to expected returns on the dollar is exactly this variance, so it makes sense that the contribution to expected excess returns of hedged U.S. equity from a yen perspective is this coefficient times the variance, which is simply the above-mentioned covariance. This covariance effect implies that the following two relationships hold: A = A + Oxu = A ~ x<y {6.9) Aj=A+0xj=^J-xj (6.10) We have now seen that there is a set of equations relating expected excess returns from a yen perspective to the expected returns from a dollar perspective (and, of course, vice versa). We can search over either the dollar-based or the yen-based expected excess returns, and the other set will be determined. Let us now consider a simple example. The following inputs allow us to solve for a simple two-country "universal hedging" equilibrium: U.S. market cap = 80 Japan market cap = 20 U.S. wealth = 80 Japan wealth = 20 U.S. risk aversion = Japan risk aversion = 2 U.S. equity volatility =15% Japan equity volatility = 17% Correlation between U.S. and Japan equity = .5 Dollar/yen volatility = 10% Correlation between U.S. equity and yen = .06 Correlation between Japan equity and yen = .1 Given these inputs, the covariance matrix for a U.S. investor is as shown in Table 6.1. The covariance matrix for a Japanese investor is only slightly different (see Table 6.2); the covariances between equity returns and the foreign currency have the opposite sign. If U.S. equity returns are positively correlated with returns on TABLE G.1 Covariance Matrix for a U.S. Investor U.S. Equity Japan Equity Yen U.S. equity .0225 .0128 .0009 Japan equity .0128 .0289 .0017 Yen .0009 .0017 .0100