Standard equity factors are autocorrelated. Hence, it is not surprising that factor strategies have also displayed momentum: past returns have historically predicted future returns. Indeed, factor momentum seems to explain all return momentum in individual stocks and across industries. Momentum has been concentrated on a subset of factors, most notably those related to “betting against beta”, a leveraged strategy that is long high-beta stocks and short low beta stocks. Also, factor return autocorrelation has been changing over time. Measures of continuation in factor returns can indicate “momentum crashes”. A plausible cause of factor momentum is mispricing, i.e. drifts of prices in accordance with fundamental gravity, if positions that exploit the mispricing bear systematic risk.

Arnott, Robert, Mark Clements, Vitali Kalesnik, and Juhani Linnainmaa (2021), “Factor Momentum”

Ehsani, Sina and Juhani Linnainmaa (2019), “Factor Momentum and the Momentum Factor”, NBER Working Paper No. 25551

Fan Minyou, Youwei Li, Ming Liao, Jiadong Liu (2021), “A Re-examination of Factor Momentum: How Strong Is It?”

The below are quotes from the papers. Emphasis, headings, and text in brackets have been added for clarity.

This post ties in with this site’s summary on macro trends.

### What is factor momentum?

“[Standard equity factors include] accruals, betting against beta, cash-flow to price, investment, earnings to price, book-to-market, liquidity, long-term reversals, net share issues, quality minus junk, profitability, residual variance, market value of equity, short-term reversals, and momentum.” [Ehsani and Linnainmaa]

“Factors, just as industries, are combinations of individual assets.” [Arnott, Clements, Kalesnik, and Linnainmaa]

“Factor momentum strategies, similar to stock momentum strategies, __select stocks based on their prior returns__.” [Arnott, Clements, Kalesnik, and Linnainmaa]

“[Academic research] documented a strong and pervasive __momentum effect in most financial market anomalies__, called factor momentum. A factor momentum strategy is long recent top-performing factors and short poorly performing factors. Therefore, it is by nature a type of factor timing strategy…Factor momentum has significant investment performance compared to traditional individual stock momentum and that factor momentum can explain both individual stock momentum and industry momentum.” [Fan, Li, Liao and Liu]

“__Factor momentum is a strategy that bets on these autocorrelations in factor returns__…It is long the factors with positive returns and short those with negative returns. This time-series momentum strategy [has historically earned] an annualized return of 4.2% [per year]…It is a pure bet on the positive autocorrelations in factor returns…High return on any factor predicts high returns on all factors.” [Ehsani and Linnainmaa]

### The evidence for factor momentum

“Most [standard equity] __factors show strong autocorrelation__, supporting the existence of the suggested factor momentum.” [Fan, Li, Liao and Liu]

“Positive autocorrelation is a pervasive feature of factor returns…__Factors’ prior returns are informative about their future__ returns. Small stocks, for example, are likely to outperform big stocks when they have done so over the prior year. This effect is economically and statistically large among the 20 factors we study: The average factor earns 52 basis points per month following a year of gains but just 2 basis points following a year of losses. The difference in these average returns is [statistically] significant.” [Ehsani and Linnainmaa]

“__Factors’ autocorrelations, however, vary over time__, and an investor trading stock momentum loses when they turn negative. We show that a simple measure of the continuation in factor returns determines both when momentum crashes and when it earns outsized profits.” [Ehsani and Linnainmaa]

“Time-series factor momentum dominates cross-sectional factor momentum.” [Fan, Li, Liao and Liu]

“Momentum in factor returns transmits into the cross section of security returns, and the amount that transmits depends on the dispersion in factor loadings. The more these loadings differ across assets, the more of the factor momentum shows up as cross-sectional momentum in individual security returns.” [Ehsani and Linnainmaa]

“Our results imply that __momentum is not a distinct factor; rather, a momentum ‘factor’ is the summation of the autocorrelations found in the other factors__. An investor who trades momentum indirectly times factors. The profits and losses of this strategy therefore ultimately depend on whether the autocorrelations in factor returns remain positive.” [Ehsani and Linnainmaa]

### What causes factor momentum?

“Our results on the connection between factor momentum and investor sentiment suggest that the __autocorrelation in factor returns, and, by extension, individual stock momentum, may stem from mispricing__. Factor returns may positively autocorrelate because mispricings slowly mean-revert: prices of assets that have been pushed away from fundamentals must later drift towards these fundamental values as arbitrageurs enter to profit from the mispricings.” [Ehsani and Linnainmaa]

“In a world absent of near-arbitrage opportunities, non-systematic returns cannot display momentum because arbitrageurs could profit from such mispricings without assuming any risk…This argument does not depend on whether factors reflect risks or mispricing. Even if all variation in expected returns stems from mispricing, only those mispricings that align with systematic risk (even just by luck!) can survive the onslaught of arbitrageurs in equilibrium.” [Arnott, Clements, Kalesnik, and Linnainmaa]

*The is evidence that factor timing has been related to macroeconomic conditions, particularly at business cycle frequency (view post here).*

### Return continuation factors

“We take a step further and examine the pervasiveness of factor momentum effect at the individual factor level…We find that __only six factors…show a strong momentum effect and dominate the factor momentum__…We call these six factors return continuation factors and…find that [they] can explain individual stock momentum and industry momentum.” [Fan, Li, Liao and Liu]

“The momentum profit generated by the return continuation factors (6.43%) is substantially greater than the profit of either the portfolio with the 14 [other factors] (3.07%) or the entire portfolio with 20 factors (4.07%). The factor momentum across return continuation factors accounts for 48.03% of the profits of the factor momentum portfolio sampling all 20 factors.” [Fan, Li, Liao and Liu]

“The __ability of factor momentum to explain individual momentum trading schemes stems from return continuation factors__…Only the six return continuation factors fully span the individual stock momentum.” [Fan, Li, Liao and Liu]

“The **betting against beta factors** show a much stronger factor momentum effect than the other financial anomalies…The factor [is] defined as a symmetric portfolio that buys low-beta stocks, leveraged to a beta of one, and sells high-beta stocks, deleveraged to a beta of one…Stock selection refers to the initial low-minus-high-beta portfolio in an equal-weighted scheme. Then, the rank weighting scheme assigns larger weights to the lower (higher) beta securities in the long (short) leg. Finally, the beta-parity approach rescales the long and short legs to make the portfolio market neutral…The __betting against beta factor…accounts for more than 25% of the total factor momentum__…The superior return persistence…is mostly caused by its unique weighting method, i.e., the rank weighting scheme. Distinct from the other anomalies that use the value-weighted method to construct the factor portfolio, the beta ranking method assigns more weight to small firms…as firm size is negatively related to the beta coefficient.” [Fan, Li, Liao and Liu]

### Factors explain individual stock and industry momentum

“__The [conventional] momentum factor of Jegadeesh and Titman (1993) is an aggregation of autocorrelation from all other financial anomalies__ rather than an independent risk factor…The profits created by the autocorrelations of factors are significantly related to the returns of the momentum factor.” [Fan, Li, Liao and Liu]

“Momentum in individual stock returns emanates from momentum in factor returns…__Factor momentum explains all forms of individual stock momentum__…The autocorrelations in factor returns transmit into the cross section of stock returns through the variation in stocks’ factor loadings. Consistent with this decomposition, we show that factor momentum explains both…’standard’ momentum…and other forms of it: industry-adjusted momentum, industry momentum, intermediate momentum, and Sharpe momentum.” [Ehsani and Linnainmaa]

“Industry momentum is not about industries, but rather about the factors against which the industries load. Factor momentum transmits into the cross-section of industry returns through the differences in industries’ factor loadings. We show there is little to no industry momentum net of factor momentum.” [Arnott, Clements, Kalesnik, and Linnainmaa]

“Our explanation for industry momentum builds on variation in betas. If factors display momentum and industries have different factor exposures, factor momentum transmits into the cross-section of industry returns. We illustrate this mechanism using simulations in which only factors display momentum. The more the factor exposures vary across industries, the stronger the industry momentum in these simulations”. [Arnott, Clements, Kalesnik, and Linnainmaa]