Arbitrage Pricing Theory

Please show your work.

You estimate a 2-factor return-generating process for 4 large portfolios with the following results.

r_A = 4 + 1.2 F1 + 0.5F2

r_B = 1 + 0.8F1 - 0.5F2

r_C = 6 - 1.2F1 + 0.5F2

r_D = 2 + 1.2F1 + 0.5F2

QUESTIONS:

(1) Which 2 portfolios are functional equivalents according to the Arbitrage Pricing Theory?

(2) Suppose you are in the APT world and:

₀ = 3%,

₁ = 6% and

₂ = 8%.

What is the expected return on portfolio D?