Financial Risk Manager Part 1

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A manager uses a two-factor model to examine the returns of two assets, X and Y. The two factors are unexpected percentage changes in inflation (IF) and consumer sentiment (CS). The following data has also been given:

$E(R_X) = 10\%$
$E(R_Y) = 12\%$
$\beta_{X,IF} = \beta_{Y,IF} = 2$
$\beta_{X,CS} = \beta_{Y,CS} = 2$

All other factors constant, which of the following statements is true?

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TTanishq

Asset X is undervalued relative to Asset Y

Asset Y is undervalued relative to Asset X

Both assets are fairly priced

The information is insufficient to determine which asset is undervalued

Both assets are undervalued

Both assets are overvalued

Explanation:

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._

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