Reference no: EM133121802
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 + βX,1 λ1 +βX,2 λ2; use all the specific quantities as given above).
b) What is the risk premium per unit of factor-1 risk, λ1? What is the risk premium per unit of factor-2 risk, λ2 (Hint: Use the two expressions developed under a) to set up a system of equations and solve for λ1 and λ2)
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 perdollar expected gain from P(C)?
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