If1\w1 kK; (6.31; And, using (6.22), the equilibrium portfolio demands are: A - 12" H^rV   = 1 2h w+1 ' 1 ^ -1 -i HiZi-^it/'/r/'^-W-;) 1.32)   \-i _ i2n - J-w+l ' 1 ^ x\ H^rrrns-w-r, and for 2' not equal to 1: 2"-l SjVi H;l v^iy In H-.272-1 v^, H.-fe1   = 1 _ 12^ f 1 ^ e 1 ' vxX(y     .72r12i(/7r1/(*-W-;) + \-l j(J'jpj'(s-w-j: (6.33; We now have equations that give the equilibrium expected excess returns, the optimal portfolio weights, and the portfolio demands for equities and bills, all as a function of the covariances of returns, and market capitalizations, wealth, and risk aversions of investors around the world. Fischer Black's universal hedging equilibrium is a special case that arises when market capitalizations equal wealth in each country and risk aversions are the same in all countries. To see this, let us use the notation X for the common risk aversion, and look a little more closely at the demand equations: \-i Ln+1 tX nj'jri'(s-w-j)- x H -\2n-l (6.34; To examine the currency hedging in country i, we look at the demand vector, dc The currency hedging of the foreign equity held in country / is the negative of the ratio of the bill holding in country / to the equity holding in country /. Thus, we examine the negative of ratio of the n + /th element to the /'th element. The uni-