The Time Variation of Risk and Return in the Foreign Exchange and Stock Markets

Recent empirical work indicates that, in a variety of financial markets, both conditional expectations and conditional variances of asset returns are time-varying. The purpose of this paper is to determine whether these joint fluctuations of conditional first and second moments are consistent with the Sharpe-Lintner-Mossin capital-asset-pricing model (CAPM). We test the mean-variance model under several different assumptions about the time-variation of conditional second moments of returns, using weekly data from July 1974 to December 1986 on returns to a portfolio composed of dollar, Deutschmark, sterling, and Swiss franc assets, together with United States equities. The model is estimated constraining risk premia to depend on the time-varying conditional covariance matrix of the residuals of the expected returns equations. The results indicate that estimated conditional variances cannot explain the observed time-variation of risk premia. Furthermore, the constraints imposed by the static CAPM are always rejected.