Portfolio A has a factor sensitivity to inflation of 1.0. Portfolio B has a factor sensitivity to inflation of 2.5. What is the most appropriate allocation to portfolio A and B to fully hedge the inflation risk?

A. Short 0.40 of portfolio B for every $1.4 invested in portfolio A.
B. Short 0.67 of portfolio B for every $1.67 invested in portfolio A.
C. Short 0.71 of portfolio B for every $1.71 invested in portfolio A.

Correct Answer: B

To fully hedge inflation risk, set the combined weighting in portfolio A and B equal to zero and solve for the portfolio weights, ω_A and ω_B = 1 - ω_A

0 = 1.0 x ω_A + 2.5 (1 - ω_A)

ω_A = 1.67 and ω_B = 1 - ω_A = -0.67

Thus, the allocation should consist of a short position of $0.67 of portfolio B for every $1.67 invested in portfolio A.