Question

given a sharpe ratio for the market portfolio of 0.4 . calculate the expected return on stock with astardard deviation return of 0.5 and acorrelation with the market portfolio return of 0.6.the risk free rate is 5% and the stardard deviation of the market portfolio returns is 0.25

Answer 1

Sharpe ration Market = 0.40

Standard Deviation of stock = 0.50

Correlation with Market = 0.60

Risk free rate = 5%

Standard Deviation of market = 0.25

Sharpe ratio = ( Market return - Risk free rate ) / Market standard deviation

0.40 = ( Market return - 0.05 ) / 0.25

Market return = 0.15 or 15% Answer

Beta = Correlation * Standard Deviation Stock / Standard Deviation market

       = 0.60 * ( 0.50 / 0.25 )

       = 1.20

Return on stock = Market return + ( Market return - Risk free rate ) * Beta

                       = 15 + ( 15 - 5 ) * 1.20

                       = 27% Answer