.0225 .0128 -.0009 Japan equity .0128 .0289 -.0017 Dollar -.0009 -.0017 .0100 holding yen, then clearly U.S. equity returns are negatively correlated with returns on holding dollars for yen-based investors. As seen in Chapter 4, the inverses of these covariance matrixes are required to find the optimal portfolio weights. These inverse matrixes are shown in Tables 6.3 and 6.4. Now the portfolio percentage allocations follow directly from the optimization of utility as in Chapter 4. Portfolio Allocations from a U.S. Investor U.S. equity: dIJ = .5 (59.27 u,* - 26.09 u.J - .90 u.|) Japan equity: d= .5 (-26.09 u,£+ 46.44 m$ - 5.55 u,|) Yen exposure: dx = .5 (-.90 u^- 5.55 jj* + 101.02 \ix) Portfolio Allocations from a Japanese Investor U.S. equity: yu = .5 (59.27 u.£- 26.09 jij + .90 u,£) Japan equity: y = .5 (-26.09 |i£+ 46.44 \ij + 5.55 \ix) Dollar exposure: yx = .5 (.90 ■ n£+ 5.55 uj + 101.02 ■ [ix) TABLE 6.3 U.S. Investor's Inverse Covariance Matrix U.S. Equity Japan Equity Yen U.S. equity 59.27 -26.09 -.90 Japan equity -26.09 46.44 -5.55 Yen -.90 -5.55 101.02 TABLE 6.4 Japanese Investor's Inverse Covariance Matrix U.S. Equity Japan Equity Dollar   U.S. equity 59.27 -26.09 .90 Japan equity -26.09 46.44 5.55 Dollar .90 5.55 101.02