The administrator of a large pension fund wants to evaluate the performance of four portfolio managers. Each portfolio manager invests only in U.S. common stocks. Assume that during the most recent 5-year period, the average annual total rate of return including dividends on the S&P 500 was 14%, and the average nominal rate of return on government Treasury bills was 8%. The following table shows risk and return measures for each portfolio: Portfolio

Average Annual Rate of Return

Standard Deviation of Return

Beta

P

17%

20%

1.1

Q

24

18

2.1

R

11

10

0.5

S

16

14

1.5

S&P 500

14

12

1.0

Portfolio X

10%

18%

0.60

S&P 500

12

13

1.00

T-bills

6

N/A

N/A

Calculate the Treynor and Sharpe measures 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 ratio.

b. On the basis of 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 ratio.