demand = U.S. wealth du + Japan wealth yu (6-11) Japan equity demand = U.S. wealth d + Japan wealth y (6.12) Demand for borrowing in yen comes from U.S. investors who want to hedge some of their equity exposure. In particular, total yen exposure is the difference between the holdings of Japanese equity and the yen borrowing that hedges the currency exposure. To simplify notation, let us denote yen lending by dollar investors (yen lending is just -1 times yen borrowing) by dY. Then dx = d, + dY. Thus, yen lending by dollar-based investors is given by the equation dY = dx- d,. Similarly, dollar lending by yen investors, denoted yp is given by the equation y" =yx- yu- Dollar lending by dollar-based investors is whatever is left after U.S. investors purchase U.S. equity, purchase Japanese equity, and participate in yen lending. Thus, dollar lending by dollar-based investors, denoted d%> is given by d% = (1 - dfJ - d,- dY). Similarly, yen lending by yen-based investors, denoted yY is given by yY = (l-yu-yj-ys). These equations allow us to complete the demand functions: Demand for dollar lending = U.S. wealth d$ + Japan wealth y$ (6.13) Demand for yen lending = U.S. wealth dY + Japan wealth yY (6-14) Equilibrium is the condition that demand equals supply; thus our equilibrium conditions are as follows: U.S. wealth du + Japan wealth yu = Market cap of U.S. equity = 80 (6.15) U.S. wealth d, + Japan wealth y, = Market cap of Japan equity = 20 (6.16) U.S. wealth d$ + Japan wealth y$ = Net supply of dollar lending = 0 (6.17) U.S. wealth d + Japan wealth y = Net supply of yen lending = 0 (6.18) In this simple economy, we can solve for the values of the dollar-based expected excess returns for which these equilibrium conditions are satisfied. The interested reader may verify that the equilibrium expected excess returns are: H* =4.128% nj = 3.230% H| = .412% and that the resulting yen-based equilibrium expected excess returns are: \i* = 4.038% M.J = 3.060% )4=.588%