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?

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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* 1926–2012 3.58 8.10 20.48 11.67 0.40 18.22 1989–2012 11.10 3.52 7.59 0.42 0.94 7.48 0.21 1968–1988 10.91 3.44 16.71 0.50 2.28 1947–1967 15.35 13.08 17.66 0.74 0.24 27.95 1926–1946 9.40 1.04 8.36 0.30 0.71