• Trend-following is one of the oldest investment methods
  • Labeled as technical analysis, trend-following went largely un-researched by academics
  • Research of cross-sectional momentum exploded after Narasimhan Jegadeesh and Sheridan Titman published their seminal 1992 study, but time-series momentum remained largely ignored until after 2008
  • Price-based trend-following techniques, like moving average systems, remained separate from return-based time-series momentum techniques.
  • New research shows that moving average systems and time-series momentum­ are mathematically-linked techniques

In 1838, James Grant published The Great Metropolis, Volume 2.  Within, he spoke of David Ricardo, an English political economist that was active in the London markets in the late 1700s and early 1800s.  Ricardo amassed a large fortune trading both bonds and stocks.  According to Grant, Ricardo’s success was attributed to three golden rules:

“As I have mentioned the name of Mr. Ricardo, I may observe that he amassed his immense fortune by a scrupulous attention to what he called his own three golden rules, the observance of which he used to press on his private friends. These were, “Never refuse an option* when you can get it,”—”Cut short your losses,”—”Let your profits run on.” By cutting short one’s losses, Mr. Ricardo meant that when a member had made a purchase of stock, and prices were falling, he ought to resell immediately. And by letting one’s profits run on he meant, that when a member possessed stock, and prices were raising, he ought not to sell until prices had reached their highest, and were beginning again to fall. These are, indeed, golden rules, and may be applied with advantage to innumerable other transactions than those connected with the Stock Exchange.”

“Cut short your losses” and “let your profits run on” became the core tenets of trend-following.

Other prominent early trend-followers include:

  • Charles H. Dow, founder and first editor of the Wall Street Journal as well as co-founder of Dow Jones and Company
  • Jesse Livermore, who is quoted by Edwin Lefèvre as having said, “[t]he big money was not in the individual fluctuations but in the main movements … sizing up the entire market and its trend.”
  • Richard Wyckoff, whose method involved entering long positions only when the market was trending up and shorting when the market was trending down.

There was even an early academic study of trend-following performed by Alfred Cowles III and Herbert Jones in 1933.  In the study, titled Some A Posteriori Probabilities in Stock Market Action, they focus on counting the number of sequences – times when positive returns were followed by positive returns, or negative returns were followed by negative returns – to reversals – times when positive returns are followed by negative returns, and vice versa.

Cowles and Jones evaluated the ratio of these sequences and reversals in stock prices over periods ranging 20 minutes to 3 years.  Their results:

It was found that, for every series with intervals between observations of from 20 minutes up to and including 3 years, the sequences out-numbered the reversals.  For example, in the case of the monthly series from 1835 to 1935, a total of 1200 observations, there were 748 sequences and 450 reversals.  That is, the probability appeared to be .625 that, if the market had risen in a given month, it would rise in the succeeding month, or, if it had fallen, that it would continue to decline for another month.  The standard deviation for such a long series constructed by random penny tossing would be 17.3; therefore the deviation of 149 from the expected value of 599 is in excess of eight times the standard deviation.  The probability of obtaining such a result in a penny-tossing series is infinitesimal.

cowles-jobes-graph cowles-jones-table

Despite promising empirical and theoretical results for trend-following, the next academic studies would not come until nearly a century later.

In 1934, Benjamin Graham and David Dodd published Security Analysis.  Later, in 1949, they published The Intelligent Investor.

In these weighty tomes, they outline their methods for successful investing.  Graham and Dodd’s method focused on evaluating the financial state of the underlying business.  Their objective was to identify a company’s intrinsic value and purchase stock when the market offered a substantial discount to that value.

For Graham and Dodd, anything else was mere speculation.

Graham and Dodd gave fundamental investors – and specifically value investors ­– their bible.

Anything, then, that was not fundamental investing was technical analysis.  And since trend-following relied only on evaluating past prices, it was labeled technical analysis.

Unfortunately, academics largely dismissed technical analysis through the 1900s.  This is likely due to the fact that it was difficult to study and test.  Practitioners follow a large number of different techniques.  Sometimes these different techniques can lead to contradictory predictions between technicians.

But in 1993, Narasimhan Jegadeesh and Sheridan Titman published Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency.  In their paper, they outlined an investment strategy that purchased stocks that had outperformed their peers and sold stocks that had underperformed.

Jegadeesh and Titman called their approach relative strength – a term that had been long used by technicians.  Now it is sometimes called cross-sectional momentum, relative momentum, or often just momentum.

This simple method outlined by Jegadeesh and Titman created statistically significant positive returns that could not be explained by common risk factors.

This paper ushered in an era of momentum research, with academics exploring how the technique fared across geographies, time-frames, and asset classes.  The results were that momentum was surprisingly robust.

Despite the success of relative strength, interest in its close cousin trend-following was still nowhere to be found.

Until the financial crisis of 2008.

Technically, one of the most popular research papers about trend-following – Mebane Faber’s A Quantitative Approach to Tactical Asset Allocation – was published in 2006.  But the majority of interest from academics occurred post-2008.

We attribute this interest to trend-following’s risk mitigation properties.

The studies typically fall into two camps.

In the first camp was the study of trend-following, which tended to follow simple mechanical systems, like moving averages.  Faber (2006) fell into this camp, using a 10-month moving average cross-over.

There are several variations of these systems.  For example, one might use the cross of price over the moving average as a signal.  Another might use the cross of a shorter moving average over a longer.  Finally, some may even use directional changes in the moving average as the signal.

Trend Following - 2015-07-26

Others tended to focus on what would become known as time-series momentum­. In time-series momentum, the trading signal is generated when the total return over a given period crosses over the zero-line.

Time Series Momentum - 2015-07-26

One of the most prominent studies for time-series momentum was Moskowitz, Ooi, and Pedersen (2011), which demonstrated the anomaly was significant in 58 liquid equity index, currency, commodity, and bond futures.

Trend-following moving average rules were still considered to be technical trading rules versus the quantitative approach of time-series momentum.  Perhaps the biggest difference is that the trend-following camp tended to focus on techniques using prices while the momentum camp focused on returns.

However, research over the last half-decade actually shows that they are mathematically related strategies.

Bruder, Dao, Richard, and Roncalli’s 2011 Trend Filtering Methods for Momentum Strategies united moving-average cross-over strategies and time-series momentum by showing that cross-overs were really just an alternative weighting scheme for returns in time-series momentum.  To quote,

The weighting of each return … forms a triangle, and the biggest weighting is given at the horizon of the smallest moving average.  Therefore, depending on the horizon n2 of the shortest moving average, the indicator can be focused toward the current trend (if n2 is small) or toward past trends (if n2 is as large as n1/2 for instance).

Bruder Dao  Richard and Roncalli

In Marshall, Nguyen and Visaltanachoti’s Time-Series Momentum versus Moving Average Trading Rules, published in 2012, time-series momentum is shown to be related to changes in direction of a moving average.  In fact, time-series momentum signals will not occur until the moving average changes direction.

Therefore, moving average rules which rely on price crossing the moving average are likely to occur before a change in signal from time-series momentum.

Similar to Bruder, Dao, Richard, and Roncalli, Levine and Pedersen show that time-series momentum and moving average cross-overs are highly related in their 2015 paper Which Trend is Your Friend?.  They also find that time-series momentum and moving-average cross-over strategies perform similarly across 58 liquid futures and forward contracts.

In their 2015 paper Uncovering Trend Rules, Beekhuizen and Hallerbach also link moving averages with returns, but further explore trend rules with skip periods and the popular MACD (moving average convergence divergence) rule.  Using the implied link of moving averages and returns, they show that the MACD is as much trend following as it is mean-reversion.

Beekhuizen Hallerbach MACD

These studies are important because they help validate the approach of price-based systems.  Being mathematically linked, technical approaches like moving averages can now be linked to the same theoretical basis as the growing body of work in time-series momentum.

Market practitioners have long held that the trend is your friend and academic literature has finally begun to agree.

But perhaps, most importantly, we now know that it doesn’t matter whether you take the technical approach using moving averages or the quantitative approach of measuring returns.  At the end of the day, they’re more or less the same thing.

Corey is co-founder and Chief Investment Officer of Newfound Research, a quantitative asset manager offering a suite of separately managed accounts and mutual funds. At Newfound, Corey is responsible for portfolio management, investment research, strategy development, and communication of the firm's views to clients. Prior to offering asset management services, Newfound licensed research from the quantitative investment models developed by Corey. At peak, this research helped steer the tactical allocation decisions for upwards of $10bn. Corey holds a Master of Science in Computational Finance from Carnegie Mellon University and a Bachelor of Science in Computer Science, cum laude, from Cornell University. You can connect with Corey on LinkedIn or Twitter.