portion of the expected return vector from country i. The (1I.J') is the formula for the covariance matrix of country z, as a function of the covariance matrix of the home country. Finally, the l^"1 vector picks off the column of the covariance matrix that corresponds to the home country currency covariance with each of the country i assets. This covariance is the appropriate numerator for the coefficient of the projection of that asset's return on the home country currency. Next, we form the optimal portfolio weights for each country's optimal asset allocation. This portfolio weight vector, w , is the CAPM optimal portfolio. Thus, from Chapter 4 the vector of portfolio weights is given by the formula: .urMzrV     zrV,- i.-m+l w(- \ilit ir1 zrVi+i^r1 i.21: Using the preceding formula we now form the country i ^-dimensional demand vector for equities and lending: d- =l2n-   H-\2n-l   zrV mi M = 1 = 1 = 1 In In In   r-l   '~1] irVi   Hi2n-l iK+1 HiK1\ (6.22) Finally, we solve for an equilibrium set of expected excess returns in the home country. Set total demand equal to the exogenously given supplies of equities and zero net lending. EQUILIBRIUM CONDITION s.-i WX = S i.23) Where Wt is the proportion of wealth held in country i, and the vector of supply, s, is the 2n-dimensional vector whose first n elements are proportion of market capitalization weight held in each country and next n elements are zeros.