Question

Refer the table below on the average risk premium of the S&P 500 over T-bills and...

Refer the table below on the average risk premium of the S&P 500 over T-bills and the standard deviation of that risk premium. Suppose that the S&P 500 is your risky portfolio.

Average Annual Returns S&P 500 Portfolio
Period S&P 500
Portfolio		 1-Month
T-Bills		 Risk
Premium		 Standard
Deviation		 Sharpe
Ratio
1926–2015 11.77 3.47 8.30 20.59 0.40
1992–2015 10.79 2.66 8.13 18.29 0.44
1970–1991 12.87 7.54 5.33 18.20 0.29
1948–1969 14.14 2.70 11.44 17.67 0.65
1926–1947 9.25 0.91 8.33 27.99 0.30

a. If your risk-aversion coefficient is A = 5.8 and you believe that the entire 1926–2015 period is representative of future expected performance, what fraction of your portfolio should be allocated to T-bills and what fraction to equity? Assume your utility function is U= E(r) – 0.5 × Aσ2. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

b. If your risk-aversion coefficient is A = 5.8 and you believe that the entire 1970–1991 period is representative of future expected performance, what fraction of your portfolio should be allocated to T-bills and what fraction to equity?

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Homework Answers

Answer #1

The main idea to solve this question is to first maximize the portfolio utility function. We would also need to analytically solve for the E(r) of the portfolio, as well as the Std dev of the portfolio.

Part A

We can calculate Portfolio SD from Sharpe ratio, as below:

Portfolio SD = Er - Rf / SR

Similarly

Part B

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