(CFA Level I): 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 table below provides the average annual rate of return for Portfolio X, the market portfolio (as measured by S&P500 Index), and U.S. Treasury bills (T-bills) during the past 8 years.

Fund	Annual average rate of return	Standard deviation of return	Beta
Portfolio X	10%	18%	0.6
S&P 500	12	13	1.0
T-bills	6

A- Calculate both the Treynor measure and the Sharpe measure for both Portfolio X and the S&P 500. Briefly explain whether Portfolio X underperformed, equaled, or outperformed the S&P 500 on a risk-adjusted basis using both the Treynor measure and the Sharpe measure.

B- Based on the performance of Portfolio X relative to the S&P 500 calculated in Part a, briefly explain the reason for conflicting results when using the Treynor measure versus the Sharpe measure.