where jiY = Expected excess return for a yen-based investor holding Japanese equity V>1 = Expected excess return for a yen-based investor holding currency hedged U.S. equity i4 = Expected excess return on holding dollars for a yen-based investor The risk of this yen-denominated portfolio is given by the volatility, oj, determined as follows by the variances and covariances of yen-based risky assets: (op) =^a={u,j,x\^b={uj,x}(yayb^Ib) (6-4) where oJb is the covariance (or variance if a = b) of returns of asset a with asset b from a yen investor's point of view. Note that for the dollar-based investor the foreign exchange asset represented by the subscript X is a yen exposure; for the yen-based investor, the asset represented by the subscript X is a dollar exposure. The equilibrium for this model is a set of expected excess returns that clear markets. The markets that need to clear are equities and short-term borrowing. Note that in the context of the domestic CAPM we did not explicitly require equilibrium for short-term borrowing. In that context if wealth equals market capitalization, then the net demand for cash must be zero. In the international context there is more than one source of cash or short-term borrowing; we will refer to these alternative supplies as "bills." The supply of equities is taken to be the fixed market capitalization. The net supply of borrowing (i.e., bills) in each currency is assumed to be zero. Demands are generated from the optimization of investors' utility, which is assumed to have the same form as in the domestic CAPM. Investors maximize a utility function: Utility of investors in country c (either $ or Y) is given by where X is the risk aversion parameter. In the global example we consider here, we differentiate U.S. investors from Japanese investors, and we solve each of their optimization problems separately. We sum the demands of each type of investor for U.S. equities and for Japanese equities, and we sum the demands for short-term lending in each country. Finally, we search for equilibrium values of expected excess returns, which are defined as those for which the total demand for each type of equity equals the supply and such that the net demand for short-term lending is zero. The zero net demand condition requires that U.S. investors are comfortable lending to Japanese investors the amount of dollars that they want to borrow, and vice versa. Before we can solve for the equilibrium expected excess returns, though, we have to recognize that there are relationships between the dollar-based expected