Answer: Short sell a hedge portfolio with 30% allocation to factor A portfolio, 50% allocation to factor B portfolio, and 20% allocation to the risk-free asset.

## Explanation The correct strategy to hedge away all exposure to both risk factors A and B without selling the portfolio is to **short sell a hedge portfolio with 30% allocation to factor A portfolio, 50% allocation to factor B portfolio, and 20% allocation to the risk-free asset**. ### Key Concepts: - **Factor Portfolios**: Well-diversified portfolios designed to have beta = 1 for one risk factor and beta = 0 for all other factors - **Hedging Principle**: To hedge factor exposures, we need to create offsetting positions ### Mathematical Basis: Portfolio Z has: - Factor A beta = 0.3 - Factor B beta = 0.5 To hedge these exposures, we need a hedge portfolio with matching betas: - Factor A beta = 0.3 - Factor B beta = 0.5 By short selling this hedge portfolio, we create negative exposures: - Factor A beta = -0.3 - Factor B beta = -0.5 When combined with Portfolio Z: - Total Factor A exposure = 0.3 + (-0.3) = 0 - Total Factor B exposure = 0.5 + (-0.5) = 0 ### Why Other Options Are Incorrect: - **Option A**: Has reversed allocations (50% to A, 30% to B) which would over-hedge factor A and under-hedge factor B - **Option C & D**: Buying hedge portfolios would increase rather than decrease exposure to the risk factors This strategy allows the manager to maintain the original portfolio while completely eliminating the systematic risk exposure to both factors A and B.

Author: Tanishq Prabhu