A portfolio invests in a risk-free asset and the market portfolio has an expected return of 7% and a standard deviation of 10%. Suppose risk-free rate is 5%, and the standard deviation on the market portfolio is 22%. For simplicity, assume that correlation between risk-free asset and the market portfolio is zero and the risk-free asset has a zero standard deviation. According to the CAPM, which of the following statement is/are correct?
a. This portfolio has invested roughly 54.55% in the market portfolio
b. This portfolio has a reward to risk ratio that is higher than market average
c. This portfolio beta is roughly 0.5455
d. Market risk premium is roughly 6.6%
e. Statements a and b are both correct
According to the CAPM, the following statement is correct
Market risk premium is roughly 6.6%
Market beta is equal to 1, so if Option A were correct then Option C would have to be correct as well (beta of portfolio=54.55%*1=0.5455). But we can select only one option and there is no Option which says Option A and Option C are correct. Therefore, we can rule out Option, Option C, Option E (because in Option E, if A were correct then C would also have to be correct). Option B is incorrect because as per CAPM, the reward to risk ratio of any portfolio can not be higher than market average and also, as the portfolio is created using market portfolio and risk free asset, the reward to risk must be equal to that of the market portfolio.
We are left with Option D
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