Steve’s risk-adjusted return analysis shows the following:

	XYZ Fund	Market
Average return	12%	10%
Beta	1.2	1.0
Standard deviation	26%	24%

Sharpe = (r_p – r_f )/ sd

Fund                (12– 4)/26 = .31

Market             (10– 4)/24  = .25

 

Jensen = r_p – [r_f + ß_p (r_m – r_f)]

Fund alpha =  12 – [4 + 1.2 (10– 4) ]= 0.8%

Market alpha = 0

 

Treynor = (r_p – r_f )/ ß_p

Fund                (12– 4)/1.2 = 6.7

Market             (10– 4)/1.0 = 6.0

 

Because each of the fund ratios was higher than the market ratios, Steve’s XYZ fund outperformed the market in terms of the Jensen, Treynor, and Sharpe measures.