(a) In a market in which the Arbitrage Pricing Theory (APT) model holds, the return on assets is given by the equation: E[R] = 20+bi,1+bi,2+... Assume the risk-free rate is 5%. Consider two well-diversified portfolios P; with the following features in a two factor model: P P2 ER] 16% 12% bi.l (x) (y) bi.2 1.4 0.8 Determine the values (x) and (y) for = 0.055 and 2 =0.07. (b) Consider a market with one risky asset and one riskless asset, and the market in discrete time. The interest rate p is time varying, with p = , P2 = 1, and p = . The share prices at times 0, 1, 2, and 3 are defined by So=2, S = SoY1, S2 = S1Y2, S3 = S2Y3 where Y, Y, and Y3 are independent random variables with P(Y = u)+P(Y = d) = 1, u = 2, d = 1 == P(Y2=u2)+P(Y = d2) = 1, u2 = 3, d = 2 P(Y3u3)+P(Y3d3) = 1, u3 = 2, d3 = 1 Write down the three time period binomial tree and find the time-0 option price of the option claim C = (S3 - 12)+.