In: Finance
"The characteristics of two stocks traded in the economy are as follows: Stock A, expected return=13%, standard deviation=60%; Stock B, expected return=8%, standard deviation=40%. Correlation between A and B is -1. If the market risk premium is 4%, what is the expected return for a portfolio with a beta of 3 in a CAPM universe?"
15%
18%
22%
None of the above
Stock A
Expected Return = 13%
Standard Deviaton =60%
Stock B
Expected Return = 8%
Standard Deviation =40%
Market Risk Premium = 4%
The correlation between A and B is -1, therefore the portfolio formed by A and B is a risk free portfolio.
Also, we know standard deviation of risk free portfolio is 0
let weight of A be Wa and weight of B = 1-Wa
Therefore,
Standard deviation of portfolio = (standard deviation of A x Weight of A ) - (standard deviation of B x weight of B
0 = 60% x Wa - 40% (1-Wa)
0 = 60% Wa - 40% + 40% Wa
40%/100% = Wa
Weight in stock A = 40%
Weight in stock B =60%
Return on portfolio = weight in stock A x return in stock A + weight in stock B x Return in stock B
Return on portfolio = 40% x 13% + 60% x 8%
Retrun on portfolio = 10%
As per CAPM,
Expected Return = Risk free Rate + (Beta x Market Risk Premium)
Expected Return = 10% + (2 x 4%)
Expected Return = 18%
The correct answer is option B i.e. 18%
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