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.