Financial Risk Manager Part 1

Explanation

In a two-factor model, the expected return of an asset is given by:

$E(R_i) = R_f + \beta_{i,IF} \times \lambda_{IF} + \beta_{i,CS} \times \lambda_{CS}$

Where:

• $R_f$ is the risk-free rate
• $\lambda_{IF}$ is the risk premium for inflation factor
• $\lambda_{CS}$ is the risk premium for consumer sentiment factor

Given that both assets have identical factor exposures:

• $\beta_{X,IF} = \beta_{Y,IF} = 2$
• $\beta_{X,CS} = \beta_{Y,CS} = 2$

This means both assets should have the same expected return if they are fairly priced. However, we observe:

• $E(R_X) = 10\%$
• $E(R_Y) = 12\%$

Since both assets have identical factor sensitivities, they should command the same risk premium. Therefore, the asset with the lower expected return (Asset X) is undervalued relative to the asset with the higher expected return (Asset Y).

Key Insight: When two assets have identical factor exposures, they should have identical expected returns. Any difference in expected returns indicates mispricing, with the lower-return asset being undervalued relative to the higher-return asset._