Thinking a little differently about crisis alpha - Conditional drawdown at risk

There has been significant discussion about crisis alpha, but there may need to be a more general approach to the value of certain strategies in up and down markets. Perhaps an effective approach is to look at the upside risk and the downside risk conditional on a drawdown. This is a variation on upside and downside risk and asks a conditional question of how a strategy will do when the market is in a drawdown. See "Capital Asset Pricing Model (CAPM) with drawdown measure".

The question is simple. What happens to a given asset when the market is in a drawdown versus all other times. All crises will be subsets to market drawdowns. First, it is not hard to calculate the conditional drawdown at risk (CDaR) for any asset. From the CDaR, a drawdown beta can be found which is the beta when in a drawdown. This provides useful information on how any asset drawdown is related to the market returns (beta). 

If the drawdown beta can be calculated, there can be calculated a drawdown alpha which is different from crisis alpha; however, it is good comparative measure that is consistent over any other beta and alpha calculation. The drawdown alpha and beta can be used to compare hedge fund strategies. 

It is found that trend-following provides good drawdown beta and drawdown alpha relative to other hedge fund styles. There are other hedge fund styles that will also give you good drawdown beta and alpha. For example, a multi-strat approach and some fixed income RV can also do a good job. Hence, investors can form a defensive portfolio based on the drawdown beta and alpha to protect against a market decline. This approach can be an actionable way to build a crisis prevention portfolio.