Suppose an investor has to choose what fraction of her savings, b, she invests into the stock market (risky asset). The remaining fraction 1-b is invested in risk-free Treasury bills. Let U(Rp,p) = 4 + 2p 2. Let the expected return of the risk-free asset be Rf = 2, and the expected return of the risky asset be Rm = 4. Finally, let the standard deviation of the risky asset be m = 2.

a. Find the optimal fraction to invest in the stock market?

b. Plot the indifference curves, budget line, and optimal portfolio bundle.