this additional uncertainty into account. Over a short period of time, the return to a U.S. investor from holding Japanese equity will have two components, the return on the equity earned by domestic Japanese investors plus the return earned by U.S. investors from holding yen-denominated assets. A U.S. investor holds portfolio weights du and d respectively, in the equity of the United States and Japan, and may choose to hedge (or increase) the currency exposure of the Japanese equity such that there is an outstanding yen exposure in the amount dx. These weights, dm dp and d^ are all expressed as percentages of the wealth of the dollar investor. The expected excess return over the risk-free rate, denominated in dollars, for an investor in the United States holding these weights is given by: M-p = M-u^i7 + M-/^/+M-x*^x (6-1) where u,^ = uj = Expected excess return for a dollar-based investor holding U.S. equity Expected excess return for a dollar-based investor holding currency 4 = hedged Japanese equity6 Expected excess return on holding yen for a U.S. dollar-based investor As we shall see, it turns out that even when the currency risk is hedged, the expected excess return on Japanese equity for a dollar-based investor will generally differ from that of a yen-based investor because the investors in different countries measure their expected returns in terms of different units (currencies). The risk of this portfolio for the U.S. dollar-based investor is given by the volatility, o^, determined as follows by the variances and covariances of dollar-based risky assets: (op) =K={u,j,x£b={u,j,x\(dJboib) (6-2> where Oa$&is the covariance (or variance if a = b) of returns of asset a with asset b from a dollar investor's point of view. Similarly, the expected return, denominated in yen, for an investor in Japan holding weights y, and yu, respectively, in the equities of Japan and the United States, and hedging the currency exposure on U.S. equity such that there is a net dollar exposure of an amount, yx, is given by: sThe excess return on foreign currency exposures is given by rs = (F/+1 - Xt+1)/Xt, where Ff+1 is the one-period forward exchange rate at time t, that is, the forward rate at time t at which you can contract to exchange yen for dollars at time t + 1. In terms of short-term deposit rates in the United States and Japan, K$ and Ky, covered interest parity requires that F*+1 = (1 + Ry) X(/(l + K$). The currency hedged excess return on Japanese equity from time t to t + 1 is given by r= [(P(+]/X(+])/(P/X() - 1] - R$ - (1 - R$) rt where P( is the yen price of the Japanese equity at time t.