Time-series momentum examines the trend of an asset with respect to its own past performance. This is very different than cross-sectional momentum (often referred to as Carhart momentum), which compares the performance of an asset with respect to the performance of another asset.

Ian D’Souza, Voraphat Srichanachaichok, George Jiaguo Wang and Chelsea Yaqiong Yao, who authored the 2016 study “The Enduring Effect of Time-Series Momentum on Stock Returns Over Nearly 100 Years,” provide evidence that supports the view that time-series momentum (also referred to as trend-following) is one of the few investment factors that meet five important criteria for inclusion in a portfolio; specifically, it is persistent, pervasive, robust, investable and intuitive. Their study covered the 88-year period from 1927 to 2014.

**Study Results**

Following is a summary of their findings:

- A value-weighted strategy of going long stocks with positive returns in the prior 12 months (skipping the most recent month) 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 down markets, producing an average monthly return of 0.57% (with a t-statistic of 2.09) following down markets 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.
- 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.
- Time-series stock momentum was profitable regardless of formation and holding periods for 16 different combinations.
- The common investment factors of market beta, size and value have little power to explain time-series momentum.
- Unlike with cross-sectional momentum, time-series momentum does not experience losses in January (a seasonal effect) or crashes (which occur with cross-sectional momentum during reversals).
- The time-series momentum premium can be at least partially explained by two prominent theories describing investor underreaction (both the gradual information diffusion model and what is 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). Indeed, the authors found 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 a frog will 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, it induces strong persistent return continuation. The authors found a monotonic increase in momentum profits for stocks with discrete information compared to stocks with continuous information. Thus, we have evidence that time-series momentum meets the explanation criteria.

**Further Evidence**

In a 2014 paper, “A Century of Evidence on Trend-Following Investing,” which used historical data from a number of sources, AQR Capital Management constructed a time-series momentum strategy all the way back to 1880 and found that it was consistently profitable throughout the past 134 years. AQR’s researchers constructed an equal-weighted combination of one-month, three-month and 12-month time-series momentum strategies for 67 markets across four major asset classes (29 commodities, 11 equity indexes, 15 bond markets and 12 currency pairs) from January 1880 to December 2013.

Their results include implementation costs based on estimates of trading costs in the four asset classes. They further assumed management fees of 2% of asset value and 20% of profits, the traditional fee for hedge funds. Following is a summary of AQR’s findings:

- Performance was remarkably consistent over an extensive time horizon that included the Great Depression, multiple recessions and expansions, multiple wars, stagflation, the global financial crisis of 2008 and periods of rising and falling interest rates.
- Annualized gross returns were 14.9% over the full period, with net returns (after fees) of 11.2%, higher than the return to equities, but with about half the volatility (an annual standard deviation of 9.7%).
- Net returns were positive in every decade, with the lowest net return being the 5.7% return for the period beginning in 1910. There were also only five periods in which net returns were in the single digits.
- There was virtually no correlation to either stocks or bonds. Thus, the strategy provides strong diversification benefits while producing a high Sharpe ratio (a measure of risk-adjusted returns) of 0.77. Even if future returns are not as strong, the diversification benefits would justify an allocation to the strategy.

Researchers at AQR observed that “a large body of research has shown that price trends exist in part due to long-standing behavioral biases exhibited by investors, such as anchoring and herding (and we would add the disposition effect and confirmation bias), as well as the trading activity of non-profit-seeking participants, such as central banks and corporate hedging programs. For instance, when central banks intervene to reduce currency and interest-rate volatility, they slow down the rate at which information is incorporated into prices, thus creating trends.”

The authors continue: “The fact that trend-following strategies have performed well historically indicates that these behavioral biases and non-profit-seeking market participants have likely existed for a long time.”

They noted that trend-following has done particularly well in extreme up or down years for the stock market, including the most recent global financial crisis of 2008. In fact, they found that during the 10 largest drawdowns experienced by the traditional 60/40 portfolio over the past 135 years, the time-series momentum strategy experienced positive returns in eight of these stress periods and delivered significant positive returns during a number of these events.

**Momentum & CTAs**

Nick Baltas and Robert Kosowski contribute to the literature on time-series momentum with their 2013 study, “Momentum Strategies in Futures Markets and Trend-Following Funds.” They studied “the relationship between time-series momentum strategies in futures markets and commodity trading advisors (CTAs), a subgroup of the hedge fund universe that was one of the few profitable hedge fund styles during the financial crisis of 2008, hence attracting much attention and inflows in its aftermath.”

They noted that following inflows over the subsequent years, the size of the CTA fund industry had grown substantially and exceeded $300 billion of the total $2 trillion in assets under management invested in hedge funds by the end of 2011. Their study covered the period December 1974 through January 2012 and included 71 futures contracts across assets classes: 26 commodities, 23 equity indices, 7 currencies and 15 intermediate-term and long-term bonds.

Following is a summary of their findings:

- Time-series momentum exhibits strong effects across monthly, weekly and daily frequencies.
- Strategies with different rebalancing frequencies have low cross-correlations and therefore capture distinct return patterns.
- Momentum patterns are pervasive and fairly robust over the entire evaluation period and within subperiods.
- Different strategies achieve annualized Sharpe ratios above 1.2 and perform well in both up and down markets, which should make them good diversifiers in equity bear markets.
- Commodity futures-based momentum strategies have low correlation with other futures strategies. Thus, despite the fact that they have a relatively low return, they do provide additional diversification benefits.

Importantly, Baltas and Kosowski found that momentum profitability is not limited to illiquid contracts. Momentum strategies are typically implemented by means of exchange-traded futures contracts and forward contracts, which are considered relatively liquid and to have relatively low transaction costs compared to cash, equity or bond markets.

In fact, they found that “for most of the assets, the demanded number of contracts for the construction of the strategy does not exceed the contemporaneous open interest reported by the Commodity Futures Trading Commission (CFTC) over the period 1986 to 2011.” The authors also found that the “notional amount invested in futures contracts in this hypothetical scenario is a small fraction of the global OTC derivatives markets (2.3% for commodities, 0.2% for currencies, 2.9% for equities and 0.9% for interest rates at end of 2011).”

Finally, they concluded: “Our analyses based on the performance-flow regressions and the hypothetical open interest exceedance scenario do not find statistically or economically significant evidence of capacity constraints in time-series momentum strategies.”

**Summary**

The evidence on time-series momentum has been found to be persistent across time and economic regimes, and pervasive across asset classes. Additionally, it has been found to be robust to various definitions. And it also has been shown to be implementable, with little to no evidence of significant capacity constraints. These are all strong points in favor of considering this “alternative” investment strategy for inclusion in your portfolio.

The strongest challenge to time-series momentum is the lack of a risk-based explanation. However, behavioral explanations can also lead to the persistence of premiums. And time-series momentum does have several behavioral explanations, including investor underreaction (both the gradual information diffusion model and the frog-in-the-pan model) as well as anchoring, herding, the disposition effect and confirmation bias.

In addition, trading activity by non-profit-seeking market participants (such as corporate hedging programs and central banks) can lead to the development of trends. Human behavior tends to be highly persistent, and there doesn’t seem to be any reason to believe that market interventions by central banks and hedging programs won’t persist in the future.

The bottom line is that, given their diversification benefits and downside (tail risk) hedging properties, a moderate portfolio allocation to trend-following strategies merits consideration. One important note, however, is that the generally high turnover of trend-following strategies renders them relatively tax inefficient. Thus, there should be a strong preference to hold them in tax-advantaged accounts.

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