Consider two well-diversified portfolios A and B that conform to a two-factor model (the two shocks to factors, F1,t and F2,t, have zero means), that is, their alphas are equal to zero, and the risk-free rate (assume that you may both lend and borrow at the risk-free rate). All returns are expressed in percentage points:

rA,t = 12.5 + 0.6 F1,t + 0.9 F2,t ;

rB,t = 18.5 + 1.2 F1,t + 1.3 F2,t ;

rf = 2.

a) Write the expressions for the expected rates of return on portfolios A and B according to the two-factor model (Hint: The general form is E(rX) = rf + X,1 1 +X,2 2; use all the specific quantities as given above).

b) What is the risk premium per unit of factor-1 risk, 1? What is the risk premium per unit of factor-2 risk, 2 (Hint: Use the two expressions developed under a) to set up a system of equations and solve for 1 and 2)

c) Construct factor portfolios FP1 and FP2. Report the portfolio compositions for the two factor portfolios (the weights that they place on A, B, and the risk-free asset).

d) What is the expected rate of return predicted by the two-factor model for portfolio C (Hint: Is the alpha of portfolio C equal to zero?): rC,t = 13.3 + 1.4 F1,t + 0.7 F2,t.

e) Use portfolios A, B, and C, and the risk-free asset to construct a zero-cost portfolio P(C) that would generate arbitrage profits. Report the resulting positions on A, B, C, and the risk-free asset (assume the absolute value of the position in C is $1 to set the scale of arbitrage). What is the per dollar expected gain from P(C)?

Answer rating: 100% (QA)

Solutions for the twofactor model problem a Expected returns of portfolios A and B Following the given twofactor model formula ErAt rf A1 F12 A2 F22wh... View the full answer