Question

Assume the CAPM holds. The risk-free rate is 5% and the market portfolio expected return is 15% with a standard deviation of 20%. An asset has an expected return of 16% and a beta of 0.8.

a) Is this asset return consistent with the CAPM? If not, what expected return is consistent with the CAPM?

b) How could an arbitrage profit be made if this asset is observed?

c) Would such a situation be expected to exist in the longer term?

Answer 1

a) As per CAPM ,

Required rate of return = Risk free rate + ( Market return - risk free rate ) * beta

= 5+ ( 15 -5) * 0.8

= 13%

the return is not consistent with CAPM.

13% is consistent with CAPM.

b)

The expected rate of return is less than the required rate of return. Hence the stock is trading cheap and investor should go long the stock.

c) Such situation wont exist for a longer term as more and more people come to know about it they will start expoliting the situation and the expected price will reach out to actual price and the arbitrage opportunity will close.