Consider a riskaverse investor with an increasing and concave utility function. Suppose that the inventor wants to maximize the expected utility of her endofperiod wealth by investing the amount w in two securities with the rate of return R1 and R2. Assume that the endofperiod wealth W = w + Lu'l-Rl +sz. is a normal random variable. Set [.91 13 0 and (.02 2 I], where w = ml + [.92. Suppose that the riskfree rate is zero. Assume the validity of the Capital Asset Pricing Model (CAPM) as in Section 9.5, i.e., R1 = 31Rm+el and R2 = 82R", +62 for some constants 31 and 32; also el and e2 are independent normal random variables with mean zero and variance 03, they are also independent from the marker rate of return Rm. Variance ome is denoted by 0?\". Suppose that ml E om) is invested in security 1 and m E (1 oc)m is invested in security 2; 0 E o S 1. Show that if the expected rate of return of both securities is zero, the optimal fraction to invest in security 1 will be a = '73 + 03.;32(2 131) 203 + (32 - ll203n