Question

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 10.79 2.66 12.87 7.54 14.14 2.70 9.25 0.91 S&P 500 Portfolio Risk Standard Premium Deviation 8.30 20.59 8.13 18.29 5.33 18.20 11.44 17.67 8.33 27.99 Sharpe Ratio 0.40 0.44 0.29 0.65 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= En-0.5 Ao?. (Do not round intermediate calculations. Round your answers to 2 decimal places.) T-bills Equity

Answer 1

Weight in Equity=(rp-rf)/(A*(sp)^2)
Weight in Tbills=1-Weight in Equity

1.
=1-(11.77%-3.47%)/(5.8*(20.59%)^2)=66.2450549310489%

2.
=(11.77%-3.47%)/(5.8*(20.59%)^2)=33.7549450689511%

3.
=1-(12.87%-7.54%)/(5.8*(18.2%)^2)=72.2568072321767%

4.
=(12.87%-7.54%)/(5.8*(18.2%)^2)=27.7431927678233%