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2. A Two-Factor APT Consider an economy in which the random return i on each individual asset i is given by i = E(fi) + Bim[im E(m)] + Bi,smb[SMB E(smb)] + i where, as we discussed in class, E(i) equals the expected return on asset i, im is the random return on the market portfolio, ismi is the random return on a "small-minus-big" portfolio that takes a long position in shares of stock issued by smaller, overlooked companies and a corresponding short position is shares of stock issued by larger, more popular companies. ; is an idiosyncratic, firm-specific component, and Bim and Bi,sms are the "factor loadings" that measure the extent to which the return on asset i is correlated with the return on the market and "small-minus-big" portfolios. Assume, as Stephen Ross did when developing the arbitrage pricing theory (APT), that there are enough individual assets for investors to form many well-diversified portfolios and that investors act to eliminate all arbitrage opportunities that may arise across all well-diversified portfolios. a. Consider, first, a well-diversified portfolio that has Bw,m = Bw,SMB = 0. Write down the equation, implied by the APT, that links the expected return E(FH) on this portfolio to the return ry on a portfolio of risk-free assets. b. Consider, next, two more well-diversified portfolios. Portfolio two with Bw,m= 1 and Bw.SMB = 0 and portfolio three with Bw,m= 0 and Bw.SMB = 1. Write down the equations, implied by this version of the APT, that link the expected returns E(73) and E(73) on each of these two portfolios to E(im), and Effsmb). c. Suppose you find a fourth well-diversified portfolio that has non-zero values of both Bw,m and Bw.sms and that has expected return E (7) = rf + Bw.m[E (M) rs]+Bw,smBE(sMB) +A where A