Course Name: Momentum Trading Strategies, Section No: 10, Unit No: 1, Unit type: Video
Why the time series momentum is positively skewed, while the cross section momentum is negatively skewed?
This is a very keen observation and a really good question. One way to think about it is like this - both time series momentum (TSMOM or trend following) and cross sectional momentum (XSMOM) has changing beta profile to the overall market (despite XSMOM being market neutral). For TSMOM, the beta is usually low in a normal market, but become strongly positive (negative) in an up (down) market. This is similar to a long straddle position and results in a outperformance in both strong bull or bear market - introducing a positive skew. On the other hand, XSMOM has a similar but fundamentally different beta profile, while maintainig overall market neutrality. In downmarket, it shorts the past losers. It is observed, that at least in equities market, such past losers exhibit strong asymmetric beta - a low down-beta (beta to further market sell off) and a high up-beta (beta to a market rebound). As a result a rebound in a down market results in the so called "momentum crash" - heavy losses in the shorts which are barely covered by the longs. This effect (asymmetric beta) is not observed for the winners in a up market - introducing this negative skew.
In more technical terms,
1. TSMOM returns are long auto-covariance (past up move of stock X predicting future up move of X is good) + long average squared returns (high trend of the overall markets, positive or negative, is good), whereas
2. XSMOM returns are long auto-covariance (same as above) + long cross-sectional variance of mean returns (high variations of individual stock trends, rather than strong overall trends, are good) + short cross-covariance (past up move of X predicting future up move of Y is very bad).
In both cases, the last terms are responsible for their skewness - the whole difference boils down to how they are constructed - market neutral or not. If you are interested for more technical stuff on this, read "time series momentum" and "momentum crash" by Moskowitz and Perdersen, and also "risk in hedge fund strategies" by Fung and Hsieh.
Really appreciate your comprehansive explanationc and helpful resources! I will look into it!