"We defined two types of signed momentum strategies, a time-series and a cross-sectional strategy, the former already well-known in the literature. We consider two forms of volatility weighting: weighting a strategy by its own (predicted) volatility and weighting each of the underlying assets (normalized returns). In the former case we see that the intuition that if returns are negatively related to ex-ante volatility, then volatility weighting will be beneficial is only partially accurate. We consider using normalized returns in both a time-series and cross-sectional setting, deriving some simple results."

"We distinguish between a timing effect and a stabilizing effect in volatility weighting. The latter is important when the relationship between returns and volatility is negative. These effects are hard to disentangle, but we find that both are important. Our empirical results confirm that weighting a strategy with its own volatility as well as using normalized returns adds value: the Sharpe ratio increases and the kurtosis decreases. Weighting a strategy with its own volatility seems to work at least when the relationship with volatility is negative and using normalized returns is almost always effective. Dispersion weighting, however, seems to be less effective, though still improving the Sharpe ratio."
 

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