1 Arbitrage Pricing Theory (20 points) (1) Contrast the CAPM and the APT main assumptions. (2) Consider the Fama-French three-factor model: i =E(i) + Bi,m(rm - E(rm)) + i,s(SMB - E(SMB)) + Bih (HML - E(HML))+i where m is the random return on the market portfolio, SMB is the random return on the "small-minus- big" portfolio (size factor), and HML is the random return on the "high-minus-low" book-to-market value portfolio (book-to-market value factor). Assume that for a specific well-diversified portfolio, portfolio 1, Bw,m =0.9, Bw,s = 0.3, Bw.h = 0.2. The market beta is the same for the CAPM and the three-factor model. Let the market, the size, and the book-to-market risk premiums be 12%, 6%, and 5%, respectively. The risk-free interest rate is 3%. a) If you believe the CAPM to be valid, what should be the expected return on portfolio 1? b) Assume you believe the the three-factor model to be more accurate. i. What should the expected return be on portfolio 1? ii. Suppose there is another well-diversified portfolio, portfolio 2, with betas half the size of those of portfolio 1, but with the same expected return. Would an arbitrage opportunity exist? If so, what would be the arbitrage strategy?