Inflation is expected to increase by 4% annually, and both expect their salaries to increase at the same rate (4%). They generally believe that the S&P 500 is a good measure of the markets overall performance, and it has a historical rate of return of 12%, which they expect to continue. The Maclures have a required rate of return of 9%. Part of their portfolio holdings consists of short-term treasury bills and the rate you will calculate for those treasury bills should be applied as the risk free rate for any questions that require risk free rate information.

They consider themselves to be moderate to moderate-aggressive investors. They are in the 28% marginal income tax bracket for federal income tax purposes. As residents of Tennessee they pay no state income tax.

The Maclures are considering hiring a money manager to deal with their growing portfolio, and they have narrowed down their choices to the following management firms. For each firm, you have details on the historical mean return, portfolio standard deviation, and the risk free rate (see table).

	Benchmark	Manager 2	Manager 3	Manager 4	Manager 5
Mean	9.52%	16.00%	9.20%	18.00%	7.00%
Standard Deviation	10.65%	15.00%	5.60%	25.00%	6.00%
Risk-Free Rate	3.50%	3.50%	3.50%	3.50%	3.50%

Use the Modigliani measure to derive an estimate of what each money managers return should have been given the amount of risk taken for Manager 2 and 4.