1) how to find the lamda in APT

2) what the strategy and the expected return

3) what is the value of those 3 beta

(30%) Consider a 4-factor model with factors F1, F2, F3 and F4 and the risk-free rate of 2%. The following are the sensitivities bij (to factor Fi) and expected returns {pi: i=1,...,5} of 5 well-diversified portfolios: Portfolio 1 2 3 4 5 bil 2.0 1.0 0.0 0.0 1.0 bi2 -1.0 1.0 0.0 0.0 2.0 biz 0.0 0.0 -1.0 0.0 1.0 bi4 0.0 0.0 0.0 1.0 -2.0 Hi 5.0% 11.0% 5.0% 6.5% 3.0% (a) Based on Portfolios 1, 2, 3, 4 and the risk-free rate, compute the factor risk premiums (s) in the Arbitrage Pricing Theorem. (b) Suppose that Portfolio 5 is also taken into consideration. Is there any arbitrage opportunity? If so, construct an arbitrage strategy and compute the expected return of the strategy. (c) Assume that the equilibrium conditions hold so that the CAPM can be applied. Suppose that BF3M = Cov(F3, M) = -1.5, where M is the market portfolio. What are the values of BF, M, BFM and BEAM? (30%) Consider a 4-factor model with factors F1, F2, F3 and F4 and the risk-free rate of 2%. The following are the sensitivities bij (to factor Fi) and expected returns {pi: i=1,...,5} of 5 well-diversified portfolios: Portfolio 1 2 3 4 5 bil 2.0 1.0 0.0 0.0 1.0 bi2 -1.0 1.0 0.0 0.0 2.0 biz 0.0 0.0 -1.0 0.0 1.0 bi4 0.0 0.0 0.0 1.0 -2.0 Hi 5.0% 11.0% 5.0% 6.5% 3.0% (a) Based on Portfolios 1, 2, 3, 4 and the risk-free rate, compute the factor risk premiums (s) in the Arbitrage Pricing Theorem. (b) Suppose that Portfolio 5 is also taken into consideration. Is there any arbitrage opportunity? If so, construct an arbitrage strategy and compute the expected return of the strategy. (c) Assume that the equilibrium conditions hold so that the CAPM can be applied. Suppose that BF3M = Cov(F3, M) = -1.5, where M is the market portfolio. What are the values of BF, M, BFM and BEAM