Beta-Hedging Equity and Credit Returns to Isolate Excess Performance

Summary

The note explains why analysts may adjust equity returns by their beta to a credit index when comparing performance. Its example models equity return Y as beta times credit return X plus an excess-return component, then considers a portfolio that holds equity and shorts a weighted amount of credit. The expected return and variance of this hedge depend on the difference between the equity beta and the hedge weight, alongside the variance of the excess component.

Setting the hedge weight equal to beta removes the modeled credit exposure, leaving the excess-return component as the remaining source of return variation. This helps distinguish performance associated with shared market movement from relative performance. The argument assumes a linear relationship, a zero intercept, and the stated return decomposition; it does not establish that the hedge is practical, stable, or complete. The source presents the framework as an explanation, without empirical evidence or discussion of estimation error, transaction costs, or changing correlations.

Key ideas

• Beta adjustment can frame equity performance relative to credit as a hedged return comparison.
• The example represents equity returns as beta-scaled credit returns plus an excess component.
• A hedge weight equal to beta cancels the modeled credit exposure.
• The remaining variance is attributed to the excess-return component under the stated assumptions.

Tags

# Equity vs Credit Performance


# Equity vs Credit Performance












When comparing performance of equities (for example S&P 500) versus credit indices (for example US HY) people often adjust equity returns by its beta relative to credit.

Can someone please explain what’s the reason?

For example, if you do invest in both securities your overall return will be return on equity investment versus the return on the credit investment. Thank you.

## Answer by TickaJules (score 0, accepted)

https://quant.stackexchange.com/a/73288

Not sure if this is the argument you are looking for but....Say you buy a unit of equity ($Y$) and hedge with $w$ units of credit ($X$). Your return is $R = Y - wX$. Assume $E(Y)=\beta E(X) + \alpha$ is your regression line, with $\alpha$ assumed to be 0. Rewrite $Y=\beta X + e$ ($e$ here is the excess return) with $E(e)=0$ and $\sigma^2(e)=V$ for some $V$. You can then show that $E(R)=(\beta-w)E(X)$ and $\sigma^2(R)=\sigma^2(X) (\beta-w)^2+V$. Then if you pick $w=\beta$, you see that the only thing that matters now is $V$ (the variance of the excess returns).

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.