Question 1. Assume that there are two countries with investments in each country that pay r1 and r2 respectively, where r1 (r2) has mean r1 (r2) and variance 0% (0%) (assume 012 = 0). Agents in country 1 have preferences given by U(W) = E(W) VAR(W) where W 2 sun + (1 x)r2 a) Derive the optimal portfolio share a: for the home country. Show that in a fully symmetric environment with equal means and variances that a: = 5 b) Now assume that F2 2 0.5, a? = 0% = 0.1, and p = 3. How much would the expected return on home country stocks have to be for the home country investors to have a 0.75 share in the home (good 1) stock (i.e. to have home bias of 0.25). c) Alternatively assume that 71 = r2, but that p = 3 and of = 0% = 0.1. But now assume that the home consumer perceives that the foreign stock: is more uncertain than it is in reality. That is, the home consumer perceives the return F2 2 r2 + big, where E (U2) 2 0. What would the variance of 11.2 (the home consumer's misperception) have to be in order for rs = .75 to be optimal for the home consumer? d) The expected return on the portfolio is R = 56771 + (1 w)r'2, and the variance is V = $20? + (1 @203. Assume 772 > 171. Show that the portfolio frontier, the relation- ship between V and R, is negatively sloped for all as below the minimum variance share 2 '72 2 2 - 01 +02 m