Question

1. 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. b. Calculate the alpha for each stock. c. Calculate the Treynor ratio for each stock. d. Which stock is the best choice under the following circumstances? i. This is the only risky asset to be held by the investor. ii. This stock will be mixed with the rest of the investor's portfolio, currently composed solely of holdings in the market-index fund.

Answer 1

Sharpe Ratio of Stock

= (Rs-Rf)/$\sigma s$

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

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

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

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alpha = rate of return - risk free rate - $\beta$ (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%

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treynor ratio = (rs-rf)/Beta

where rs = return on a

stock, rf = risk free rate, beta = beta of stock

treynor ratio of stock A

= (12-5)/0.7 = 10

treynor ratio of stock B

=(16-5)/1.4 = 7.86

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D (1)

if only one risky asset has to be chosen, then its stock B as it has a higher return of 16% as compared to stock A with a return of 12%

D(2)

Stock B should be included owing to higher return than stock A