Question

Assume that the CAPM holds. The expected return of the market portfolio is 15%, and the standard deviation of the market portfolio is 25%. The risk free rate is 5%. A friend of yours now claims that a portfolio exists that has an expected return of 12% with a standard deviation of 10%. Is it possible that this claim is true and this portfolio exists under this scenario? Why? You do not have to show your calculations. Just describe why your calculations lead you to your answer.

Answer 1

Given that,

Expected return on market Rm = 15%

Standard deviation on market portfolio is SDm = 25%

Risk free rate Rf = 5%

So, reward-to-variability ratio = (Rm - Rf)/SDm = (15 - 5)/25 = 0.4

A friend claims that a portfolio exists that has an expected return of 12% with a standard deviation of 10%

reward-to-variability ratio of portfolio = (12 - 5)/10 = 0.7

This portfolio can not exists in a CAPM scenario because CAPM assume that market portfolio has best reward-to-variability ratio and no other portfolio can have it more than market. So, this portfolio can not exists.