UMUULIVALU PHILI (a) State and interpret the Euler equation from the Lucas Tree model. [3] (b) Briefly show how to use the Euler equation to derive the Consumption CAPM. [2] (c) Briefly discuss two other risk factors, beyond the standard factors in the 3-factor Fama-French model, that have been used to explain the cross-section of stock returns. [5] (d) Suppose that a three-factor Arbitrage Pricing Theory equation is given by: Elr.) = 1% + 5%B.,m + 2%Bus +2.5%Bs where M is the market portfolio, S is the size factor, and V is the value risk factor. Consider the following information on well-diversified portfolios: Portfolio Expected return (%) Bim A 6.05% 0.70 B 10.50% 2.00 C 7.5% 1.20 Bus 0.40 -0.50 0.50 0,30 0.20 -0.20 Portfolio D has the following factor loadings: Bam = 1.4.Bes = 0.2 and 1.0.24. i) What expected return should portfolio D earn if it were to satisfy the APT equation? [3] il) Applying financial Analysis techniques, you find that portfolio D offers an expected retum E) - 7%, that is, you find that portfolio D does not satisfy the APT equation. Brictly outline (without calculations) how you might exploit the arbitrage opportunity that D offers [2] iii) Calculate the positions in the combination portfolio that invests in A, B and C with amounts and rc, respectively, to match the factor loadings on portfolio D. The remainder, 1-(A + 8 +0), is funded or invested at the risk-free rate: Illustrate how to implement the arbitrage opportunity. Paragraph E + + UMUULIVALU PHILI (a) State and interpret the Euler equation from the Lucas Tree model. [3] (b) Briefly show how to use the Euler equation to derive the Consumption CAPM. [2] (c) Briefly discuss two other risk factors, beyond the standard factors in the 3-factor Fama-French model, that have been used to explain the cross-section of stock returns. [5] (d) Suppose that a three-factor Arbitrage Pricing Theory equation is given by: Elr.) = 1% + 5%B.,m + 2%Bus +2.5%Bs where M is the market portfolio, S is the size factor, and V is the value risk factor. Consider the following information on well-diversified portfolios: Portfolio Expected return (%) Bim A 6.05% 0.70 B 10.50% 2.00 C 7.5% 1.20 Bus 0.40 -0.50 0.50 0,30 0.20 -0.20 Portfolio D has the following factor loadings: Bam = 1.4.Bes = 0.2 and 1.0.24. i) What expected return should portfolio D earn if it were to satisfy the APT equation? [3] il) Applying financial Analysis techniques, you find that portfolio D offers an expected retum E) - 7%, that is, you find that portfolio D does not satisfy the APT equation. Brictly outline (without calculations) how you might exploit the arbitrage opportunity that D offers [2] iii) Calculate the positions in the combination portfolio that invests in A, B and C with amounts and rc, respectively, to match the factor loadings on portfolio D. The remainder, 1-(A + 8 +0), is funded or invested at the risk-free rate: Illustrate how to implement the arbitrage opportunity. Paragraph E + +