Manage coskewness and improve momentum trading

I am biased toward momentum trading whether cross-sectionally or as a time series. It is simple to implement and has been a consistent risk factor across long periods of time. Of course, it may fall out of favor over short periods, but it has generally produced strong returns over the long run. Unfortunately, a problem exists. 

Momentum is subject to crashes and shows negative skew.  Past returns winners show negative skew while past losers show less skew. The net result is that a winners minus losers portfolio will have negative skew. The gains from momentum are balanced against the pain from these periodic crashes. If only the negative skew problem could be solved, momentum would be an even better core strategy. 

What must be managed is the coskew, the covariance between asset returns and squared market returns. Coskew is higher with stocks that have extremes. If the coskew is negative, returns will fall when market volatility increases. Some will even argue that the excess returns of a momentum portfolio are compensation for the risk of holding a coskewed basket. 

Crashes are more likely when volatility is high. Hence, if momentum portfolios are conditioned on volatility or more importantly coskew, there is the potential for improvement versus a momentum portfolio that is not adjusted for this factor. This issue is addressed in the paper, "Coskewness and Reversal of Momentum Returns: The US and International Evidence". 

The authors find that coskew for stocks is important especially during less volatile periods. Momentum returns reverse during high volatility periods but not from coskew. Overall, if coskew rises (falls) above (below) a certain level, it makes sense to cut (increase) momentum exposure. This simple rule will reduce the change of a momentum crash and improve the overall return from holding winners minus loser momentum portfolios.