Question

Consider the two (excess return) index-model regression results for stocks A and B. The risk-free rate over the period was 8%, and the market's average return was 16%. Performance is measured using an index model regression on excess returns. Stock 18 + 1.2 (ry - rp) 0.677 Index model regression estimates R-square Residual standard deviation, (e) Standard deviation of excess returns Stock B 28 +0.8(IN - rf) 0.487 20.88 28.30 126 23.38 a. Calculate the following statistics for each stock: (Round your answers to 4 decimal places.) Stock A Stock B 1. Alpha . Information ratio W. Sharpe ratio iv. Treynor measure b. Which stock is the best choice under the following circumstances? < Prev 4 of 6 !!! Next >

Answer 1

a).

i). Alpha(a) = Intercept of the Regression

Stock A's Alpha = 1%;

Stock B's Alpha = 2%;

ii). Information Ratio = Alpha / Residual standard deviation

Stock A's Information Ratio = 1% / 12% = 0.0833

Stock B's Information Ratio = 2% / 20.8% = 0.0962

iii). Sharpe measure = (r_p – r_f) / Standard Deviation

Stock A's Sharpe Ratio = [1% + 1.2(16% - 8%)] / 23.3%

= [1% + 9.6%] / 23.3%

= 10.6% / 23.3% = 0.4549

Stock B's Sharpe Ratio = [2% + 0.8(16% - 8%)] / 28.3%

= [2% + 6.4%] / 28.3%

= 8.4% / 28.3% = 0.2968

iv). Treynor measure = (r_p – r_f)/ b

Stock A's Treynor measure = [1% + 1.2(16% - 8%)] / 1.2

= [1% + 9.6%] / 1.2

= 10.6% / 1.2 = 8.8333%

Stock B's Treynor measure = [2% + 0.8(16% - 8%)] / 0.8

= [2% + 6.4%] / 0.8

= 8.4% / 0.8 = 10.5%

b). Stock B is better off in terms of Alpha, Information Ratio and Treynor Measure.

Stock A is better off in terms of sharpe ratio.