We have one risk-free asset with a return r, = 0.06 (i.c., 6 %) and one risky asset. There are three states of nature. State 1 occurs with a probability of p,=0.25, State 2 occurs with a probability of p=0.50, and State 3 with a probability of p, 0.25. The rate of return in the different states are r=0.00, r=0.12, and r, = 0.20. b) As discussed in class, the expected return of the optimal portfolio, E(r)=r can be written as: r=r, +%, (n-). where is the standard deviation in the return of the total portfolio. Assume an investor who has the mean-variance utility function: u = r.5 30r0.5. The investors utility maximization problem is: =r + %, (r, -r). Max u=r05-3or5 s.t. r=r What is the expected return there is an interior solution, i.e., r,