Consider the two (excess retum) index-model regression results for stocks A and
ID: 2799974 • Letter: C
Question
Consider the two (excess retum) index-model regression results for stocks A and B. The riskfree rate over the period was 6%, and the market's average return was 14% Performance is measured using an index model regression on excess retums. Stock A Stock B index model regression estimates | 1% + 12(rM-M | 2% + 8(rM_m R-square 576 436 Residual standard deviation, (e) 10 3% 19.1% Standard deviation of excess returns 21.6% 24.9% a. Calculate the following statistics for each stock i. Alpha ii. Information ratio ii Sharpe ratio iv. Treynor measure b. Which stock is the best choice under the following circumstances? i. This is the only risky asset to be held by the investor ii. This stock will be mixed with the rest of the investor's portfolio, currently composed solely of holdings in the market-index fund i. This is one of many stocks that the investor is analyzing to form an actively managed stock portfolioExplanation / Answer
Solution:
a. Stock A Stock B
i. Alpha (Regression Intercept) 1% 2%
ii. Information Ratio = alpha/e 1/10.3 = 0.0971 2/19.1 = 0.1047
iii. Sharpe measure = (rp - rf)/p [1 + 1.2 (14 - 6)]/21.6 = 0.4907 [2 + 0.8 (14 - 6)]/24.9 = 0.337
iv. Treynor measure = (rp - rf)/p [1 + 1.2 (14 - 6)]/1.2 = 8.833 [2 + 0.8 (14 - 6)]/0.8 = 10.5
b.
i. If this is the only risky asset held by the investor, the Sharpe’s measure is the appropriate measure. Since the Sharpe measure is high for Stock A, and then A is the best choice.
ii. If the stock is mixed with the market index fund, then the contribution to overall Sharpe measure is determined by the information ratio and hence Stock B is preferred.
iii. If the stock is one of many stocks, then Treynor’s measure is the appropriate measure, and Stock B is preferred.