An Important Analysis of Stock Momentum and Reversal Factors

So much was written about stock momentum since the Jegadeesh and Titman (1993) that it might have started to be confusing. Still, there seems to be a consensus among academics and practitioners that there is a stock momentum based on past twelve returns and short-term reversal based on the past month. However, there is also an industry momentum, sector momentum, peers momentum, and the newest addition is the factor momentum. These numerous anomalies raise a question – can be the initial momentum explained by industry, sector or factor momentum? Moreover, similar question could be raised about the short-term reversal. 

The novel research by Li and Turkington (2021) uses a robust regression model where variables are standardized and include returns of individual securities as the dependent variable. The explanatory variables include returns over the industry, industry over industry group, industry group over the sector, sector over the market, various risk factors and even returns of statistical peers (measured by Mahalanobis distance). As a result, the authors provide an in-depth analysis of both momentum and reversal anomalies, and the approach yields compelling results. These analyses are even divided into a more prolonged sample and the most recent period of 2010-2020. 

The individual momentum anomaly that broader market groups do not fully explain exists in the whole sample but is statistically weak. On the other hand, the reversal anomaly is highly significant. Secondly, the traditional 12-months momentum can be better explained by the factor momentum than the industry or sector momentum. Still, the industries, industry groups, sectors, and even factors have distinct drivers, and the anomalies seem different. 

The most recent sample offers captivating results too. Firstly, it seems that the 12-month momentum in industries does not exist anymore, but the opposite holds for a 1-month reversal. The reversal in industries or sectors is even more apparent. 

To sum it up, there are several takeaways for every quant investor, and we highly recommend diving deeper into the paper. 

Authors: Yimou Li and David Turkington

Title: Mapping Momentum



Findings on momentum and reversal effects in the stock market are often disparate. Differences in methodology, calibration, data universe, and the granularity of tests have made it challenging to reconcile and unify the various documented relationships. Our goal is to attribute stock return predictability to a variety of distinct momentum (and reversal) components within a single coherent framework. We focus on S&P 500 stocks and implement consistent data transformations, nested sets of excess returns, and panel regressions to facilitate this attribution. We find that sector and factor momentum coexist, but they operate on different horizons, and sector momentum is more prone to crash during volatile markets. Collectively, sector and factor momentum explains away most of the security-specific 12-month momentum effect, with factors explaining more. Traditional 12-month momentum is much more prevalent for past “loser” stocks whereas crashes and reversals are found mostly among past “winners.” Lastly, we show that in the decade after the 2008-2009 financial crisis compared to the decade prior, sector and industry momentum disappeared at the 12-month horizon but intensified in terms of 1-month reversals.

As always we present several interesting figures:

Notable quotations from the academic research paper:

“We analyze stocks in the S&P 500 universe between 1995 and 2020. We choose this large capitalization and highly liquid market to remove concerns that pricing anomalies are mere artifacts of market frictions, or that the predictive relationships we identify would not have been implementable in practice, or accessible at scale. We run pooled panel regressions on individual stock returns. Our dependent variable is
the total return of stock i for the following month, normalized as a cross-sectional percent rank and centered to have zero mean. After this normalization, it is nearly impossible for a few outliers to have an undue influence on results – a concern that would otherwise loom large for stock returns. It also mitigates heteroskedasticity in errors, leading to more robust statistical inference. And, since there are months in which stocks mostly rise (bull markets) or mostly fall (bear markets), the cross-sectional ranking keeps our focus on relative “winners” and “losers.” We compute returns from trading day t+4 to trading day t+23 to reflect a subsequent onemonth period plus a 3-day implementation lag.

As explanatory variables, we include a variety of trailing one year (day t-250 to t-20) and one month (day t-20 to t) price returns that are related to stock i. We consider four categories of price signals.

First, we include the returns of the hierarchical industry portfolios that contain stock i, according to the Global Industry Classification System (GICS). We measure industry returns in a nested fashion, taking the excess return of each more granular segment above and beyond the return of the broader class to which it belongs. We compute a stock’s level 1 sector return in excess of the broad market, its level 2 industry group return in excess of its level 1 sector return, and its level 3 industry return in excess of its level 2 industry group return. In each case, we percent rank the excess return against the relevant set of cross-sectional comparisons. This approach avoids multicollinearity and provides a clean attribution across levels.

Second, we include the return of stock i in excess of its level 3 industry return. These stock-specific excess returns are ranked across all stocks in the universe at time t.

Third, we include size, value, investment and profitability factors as proposed by Fama and French (2015). We treat these factors based on observable attributes the same way we treat industry classifications. Specifically, we form decile portfolios by ranking stocks cross-sectionally on a given attribute (such as book-to-market for the value factor) and identify the portfolio that contains stock i. For that stock, we record the cross-sectional rank of that decile portfolio’s trailing returns compared to the nine other decile portfolios. We re-rank for each attribute, so these groups are not nested like the industry classifications. Mathematically, it must be the case that if factor momentum occurs for groups of stocks, the stocks that compose the factor portfolio at any point in time must “inherit” the performance trends of the composite factor as a component of their own trailing return.

Fourth, we include the returns of an index of “peer” stocks whose price behavior is statistically most similar to that of stock i as of time t. This statistically defined factor may identify dimensions of similarity beyond the traditional ones we enumerated previously, but which are reflected in prices nonetheless. It might pick up on broad-based factors that we did not include explicitly. Alternatively, it might pick up on narrow similarities in circumstances across firms. Or, it might reflect other effects such as pairs of stocks that tend to be held together by large mutual funds or ETFs or groups of stocks that react similarly to certain news events. To identify the statistical peers of stock i, we measure the Mahalanobis distance of every other stock in our universe to stock i and select the 3 with the shortest distance. Once we identify the 3 closest peers for stock i, we equally weight them as an index and compute their trailing 12 or 1 month returns in the same fashion as for industries and factors. We repeat this process for every stock and compute the cross-sectional percent rank of peer returns.

These results reveal that the cross-sectional predictability of trailing returns comes from many coincident and distinct sources. We are able to compare the strength of these effects directly, and in common units. The findings suggest that 12-month single stock momentum is subsumed by other forms of momentum, but single stock 1-month reversal is not. The influence of industry classifications and factors appears to differ. Industries and sectors exhibit strong reversal effects, whereas positive momentum appears to be dominated by factors. It is premature, however, to conclude that factor momentum explains industry-related momentum on this basis. We show in the next section that positive industry and sector momentum is indeed a prevalent force, but it is obscured in the full sample by occasional crashes.

The low volatility (dark blue) results in Exhibit 4 are qualitatively similar to the unconditional results in Exhibit 3. The notable exceptions are that 12-month momentum for security-specific, industry, industry group, and especially sector are now much more significant. Each of these effects reverses meaningfully in volatile periods, which explains why they were not identified in the full sample regression. The same dynamic applies to the 12-month investment factor and statistical peer group momentum, but less so. Size and value merely cease to work at the 12-month frequency, while profitability is the only 12-month effect that works better in volatile times. Most of the one month effects, both reversals and positive momentum, simply fail to generate reliable results of any kind when volatility is high. The one exception is the investment factor.

Why do industry and sector momentum signals reverse so strongly during volatile periods while factor-based momentum signals do not?

One possible reason is the relative stability of sector and industry groups, compared to the revolving composition of factor portfolios. Persistent momentum in a sector will inflate the value of a stock within it, and since stocks do not change sectors often, it will continue to experience sector-driven momentum until it is overvalued and eventually crashes. Persistent factor momentum likely has a different impact on stocks, because stocks that are included in the factor eventually rotate out and are replaced by others. To the extent some stocks are temporarily overvalued as a result, they may correct more gradually. Therefore, we speculate that perhaps bubble-like behavior in sectors leads to more spectacular crashes than does similar bubble-like behavior in factors.

As an extension to the results shown in Exhibit 4, we perform a similar analysis to determine whether the sector/industry effects or the factor effects explain more of the security-specific 12-month momentum. In particular, we include only the sector/industry variables or only the factor variables along with security-specific momentum, and we report these results in the Appendix. Our main takeaway from these experiments is that sector/industry variables by themselves only explain a modest portion of security-specific momentum, which still retains a highly significant t-statistic of 2.85. However, factor-based signals on their own reduce the t-statistic of security-specific momentum to 1.27.

Overall, the piecewise regression results show that momentum effects manifest disproportionately as negative return outcomes. In particular:

Momentum in 12-month returns occurs mostly among past losers during calm markets. Large negative relationships occur mostly for winners, either as 1-month reversals during calm markets or as crashes of 12-month momentum during volatile markets. This finding is consistent with the intuition that it is easier for overweight positions to build up when the market is quiet, leading to crowded overweight positions and eventually crashes due to market shocks.

The more recent period from 2010-2020 reveals a few interesting trends:

12-month momentum in sectors and industries has diminished. 1-month reversals in sectors and industries have become more pronounced, and occur at every level of sector/industry stratification, and for close statistical peers. There is instability in the 12-month versus 1-month dynamics of factor effects. Between the two time periods, size and value migrated from a 1-month to a 12-month effect, but the opposite occurred for investment and profitability. When interpreting the factor results, it is important to keep in mind that momentum could occur on either side of a trade. For example, the main momentum that occurred for value cohorts during 2010-2020 was one in which the value factor lost money.”

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