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"The characteristics of two stocks traded in the economy are as follows: Stock A, expected return=13%,...

"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

Solutions

Expert Solution

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%

Thumbs Up Please! Thank You

jeff jeffy answered 1 year ago
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