Ella owns a stock with a beta of 1.34 and a standard deviation of 16.4%. The stock has a total return of 14.8%. The market risk premium is 8.5%, while the return on the market portfolio was 12.0%. What is the value of Sharpe's measure for Ella's portfolio?
A) 0.21
B) 0.38
C) 0.69
D) 0.90

Question

Quizplus · Accepted Answer

Sharpe's measure (S) = (Return on portfolio - Risk-free rate) / Portfolio standard deviation
First, we need to calculate the expected return on Ella's stock using the CAPM formula:
Expected return = Risk-free rate + Beta * Market risk premium
Expected return = 2.55% + 1.34 * 8.5% = 14.05%
Next, we can calculate the excess return on Ella's stock:
Excess return = Total return - Risk-free rate
Excess return = 14.8% - 2.55% = 12.25%
Finally, we can calculate Sharpe's measure:
S = (12.25% - 2.55%) / 16.4% = 0.688
Therefore, the closest answer choice is C: 0.69.

Ella Owns a Stock with a Beta of 1