Question

Security A has a beta of 1.0 and an expected return of 12%. Security B has a beta of 0.75 and an expected return of 11%. The risk-free rate is 6%. Both these two securities are in the same market. Explain the arbitrage opportunity that exists; explain how an investor can take advantage of it. Give specific details about how to form the portfolio, what to buy and what to sell (we assume that the company-specific risk can be neglected). I need a detailed answer for 20 marks.

Answer 1

An arbitrage opportunity is existing between security A and security B, because it is possible to form a Portfolio of security A and risk free assets that has a beta of. 75 and a different expected return than security B.

The investor can use the the differential weight as building a Portfolio by choosing. 75 as weight in security A and.25 of weight in risk free assets.

So then the portfolio will have Expected Rate of Return-

E(rp)=[ [.75×12%]+ [.25×6%]]

=[ 9%+1.5%]

= 10.5%

This expected rate of return of 10.5% is lesser than expected rate of return of security B which is 11%.

There is an arbitrage opportunity existing which could be exploited by buying of security B and financing the purchase of security B by short selling of security A and borrowing the risk-free Asset.