Consider the two (excess return) index-model regression results for stocks A and

Question

Consider the two (excess return) index-model regression results for stocks Aand B. The risk-free rate over the period was 6%, and the market’s average return was 15%. Performance is measured using an index model regression on excess returns.

a. Calculate the following statistics for each stock: (Round your answers to 4 decimal places.)

Stock A Stock B Index model regression estimates 1% + 1.2(rM rf) 2% + 0.8(rM rf) R-square 0.594 0.445 Residual standard deviation, (e) 10.6% 19.4% Standard deviation of excess returns 21.9% 25.5%

Explanation / Answer

1)

Alpha = regression intercept

Stock A = 1% Stock B = 2%

2)

information ratio = alpha / Residual standard deviation

Stock A = 1% / 10.6% = 0.0943

Stock B = 2% / 19.4% = 0.1031

3)

Sharpe ratio = (Rp - Rf) / SD =

Stock A

Rp - Rf = 1% + 1.2*(15% - 6%) = 11.8%

Sharpe ratio = (11.8%) / 21.9% = 0.5388

Stock B

Rp - Rf = 2% + 0.8*(15% - 6%) = 9.2%

Sharpe ratio = (9.2%) / 25.5% = 0.3608

4)

Treynor measure = (Rp - Rf) / Beta

Stock A

Rp - Rf = 1% + 1.2*(15% - 6%) = 11.8%

Sharpe ratio = (11.8%) / 1.2 = 9.8333%

Stock B

Rp - Rf = 2% + 0.8*(15% - 6%) = 9.2%

Sharpe ratio = (9.2%) / 0.8 = 11.5000%

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