III. Discussion The evidence above confirms the inferences of Levine (1989, 1991) and Huang (1990) that deviations from real interest rate parity alone cannot account for exchange premia. Indeed, as found by Levine (1991), deviations from PPP are the primary factor explaining such premia, accounting for nearly 80 to 90 percent of their time variation. This is an important stylized fact which relates to a number of strands of ongoing investigation. A variety of theoretical models have examined international asset pricing under the assumption that relative purchasing power parity holds.’ Equation (1) shows that any foreign exchange risk premium in such models must correspond directly to differentials in real interest rates (since deviations from PPP are zero). As we have seen that real interest rate differentials can account for only a small
Risk premia
in ,Jiweign eschange:
Timorhy
C Coke)
proportion of ex ante returns to holding foreign exchange, it would seem that models based on the PPP assumption cannot account for this phenomenon. Therefore, an important implication of the results here is that deviations from EPPP must play a significant role in any serious theoretical or empirical model attempting to account for exchange premia. The results here also shed light on the finding by Fama (1984) that risk premia in foreign exchange and expected changes in the spot rate covary negatively.” Fama finds this result surprising and somewhat anomalous, while Hodrick and Srivastava (1986) give an involved example of how such a phenomenon could arise in a PPP setting. Gokey (1991) finds the correlation noted by Fama is in fact nearly perfect, which is particularly difficult to explain in a PPP context since such a setting necessarily relies on a relatively indirect mechanism relating to real interest rates in the two countries. However, in a framework which does not impose PPP, equation (1) suggests that expected changes in the exchange rate can translate directly into excess returns to foreign exchange via deviations from EPPP. The finding that most of the variation in risk premia is in fact due to deviations from EPPP therefore explains both the direction and high degree of correlation between risk premia and expected exchange rate changes. Appendix This Appendix describes the Monte Carlo experiment used to derive the standard errors reported in Table 1. A system estimator is employed to jointly estimate the coefficients for the projection equations for deviations from RIRP and EPPP for each country (it is easily verified that the coefficients for the projection equation for excess returns may be obtained in all cases from the sum of the coefficients in the other two equations). Although the system estimator does not increase the power of the estimation (since the variables in each equation are the same), it does yield a covariance matrix for the coefficients both within and across the two equations. Using a multivariate normal distribution with mean vector and covariance matrix given by the system estimator, a random sample of 500 observations of the vector of 14 coefficients in the two projection equations are generated for each country. For each observation, the variances of predictable returns and deviations from RIRP and PPP are calculated using coefficients for the linear projection generated from the normal distribution and the actual data for the independent variables. For each of the 500 observations, the variance ratios (including interaction effect) are then calculated, and the standard errors reported in Table 1 are the standard deviations of the resulting 500 sets of variance ratios.
Notes 1. For an extensive
2.
3.
4.
survey of work showing the existence of predictable components, see Hodrick (1987). Examples ofmore recent investigations include Cumby (1988) Korajczyk and Viallet (1992), and Bekaert and Hodrick (1993). Examples of recent papers examining pricing of foreign exchange contracts include Mark (1988) Cumby (1988) and Korajczyk and Viallet (1992). For a survey of previous work. see Hodrick (1987). Derivation begins with the definition of real interest rates rj’ - r;’ = (ii - n{) - (if - 7~:). This can be rewritten as r/- rp = (i{ - i;’ + ds,) + (7~:- Z{ - rls,). Taking conditional expectations and rearranging yields (1). Including Fama (1984), Korajczyk (1985), Mark (1988), and Huang (1990), among others. As is well known, it is not possible with the Harris Bank data set to achieve correct thereby introducing a degree of alignment of forward and future spot observations,
Risk premier in ,foreiyn e.vchangr: Timothy C Gokq
5.
6.
7.
8.
9.
IO.
unavoidable measurement error into the data. We use lagged values as instrumental variables as suggested by Cornell (1989) to address this issue, and it should not affect the results here. See also Bekaert and Hodrick (1993). Many thanks to Professor Stephen Nickel1 and the Institute of Economics and Statistics at Oxford University for funding to purchase the Harris Bank data. Index values are taken to represent end-of-month prices, and local CPI’s are translated into dollars using end-of-month exchange rates. Although index values are actually more (1990) compares end-of-month and representative of mid-month prices, Huang mid-month assumptions and finds very little difference in results. Forward premia for the UK, Germany, Japan, France and Italy are employed for all equations. The number of forward premia is limited to five to facilitate the Monte Carlo experiment used to derive standard errors (described in the Appendix). Results using the instrument set here are qualitatively similar to those based on all nine forward premia (available from the author on request). Of course, the linear projection is subject to the usual caveats about potential misspecification (e.g. omitted variable biases, potential non-linearity of conditional expectations). The larger standard errors for the 1970s versus the 1980s or the overall period are driven by greater imprecision in the linear projections as well as by smaller predictable variation. This is in keeping with the findings of many investigators that the predictability of excess returns was much poorer in the 1970s than in the 1980s. See, for example, Bekaert and Hodrick (1993). These results are available from the author upon request. They attribute somewhat more influence to the interaction effect and somewhat less to deviations from PPP, but the influence of deviations from RIRP is still small. The results in Table 1 are preferred because the projection equations using the alternative instrument set have significantly higher standard errors and lower explanatory power. Grauer et al. (1976). Hodrick (1981, 1989) and Bekaert (1994) are illustrative of several approaches. Bekaert (1994) examines a decomposition similar to the one here as one explanation for his model’s lack of explanatory power. Note that ex ante excess returns as defined here are the negative of the risk premium as defined by Fama. Therefore. in the notation here, the issue is positice covariation of ex ante excess returns with expected changes in the spot exchange rate.
References ADLER, MICHAEL AND BERNARD DUMAS, ‘International portfolio choice and corporation finance: a synthesis,’ Journal of’Finunce, June 1983, 38: 925-983. BEKAERT, GEERT. ‘Exchange rate volatility and deviations from unbiasedness in a cash-in-advance model,’ Journal of’ International Economics, February 1994, 36: 29-52. BEKAERT,GEERT AND ROBERTJ. HODRICK, ‘On biases in the measurement of foreign exchange risk premiums,’ Journal of Internationul Money und Finance, April 1993, 12: 115-138. CORNELL, BRADFORD, ‘The jmpact of data errors on measurement of the forward exchange risk premium,’ Journal of International Money and Finance, March 1989, 8: 147-157. CUMBY, ROBERT E., ‘Is it risk? Explaining deviations from uncovered interest parity,’ Journal of Monetary Economics, September 1988, 22: 279-299. FAMA, EUCZN~ F.. ‘Forward and spot exchange rates,’ Journal of Monetury Economics. November 1984. 14: 319-338. FRANKEL, JEFFREY A. AND ALAN T. MACARTHUR. ‘Political versus currency premia in international real interest differentials: a study of forward rates for 24 countries,’ Europwn Economic Review, January 1988, 32: 1083-l 121. GOKEY, TIMOTHY C., Internationcrl Asset Pricing and the Foreign E.vchange Risk Premium: Theory and Evidence, unpublished D.Phil. Thesis, Oxford University, 1991. GRAUER, FREDERICK L. A., ROBERT H. LITZENBERGERAND RICHARD E. STEHLE, ‘Sharing rules and equilibrium in an international capital market under uncertainty,’ Journal sfFinancia1 Economics, June 1976, 3: 233-256.
HODRICK, ROBERT J., ‘International asset pricing with time-varying risk premia,’ Journul of International Economics, November 1981, 11: 573-587. HODRICK, ROBERT J.,The Empirical Evidence on the !?fji’cienc_yaf’Forward and Futures Foreign Exchange Markets, Harwood Academic Publishers, Chur, 1987. HODRICK, ROBERTJ., ‘Risk, uncertainty. and exchange rates,’ Journal of’Monetary Economics. May 1989. 23: 433-459. HODRICK, ROBERTJ. AND SANJAY SRIVASTAVA,‘The covariation of risk premiums and expected future spot exchange rates,‘Journalqf’lnternational Money and Finance, April 1986,5: S5-21. HUANG, ROGER D., ‘Risk and parity in purchasing power,’ Journal of‘ Money, Credit and Banking, August 1990, 22: 339-356. KORAICZYK, ROBERT A., ‘The pricing of forward contracts for foreign exchange,’ Journal of Political Economy, April 1985, 93: 346-368. KORAJCZYK, ROBERTA. AND CLAUDE J. VIALLET, ‘Equity risk premia and the pricing of foreign exchange risk,’ Journal qf’international Economics, November 1992, 33: 199-219. LEVINE, Ross, ‘The pricing of forward exchange rates,’ Journal of‘ International Money and Finance, June 1989. 8: 163-179. LEVINE, Ross, ‘An empirical inquiry into the nature of the forward exchange rate bias,’ Journal qf’lnternational Economics. May 1991, 30: 359-369. MARK, NELSON C., ‘Time-varying betas and risk premia in the pricing of forward foreign exchange contracts,’ Journal of Financial Economics, December 1988, 22: 335-354. SOLNIK, BRUNO H., ‘An equilibrium model of the international capital market,’ Journal of Economic Theory, August 1974, 5: 500-524.
738
Money and Finance 1994 13(6) 729-738
What explains the risk premium in foreign exchange returns? TIMOTHY C GOKEY* McKinsey
& Company,
Minneapolis,
MN 55402, USA
We decompose excess returns to holding foreign exchange into components associated with deviations from real interest rate parity and purchasing power parity, respectively. We find that deviations from purchasing power parity account for over 80 percent of the predictable variation in excess returns to holding foreign exchange in the period 1974489 and that deviations from real interest rate parity play a relatively minor role. (JEL
F31, G12, G15). For some time now, there has been a considerable body of evidence showing the existence of predictable components in excess returns to holding foreign exchange.’ The most popular explanation for such components is that non-zero expected returns represent compensation for economic risk. Nevertheless, a substantial amount of empirical research has failed to demonstrate a measure of foreign exchange risk which can account for observed predictable components in foreign exchange or, indeed, which is even priced. At least since Solnik (1974), and particularly since Adler and Dumas (1983), one strong current in literature has been that deviations from purchasing power parity (PPP) are the distinguishing feature of asset pricing in an international context. Yet empirical work seeking to apply asset pricing models to foreign exchange has continued to focus on models which assume purchasing power parity.2 These models imply that the risk premium on foreign exchange is identically equal to real interest rate differentials across countries. The implicit argument in empirical work pursuing this approach is that deviations from PPP are of secondary importance for explaining risk premia on foreign exchange. This point of view was bolstered by the widely cited empirical paper of Korajczyk (1985) who could not reject the hypothesis that real interest rate differentials completely account for risk premia on foreign exchange. While more recent evidence has shown that Korajczyk’s tests lacked power and that deviations from PPP must play some role in pricing foreign exchange, the key question of just how important they really are in explaining predictable returns remains unclear. *This paper is derived from chapter 2 of the author’s doctoral dissertation at Oxford University. I wish to thank Michael Adler, Stephen Bond, Derek Morris, Tim Jenkinson, Stewart Hodges, James Lothian and two anonymous referees for helpful comments. All remaining errors are the author’s responsibility. Financial support from the Rhodes Trust and Harry S Truman Foundation is gratefully acknowledged. 0261.-5606/94/06072910
I$ 1994 Butterworth-Heinemann
Ltd
In this paper we decompose ex ante exchange risk premia into components associated with deviations from real interest rate parity (RIRP) and ex ante purchasing power parity (EPPP), respectively. We find that the latter is of far greater significance than the former, accounting for over 80 percent of the predictable variation in excess returns to holding foreign exchange in the period 1974 to 1989. This finding complements and confirms the work of Levine (1989, 1991) and strongly suggests that an asset pricing model which accounts for deviations from purchasing power parity is required in order to seriously address the issue of pricing of foreign exchange risk. The paper is organized as follows: Section I provides the relevant background; Section II describes the methodology and results and Section III concludes.
I. Background The evidence we review below is based on a simple decomposition of excess returns to holding foreign currency into deviations from purchasing power parity and differences across countries in real interest rates. This well-known decomposition may be stated as follows: E,_,(i/-$+ds,) (1)
= E,_,(r[-r;)
+ E,_,(~s,-~c~+?I[),
Ex ante excess
Real interest
Ex ante
return to
differential
deviation
foreign exchange
from
relative PPP
where rl and i, are the real and nominal interest rates from t - 1 to t, rc, is the rate of inflation from t - 1 to t (all stated in continuously compounded terms), ds, is the change in the log of the exchange rate (domestic currency per unit foreign currency) from t - 1 to r, and superscripts r and d refer to foreign and domestic values3 In (I), the operator E,_ 1 indicates that all values are conditional on information available at time t - 1, but the identity also holds in ex post form. Note that the excess return as defined here is the dollar denominated excess return to holding foreign currency. The decomposition (1) has motivated several empirical investigations. In a widely cited study, Korajczyk (1985) could not reject the hypothesis that expected excess returns to holding foreign exchange are equal to expected real interest differentials. Using more powerful instruments, Levine (1989) does reject the hypothesis that real interest rate differentials fully account for predictable components of returns. Going further, Levine (1991) cannot reject the hypothesis that predictable components in real exchange rates (deviations from PPP) fully account for predictable components in returns, implying that real rate differentials play no role. Although focusing on deviations from EPPP, Huang (1990) also provides evidence which links such deviations to risk premia in forward foreign exchange. Applying a regression methodology analogous to that of Fama (1984), Huang demonstrates that the variability of time-varying deviations from EPPP exceeds the variation in ex ante real interest rate differentials and that the variation in ex ante real interest rate differentials is too low to account for the systematic
Risk premia
in ,fiwign
exchange:
Timo/hy
C Gokq,
UK 30
20
10
0
-10
I
-20
I
I
1978
I
1
I
I
i 982
1980
I
I
1984
I
i 986
I
I
1988
20
10
0
-10
-20
I
I
I
1978
I
1980
I
I
I
1982
I
I
1984
I
1986
I
I
1988
Year FIGURE
Journul
of Intcmational
1. Decomposition
Mane),
and Finance
of ex post exchange
1994 Volume
13 Number
risk premia.
6
731
Germany
30:
_^
I
differentia
Deviation from PPP
1980
1978
1982
1984
1988
1986
Year
Canada
20
10
Exchange
Real
interest
premium
differential
0
-10
-20
I
1978
I
I
1980
I
I
I
I
1984
1982
Year
732
I
I
1986
I
,
1988
I
Ri.yk premix
in forrign
eschange:
Timoth),
C Coke),
failure of EPPP, implying that predictable components in nominal returns and deviations from EPPP must be related. He also uses a latent variable model to show that the forward exchange risk premium and deviations from EPPP move together. Due to the inherent unobservability of the risk premium, Korajczyk, Levine and Huang employ somewhat indirect methods to arrive at their conclusions. Moreover, while it seems that both deviations from EPPP and real interest rate differentials must play some part in explaining risk premia in foreign exchange, the relative importance of the two components remains unclear.
II. Evidence
from a direct decomposition
In order to address these issues, we employ an approach based on direct examination of the decomposition (1). The findings complement previous results discussed above and strongly suggest that deviations from EPPP play the primary role.
ZZ.A. Description qf data We consider spot exchange and eurodeposit rates for nine countries versus the US dollar over the period 1974:l to 1989: 12. The data are obtained from the Foreign E_whange Weekly tape from the Harris Trust and Savings Bank of Chicago, IL. The Harris Bank data are chosen because of its extensive use by previous investigators.4 The underlying data are weekly, and monthly observations are created by sampling the Friday closest to the end of each month. Extensive diagnostics are undertaken and the data are in most cases cross-checked against a second source. Local inflation is based on consumer price indices as reported by the International Monetary Fund’s International Financial Statistics data tape.5 To set the context, Figure 1 displays the decomposition (1) in ex post form. Several previous investigators (e.g. Frankel and MacArthur, 1988) have conducted such examinations. However, their focus and data sets typically provide a snapshot of one time period only. In order to address the issue of time-variation, we examine every possible 36 month sub-period between 1974:l and 1989:12. Figure 1 presents the results for four countries; the others are qualitatively similar. Each observation represents the average ex post outcome for each quantity over the previous 36 months. The important role played by deviations from purchasing power parity is illustrated by their much greater magnitude and time variation compared to real interest rate differentials. The result is very high correlation between deviations from PPP and exchange premia, while real interest rate differentials appear to play a much smaller role. One reason to be cautious about the results in Figure 1 is that a substantial portion of the apparent relation between ex post excess returns and PPP deviations could be due to shared unpredictable components related to changes in the exchange rate. Journal
of Inirrnutionnl
Mane>, und Finance
1994 Volume
I3 Number 6
733
0.892 (0.125)
0.799 (0.080)
0.815 (0.121)
0.051 (0.042)
0.035 (0.025)
0.047 (0.035)
0.093 (0.066)
0.037 (0.024)
0.035 (0.032)
0.083 (0.059)
UK
Germany
Japan
Canada
Belgium
France
Italy
Netherlands
0.120 (0.096) 0.125 (0.115) 0.042 (0.036) 0.119
0.257 (0.092) - 0.006 (0.138) 0.102 (0.209) 0.115
0.660 (0.103)
0.967 (0.130)
0.800 (0.177)
0.827
0.039 (0.027)
0.098 (0.093)
0.058
Switzerland
Average
0.989
0.974 (0.145)
1.206 (0.260)
0.709 (0.182)
0.894 (0.114)
1.203 (0.286)
0.028 (0.028)
1.028 (0.338)
0.153 (0.253)
0.132 (0.163)
0.135 (0.094)
1.028 (0.454)
0.191 (0.248)
0.138 (0.114)
0.830 (0.101)
0.979 (0.108)
0.025 (0.036)
0.166 (0.072)
0.134 (0.137)
0.877 (0.370)
0.254 (0.215)
0.057 (0.130)
0.053 (0.101)
Deviation from PPP
Real rate difference
Interaction effect
variation
by component.
-0.108
-0.016 (0.155)
-0.331 (0.316)
0.171 (0.208)
0.077 (0.122)
-0.337 (0.372)
-0.181 (0.542)
-0.219 (0.641)
0.036
0.030 (0.026)
0.020 (0.014)
0.030 (0.019)
0.018 (0.013)
0.012 (0.009)
0.147 (0.128)
0.034 (0.028)
0.012 (0.010)
- 0.004 (0.115)
0.025 (0.016)
Real rate difference
-0.131 (0.491)
Interaction effect
B. 1974:1-1980:12
of predictable
0.910 (0.100)
0.775 (0.167)
Deviation from PPP
Real rate difference
A. 1974:lL1989:12
TABLE 1. Decomposition
0.838
0.819 (0.087)
0.862 (0.074)
0.845 (0.083)
0.871 (0.069)
0.864 (0.059)
0.776 (0.237)
0.804 (0.096)
0.859 (0.056)
0.842 (0.08 1)
Deviation from PPP
C. 1981:1-1989:12
0.126
0.151 (0.083)
0.118 (0.068)
0.125 (0.078)
0.111 (0.066)
0.124 (0.052)
0.077 (0.270)
0.162 (0.084)
0.129 (0.051)
0.133 (0.074)
Interaction effect
.j-
;
P ,Z-
g
6 2 ;r. 4 2 $5
5’
2.
II.B. Ex ante results To investigate the ex ante (predictable) components in which we are chiefly interested, we examine the variability of fitted values from a linear projection of each quantity onto an instrument set available at time t - 1. This has the effect of purging each series of expectational errors and focusing attention on ex ante components. The instrument set employed here consists of a constant, five of the nine forward premia (lagged one period to avoid problems due to measurement error),6 and the time t - 1 own country inflation differential versus the USA. Using the simple identity Var(a + b) = Var(a) + Var(b) + 2 Cov(a, b), we are able to decompose the total ex ante variation in risk premium into components due to variation in ex ante real interest rate differentials, variation in deviations from EPPP and interaction between the two. We then normalize by the ex ante variation in excess returns so that each component is expressed as a percentage of the total variance and the three components sum to one. The results are presented in Table 1. They provide further support for the qualitative story of Figure 1. Over the full period 1974 to 1989, variation in ex ante real rate differentials accounted for less than 6 percent of the total predictable variation in excess returns on foreign exchange, while deviations from EPPP accounted for over 80 percent. Sub-period results, also reported in Table 1, confirm these findings. For 1974480, deviations from RIRP explain about 12 percent of predictable variation in excess returns; for 1981-89, they account for less than 4 percent. The robustness of the findings in Table 1 is investigated in two ways. First, a small Monte Carlo experiment, described in the Appendix, is conducted to assess the potential impact of sampling error in the linear projection equations. Resulting standard errors are reported in parentheses in Table 1. The implication that deviations from PPP account for the major proportion of predictable variation and that deviations from RIRP play a much smaller role is strongly confirmed in all cases.’ As a final check, the analysis of Table 1 is repeated with an alternative instrument set consisting of a constant, the own forward premium, exchange rate change, and inflation differential (all lagged one period). The results are qualitatively similar to those reported here.8
III. Discussion The evidence above confirms the inferences of Levine (1989, 1991) and Huang (1990) that deviations from real interest rate parity alone cannot account for exchange premia. Indeed, as found by Levine (1991), deviations from PPP are the primary factor explaining such premia, accounting for nearly 80 to 90 percent of their time variation. This is an important stylized fact which relates to a number of strands of ongoing investigation. A variety of theoretical models have examined international asset pricing under the assumption that relative purchasing power parity holds.’ Equation (1) shows that any foreign exchange risk premium in such models must correspond directly to differentials in real interest rates (since deviations from PPP are zero). As we have seen that real interest rate differentials can account for only a small
Risk premia
in ,Jiweign eschange:
Timorhy
C Coke)
proportion of ex ante returns to holding foreign exchange, it would seem that models based on the PPP assumption cannot account for this phenomenon. Therefore, an important implication of the results here is that deviations from EPPP must play a significant role in any serious theoretical or empirical model attempting to account for exchange premia. The results here also shed light on the finding by Fama (1984) that risk premia in foreign exchange and expected changes in the spot rate covary negatively.” Fama finds this result surprising and somewhat anomalous, while Hodrick and Srivastava (1986) give an involved example of how such a phenomenon could arise in a PPP setting. Gokey (1991) finds the correlation noted by Fama is in fact nearly perfect, which is particularly difficult to explain in a PPP context since such a setting necessarily relies on a relatively indirect mechanism relating to real interest rates in the two countries. However, in a framework which does not impose PPP, equation (1) suggests that expected changes in the exchange rate can translate directly into excess returns to foreign exchange via deviations from EPPP. The finding that most of the variation in risk premia is in fact due to deviations from EPPP therefore explains both the direction and high degree of correlation between risk premia and expected exchange rate changes. Appendix This Appendix describes the Monte Carlo experiment used to derive the standard errors reported in Table 1. A system estimator is employed to jointly estimate the coefficients for the projection equations for deviations from RIRP and EPPP for each country (it is easily verified that the coefficients for the projection equation for excess returns may be obtained in all cases from the sum of the coefficients in the other two equations). Although the system estimator does not increase the power of the estimation (since the variables in each equation are the same), it does yield a covariance matrix for the coefficients both within and across the two equations. Using a multivariate normal distribution with mean vector and covariance matrix given by the system estimator, a random sample of 500 observations of the vector of 14 coefficients in the two projection equations are generated for each country. For each observation, the variances of predictable returns and deviations from RIRP and PPP are calculated using coefficients for the linear projection generated from the normal distribution and the actual data for the independent variables. For each of the 500 observations, the variance ratios (including interaction effect) are then calculated, and the standard errors reported in Table 1 are the standard deviations of the resulting 500 sets of variance ratios.
Notes 1. For an extensive
2.
3.
4.
survey of work showing the existence of predictable components, see Hodrick (1987). Examples ofmore recent investigations include Cumby (1988) Korajczyk and Viallet (1992), and Bekaert and Hodrick (1993). Examples of recent papers examining pricing of foreign exchange contracts include Mark (1988) Cumby (1988) and Korajczyk and Viallet (1992). For a survey of previous work. see Hodrick (1987). Derivation begins with the definition of real interest rates rj’ - r;’ = (ii - n{) - (if - 7~:). This can be rewritten as r/- rp = (i{ - i;’ + ds,) + (7~:- Z{ - rls,). Taking conditional expectations and rearranging yields (1). Including Fama (1984), Korajczyk (1985), Mark (1988), and Huang (1990), among others. As is well known, it is not possible with the Harris Bank data set to achieve correct thereby introducing a degree of alignment of forward and future spot observations,
Risk premier in ,foreiyn e.vchangr: Timothy C Gokq
5.
6.
7.
8.
9.
IO.
unavoidable measurement error into the data. We use lagged values as instrumental variables as suggested by Cornell (1989) to address this issue, and it should not affect the results here. See also Bekaert and Hodrick (1993). Many thanks to Professor Stephen Nickel1 and the Institute of Economics and Statistics at Oxford University for funding to purchase the Harris Bank data. Index values are taken to represent end-of-month prices, and local CPI’s are translated into dollars using end-of-month exchange rates. Although index values are actually more (1990) compares end-of-month and representative of mid-month prices, Huang mid-month assumptions and finds very little difference in results. Forward premia for the UK, Germany, Japan, France and Italy are employed for all equations. The number of forward premia is limited to five to facilitate the Monte Carlo experiment used to derive standard errors (described in the Appendix). Results using the instrument set here are qualitatively similar to those based on all nine forward premia (available from the author on request). Of course, the linear projection is subject to the usual caveats about potential misspecification (e.g. omitted variable biases, potential non-linearity of conditional expectations). The larger standard errors for the 1970s versus the 1980s or the overall period are driven by greater imprecision in the linear projections as well as by smaller predictable variation. This is in keeping with the findings of many investigators that the predictability of excess returns was much poorer in the 1970s than in the 1980s. See, for example, Bekaert and Hodrick (1993). These results are available from the author upon request. They attribute somewhat more influence to the interaction effect and somewhat less to deviations from PPP, but the influence of deviations from RIRP is still small. The results in Table 1 are preferred because the projection equations using the alternative instrument set have significantly higher standard errors and lower explanatory power. Grauer et al. (1976). Hodrick (1981, 1989) and Bekaert (1994) are illustrative of several approaches. Bekaert (1994) examines a decomposition similar to the one here as one explanation for his model’s lack of explanatory power. Note that ex ante excess returns as defined here are the negative of the risk premium as defined by Fama. Therefore. in the notation here, the issue is positice covariation of ex ante excess returns with expected changes in the spot exchange rate.
References ADLER, MICHAEL AND BERNARD DUMAS, ‘International portfolio choice and corporation finance: a synthesis,’ Journal of’Finunce, June 1983, 38: 925-983. BEKAERT, GEERT. ‘Exchange rate volatility and deviations from unbiasedness in a cash-in-advance model,’ Journal of’ International Economics, February 1994, 36: 29-52. BEKAERT,GEERT AND ROBERTJ. HODRICK, ‘On biases in the measurement of foreign exchange risk premiums,’ Journal of Internationul Money und Finance, April 1993, 12: 115-138. CORNELL, BRADFORD, ‘The jmpact of data errors on measurement of the forward exchange risk premium,’ Journal of International Money and Finance, March 1989, 8: 147-157. CUMBY, ROBERT E., ‘Is it risk? Explaining deviations from uncovered interest parity,’ Journal of Monetary Economics, September 1988, 22: 279-299. FAMA, EUCZN~ F.. ‘Forward and spot exchange rates,’ Journal of Monetury Economics. November 1984. 14: 319-338. FRANKEL, JEFFREY A. AND ALAN T. MACARTHUR. ‘Political versus currency premia in international real interest differentials: a study of forward rates for 24 countries,’ Europwn Economic Review, January 1988, 32: 1083-l 121. GOKEY, TIMOTHY C., Internationcrl Asset Pricing and the Foreign E.vchange Risk Premium: Theory and Evidence, unpublished D.Phil. Thesis, Oxford University, 1991. GRAUER, FREDERICK L. A., ROBERT H. LITZENBERGERAND RICHARD E. STEHLE, ‘Sharing rules and equilibrium in an international capital market under uncertainty,’ Journal sfFinancia1 Economics, June 1976, 3: 233-256.
HODRICK, ROBERT J., ‘International asset pricing with time-varying risk premia,’ Journul of International Economics, November 1981, 11: 573-587. HODRICK, ROBERT J.,The Empirical Evidence on the !?fji’cienc_yaf’Forward and Futures Foreign Exchange Markets, Harwood Academic Publishers, Chur, 1987. HODRICK, ROBERTJ., ‘Risk, uncertainty. and exchange rates,’ Journal of’Monetary Economics. May 1989. 23: 433-459. HODRICK, ROBERTJ. AND SANJAY SRIVASTAVA,‘The covariation of risk premiums and expected future spot exchange rates,‘Journalqf’lnternational Money and Finance, April 1986,5: S5-21. HUANG, ROGER D., ‘Risk and parity in purchasing power,’ Journal of‘ Money, Credit and Banking, August 1990, 22: 339-356. KORAICZYK, ROBERT A., ‘The pricing of forward contracts for foreign exchange,’ Journal of Political Economy, April 1985, 93: 346-368. KORAJCZYK, ROBERTA. AND CLAUDE J. VIALLET, ‘Equity risk premia and the pricing of foreign exchange risk,’ Journal qf’international Economics, November 1992, 33: 199-219. LEVINE, Ross, ‘The pricing of forward exchange rates,’ Journal of‘ International Money and Finance, June 1989. 8: 163-179. LEVINE, Ross, ‘An empirical inquiry into the nature of the forward exchange rate bias,’ Journal qf’lnternational Economics. May 1991, 30: 359-369. MARK, NELSON C., ‘Time-varying betas and risk premia in the pricing of forward foreign exchange contracts,’ Journal of Financial Economics, December 1988, 22: 335-354. SOLNIK, BRUNO H., ‘An equilibrium model of the international capital market,’ Journal of Economic Theory, August 1974, 5: 500-524.
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