Question

Assume that you are using a two-factor APT model, with factors A and B, to find the fair expected return on a well-diversified portfolio Q that has an actual expected return of 18%. Portfolio Q's factor loadings (i.e., Q's betas on each of the two factors) and the factors' risk premiums are shown in the table below. Portfolios for factors A and B are tradable (i.e., you can take long or short positions in them). The risk-free rate is 3.5%. Factor Factor Risk Premium Q's factor loading (Beta) 12.0% 1.4 0.8 -3.5% a) Is there an arbitrage opportunity in this economy? If so, what is the arbitrage return (in %) per dollar bought/sold of Q ? Explain how you would attain this arbitrage return, i.e., specify your net dollar position, per dollar traded in portfolio Q, in each of the portfolios Q, A, B, and in the risk-free asset (e.g., "for each dollar bought/sold of Q, buy/sell $X of A, etc.)

Answer 1

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& R = RE + FRI, A + FRP2 B2 t - - -- + frig Bk factor Bisk foenicom 61B) = 3.5+ 12/14) - 3.5(18) = 3.5+ 16.8 - 2.8 for ElR)= 17.5 Khan (9) Re = 175 E)R) = 184 ER) > Pe this expedien is 17.5 but actum is ist that means acted expected vader parking undes piring - Yes, arbihage offertumity is there If we fany portfolio & in then this resercing 13.0-1715 lie as ut arbitrage schum is there