Refer the table below on the average excess return of the U.S. equity market and the standard deviation of that excess return. Suppose that the U.S. market is your risky portfolio.

	Average Annual Returns	U.S. Equity Market
Period	U.S. equity	1-Month T-Bills	Excess return	Standard Deviation	Sharpe Ratio
19272021	12.17	3.30	8.87	20.25	0.44
19271950	10.26	0.93	9.33	26.57	0.35
19511974	10.21	3.59	6.62	20.32	0.33
19751998	17.97	6.98	10.99	14.40	0.76
19992021	10.16	1.66	8.50	18.85	0.45

Required:

If your risk-aversion coefficient is A = 4.1 and you believe that the entire 19272021 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 A²squared.

What if you believe that the 19751998 period is representative?