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A stock has a correlation with the market of 0.4. If the Sharpe ratio of the...

A stock has a correlation with the market of 0.4. If the Sharpe ratio of the market portfolio is 0.7, what is the Sharpe ratio of the stock? (Hint: algebraically manipulate the SML equation.)

A. 0.28

B. 0.75

C. 0.60

D. 0.55

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Answer #1

Sharpe ratio=(return-risk free rate)/standard deviation
Sharpe ratio of market=0.7
=>(return of market-risk free rate)/standard deviation of market=0.7

return of stock usign CAPM=risk free rate+beta*(market return-risk free rate)=risk free rate+correlation of stock with market*standard deviation of stock/standard deviation of market*(market return-risk free rate)
Sharpe ratio of stock=(return of stock-risk free rate)/standard deviation of stock=(risk free rate+correlation*standard deviation of stock/standard deviation of market*(market return-risk free rate)-risk free rate)/standard deviation of stock=correlation*(market return-risk free rate)/standard deviation of market=0.4*0.7=0.28

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