3. The returns on stocks A and B are 12% and 16%, respectively. The SD of the returns on stocks A and B are 31% and 12%, respectively. The beta of A is 0.7, while that of B is 1.4. The risk free rate over the period was 5%, the market’s average return was 13%. a. Calculate the Sharpe ratio for each stock (10 points). b. Calculate the alpha for each stock (10 points). c. Which stock is the best choice if this stock will be mixed with the rest of the investor’s portfolio, currently composed solely of holdings in the market-index fund (15 points).

a. The Sharpe ratio of Stock A is 0.23

The Sharpe ratio of  Stock B is 0.92

b. The alpha of stock A is 1.4%

The alpha of stock B is -0.2%

c. If this stock will be mixed with the rest of the investor’s portfolio, Stock B should be included owing to higher return than stock A

Explanation:

a. In order to calculate the Sharpe ratio for each stock we woud have to use the following formula:

Sharpe Ratio of Stock

= (Rs-Rf)/σ s

where Rs = return on stock , σ s = standard deviation of stocks excess return, rf = risk-free rate

Sharpe ratio Stock A = ( 12-5)/31 = 0.23

Sharpe ratio  Stock B = (16-5)/12 = 0.92

b. In order to calculate the alpha for each stock we woud have to use the following formula:

alpha = rate of return - risk free rate - β (market return - risk free rate)

alpha of stock A = 12-5-0.7(13-5) = 1.4%

alpha of stock B = 16-5-1.4(13-5) = -0.2%

c. If this stock will be mixed with the rest of the investor’s portfolio, Stock B should be included owing to higher return than stock A

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