Problem 18-02

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 Standard and Poors 500 Index), and U.S. Treasury bills (T-bills) during the past eight years.

	Annual Average		Standard Deviation
	Rate of Return		of Return		Beta
Portfolio X	11	%	15	%	0.40
S&P 500	12		11		1.00
T-bills	6		n/a		n/a
n/a = not applicable

Based on the Sharpe measure Portfolio X -Select-underperformedequaledoutperformedItem 7 the market index because Sharpe measure for Portfolio X is -Select-greaterlessItem 8 than Sharpe measure for the S&P 500.

1. Calculate both the Treynor measure and the Sharpe measure for both Portfolio X and the S&P 500. Round your answers for the Treynor measure to one decimal place and for the Sharpe measure to three decimal places.

   	Treynor measure	Sharpe measure
   Portfolio X	%
   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.

   Based on the Treynor measure Portfolio X -Select-underperformedequaledoutperformedItem 5 the market index because Treynor measure for Portfolio X is -Select-greaterlessItem 6 than Treynor measure for the S&P 500.

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

   As Treynor measure considers -Select-only systematiconly unsystematicboth systematic and unsystematicItem 9 risk while Sharpe measures considers -Select-only systematiconly unsystematicboth systematic and unsystematicItem 10 risk so a -Select-poorlyperfectlyItem 11 diversified portfolio could show better performance relative to the market if the Treynor measure is used but lower performance relative to the market if the Sharpe measure is used. As a result, Portfolio X has a large amount of -Select-systematicunsystematicItem 12 risk.