Risky assets offer a higher expected rate of return, otherwise risk-averse investors would not hold them. The difference between this expected return and the return on a riskless, `safe' asset is called the risk premium. In foreign exchange markets, the relative risk premium is the expected reward for holding assets denominated in one currency relative to holding assets in another currency. Economists have sought to explain the foreign exchange risk premium by extending the Capital Asset Pricing Model (CAPM) to an international context, relating the expected relative return on a given asset over some period to investors' holdings of assets at the beginning of the period. Unfortunately empirical studies using this approach have generally failed to explain foreign exchange risk premia.
In Discussion Paper No. 354, Stephen Thomas and Research Fellow Michael Wickens suggest why such exercises have been disappointing and attempt new tests, avoiding earlier failings. Typically researchers have considered investment portfolios consisting of the outstanding bond stocks of the major industrialized countries, omitting equities and other assets. Thomas and Wickens include them and also argue that greater care should be exercised when constructing rate of return data for the various assets considered. For government bonds, the data should reflect bond price changes and coupons as well as exchange rate changes.
There is also a basic statistical problem in seeking to explain highly variable relative returns by stocks of financial assets which change little. If the conditional variance of excess returns varies over time then so, in all probability, will the risk premium. Researchers have attempted to represent this time variation by introducing autoregressive conditional heteroskedasticity (ARCH)-in-mean effects in the CAPM, so that the conditional variance of excess returns has an autoregressive structure. But this has also failed to produce significant estimates for investors' relative risk aversion, implying that the risk premium cannot be explained in this way.
Thomas and Wickens estimate a series of models for government bonds and equities for Germany, Japan, the United States and United Kingdom, using a new, carefully constructed monthly data set for 1973-87, with special emphasis on calculating appropriate bond and equity returns. In particular, bond returns reflect changes in the price of bonds as well as in coupons. The authors still find little explanatory power for relative risk premia, however, even when they introduce ARCH processes in the equation errors. The data appear to be described better by an assumption of risk-neutrality. Correcting the international CAPM for the major deficiencies detected in earlier studies does not, therefore, reverse their conclusions. Thomas and Wickens suggest that it is not possible to devise a single international CAPM which covers all countries and all assets. Nor is it likely that explanations for the apparent short-run variation in risk premia will be found in ARCH-in-mean versions of these models.
The efficient markets hypothesis is based on the assumptions that investors are both rational and risk-neutral. Recent empirical work, rejecting this hypothesis for both foreign exchange and equity markets, has generally been interpreted as evidence not of irrationality, but of risk-aversion. In Discussion Paper No. 356, Wickens and Thomas pursue the issue of whether risk premia exist in the foreign exchange and equity markets.
The difficulty for empirical work is that risk premia are not directly observable and must be estimated indirectly, by postulating and fitting models for them, such as the international CAPM for the foreign exchange markets. Tests of the efficiency of equity markets have focused more on the present value model of equity prices, but the conclusions have generally been negative. Capital asset pricing theory has been used to formulate alternative models which admit a risk premium, and recent work has discovered ARCH effects.
Given the failure of parametric models of risk premia, Wickens and Thomas use non-parametric techniques to produce estimates that do not depend on any particular model of risk. Their model is based on the hypothesis that the forward rate is an unbiased predictor of the spot rate. Once the forward and spot rates are transformed to stationary series the risk premium, assuming it is stationary, can exert a detectable influence. Forward and spot rate data for exchange rates already exist. For equities, however, only the spot rate (the stock price) exists, and so the authors have to construct a forward rate. As a by-product, these data can also be used to test the efficiency of the stock market.
Wickens and Thomas use monthly data for the exchange rates of the Deutschmark, sterling and yen against the dollar and for the West German, Japanese, UK and US stock markets between May 1973 and June 1988. They obtain estimates for the whole period and for each year of the average risk premium, of a lower bound for the proportion of the variation in the rate of return due to variations in the risk premium, and of the implied coefficient of relative risk aversion. The whole-period results generally confirm previous findings that risk premia are not an important influence. The annual estimates, however, reveal considerable variability not hitherto uncovered. Since much of the literature assumes constant relative risk aversion, more effort is needed to provide models that can account for this short-run variability.
Finally, the new test of the efficiency of stock markets, based on the estimates of the equity risk premium, firmly rejects efficiency, showing that agents are either irrational or risk-averse.

International CAPM: Why Has It Failed?
Non-Parametric Estimates of the Foreign Exchange and Equity Risk Premia and Tests of Market Efficiency
M R Wickens and S H Thomas

Discussion Paper Nos. 354 and 356 November and December 1989 (IM/AM)