Consider the two (excess return) index-model regression results for stocks A and B. The risk-free rate over the period was 4%, and the market’s average return was 11%. Performance is measured using an index model regression on excess returns.
Stock A | Stock B | ||||||||||
Index model regression estimates | 1% + 1.2(rM − rf) | 2% + 0.8(rM − rf) | |||||||||
R-square | 0.683 | 0.49 | |||||||||
Residual standard deviation, σ(e) | 12.1% | 20.9% | |||||||||
Standard deviation of excess returns | 23.4% | 28.5% | |||||||||
a. Calculate the following statistics for each stock: (Round your answers to 4 decimal places.)
Stock A Stock B
Alpha
Information ratio
Sharpe ratio
Treynor Measure
a). Alpha = Intercept of the Regression
Stock A's Alpha = 1%
Stock B's Alpha = 2%
ii). Information Ratio = Alpha / σ(e)
Stock A's Information Ratio = 1% / 12.1% = 0.0826
Stock B's Information Ratio = 2% / 20.9% = 0.0957
iii). Sharpe Ratio = (rp - rf) / standard deviation
Stock A's Sharpe Ratio = [1% + 1.2(11% - 4%)]/23.4% = 9.4%/23.4% = 0.4017
Stock B's Sharpe Ratio = [2% + 0.8(11% - 4%)]/28.5% = 7.6%/28.5% = 0.2667
iv). Treynor measure = (rp - rf)/Beta
Stock A's Treynor measure = [1% + 1.2(11% - 4%)]/1.2 = 9.4%/1.2 = 7.83%, or 0.0783
Stock B's Treynor measure = [2% + 0.8(11% - 4%)]/0.8 = 7.6%/0.8 = 9.50%, or 0.0950
Consider the two (excess return) index-model regression results for stocks A and B. The risk-free rate...
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