Please answer all parts and show work. Thanks!

4. Consider two assets with the following returns: State Prob. of state R1 R2 2/3 .03 .05 1/3 .02 (a) Compute the optimal portfolio for an investor having a Bernoulli utility of net returns u(r) = lnr. In other words, the investor maximizes max Eu [aR + (1 a) R2] (b) Compute the certainty equivalent of the optimal portfolio. 4. Consider two assets with the following returns: State Prob. of state R1 R2 2/3 .03 .05 1/3 .02 (a) Compute the optimal portfolio for an investor having a Bernoulli utility of net returns u(r) = lnr. In other words, the investor maximizes max Eu [aR + (1 a) R2] (b) Compute the certainty equivalent of the optimal portfolio