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?

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.