Question

Problem 6-20 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. Period 1926-2015 1992-2015 1970-1991 1948-1969 1926-1947 Average Annual Returns S&P 500 1 -Month Portfolio T-Bills 11.77 3.47 18.79 2.66 12.87 7.54 14.14 2.70 9.25 @.91 Risk Premium 8.30 8.13 5.33 11.44 8.33 S&P 500 Portfolio Standard Deviation 20.59 18.29 18.20 17.67 27.99 Sharpe Ratio 0.40 8.44 0.29 0.65 0.30 a. If your risk-aversion coefficient is A = 3.9 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 = E1-0.5 A0? (Do not round intermediate calculations. Round your answers to 2 decimal places.) T-bills Equity b. If your risk-aversion coefficient is A = 3.9 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? (Do not round intermediate calculations. Round your answers to 2 decimal places.) T-bills Equity

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Answer 1

А 3.9 11.77% 3.47% 8.30% 20.59% 50.20% 49.80% 1 a) 2 A 3 S&P Portfolio 4 1-month T-bills 5 risk premium 6 Standard deviation 7 8 % to be invested in equity 9 % to be invested in T-bills 10 11 b) 12 A 13 S&P Portfolio 14 1-month T-bills 15 risk premium 16 Standard deviation 17 18 % to be invested in equity 19 % to be invested in T-bills 3.9 12.87% 7.54% 5.33% 18.20% 41.26% 58.74%

3.9 1 a) 2 A 3 S&P Portfolio 4 1-month T-bills 5 risk premium 6 Standard deviation 0.1177 0.0347 0.083 0.2059 =B5/(B2*36*B6) =1-18 8 % to be invested in equity 9 % to be invested in T-bills 10 11 b) 12 A 13 S&P Portfolio 14 1-month T-bills 15 risk premium 16 Standard deviation 3.9 0.1287 0.0754 0.0533 0.182 17 18 % to be invested in equity 19 % to be invested in T-bills =B15/(B12*B16 B16) =1-B18 20