4. (total 2 points) Consider a portfolio of three stocks and the risk-free asset with weights wi, w2, and w3 in the three stocks and weight 1 - Wi - W2 - W3 in the risk-free asset. The return on the portfolio is of course rp = wiri + w2r2 + w3r3 + (1 - Wi - W2 W3)rf. The covariance matrix of the returns of the three stocks is 1011 =1021 031 012 022 032 013 023, 033 where Oii = o- and j = Oji. (a) (1 point) Consider op? = var(rp) = var(wr + w2r2 + wzr3). Please write down a formula that expresses this portfolio variance in terms of the portfolio weights wi and the elements Oij of the covariance matrix. (b) (1 point) Consider Olp = cov(ri, rp), that is the covariance between the return on the first stock and the return on the portfolio. Please write down a formula that expresses this covariance in terms of the portfolio weights W; and the elements Oij of the covariance matrix. (Hint: You might want to use the fact that cov(X, aY+bZ) = cov(X, aY) + cov(X, bZ) = acov(X, Y) + bcov(X, Z).) 4. (total 2 points) Consider a portfolio of three stocks and the risk-free asset with weights wi, w2, and w3 in the three stocks and weight 1 - Wi - W2 - W3 in the risk-free asset. The return on the portfolio is of course rp = wiri + w2r2 + w3r3 + (1 - Wi - W2 W3)rf. The covariance matrix of the returns of the three stocks is 1011 =1021 031 012 022 032 013 023, 033 where Oii = o- and j = Oji. (a) (1 point) Consider op? = var(rp) = var(wr + w2r2 + wzr3). Please write down a formula that expresses this portfolio variance in terms of the portfolio weights wi and the elements Oij of the covariance matrix. (b) (1 point) Consider Olp = cov(ri, rp), that is the covariance between the return on the first stock and the return on the portfolio. Please write down a formula that expresses this covariance in terms of the portfolio weights W; and the elements Oij of the covariance matrix. (Hint: You might want to use the fact that cov(X, aY+bZ) = cov(X, aY) + cov(X, bZ) = acov(X, Y) + bcov(X, Z).)