An analyst wants to evaluate portfolio X, consisting entirely of U. S. common stocks, using both the Treynor and Sharpe measures of portfolio performance. The following table provides the average annual rate of return for portfolio X, the market portfolio ( as measured by the S& P 500), and U. S. Treasury bills during the past eight years:

a. Calculate the Treynor and Sharpe measures for both portfolio X and the S& P 500. Briefly explain whether portfolio X underperformed, equalled, or outperformed the S& P 500 on a risk-adjusted basis using both the Treynor measure and the Sharpe ratio.
b. In view of the performance of portfolio X relative to the S& P 500 calculated in part ( a), briefly ex-plain the reason for the conflicting results when using the Treynor measure versus the Sharpe ratio.

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Portfolio X S&P 500 T-bills Average Annual Rate of Return (%) 10 12 6 Standand Deviation (%) 18 13 NA Beta .60 1.00 NA