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Suppose we experience a significant equity market crash. All equities are affected, but the drawdown disproportionately affects equities in a specific sector - for example, say the broad equity market is down -15%, but the energy subsector is down -30%.

Now suppose that one month after the shock, the broad market has largely recovered and its valuation multiples currently are trading in line with their levels prior to the shock. However, the energy subsector has not recovered to the same degree and its valuation multiples are still substantially below their levels prior to their shock.

My question is: should the difference in valuation levels between the energy sector and the broad market affect the energy sector's beta to the market in the current environment? Estimating conditional/time varying beta using methods like GARCH-DCC may suggest that its beta has increased because the energy sector's relative volatility is higher following the shock. However, if the energy sector has not participated in the broad market recovery and its valuation multiples are still low, that might suggest that its beta has become disconnected from the market and so it should have a lower beta and be less sensitive to another drawdown.

How (if at all) should I calculate beta in this instance? Any suggestions are appreciated.

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This is really more a subjective question (and thus not ideal to this SE) but I'd suggest you're comparing apples to pineapples. Beta is a sensitivity to broad market return, valuation multiples are really more about relative value or 'cheapness'.

A company can be cheap and have lower beta/vol or higher beta/vol than some set of its peers. Betas and valuations also vary by sector, as you'd noted. Energy in particular has had a rough go of it that last ~5 years, and even moreso of late with crude where it is due in part to covid-related drop in demand.

In short, beta still measures what it's designed to measure, the real question is whether (and how) this impacts your process.

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"if the energy sector has not participated in the broad market recovery and its valuation multiples are still low, that might suggest that its beta has become disconnected from the market and so it should have a lower beta and be less sensitive to another drawdown"

Your argument seems to be "because it's (relatively) cheap it's less likely to get cheaper". Not sure why this would hold theoretically or that it holds in practice (e.g. SX7E vs. SX5E).

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