The academic research has provided investors with strong evidence that there is a small group of factors—or sources of returns—that have provided higher returns over the long term. To be considered among this group, the evidence should have the following characteristics:

- Persistence—it holds across long periods of time and various economic regimes.
- Pervasive—it holds across countries, regions, sectors and even asset classes.
- Robust—it holds for various definitions (for instance, there’s a value premium whether we measure value by price-to-book, earnings, cash flow or sales).
- Investable—it holds up not just on paper, but also after considering trading costs.
- Intuitive—there are logical, risk-based (economic) or behavioral-based explanations for the premium and why it should continue to exist.
- It isn’t subsumed by other well-known factors.

While there have been more than 300 factors identified in the literature—so many that John Cochrane called it a “factor zoo”—there are only a handful that meet these six criteria. Ian D’Souza, Voraphat Srichanachaichok, George Wang and Chelsea Yaqiong Yao—authors of the January 2016 study “The Enduring Effect of Time-Series Momentum on Stock Returns over Nearly 100 Years”—provide evidence supportive of the view that time-series momentum (also referred to as trend-following) is one of the few that meet all of these conditions. (Time-series momentum examines the trend of an asset with respect to its own past performance; cross-sectional momentum compares an asset with respect to another asset.)

**Momentum Results**

The authors’ study covered the 88-year period from 1927 to 2014. The following is a summary of their findings:

- A value-weighted strategy of going long stocks with positive returns in the prior year and going short stocks with negative returns during the same period of time produced an average monthly return of 0.55%, and was highly significant (with a t-statistic of 5.28). It has also been present following both up and downmarkets, producing an average monthly return of 0.57% (with a t-statistic of 2.09) following downmarkets, and 0.54% (with a t-statistic of 5.30) following up markets. What’s more, it was persistent across all four subperiods the authors studied, with average monthly returns of 0.69% (with a t-statistic of 2.41) in the period 1927 through 1948, 0.47% (with a t-statistic of 3.60) in the period 1949 through 1970, 0.62% (with a t-statistic of 3.84) in the period 1971 through 1992, and 0.42% (with a t-statistic of 1.91) in the period 1993 through 2014. Thus, it meets the persistence criteria.
- Time-series momentum produced positive risk-adjusted returns in all 13 international stock markets the authors examined for the period 1975 through 2014. And it was statistically significant at the 95% confidence level in 10 of the 13 countries. The highest return for a value-weighted strategy was in Denmark, where it had a monthly return of 1.15% per month (with a t-statistic of 5.06). Thus, it meets the pervasive criteria.
- Time-series stock momentum was profitable regardless of formation and holding periods for 16 different combinations. Thus, it meets the robust criteria.
- Time-series stock momentum fully subsumes cross-sectional stock momentum, while cross-sectional stock momentum cannot capture time-series stock momentum. In addition, the other common factors of beta, size and value have little power to explain time-series momentum. Thus, it meets the criteria of not being subsumed by other factors.
- Unlike with cross-sectional momentum, time-series momentum doesn’t experience losses in January (a seasonal effect) or crashes (which occur with cross-sectional momentum during reversals).
- The time-series premium can be at least partially explained by two prominent theories describing investor underreaction (both the gradual information diffusion model and what’s called the frog-in-the-pan model). For example, if time-series momentum came from gradual information flow, there should be greater time-series momentum in small stocks (for which information diffuses more slowly). However, they found that the small size group produces the highest momentum profits (0.78% per month with an associated t-statistic of 5.52), while the large size group generates the lowest momentum profits (0.47% per month with an associated t-statistic of 4.33). The frog-in-the-pan hypothesis suggests that investors are less aware of information that arrives continuously and in small amounts than they are of information that arrives in large amounts at discrete points in time. The analogy is that frogs jump out of a pan of water following a sudden increase in temperature, but underreact to the water temperature in the pan if it is brought to a boil slowly, and so are cooked. According to the frog-in-the-pan hypothesis, if investors underreact to small amounts of information that arrive continuously, this induces strong persistent return continuation. The authors found a monotonic increase in momentum profits for stocks with discrete information compared with stocks with continuous information. Thus, we have evidence that it meets the explanation criteria.

D’Souza, Srichanachaichok, Wang and Yao also examined a strategy that combined the two (time-series and cross-sectional) momentum strategies. Their dual momentum strategy buys the strongest winner portfolio and sells short the weakest loser portfolio, basically making it a market-neutral strategy. They found that the average annualized return of the dual momentum strategy was 22.4%.

The strategy, however, was associated with high volatility (37.5% per year). The data was statistically significant and also held up to tests that employed different combinations of formation and holding periods.