Suppose that asset returns in the economy are described by the following two-factor model: R =...

Transcribed Image Text:

Suppose that asset returns in the economy are described by the following two-factor model: R₁ = a₁ + b₁₁iF₁ + b2, F2 + ei, where ai, b₁,i and b2,i are asset-specific constants. Furthermore assume that the e; have zero mean, E[e₁] = 0, and are uncorrelated across assets, E[e₁ej] = 0 for i #j. Furthermore, assume that the factors satisfy E[F₁] = E[F₂] = 0, and E[F₁F₂] = 0. Suppose there exist three well-diversified portfolios A, B, and C with the following characteristics: Portfolio A B Expected Return E(R₁) 15% 14% 10% a) Find the Factor Risk Premia 2₁ and 22. (8 marks) b) Assume portfolio E has expected return 15% and factor loadings bE,1=bE,2= 0.6. Find a combination of portfolios A, B, and C (call this portfolio D) that has the same systematic risk as portfolio E. (8 marks) c) Find the expected return on portfolio D in two different ways. bi,1 1.0 0.5 0.3 (8 marks) d) Is there an arbitrage opportunity in this market? If so, construct an arbitrage strategy using only portfolios D and E. What is the riskless gain of this strategy? What will happen to the expected return on portfolio E? (8 marks) Security e) Suppose that there is another risky asset XYZ is traded in the market with the following characteristics. XYZ bi 0.3 b₁,2 0.6 1.0 0.2 b2 2.0 O 14% Assuming that the standard deviations of the two factors are 10% and 5% respectively, calculate the asset's XYZ idiosyncratic risk. (8 marks) Suppose that asset returns in the economy are described by the following two-factor model: R₁ = a₁ + b₁₁iF₁ + b2, F2 + ei, where ai, b₁,i and b2,i are asset-specific constants. Furthermore assume that the e; have zero mean, E[e₁] = 0, and are uncorrelated across assets, E[e₁ej] = 0 for i #j. Furthermore, assume that the factors satisfy E[F₁] = E[F₂] = 0, and E[F₁F₂] = 0. Suppose there exist three well-diversified portfolios A, B, and C with the following characteristics: Portfolio A B Expected Return E(R₁) 15% 14% 10% a) Find the Factor Risk Premia 2₁ and 22. (8 marks) b) Assume portfolio E has expected return 15% and factor loadings bE,1=bE,2= 0.6. Find a combination of portfolios A, B, and C (call this portfolio D) that has the same systematic risk as portfolio E. (8 marks) c) Find the expected return on portfolio D in two different ways. bi,1 1.0 0.5 0.3 (8 marks) d) Is there an arbitrage opportunity in this market? If so, construct an arbitrage strategy using only portfolios D and E. What is the riskless gain of this strategy? What will happen to the expected return on portfolio E? (8 marks) Security e) Suppose that there is another risky asset XYZ is traded in the market with the following characteristics. XYZ bi 0.3 b₁,2 0.6 1.0 0.2 b2 2.0 O 14% Assuming that the standard deviations of the two factors are 10% and 5% respectively, calculate the asset's XYZ idiosyncratic risk. (8 marks)

Answer rating: 100% (QA)

a The factor risk premia 21 and 22 are the expected returns of the first and second factors respectively The expected return of the first factor is ca... View the full answer