Today my colleague at Buckingham Strategic Wealth, institutional services advisor Tim Jost, will look at some of the latest research on the momentum factor. The following is his analysis.

To begin, momentum is a phenomenon discovered in returns where those assets that have performed well recently will continue to perform well. Momentum has been studied extensively since 1993, when the original paper “Momentum” was published by Narasimhan Jegadeesh and Sheridan Titman. Strong proponents of efficient market theory, Eugene Fama and Ken French have referred to the momentum premium as the “premier anomaly” among those studied in the financial literature.

**Different Types Of Momentum**

Two different variations of momentum have been identified and studied by researchers—cross-sectional momentum and time series momentum. While similar in nature, cross-sectional and time series momentum have been identified as distinct premiums or sources of return in the financial literature.

Cross-sectional (CS) momentum ranks assets by recent performance and takes a long position in those that have outperformed relative to other assets, and goes short those that have underperformed. Thus, cross-sectional momentum looks at recent performance of assets on a relative basis to other assets.

Time-series (TS) momentum takes a long or short position on an asset by only looking back at its own absolute performance during the ranking period. Thus, if an asset’s price has been going up (down), a TS momentum strategy will go long (short) that asset. Managed futures strategies have typically targeted the capture of the TS momentum factor.

An important distinction between how these two strategies/factors have been defined is that CS momentum is a zero-net investment strategy—it is long the same dollar amount of assets as it is short—while TS momentum can be either net long or short through time. Because returns tend to be positive, on average, over time, TS momentum strategies tend to take larger long positions than short positions, thus having a time-varying net long investment outlay.

**Relevant Research**

In their 2012 paper “Times Series Momentum,” authors Tobias Moskowitz, Yao Hua Ooi and Lasse Pedersen claim that while time series momentum is related to cross-sectional momentum, it is ultimately a separate premium. Thus, two distinct types of momentum exist, according to their assertions. Moskowitz, Ooi and Pedersen also claim that a TS momentum strategy is more profitable than a CS momentum strategy.

Additionally, the authors conclude that TS strategies fully explain and subsume CS strategies. Given this, they recommend that a factor based on TS momentum be included in multifactor asset pricing models and suggest that this factor can help explain existing asset pricing phenomena, including CS momentum premiums.

In their July 2017 paper “Cross-Sectional and Time-Series Tests of Return Predictability: What Is the Difference?” the authors, Amit Goyal and Narasimhan Jegadeesh, respond to Moskowitz, Ooi and Pedersen’s claims and contribute to the research by concluding that TS and CS momentum are not distinct sources of return, and that differences in returns stem from the time-varying net long exposure to risky assets of TS momentum.

The authors also conclude that CS momentum strategies actually outperform TS momentum strategies when both are scaled to have similar dollar investment outlays.

**Differences In Returns Between TS, CS Momentum **

Goyal and Jegadeesh first look at similarly scaled TS and CS momentum strategies using historical U.S. common stock data. Their data covers the period 1946 through 2013. They sort returns based on a range of prior returns and holding periods (from one to 60 months). Both TS and CS strategies are scaled to have total positions, both long and short, equal to two dollars, which allows for an apples-to-apples return comparison across the two strategies.

The authors find striking differences between the excess returns of TS and CS strategies, which are similar to Moskowitz, Ooi and Pedersen’s findings when looking across international asset classes. Below are the highlights of these differences:

- For TS strategies, all earn positive excess returns that tend to increase with the length of the ranking period. However, not all CS strategies have positive excess returns, with returns generally being negative for sorts with both shorter ranking and holding periods and for both longer ranking and holding periods.
- The differences in returns between TS and CS strategies exhibit a U-shaped pattern, with the largest differences at the long and short ends, where TS strategies tend to outperform CS strategies.
- As an example, a CS strategy with a one-month ranking period and one-month holding period (1 x 1) earned -5.09%, which is consistent with the evidence of short-term reversal patterns shown in prior research on CS momentum. In comparison, a 1 x 1 TS strategy earned 4.03%.
- The 60 x 60 CS strategy earned -2.00%, which is also consistent with long-horizon return reversals shown in prior research on CS momentum, while a 60 x 60 TS strategy earned 7.71%.
- Both CS and TS 6 x 6 strategies earn significantly positive excess returns—the TS strategy earned 5.79%, and the CS strategy earned 3.90%.

Goyal and Jegadeesh attribute these differences in returns between TS and CS strategies in U.S. stocks to both market timing and time-varying net long holdings of TS strategies. The authors attribute market timing as being responsible for differences in returns for short ranking and holding periods, and time-varying net long investments in risky assets of TS strategies being responsible for differences in returns for longer ranking and holding periods.

**Adjusting For Time-Varying Net Long Exposure **

Given that TS strategies are not zero-dollar investment strategies like CS strategies and will be either net long or short at any given time, to make these strategies directly comparable, the authors add to CS strategies a time-varying investment in the equity market.

This investment is equal to the dollar value of the difference between the long and short sides of the TS strategy each month (we’ll call this the “time-varying market” or “TVM-CS strategy”). If the performances of TS strategies and TVM-CS strategies are similar, it would be a stretch to view TS momentum as a distinct source of return.

The authors find that both TS and TVM-CS strategies perform similarly within U.S. individual stocks for the horizons over which momentum strategies have been shown to be profitable. Following are highlights from their findings:

- The return differences between TS and TVM-CS strategies are small and mostly statistically insignificant.
- For ranking periods of 1 x 1 and 60 x 60, the differences in returns between TS and TVM-CS strategies are 1.18% and 0.51%, respectively.
- For strategies when ranking period equals holding period—3 x 3, 6 x 6 and 12 x 12—the alphas for the differences in returns between TS and TVM-CS strategies, using the Fama-French three-factor model, are statistically insignificant, or not different from zero.

The authors suggest that when momentum works, TS strategies pick winners and losers among individual stocks in the same manner that CS strategies do.

This is because returns are similar for TS and TVM-CS strategies over horizons where CS momentum has been shown to provide positive returns—thus, the seemingly superior performance of TS strategies over CS strategies that Moskowitz, Ooi and Pedersen claim is due entirely to TS strategies’ time-varying net long positions in the market.

Given this, and contrary to Moskowitz, Ooi and Pedersen’s claims, the authors suggest that TS momentum is not a distinct source of return and that TS strategies do not subsume CS strategies in individual stocks.

**Adjusting For Scale Differences **

Goyal and Jegadeesh also look at TS and CS strategies across international asset classes. Specifically, the authors look at 55 different futures markets across four broad asset classes of equities, bonds, commodities and currencies over the period 1985 through 2013.

The authors first compare TS and CS strategies across international asset classes that are scaled similarly, as before, for U.S. stocks to have total positions, both long and short, equal to two dollars. They find that excess returns for both strategies are similar and positive for all periods, and the differences between excess returns of TS and CS strategies are not statistically different than zero. This is consistent with the authors’ assertion that TS and CS momentum are not distinct sources of return.

In constructing TS strategies for their paper, Moskowitz, Ooi and Pedersen scale positions using an inverse volatility scaling approach that scales positions in each asset class by a factor equal to 40% divided by the lagged volatility of the asset. Using this scaling approach leads to larger cumulative positions across both long and short positions in dollar terms. This, then, ultimately magnifies the size of profits for the TS strategies.

To account for this, Goyal and Jegadeesh construct similarly scaled CS strategies to compare to TS strategies constructed using this inverse volatility-scaling approach. The authors’ main takeaways include:

- Both volatility-scaled TS and CS strategies earn positive excess returns for all ranking periods. However, the differences in returns between the similarly scaled TS and CS strategies are quite different.
- Volatility-scaled CS strategies earn bigger returns than the corresponding volatility-scaled TS strategies for all ranking periods except the longest one that looks back 60 months.
- As an example, when using 12-month ranking and one-month holding periods (12 x 1), the CS strategy earned 21.55%, while the TS strategy earned 14.75%.
- Net long positions of the volatility-scaled TS strategy are much higher than those for TS strategies that are not scaled inversely by volatility.

As with the other TS strategies analyzed, volatility-scaled TS strategies also tend to have time-varying net long positions in risky assets.

To account for this, the authors again add a time-varying investment in a market index to CS strategies. When comparing volatility-scaled TS and CS strategies with similar volatility-scaled CS strategies that have a time-varying investment in the market, the authors found that the latter outperform both the volatility scaled TS and CS strategies across all ranking periods.

**Summary**

Goyal and Jegadeesh refute Moskowitz, Ooi and Pedersen’s claims that TS and CS momentum are distinct sources of returns. They show that differences in returns between TS and CS strategies shown in prior research are primarily driven by differences in factor construction and not necessarily by differences in return phenomena.

The main difference in returns between previously studied TS and CS strategies relates to both a time-varying net long investment in risky assets of TS strategies and differences in position scaling. When controlling for scaling differences and the time-varying net long exposure that TS strategies take on, CS strategies actually outperform.

Managed futures strategies have typically implemented some form of time-series momentum strategy, also commonly referred to as “trend-following.” Even though the authors show that TS momentum is not a distinct return phenomenon from CS momentum, this doesn’t mean that having an allocation to trend-following in a portfolio isn’t advised; investors just need to understand what exposure they are actually receiving.

Goyal and Jegadeesh suggest that trend-following strategies really just provide exposure to CS momentum with an additional time-varying net long investment in risky assets. While net long over the longer term, managed futures will be net short at certain periods—for example, trend-following strategies generally tend to be net short when markets are in crisis.

This is an attractive property, since trend-following has historically provided a left-tail (the risk of large losses) hedging property during poor market periods. For some investors, my firm, Buckingham Strategic Wealth, recommends a modest allocation to managed futures strategies because of this left-tail hedging property in addition to the robust momentum premium and its lack of correlation to traditional asset classes like stocks and bonds, along with other factors or return phenomena over the long term.

*Larry Swedroe is the director of research for* *The BAM Alliance**, a community of more than 140 independent registered investment advisors throughout the country.*