3. Optimal portfolio choice with two risky asset and one risk-free asset: Jessica has $10,000. She can invest the money in (1) a corporate bond, (2) a stock, and (3) the risk-free T-bill. The table below provides these assets expected returns and standard deviations:

Bond (D) Stock (E)

T-Bill Expected Return, Bond D(7%), Stock E(14%), T-Bill(2%)

Standard Deviation, Bond D(15%), Stock E(25%), T-Bill(0%)

The coefficient of correlation (DE) between the corporate bond and the stock is 20%. Jessica has a risk aversion A=4.

(a) Which risky asset (bond or stock) has a higher Sharpe ratio? (5 points)

(b) What are the weights of the bond and the stock in the optimal risky portfolio of two risky assets? (10%) 3

(c) Does the optimal risky portfolio have a higher or lower Sharpe ratio than the stock and the bond and why? (10%)

(d) What are the optimal weights that Jessica chooses for the optimal risky portfolio and for the risk-free T-bill in her overall portfolio? How many dollars should Jessica invest in the corporate bond, the stock, and the T-bill, respectively in the optimal portfolio? (10 points)

(e) Suppose that Jessica has not taken the investment class. For her risky portfolio, she invests 10% in the bond and 90% in the stock. Is the Sharpe ratio of her risky portfolio higher or lower than the Sharpe ratio of the optimal portfolio that you construct in (b) and why? (5%)

(f) Jim has risk aversion A=3. Would Jims optimal risky portfolio be the same as that in question (b)? Would Jim and Jessica choose the same overall optimal portfolio in question (d)? Explain. (5%)

(g) Suppose the coefficient of correlation between the stock and the bond decreases to 0. Would the change increase or decrease the Sharpe ratio of the optimal risky portfolio in question (b) and why? (5%)