We assume that the risk-free is 4.5 percent per year. We assume S&P 500 index has a standard deviation of 15 percent over a 10-year period. Managers X, Y, and Z have risk-return measures in the following table. Compute Treynor, Sharpe, and Jensen indexes for each manager. Compute selectivity, diversification, and net selectivity indexes. Rank managers according to each index.

Manager	Average Return	Portfolio Standard Deviation	Beta
S&P 500	0.10	0.15	1.00
Manager X	0.12	0.11	0.90
Manager Y	0.16	0.2	1.10
Manager Z	0.18	0.27	1.20

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