Equity vs Credit Performance [closed]

Question

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 1

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).