#### October 2024 -- Xilin Chen, Weichuan Deng, Boyu Fang & Milind Sharma

*Thanks to Oleg Kolesnikov & Amit Sardar for technical input*

### Introduction

This paper aims to replicate, validate, and extend the existing literature on factor momentum using a proprietary dataset that has been deployed in live trading for the past 5.75 years in addition to the full 24.75-year history used in documenting the existence of factor momentum via Time Series Momentum (TSMOM) strategies applied to the 18 QuantZ Enhanced Smart Beta (ESB) composites. We demonstrate that TSMOM improves risk-adjusted returns when applied to these ESBs. Such outperformance is corroborated by testing the TSMOM strategies with 5.75 years of live trading data.

The best-performing ESB-based TSMOM strategies outperform both the equal-weighted QuantZ ESBs benchmark and the QuantZ Enterprise 18 composites in terms of risk-adjusted returns (i.e., Sharpe, Sortino, and Calmar ratios) in our 24.75-year full history backtesting. Further, we validate that excluding cross-sectional momentum ESBs can enhance the performance of TSMOM strategies as previously documented in the literature. The litmus test is outperformance in the 5.75-year live trading data which also exhibits the defensive, downside protection characteristics noted in the TSMOM literature by Gu and Mulvey (2021) [5].

The QMIT founder has been part of multiple pioneering industry applications of factor investing in the Quantamental realm over the past 28 years. QMIT pioneered the application of Machine Learning ensembles towards the formulation of a spanning set of Enhanced Smart Beta (ESB) composites in its attempt at taming the factor zoo. These ESB composites combine hundreds of factors deployed by the author in various hedge and mutual fund strategies since the 1990s. In this paper, we deploy ESBs as the ingredients of TSMOM strategies to ascertain whether they outperform a baseline equal-weighted ESB benchmark as evidence of persistence in such ESBs.

### Literature Review

__Cross-Sectional Momentum (XSMOM)__**:**The study of momentum started with the cross-sectional momentum (XSMOM) effect, which refers to the tendency of stocks that have performed well relative to their peers to continue to perform well in the near future. XSMOM strategies focus on the cross-sectional ranking of past returns (“relative performance”) across assets, in order to construct long vs short decile, quintile, or tercile portfolios possibly with a double sort. Jegadeesh and Titman (1993) [1] showed that buying recent top quintiles (“winners”) and selling recent bottom quintiles (“losers”) among individual stocks in NYSE and AMEX can yield significant positive returns when using equal holding and lookback periods (the latter also referred to as “portfolio formation period” in some literature) ranging from 3 to 12 months, with reversals observed in the short term (out to 1 month) (Jegadeesh 1990; Lehmann 1990) as well as the long term (ranging from 3 to 5 years) (De Bondt and Thaler 1985). Carhart (1997) constructed a 4-factor model by adding the 1-year individual stock-level XSMOM effect to the original Fama-French 3-factor model (FF3), which was based purely on size, style, and beta (Fama and French 1993), and the Carhart 4-factor model greatly improved on the average pricing errors of the CAPM and FF3 (Carhart 1997).__Time Series Momentum (TSMOM)__**:**The TSMOM literature focuses on nominal past performance instead of cross-sectional rankings as in the XSMOM case. TSMOM strategies go long the assets with positive returns (“winners”) in the lookback period and short the ones with negative returns (“losers”) in the lookback period. Moskowitz, Ooi, and Pedersen (2012) presented evidence of positive TSMOM effects in all 58 financial instruments they tested (including equity index futures), and 52 of them were significantly non-zero at a 5% significance level. They noted that TSMOM has a payoff profile similar to an option straddle on the market, as per Fung and Hsieh (2001) observed in trend-following strategies, given the significantly positive coefficient on squared market returns. Namely, TSMOM performs well during extreme market conditions (both up and down), as it typically takes long positions during significant market upswings, and goes short the during market downturns (Moskowitz, Ooi, and Pedersen 2012). In particular, their TSMOM strategy outperformed the S&P 500 during the crash periods (Moskowitz, Ooi, and Pedersen 2012). Unlike XSMOM strategies, the TSMOM effects usually do not come with short-term reversals. Thus TSMOM studies, like Gu and Mulvey (2021), do not exclude the most recent month from the lookback period like the implementation of the XSMOM strategies. E.g., consider a TSMOM strategy with a 6-month lookback period and monthly rebalancing - at the rebalancing date, the strategy determines if an asset or a factor is a “winner” or a “loser” based on the sign of the cumulative return of the past 6 months.__Factor Momentum__**:**Researchers have discovered that both the XSMOM and TSMOM effects are present not only at the single asset level but also at the industry and factor levels. In the U.S. equity market, they find that factor-level momentum not only subsumes single asset- or industry-level momentum effects, but actually drives them. Arnott et al. (2021) [2] demonstrated that factor XSMOM strategy retained highly significant and positive alphas (of +70 bps and +66 bps per month, with t-stats of 6.60 and 6.12, respectively) despite controlling for the FF5 model and FF5 plus Carhart’s single stock-level momentum factor (Carhart 1997). Remarkably, the profitability of the short-term factor momentum XSMOM effect does not stem from single-stock level XSMOM effect and is a stand alone phenomenon. Arnott et al. (2021) also showed that industry XSMOM momentum is a byproduct of the factor XSMOM. Gupta and Kelly (2019) [3] and Ehsani and Linnainmaa (2022) [4] found that momentum at the individual stock level is largely driven by factor TSMOM persistence, and documented significant positive returns for factor momentum strategies (due to the positive autocorrelation in returns of most factors).__Factor Time Series Momentum__**:**Gupta and Kelly (2019) and Ehsani and Linnainmaa (2022) demonstrate that strategies based on factor TSMOM are purer, more robust, and more reliable approaches for capturing the persistence in factor performance compared to factor XSMOM strategies. Gupta and Kelly (2019) observed that factor TSMOM yields more stable returns than factor XSMOM and exhibits positive alpha when controlling for factor XSMOM, while factor XSMOM generates negative alpha when controlling for factor TSMOM, indicating that factor TSMOM subsumes factor XSMOM. Ehsani and Linnainmaa (2022) further confirm this subsumption. Inspired by the straddle-like qualities of TSMOM strategies observed in asset classes beyond equities (Moskowitz, Ooi, and Pedersen 2012), some researchers have explored whether market-neutral equity factor TSMOM could demonstrate defensive characteristics during market crashes. Gu and Mulvey (2021) investigated the potential for crash protection using a dollar-neutral factor TSMOM strategy. Their findings showed that buy-winner TSMOM strategies achieved a Sharpe ratio exceeding 2.0 during crash periods, and incorporating these strategies into their diversified core portfolios significantly enhanced risk-adjusted returns.

__Road Map:__**Correlation Analysis**section confirms the persistence of TSMOM in the returns of ESBs. The**Results**section shows the back-tested performance on our full 24.75-year history (Jan 2000 - Sept 2024) highlighting the strong performance of TSMOM strategies across different configurations and identifies the top performers. Finally, the**Corroboration**section validates the effectiveness of these strategies in 5.75Y of live trading, demonstrating their strong risk-adjusted returns and defensive performance during volatile periods. It is noteworthy that the factor construction methodology and the history of our dataset are different from Gu and Mulvey (2021) who only used 48 out of 55 factors (each constructed with a single explicitly defined ranking characteristic) from Ehsani and Linnaimaa (2019) and Kozak, Nagel, and Santosh (2020), covering the period from 1975 to 2019, while we utilize the 18 ESBs (based on hundreds of raw factors) from QuantZ, spanning January 2000 till Sept 2024.

Since our implementation of the Gu and Mulvey (2021) factor TSMOM strategy is based on QuantZ’s Enhanced Smart Betas (ESBs) it's important to describe our foundational building blocks. QuantZ provides ML-enhanced Smart Betas allowing one to express almost any linear view on Equities based on ensemble learners which determine the optimal combination of raw factors intra cohort. The ESBs were designed to be higher octane composites which could outperform naive well known factor representatives of each cohort. Definitions are presented in the appendices.

Our researchers have drawn upon their decades of collective experience to identify, clean, and test 18 factor cohorts from which we construct the 18 Enhanced Smart Betas so that you may directly deploy these indispensable building blocks cost-effectively towards the creation of quant equity strategies for which our Composite Signals (based on such ESBs) are good proxies. Given that the set of N choose k combinations in this case is quite large, it’s particularly instructive to focus on the curated signal composites we have created.

### Methodology

**Data**

We use the monthly ESB returns data between January 2000 and Sept 2024. The data from 2000-2018 are from backtesting, and the data since 2019 pertain to the live trading history. Following the tradition of momentum research, including Jegadeesh and Titman (1993) and subsequent literature, such as some notable works in factor TSMOM, like Ehsani and Linnainmaa (2022) and Gu and Mulvey (2021), we do not account for the impact of transaction costs or rebates.

If we want to include transaction cost (but still ignore short rebates): Although the mentioned papers do not address transaction costs or rebates, an important paper on factor TSMOM by Gupta and Kelly (2019) does consider transaction costs. They assume, based on Frazzini, Israel, and Moskowitz (2015), that an incremental 1% of factor-level turnover incurs a 10 basis point transaction cost. However, since most major studies do not account for rebates, we have chosen to exclude rebates from our analysis.

**Implementation**

We follow the framework and procedure in Ehsani and Linnainmaa (2022) and Gu and Mulvey (2021) to implement TSMOM strategies. For a TSMOM strategy of k-month lookback, at the beginning of each holding period, all the factors are classified into either “winners” or “losers” based on previous cumulative returns over the most recent k months before this holding period, and we construct a “winners leg” portfolio as an equal-weighted portfolio of winner ESBs, and a losers leg as an equal-weighted portfolio of “loser” ESBs:

We backtest the factor TSMOM strategies based on our 18 ESBs (not on their constituent factors or single stocks), and as Gu and Mulvey (2021) did, we include three ways of implementation:

, in which we go long the winners legs and short the losers legs,__Long-Short (LS)__, in which we buy and hold the winners legs only, and__Long winners (LW)__, in which we buy and hold the losers legs only.__Long losers (LL)__

Since each ESB is constructed as a market-neutral long-short portfolio of the individual stocks in QuantZ’s investment universe, the long-only portfolios consisting of the ESBs are also market-neutral long-short portfolios of these individual stocks.

The primary benchmark is the equal-weighted portfolio across all ESBs in the investment universe. We also bring in Enterprise 18, a plug-and-play composite signal comprised of all ESBs, as an alternative goalpost based on an active Quantamental MFM (multi-factor model) strategy. Instead of being a portfolio of the 18 ESBs, the Enterprise 18 signal captures the overlap among the underlying ESBs, resulting in a long-short market-neutral portfolio that is higher-octane and more diversified, allowing for higher returns and improved risk-adjusted performance compared to each individual ESB. While most factor studies such as Gu and Mulvey (2021) limit the analysis to dollar-neutrality we also show the beta-neutral case for contrast given that the latter is bona fide market neutral particularly since some ESBs like Risk (aka Low Vol or akin to the BAB factor) and Momentum can have substantial & time varying net betas.

We evaluate and rank the strategies predominantly by their risk-adjusted return, assessed in terms of Sharpe ratio, Sortino ratio, and Calmar ratio [6]. For all tables of performance metrics in this study, we rank the strategies based on their Sharpe Ratios.

It is noteworthy that the factor construction methodology and the history of our dataset is rather different from Gu and Mulvey (2021). Gu and Mulvey used 48 out of 55 factors (each constructed with a single explicitly defined raw ranking characteristic) from Ehsani and Linnaimaa (2019) and Kozak, Nagel, and Santosh (2020), covering the period from 1975 to 2019, while we utilize the spanning set of 18 ESBs from QuantZ, covering the most recent ~24.75y of (January 2000 till Sept 2024). The last 5.75y were collected live (hence no possibility of look ahead or survivorship biases) with daily granularity which would be rare in the academic literature. Furthermore, the QuantZ ESBs are not single company characteristics but dynamic factor composites generated by the ensemble learners. These differences may account for the resulting differences in the performance and optimal lookback periods.

__Choice of lookback period and rebalancing frequency__

The lookback period used to compute the past “absolute performance” is crucial in determining the winner and loser factor portfolios while the rebalancing frequency determines the holding period. Moskowitz, Ooi, and Pedersen (2012) used the 12-month lookback period to determine winners and losers while Gu and Mulvey (2021) tried lookbacks of 1/3/6/12/24 months. In this study, we use lookback periods of 1/3/6/12 months, with monthly or quarterly rebalancing.

__With and without Momentum__

Gu and Mulvey (2021) suggested excluding XSMOM factors in time series factor momentum strategies to avoid the impact of the correlation between factor momentum TSMOM and individual stock momentum XSMOM. Their approach is in line with the observation of Ehsani and Linnainmaa (2022), viz., that the individual stock-level XSMOM factor does not have significant returns persistence. This study will contrast the performance of the factor TSMOM strategy with and without the individual stock-level XSMOM ESBs, which are Momentum (MOM) and Enhanced Momentum (EnMOM).

__Dollar Neutral vs. Beta Neutral__

As previously noted, certain ESBs like Risk (aka Low Vol or akin to the BAB factor) and Momentum (EnMOM or MOM) can have substantial & time varying net betas which means that inferences made using the academic default of dollar-neutrality can often be substantially misleading (to wit Gu and Mulvey (2021) as well as Ehsani and Linnainmaa (2022)). Therefore, we show both dollar-neutral and beta-neutral results allowing the reader to make contrasting inferences. In particular, we note that deploying beta-neutral ESBs can improve risk-adjusted returns, which extends the existing strand of literature.

### Correlation Analysis

The success of TSMOM requires persistence of the winner/ loser factor portfolios which entails a statistically significant & positive correlation between the lookback and holding period returns. The correlation charts below are based on the full 24.75 years of our history (i.e. in-sample), which means that they cannot be used directly to select the optimal lookback period or the rebalancing frequency.

We first display the first-order autoregression, AR(1) coefficients below, in line with Gu and Mulvey (2021). Amongst the 18 dollar-neutral (or beta-neutral) ESBs, 12 (or 13) ESBs have a positive AR(1) coefficient, and in both dollar-neutral and beta-neutral cases, 6 of the ESBs are statistically significant at a 95% confidence level. This is suggestive of factor persistence i.e., profitably going long the winners while reducing exposure to (or even shorting) the losers. Indeed, the 1 month dollar-neutral (monthly rebal) chart below shows *fundamental ESB*s like * Leverage, Relative Value, Profitability, Efficiency, Growth & CSU* exhibit serial correlation while some of the technical ones like EnMom, Mom, Reversals & Short Interest mean revert (with only SIRF being statistically significant). With beta-neutrality the statistical significance is even more pronounced with ART as well as Deep Value coefficients becoming significant as well.

Figure 1: Correlation between holding period returns and lookback period returns, with the 1-month lookback period, rebalanced monthly, i.e. AR(1) (Dollar-Neutral ESBs)

Figure 2: Correlation between holding period returns and lookback period returns, with the 1-month lookback period, rebalanced monthly, i.e. AR(1) (Beta-Neutral ESBs)

However, Moskowitz, Ooi, and Pedersen (2012) noted that only using autocorrelation tests to evaluate the validity of the TSMOM effect can miss some significant predictability because for monthly data AR(1) only shows the correlation between the 1-month lookback vs forward period. Given the various combinations of {lookback x holding} periods used in the literature we generalize the notion to simply consider correlations between the lookback {1/3/6/12 months} vs forward holding periods {1 or 3 months}. As we vary the combinations of {lookback x holding} periods the correlations & their significance changes - as one might expect - with the occasional flip in sign as noted for CSU, DV and Stability.

Figure 3: Correlation between holding period returns and lookback period returns, with the 3-month lookback period, rebalanced monthly (Dollar-Neutral ESBs)

Figure 4: Correlation between holding period returns and lookback period returns, with the 3-month lookback period, rebalanced monthly (Beta-Neutral ESBs)

Amongst all combinations, the {6-month x 1-month} seems most promising given the largest number of ESBs that have a significantly positive correlation in both dollar-neutral and beta-neutral configurations. Among the 18 dollar-neutral ESBs, 12 ESBs have a positive correlation, 7 of them are statistically significant at a 95% confidence level, and only Analyst Ratings & Targets (ART) ESB has a negative correlation that is narrowly significant. Under beta-neutrality, 15 of 18 ESBs have a positive correlation, 9 of them are statistically significant at a 95% confidence level, and none of the ESBs have a significantly negative correlation. This result indicates that the 6-month lookback with monthly rebalancing configuration may be the optimal set-up for TSMOM strategies based on ESBs.

Figure 5: Correlation between holding period returns and lookback period returns, with the 6-month lookback period, rebalanced monthly (Dollar-Neutral ESBs)

Figure 6: Correlation between holding period returns and lookback period returns, with the 6-month lookback period, rebalanced monthly (Beta-Neutral ESBs)

__Performance of TSMOM Strategies (Jan 2000 - Sept 2024)__

We noted the formulation of various TSMOM strategy combinations in the implementation section above. In this section, we backtest TSMOM strategies over 24.75 years across four distinct scenarios using either dollar-neutral or beta-neutral ESBs, and either including or excluding the two XSMOM ESBs. Each scenario is coupled with three possible implementations (long-short, long winners, and long losers) for a total of 12 cases further multiplied by lookback periods (1, 3, 6, and 12 months) and 2 rebalancing frequencies (monthly and quarterly) which results in a total of 96 configurations. To recap that's 24 configurations * 4 scenarios.

The cumulative performance of each strategy is visualized as the value-added monthly index (or VAMI pegged at $1 at inception) as shown in the figures below for the top 2 Sharpe Ratio performers in each of the three ways of implementation <LS, LW, LL>. Since one of our benchmarks, Enterprise 18, has much higher returns and volatility than any ESB, its VAMI may seem to dominate all others (see Figure 7 below). Thus, in order to evaluate the strategies based on their risk-adjusted performance, **we scale their VAMIs to match the volatility level of the 18-ESB equal-weighted portfolio (EW18) benchmark** in all other VAMI plots hereafter which will also visually bring Enterprise 18 down to a comparable vol scale.

**Figure 7: **$-Neutral: Best 2 in each direction of strategy (without vol scaling)

The TSMOM strategies (like their ESB brethren) need to be anchored or initialized with enough history (for the lookback) to get started. For ESBs that means equal weighting constituent factors for the 1st 24 months before the ensembles can start learning. Similarly, each TSMOM strategy sits in the EW18 benchmark portfolio till it accumulates enough data for its lookback period to start picking winners & losers. Ironically, the NASDAQ crash years at the beginning of the 24.75 year period are in fact the strongest for our ESBs hence any methodology such as sitting in cash would dramatically handicap longer lookbacks.

Implementation - (LS/LW/LL): In all four scenarios {BN/DN x with/without XSMOM ESBs}, we observe that the Long Winners implementation of TSMOM strategies systematically outperforms all others, with the Long Losers trailing significantly behind. This highlights the dominance of the time series momentum (TSMOM) effect over the 24.75-year history. However, it's noteworthy that even the laggard Long Losers generated positive returns with the best of the cohort being as high as 0.88 Sharpe (LL, BN, 3mo/3mo, with XSMOM) which is quite good on a stand-alone basis. That's why the Long/Short implementation is stymied by the strength of the shorts.

Beta vs $ Neutrality: We also observed that beta-neutral configurations generally exhibit much higher risk-adjusted returns for the top-performing strategies than the dollar-neutral ones, ceteris paribus due to significantly lower volatility and downside deviation.

With/ Without XSMOM: Furthermore, in both dollar-neutral and beta-neutral configurations, the exclusion of XSMOM ESBs resulted in an overall increase in the risk-adjusted returns for TSMOM strategies, especially for dollar-neutral cases.

Best strategy {Lookback x Rebal period) -- Amongst all TSMOM strategies, the Long Winners TSMOM strategies with a 6-month lookback period and rebalanced monthly (LW 6m/1m) performed the best in all four scenarios, followed by Long Winners TSMOM strategies with a 6-month lookback period and rebalanced quarterly (LW 6m/3m). *LW 6m/1m TSMOM strategy outperformed both benchmarks in all 4 scenarios under all 3 risk-adjusted metrics as per Tables 1-a & 1-b below.*

**Table 1-a: **Dollar-Neutral ESBs

**Table 1-b: **Beta-Neutral ESBs

** Table 1:** Performance of the TSMOM Strategy for 24.75y

Take the top risk-adjusted TSMOM strategies, LW 6m/1m, for instance. In the dollar-neutral scenarios, the Sharpe ratio of the EW18 benchmark is 1.01. For the dollar-neutral LW 6m/1m strategies, the one with XSMOM ESBs obtained a Sharpe ratio of 1.08, and the one excluding XSMOM ESBs significantly raised the Sharpe ratio to 1.22 (which is higher than the EW18 benchmark and higher than the one with XSMOM ESBs). The dollar-neutral LW 6m/1m strategy (excluding XSMOM) also improved the Sortino ratio by 26.1% and the Calmar ratio by 50% compared to the EW16 benchmark.

**Figure 8: **VAMI of TSMOM Strategies - 16 ESBs ($-Neutral; ex-XSMOM) for 24.75y (vol scaled)

**Table 2**:Performance of Top-10 Strategies - 16 ESBs ($-Neutral; ex-XSMOM) for 24.75y

Although using TSMOM is also helpful in beta-neutral scenarios, it is noteworthy that the relative improvement in the Sharpe ratio for the top TSMOM strategies is much higher in the dollar-neutral scenarios because the benchmark has a much lower Sharpe ratio to start with. In the beta-neutral scenarios, the Sharpe ratio of the equal-weighted benchmark (EW16) is 1.53 (a tough bar to clear). For the beta-neutral LW 6m/1m strategies, the one with XSMOM ESBs obtained a trivially higher Sharpe ratio of 1.65, and the one excluding XSMOM ESBs further raised the Sharpe ratio to 1.72, and increased the Sharpe ratio by around 12.4% relative to the EW16 benchmark. The relative improvement in the other two risk-adjusted return metrics, Sortino and Calmar, is also lower than the dollar-neutral case, but the magnitude in each case is close to 30%, which is substantial.

**Figure 9: **VAMI of TSMOM Strategies - 16 ESBs (Beta-Neutral; ex-XSMOM) for 24.75y (vol scaled)

**Table 3**: Performance of Top-10 Strategies - 16 ESBs (Beta-Neutral; ex-XSMOM) for 24.75y [7]

The backtesting shows that using monthly-rebalanced Long Winner TSMOM strategies on the 16 non-XSMOM ESBs with a 6-month lookback period can help investors significantly improve the Sortino ratio and the Calmar ratio of their ESB-based strategies in comparison to the EW16 strategy and the Enterprise 18 composite, with Sharpe ratio at a comparable level or even improved (especially in the dollar-neutral cases). The desirable characteristics in terms of downside deviation and maximum drawdown (MDD) are in line with other studies such as Gu and Mulvey (2021).

### Robustness checks

Considering that the extraordinarily profitable NASDAQ crash episode may distort the full period performance of the strategies, we first re-evaluate the performance of the strategies with beta-neutral ESBs (without XSMOM ESBs) using the 22.75-year data starting with the 25th month (Jan. 2002) as robustness check in order to 1) remove the impact of the positive outlier NASDAQ crash episode, and 2) omit the anchoring period of the ensembles when they simply match the equal-weighted benchmark (EW16) as with our TSMOM strategies. The Long Winner TSMOM strategies on the 16 non-XSMOM ESBs with a 6-month lookback still performed the best among all TSMOM strategies. However, it obtained a Sharpe ratio of 1.55, which is slightly higher than the one of the EW16 (1.54) but lower than the Sharpe ratio of the Enterprise 18 composite (1.57). However, using the top TSMOM strategy still helps investors manage the downside deviation and drawdowns much better, cutting down both by more than 50% resulting in a much higher Sortino ratio (3.89) and Calmar ratio (1.34) than the ones of the EW16 and the Enterprise 18 composite (see Appendix II).

### Drivers of Performance

The dynamic regime dependent choice of ESBs in the <LW, LL, LS> portfolios may explain why the top TSMOM strategies have downside deviations and MDDs comparable to the equal-weighted benchmark yet monetize a higher return. To further evaluate the potential drivers of performance we consider how the TSMOM strategy bets on each ESB. In Figure 10 and Figure 11, we visualize the number of ESBs in the winners leg for each period and the winning rate of each ESB in the beta-neutral LW 6m/1m strategies. To aid visualization, we use the risk-off-risk-on spread (RORO), which is the difference between the mean return of all risk-off ESBs and the mean return of all risk-on ESBs, as a contemporaneous proxy for the market regime. A lower RORO spread (like in 2008) is indicative of a Risk-Off episode.

Figure 10: Number of ESBs in the Winners Leg of the LW 6m/1m Strategy, 16 ESBs (Beta-Neutral; ex-XSMOM) for 24.75y

Figure 11: Winning Rate of each ESB in the LW 6m/1m Strategy, 16 ESBs (Beta-Neutral; ex-XSMOM) for 24.75y

From Figure 10 we can observe that the Winners Leg of the LW 6m/1m Strategy encompasses nearly all ESBs (EW16) during the Risk-On periods when most ESBs will likely be positive over the lookback period. Empirically, the strategies based on a 6-month lookback period seem to be sufficiently responsive to market changes without excessive turnover.

For the given horizon in Figure 11, Leverage (lev), Risk (risk), Profitability (prof) and Stability (stab) ESBs register a winning rate of around 80% in the 24.75-year history, consistent with the correlation analysis (Figure 6) and the positive hit rate for these ESBs. The winning 6-month lookback balances turnover with reaction time to regime changes.

### LIVE Corroboration (Jan 2019 - Sept 2024)

We have 24.75 years of returns for our ESBs with the recent 5.75y post-2019 being live-trading record (while the prior 19 years are back-tested). To corroborate the validity of the strategy, we re-evaluate the TSMOM strategies with the 5.75-year live-trading data. Figure 12 and Table 4 visualize the performance of TSMOM strategies based on beta-neutral ESBs (excluding XSMOM ESBs) over the live-trading history.

**Figure 12: **VAMI of TSMOM Strategies - 16 ESBs (Beta-Neutral; ex-XSMOM) for 5.75y (vol scaled)

As with the 24.75-year and 22.75-year history, the Long Winners TSMOM strategies with a 6-month lookback period and rebalanced monthly (LW 6m/1m) still performed the best among all TSMOM strategies once again over the 5.75-year live-trading data, with a Sharpe ratio of 1.47, which is higher than Sharpe ratio of the EW16 benchmark (1.21), and is higher than one of the Enterprise (1.24).

We also observe that the outperformance of long-winner TSMOM strategies compared to the benchmarks was largely established between March 2020 to early 2021 when Covid (for obvious reasons) resulted in significant strategy dispersion whereas subsequent performance has marched more in tandem. Relative to the benchmark, the best TSMOM (LW, 6m/1m) strategy essentially doubles the cumulative return with a similar MDD resulting in a far superior risk adjusted profile showing good downside protection during volatile periods similar to what Gu and Mulvey (2021) observed.

In Table 4, we observe that, compared to the outcome on a longer history, the annualized returns of long-winner TSMOM strategies are now a bit higher in magnitude and are closer to 70% of Enterprise 18 now (in comparison to around 50% in the longer horizons discussed above). Also, we observe that the long-winners strategies outperform the benchmarks in trend between early 2020 and 2021 (the heavily COVID-impacted period).

**Table 4**: Performance of Top-10 Strategies - 16 ESBs (Beta-Neutral; ex-XSMOM) for 5.75y

### Publication Decay

The publication of a strategy may result in performance decay, as noted by McLean and Pontiff (2016), potentially diminishing the strategy's alpha or lowering its Sharpe ratio. For factor TSMOM strategies, the most closely related and frequently cited works, such as Gupta and Kelly (2019) and Ehsani and Linnainmaa (2022), utilize U.S. equity factor data spanning from 1963 to 2016 (for the latter) or 2017 (for the former). Additionally, their initial working papers were likely released before their formal journal publications, suggesting that the market could have started to incorporate the strategies' insights before their official release.

The first draft of Ehsani and Linnainmaa (2022) was published in March 2017, while the earliest available version of Gupta and Kelly (2019) appeared as a Yale ICF working paper in November 2018. Following McLean and Pontiff (2016), who argue that the dissemination of research ideas likely begins when the first working paper is released - and potentially even earlier due to conference presentations or discussions - we therefore hypothesize that publication decay (if any) ought to gradually manifest from 2017 onwards. Based on this, we divide the historical data into two distinct periods:

Pre-publication History: Jan. 2002- Dec. 2016 (to exclude the NASDAQ crash period, during which QuantZ ESBs performs particularly well through the history and there was insufficient history for the lookback periods of the TSMOM strategies)

Post-publication History: Jan. 2017- Sept 2024

The analysis then focuses on assessing the post-publication decay of these three beta-neutral, TSMOM strategies:

**LW 6m/1m**: This is the best performer during our 24.75/22.75/5.75-yr history**LW 1m/1m**: This is the best performer in our history from backtesting (2002-2018), and was mentioned as the best strategy in Gu and Mulvey (2021)**LW 12m/1m**: Considered the paradigm of the TSMOM strategies in the late 2010s, this strategy is the most researched and frequently mentioned. It was central to the construction of factor TSMOM strategy by Gupta and Kelly (2019), Arnott et al. (2021) and Ehsani and Linnainmaa (2022).

We assess the performance decay by comparison against two benchmarks (EW18 and EW16) and Enterprise 18, giving precedence to the EW18 and EW16, which themselves show the post publication Sharpe decays of -45.0% and -50.5%, down to Sharpe ratios of 1.10 and 1.08, respectively. Interestingly, of the 3 TSMOM strategies considered, the most-researched LW 12m/1m shows a decay of -45.8%, which is pretty much in line, while the LW 1m/1m decay of -58.2% is much worse in contrast to the much milder decay of only -39.4% for the LW 6m/1m case. Hence, while there is prima facie strong evidence of post-publication decay; it is just as strong for the benchmarks which means that risk adjusted decay is structural, pervasive and may not be specific to a post publication effect at least based on Sharpe ratios. Based on alphas there is not much evidence of decay in the nominal intercept values either for the EW18 benchmark or the best strategies like LW 6m/1m.

Table 5: Performance Decay: Pre- and Post-Publication Analysis (2003-2024 Sept)

Table 5 illustrates the performance decay in key investment strategies, comparing metrics from the pre-publication period (January 2003 to December 2016) and the post-publication period (January 2017 to Sept 2024). Percentage changes are reported as positive (e.g., "+X%") for post-publication increases and negative (e.g., "-X%") for decreases.

The LW 6m/1m strategy stands out with a less pronounced performance decline in risk-adjusted return ratios compared to other strategies, despite its declines in the Sharpe, Sortino, and Calmar Ratios (-39.4%, -26.9%, and -22%, respectively). This strategy maintains positive FF5 alpha (+20.6%) and FF5 + WML alpha (+14.7%), indicating a relatively resilient performance post-publication.

**Table 6**: Alphas and Risk-adjusted Returns in 22.75-year / Pre-publication / Post-publication / 5.75-year History

where alphas are in % and t-statistics are written in the parenthesis “()”. All adjusted R2’s are in squared brackets “[]”. Both are under the alpha values.

### Conclusion

Our study documents TSMOM persistence in QuantZ's proprietary live factor set of ESBs, which demonstrates the superior risk-adjusted profile of the long-winner (long only) TSMOM strategy with a 6-month lookback period and monthly rebalancing particularly during crashes such as the COVID period of 2020. Notably the LW portfolios also did remarkably well amidst the Nov 2020 Momentum crash & the L/S 1m, 3m did even better. Amongst all 3 horizons evaluated (24.75/22.75/5.75 years till Sept 2024), the LW 6m, 1m not only performs the best among all TSMOM strategies, but also outperforms both benchmarks in 24.75-year and 5.75-year horizons As for the 22.75-year horizon, although it obtains nearly identical Sharpe as the Enterprise 18 composite, it reduces the downside deviation and MDD by more than 50% and thus it obtains higher Sortino and Calmar ratios.

You may notice that our top lookback period (6 months) is different from the optimal lookback period in Gu and Mulvey (2021), which is 1 month. This could be due to differences in the factors in our pool (as well as ensembling at the ESB level) vs their factor zoo (since they do not ensemble), and the different horizons. Finally, we postulate that the factor timing of TSMOM strategies could reflect a potentially regime-aware quality: it benefits from holding a well-diversified set of ESBs similar to the equal-weighted portfolio during normal risk-on periods, and when a crash happens, the strategy rapidly pivots towards the subset of risk-off ESBs (given monthly rebal) which should continue to be the winners in a tumultuous tape. The strategies based on a 6-month lookback period seem to strike the right balance of controlled turnover despite responsiveness to changing markets particularly in a downdraft.

In conclusion, we have replicated, validated, and extended the existing literature on factor momentum to QMIT's proprietary dataset of smart betas which includes 5.75y of live data.

### APPENDIX I: __24.75y Results __

(Beta Neutral: without XSMOM)

__(Dollar Neutral: without XSMOM)__

__(Beta Neutral: with XSMOM)__

__(Dollar Neutral: with XSMOM)__

### APPENDIX II: 22.75y Results

__(Beta Neutral: without XSMOM)__

(Dollar Neutral: without XSMOM)

__(Beta Neutral: with XSMOM)__

__(Dollar Neutral: with XSMOM)__

### APPENDIX III: LIVE 5.75y Results

__(Beta Neutral: without XSMOM)__

__(Dollar Neutral: without XSMOM)__

__(Beta Neutral: with XSMOM)__

__(Dollar Neutral: with XSMOM)__

### APPENDIX IV: __Enhanced Smart Beta Definitions__

ARS: This smart beta composite shows our Analyst Revisions cohort based on measures of estimate revisions, dispersion, Standardized Unexpected Earnings surprise (SUE score) & consensus change in both earnings as well as revenues which can outperform traditional metrics like a 1mo consensus change.

ART: This smart beta composite shows our Analyst Ratings & Targets cohort based on measures of analyst recommendations, target price, changes & diffusion which can outperform traditional metrics like a 1-month consensus change.

CSU: This smart beta composite shows our Capital Structure/Usage cohort based on measures including Buybacks, Total yield, Capex, capital usage ratios, etc which can outperform traditional metrics like Cash/MC.

Dividends: This smart beta composite shows our Dividend-related cohort based on measures including Yield, payout, growth, forward yield, etc which can outperform traditional metrics like Dividend Yield.

DV: This smart beta composite shows our Deep Value (or intrinsic value) cohort based on measures including tangible book & sales which can outperform traditional Book yield.

Efficiency: This smart beta composite shows our Efficiency cohort based on measures including Asset Turnover, Current Liabilities, Receivables, etc which can outperform traditional metrics like Asset Turnover.

EnMOM: This smart beta composite shows our Enhanced Momentum cohort which can outperform traditional 12-month price momentum in both return & risk-adjusted terms, particularly at market inflection points.

EQ: This smart beta composite shows our Earnings Quality cohort based on a variety of Accrual measures which can outperform traditional metrics like Total Accruals.

Growth: This smart beta composite shows our Historical Growth cohort based on a variety of Earnings, Sales, Margins & CF-related growth measures which can outperform traditional metrics like 3-year leverage-related Sales growth.

Leverage: This smart beta composite shows our Leverage related cohort based on measures of Balance Sheet leverage which can outperform traditional metrics like Debt To Equity.

MOM: This smart beta composite shows our MOM-related cohort which can outperform traditional 12-month price momentum using a variety of traditional momentum factors.

Profit: This smart beta composite shows our Profitability cohort based on measures like ROA, ROE, ROCE, ROTC, Margins, etc which can outperform traditional metrics like ROE.

RV: This smart beta composite shows our Relative Value cohort based on measures of EPS, CFO, EBITDA, etc which can outperform traditional Earnings yield.

Reversals: This smart beta composite shows our Reversals cohort which is comprised of metrics like short-term reversals, RSI, DMA & other technical factors that can outperform traditional metrics like a 1-month total return.

Risk: This smart beta composite shows our Risk/ Low Vol cohort which is comprised of metrics like Beta, Low volatility, etc.

SIRF: This smart beta composite shows our Short Interest cohort which is comprised of metrics related to Short Interest and its normalization by Float, trading volume, etc.

Size: This smart beta composite shows our Size cohort which is comprised of metrics related to firm size including market capitalization.

Stability: This smart beta composite shows our Stability cohort which is comprised of metrics like Dispersion of EPS/ SPS estimates as well as the stability of Margins, EPS & CFs, etc.

### APPENDIX V:

Q-Q Plots of Equal Weighted Benchmarks, Enterprise 18 and LW 6m/1m TSMOM Strategy

Long-only factor portfolios exhibit diversification benefits that truncate the left tail of the return distribution—reducing extreme negative returns—while amplifying the right tail, enhancing extreme positive returns. This pattern provides evidence of factor momentum combined with downside protection when compared to the Ent18 signal. Notably, the Ent18 signal represents a single equity market-neutral combined signal, whereas the EW18, EW16, and LW portfolios are all long-only portfolios of individual ESBs, offering diversification across different ESBs.

### APPENDIX VI:

### Endnotes:

[1] **Asset Universe:** Jegadeesh and Titman (1993) conducted their study using individual stocks listed on the New York Stock Exchange (NYSE) and the American Stock Exchange (AMEX) over the period from 1965 to 1989.

[2] **Asset Universe:** Arnott et al. (2021) utilized monthly and daily return data from the Center for Research in Securities Prices (CRSP) for ordinary common shares (share codes 10 and 11) listed on the NYSE, AMEX, and Nasdaq exchanges. They included CRSP delisting returns and imputed missing (30% for NYSE and AMEX stocks and 55% for Nasdaq stocks) performance-related delisting returns. The study constructed 43 factors based on a combination of price, return, volume, and accounting information.

[3] **Asset Universe:** Gupta and Kelly (2019) constructed 65 characteristic-based factor portfolios using U.S. stock data. These portfolios encompassed a wide range of characteristics, including valuation ratios (e.g., earnings/price, book/market), factor exposures (e.g., betting against beta), size, investment, profitability metrics (e.g., market equity, sales growth, return on equity), idiosyncratic risk measures (e.g., stock volatility and skewness), and liquidity measures (e.g., Amihud illiquidity, share volume, bid-ask spread).

[4] **Asset Universe:** Ehsani and Linnainmaa (2022) analyzed 22 "off-the-shelf" factors, comprising 15 U.S. equity anomalies and 7 global factors. Data were sourced from Kenneth French’s, AQR’s, and Robert Stambaugh’s data libraries. The U.S. factors included size, value, profitability, investment, momentum, and others. Except for the liquidity factor of Pastor and Stambaugh (2003), the return data for these factors begin in July 1963; those for the liquidity factor begin in January 1968. The seven global factors are size, value, profitability, investment, momentum, betting against beta, and quality minus junk. Except for the momentum factor, the return data for these factors begin in July 1990; those for the momentum factor begin in November 1990.

[5] **Asset Universe:** Gu and Mulvey (2021) employed two datasets for their analysis: 11 long–short anomaly portfolios from Ehsani and Linnainmaa (2019), with data from Kenneth French’s, AQR’s, and Robert Stambaugh’s data libraries; and 44 long–short portfolios based on anomaly characteristics from Kozak, Nagel, and Santosh (2020). They excluded seven momentum-related factors to avoid inducing correlation between factor momentum and individual stock momentum.

[6] **Performance Metrics Definitions:** The **Sharpe Ratio** (Sharpe, 1966) is calculated as the mean of excess returns divided by the standard deviation of returns, measuring return per unit of total risk. The **Sortino Ratio** (Sortino and Price, 1994) focuses on downside risk by using the standard deviation of negative returns instead of total volatility. The **Calmar Ratio** (Young, 1991) is calculated as the average annualized excess return divided by the maximum drawdown during the period. In this study, since the risk-free rate has already been subtracted from the returns, we employ the adjusted form of the Calmar Ratio that is prevalent in current practice.

[7] LL - Long Losers, LW - Long Winners, LS - Long Winners and Short Losers, m/m - Lookback Period/Holding Period.

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