Question

Suppose that the return on Barbie's common stock has a standard deviation of 50%, and the return on the market portfolio has a standard deviation of 15%. The expected return of the market portfolio is 12%, and the risk-free rate is 4%. Assume that the Barbie stock has an expected return of 20% under the CAPM theory. What is the correlation between the Barbie stock and the Market portfolio?

Answer 1

According to CAPM ret = Rf + Beta ( Rm - Rf )

20% = 4% + Beta ( 12% - 4% )

Beta ( 8% ) = 20% - 4%

= 16%

Beta = 16% / 8%

= 2

Beta = Correlation * SD of Stock / SD of Market

2 = Correlation * 50% / 15%

Correlation = 2 * 0.15 / 0.5

Correaltion between stock and Market = 0.6

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