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 return on large stocks and 1-month T-bills; standard deviation and Sharpe ratio of large stocks over time
*The probability that the estimate of the Sharpe ratio over 1926-2012 equals the true value and that we observe the reported, or an even more different Sharpe ratio for the sub period.
a. If your risk-aversion coefficient is A = 3.5 and you believe that the entire 1926-2012 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.
b. If your risk-aversion coefficient is A = 3.5 and you believe that the entire 1968-1988 period is representative of future expected performance, what fraction of your portfolio should be allocated to T-bills and what fraction to equity?

Average Annual Returns S&P 500 Portfolio Sharpe Ratio (Reward-to- Volatility) S&P 500 1-Month Risk Standard Premium Deviation Period Portfolio T-Bills Probability* 3.58 1926-2012 11.67 8.10 20.48 0.40 3.52 7.59 19892012 11.10 18.22 0.42 0.94 10.91 3.44 19681988 7.48 16.71 0.21 0.50 0.74 1947-1967 15.35 2.28 13.08 17.66 0.24 19261946 9.40 1.04 8.36 27.95 0.30 0.71