Suppose investors can invest in two risky assets deriving returns R, R2 and in a riskless asset deriving a return Rf. Consider a portfolio P of risky assets with return Rp=wR+(1-w) R where w is a real number. (a) Express E(Rp) and Var(Rp) in terms of w, = E(R), 2= E(R), of = Var (R), 02= Var (R) and 12 = Cov(R, R). (b) Explain why one has to maximize the function g(w): = (-R)w+(-R)(1-w) ow +0(1-w) +202w(1 w) - in order to obtain the efficient frontier of investment strategies when short selling is allowed and the risk-free lending and borrowing rates are both equal to Rf. (c) Let c = R, for i=1,2. Show that when g'(w) = w=w* = C102-C012 c0+007-C1012 - 02012 and when c0+ c07-C1012-C2012 > 0, the portfolio (w*, 1-w*) of risky assets is on the efficient frontier of investment strategies. [Hint: You may use the fact that the derivative of g(w) with respect to w is without proof.] (-0-0+9012 + C012)w + (c02 - C012) [ow +0(1-w) + 2012w(1-w)1/2