In the academic literature, I found that momentum returns are negatively skewed (e.g. Daniel and Moskowitz, 2002). As far as I understand, this usually happens when the "past losers" rebound causing heavy losses on the short leg of the strategy.

Nonetheless, I noticed that many CTA/trend-following funds are convex (and have returns similar to the payoff of a straddle: they don't make money when prices don't move much, but they make a lot of money in tail events). This causes the distribution of returns to be positively skewed.

This is confusing. Are momentum returns positively or negatively skewed? Do time-series momentum and cross-sectional momentum have different skewness characteristics?

Thank you in advance

  • 1
    $\begingroup$ Are you looking at crossectional (CSMOM) momentum or time series (TSMOM) momentum? $\endgroup$ – noob2 Sep 10 '20 at 2:53
  • $\begingroup$ Hi noob2, both ideally. Do they have different skewness characteristics? $\endgroup$ – Eaglez Sep 10 '20 at 8:10
  • $\begingroup$ My impression (FWIW) is that the academic version of CSMOM (especially) and TSMOM have negatively skewed returns. The term "momentum crashes" has been employed in the literature. TF (Trend Folllowing) as commonly practiced is similar to TSMOM but tends to be implemented asymmetrically (eg enter with momentum, exit with stop loss) which can/may reduce skewness. The nice thing about academia is they define their methods precisely, whereas the CTA/TF industry is somewhat amorphous and secretive. Nevertheless there are databases of CTA returns that you could examine to answer the skewnss question. $\endgroup$ – noob2 Sep 10 '20 at 11:41

From Daniel-Moskowitz ("Momentum Crashes") you can see that equity CSMOM has negative skewness. However, this is less clear for other asset classes. From their table 11 you can see that commodity momentum has essentially zero skewness (they report a mildly positive skewness). Also e.g. this paper (Menkhoff, L., Sarno, L., Schmeling, M. and Schrimpf, A. (2012). Currency momentum strategies. JFE, 106(3), pp. 660-684) reports a mildly positive skewness for the currency momentum strategy.

Looking at the returns of CTA:s can be misleading. My impression is that few of these funds trade the type of simple mechanical trend following strategy described in the academic papers and might e.g. combine trend following with short term signals.


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