Question 1. Assume that there are two countries with investments in each country that pay H and 11; respectively, where r1 {r2} has mean #11 {g} and variance of [org]: [assume on = [1}. Agents in country 1 have preferences given by me!) = E{W} Evamw} where W = mm + {l my\": a.) Derive the optimal portfolio share .1: for the home country. Show that in a fully symmetric environment with equal means and variances that :r = %. h} Now assume that f2 = [1.5, or? = erg = {1.1, and ,o = 3. How much would the expected return on home country stocks have to he for the home country investors to have a .?5 share in the home [good 1} stock (Le. to have home bias of [1.25). c} Alternatively assume that \"Fl 2 \"g, but that p = 3 and or? = o3 2 LL]. 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 \"Fig = r2 + tag, where E{ng} = Ell. 1What would the variance of ii: [the home consumer's misperception} have to he in order for I = .375 to he optimal for the home consumer? d) The expected return on the portfolio is \"R. = xiii + [1 Elf2, and the variance is V = Ego? + {l Elgar; Assume *F-g 2} f1. Show that the portfolio frontier, the relation ship heEween V and R, is negatively sloped for all :1! below the minimum variance share 0' Ing. \"'1