Question 2: Arbitrage

Having shown your skills in the quantitative research department, your boss wants youto continue your work on stock analysis. One of the tasks the research department isinvolved in is active portfolio management, i.e., identifying mispricings and takingpositions based on these mispricings. Your boss has presented you with the followingportfolios that can be invested in:

- Portfolio A has an expected return of 15% p.a. and a market beta of 1.6

- Portfolio B has an expected return of 9% p.a. and a market beta of 0.6

a) The risk-free rate is 3%. Could you tell your boss whether any arbitrageopportunities are available? What is the arbitrage profit in percentage?

b) If you know that short-selling requires a margin deposit of 40% of the valueshorted and you have $3 million to invest in the arbitrage, how much money can you make on the arbitrage?

c) After a careful analysis, you realize that the strategy above relies on the CAPM being the correct asset pricing model. However, you realize that there may bea more appropriate 2-factor model that besides market risk also considersinterest rate risk. You have found that the market risk premium is 10% and theinterest rate risk premium is 5%. Portfolio A has a beta of 1.6 on the market riskpremium and, in addition, a beta of -1.0 on the interest rate risk premium.Portfolio B has a beta of 0.7 on the market risk premium and, in addition, a betaof -0.2 on the interest rate risk premium.

With this new 2-factor asset pricing model do you still find that there is an arbitrage opportunity? What does your new conclusion tell you about thearbitrage opportunity identified before?