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). Need a step by step answer, using correct formula

Answer 1

Step 1: An arbitrage opportunity exists because it is possible to form a portfolio of security A and the risk-free asset that has a beta of 0.75 and a different expected return than security B.

Step 2: Choose 75% as the weight in A and 25% in the risk-free asset. This portfolio would have:

E(rp) = [0.75 x 12%] + [0.25 x 6%] = 10.5%

Step 3: The return of 10.50% is less than B's 11% expected return.

Step 4: The investor should buy B and finance the purchase by short selling A and borrowing at the risk-free asset.