Part A Suppose the single-factor APT is the correct model. However, the way the APT becomes the correct model is by investors exploiting arbitrage opportunities. Suppose well-diversied portfoli A has a beta value on the factor F of A = 2, and an expected return of E(rA) = 10%. Asset B has a beta of B = 1.2 and expected return E(rB) = 6.5%. Suppose return to risk-free asset is 1%. Is there arbitrage here? Part B: Multi-Factor Models Ok, I am going to walk you through the algebra on this. I highly suggest you don't simply refer to your notes on how to do this, but instead use your notes only to nd the relevant formulas. Suppose now the two-factor APT is correct. Suppose two well-diversied portfolios A and B with betas on the two factors given by A,1 = 1,A,2 = 1.2,B,1 = .8, and B,2 = .96. Suppose E(rA) = 8% and E(rB) = 9.5%. Suppose a risk-free rate of 1%. (B.1) What is the return to A and B if the factor is F1 = 1 and F2 = .7? What if F1 = .5 and F2 = .5? What about for a general values of F1 and F2 = 1? (B.2) Ok, now suppose you put 80% of your portfolio in A, 20% in the risk free asset, and 6 100% in B. What if F1 = 1 and F2 = .7? What if F1 = .5 and F2 = .5? What about for a general values of F1 and F2 = 1? Is there arbitrage here? (B.3) What are the betas on the two factors for the strategy listed in B.2? In general, if you have two well-diversied portfolios A and B, with beta values A,1,A,2,B,1, and B,2, and you invest A in portfolio A, B in portfolio B and the rest in the risk-free asset, what are the betas of that portfolio?. Write out ALL of your algebra steps. (B.4) Given you analysis in B.3, suppose there are two factor portfolios P1 and P2, with P1,1 = 1,P1,2 = 0,P2,1 = 0 and P2,2 = 1. Suppose you invest 1 in P1, 2 in P2, and the rest in the risk free asset. What are the betas of this new portfolio? (B.5) Suppose now that the expected return to portfolio B is 10%. Suppose (from B.4) that E(rP1) = 6% and E(rP2) = 7%. Is there arbitrage in this situation?