APT. Suppose that stock returns are generated from the following linear process:

ri = E(ri) + bi,1X1 + bi,2X2 + i

where i and Xk are mean zero processses. The assumptions of Ross Arbitrage Pricing Theory hold. Consider three broadly diversified portfolios. Their returns are given approximately1 by

rA =0.06+2X1 +2X2

rB =0.05+3X1 +X2

rC =0.03+3X1

(a) Suppose there is a risk-free asset in the economy. What is its return?

(b) Determine the factor risk premia.

(c) Consider a fourth portfolio:

rD = 0.08+X1 +0.5X2

Are there arbitrage opportunities? If so, explain how you can exploit them.