Cross-Sectional Momentum

Cross-sectional momentum is the observed tendency of assets that have performed better than their peers over the past several months to continue performing better over the following months, and of relative losers to keep lagging. The term also names the strategy built on it: rank a group of assets by past return, buy the top of the ranking and sell short the bottom.

The word cross-sectional marks the comparison as one between assets at the same date. An asset can be a winner in this sense even when its own price has fallen, as long as others fell further. That separates it from time-series momentum, used in trend following, where each asset is judged only against its own past. Cross-sectional momentum is one of the most studied patterns in asset pricing and a standard factor in factor investing.

The effect was documented for US shares by Narasimhan Jegadeesh and Sheridan Titman in a 1993 paper. They formed portfolios of shares ranked on returns over the previous three to twelve months and held them for three to twelve months. Past winners beat past losers by a margin of roughly one percent a month in their sample. In 1997 Mark Carhart added a momentum factor to the three-factor model of Fama and French, and a four-factor factor model became a common benchmark for fund performance.

Later research found the pattern in many countries and in other asset classes, including equity indices, currencies, commodities and government bonds. Momentum tends to be negatively correlated with value, which is the reason the two are often combined in a value and momentum strategy. The effect poses a challenge to the weak form of the efficient market hypothesis, under which past prices should not predict future returns.

The most common ranking measure is the return over the past twelve months, leaving out the most recent month:

• $P_{t-1}$ is the price one month ago.
• $P_{t-12}$ is the price twelve months ago.

The latest month is skipped because over very short horizons returns tend to reverse, an effect known as short-term reversal. A share that traded at $80 twelve months ago and $100 one month ago has a score of 100 ÷ 80 − 1 = 25 percent.

All shares in the universe are scored and sorted. A typical academic version buys the top tenth and sells short the bottom tenth, weighting by market value, and repeats the sort each month. The return of the factor, often labeled winners-minus-losers, is the return of the long side less that of the short side. If the winner portfolio gains 1.5 percent in the next month and the loser portfolio gains 0.3 percent, the factor return is 1.2 percent. Because the two sides are of equal size, the position has little net exposure to the market on average.

There is no agreed cause. Explanations drawn from behavioral finance hold that investors react too slowly to news, so that prices adjust gradually, or that buying by trend-chasers pushes prices beyond fair value for a time. The tendency of investors to sell winning positions too early and hold losing ones too long would also delay price adjustment. Risk-based explanations argue that winners are temporarily riskier and that the return is compensation, with the occasional severe loss as the risk in question. A third view points to limits on arbitrage: the trade requires frequent turnover and short selling of small, hard-to-borrow shares, which keeps capital from removing the pattern.

The strategy's losses are infrequent but large. After a steep market decline, the loser portfolio is filled with shares that fell most, which tend to be those most sensitive to the market. When the market rebounds, these losers surge, and a portfolio that is short them suffers. This is called a momentum crash. The most cited cases followed the market lows of 1932 and 2009. Work by Kent Daniel and Tobias Moskowitz showed that such crashes are partly predictable from market conditions and that scaling the position down when volatility is high reduces them.

Momentum is a high-turnover strategy. Rankings change every month, and a large part of the portfolio is replaced several times a year. The resulting transaction costs take a significant share of the gross return, more so because much of the measured effect comes from smaller and less liquid shares and from the short side.

Practical versions soften these problems. Long-only momentum funds hold recent winners without shorting, which keeps full market exposure. Managers trade more slowly, use wider bands before replacing a holding, neutralize industry exposure so the portfolio is not a bet on one sector, or blend several look-back periods.

Cross-sectional momentum is the systematic, portfolio-level form of the idea behind discretionary momentum trading; the general concept is described under momentum. Its mirror image at short horizons is cross-sectional mean reversion, which buys recent losers. The two coexist because they operate over different periods: reversal over days to a month, momentum over several months to a year, and reversal again over three to five years. Historical returns to the factor have varied greatly by decade, and its past performance is no assurance of future results.