During my review of several quantitative trading books and papers, I kept on seeing information on two classes of trading strategies: mean reversion and momentum. I thought the things I read explained mean reversion quite clearly, but I wasn’t entirely clear on how to implement momentum investing and trading strategies, so I decided to research it more thoroughly.
This post focuses on what I have learned regarding the principles supporting the momentum class of investing and trading strategies (which I believe are superior to mean reversion).
At the end of this post, I also include a simple implementation of momentum in R on the S&P 500 (SPY) to aid in developing intuition. Over the roughly 23 year time period, such a strategy would achieve cumulative returns of around 830% with lower volatility versus 690% for the S&P 500.
Momentum is the foundation for a large number of quantitative and systematic trading strategies. It has received considerable interest from academic researchers over the past 20 years and has been repeatedly shown to be a source of consistently high risk-adjusted returns. Using the principles of momentum in combination with a simple and systematic trading strategy has produced impressive results.
This guide provides a summary of the principles of momentum, some theories on why momentum works, a curated selection of momentum research, and a simple implementation of momentum to aid in developing intuition.
Ideas Behind Momentum
Momentum is based on the empirical observation that there is persistence in an asset’s performance. An asset that has performed well in the past tends to perform well in the future, and an asset that has performed poorly in the past tends to perform poorly in the future. It’s a simple but powerful idea confirmed by hundreds of studies.
There are two types of momentum that have been identified in the literature: cross-sectional momentum and time-series momentum.
(also referred to as ) examines an asset’s past return relative to other asset’s past return. This type of momentum has received the most attention in the literature and is often applied to stocks. Most academic studies involve partitioning the universe of assets into equal segments and comparing the performance of the strongest performers to the performance of the weakest performers. The implementation most commonly cited is to rank all stocks based on their past 12-month return, then enter into a long position in the top 10 percent of stocks for one month. Some studies also enter into a short position in the bottom 10 percent of stocks.
(also referred to as ) examines an asset’s past return without considering the past return of other assets. If an asset’s return is above zero over a specified period of time, then the asset is considered to have positive momentum. An example implementation of this momentum is to enter into a long position if the past 12-month return is positive and enter into a short position if the past 12-month return is negative. Some studies calculate the performance over a specified window relative to the risk-free rate.
Both types of momentum are based on a simple rules-based implementation with the goal of identifying price trends that are likely to persist in the future. Although simple in its implementation, study after study has indicated that momentum trading strategies perform well across all asset classes, geographies, and time periods. I have reviewed the empirical evidence and it’s surprisingly strong and compelling. The core idea behind momentum has also been implemented in various investment systems and by many investment managers.
Theoretical Explanations of Momentum
There is no single accepted theory that explains why momentum works but understanding the various explanations can give you more confidence in the ideas behind momentum, insight into how markets and market participants act, and aid in developing trading strategies that use momentum.
Some researchers have attempted to explain that the excess returns from momentum are compensation for assuming additional risk, but I think the more compelling set of explanations is that momentum exists due to deeply rooted human behavioral biases and predictable but irrational behavior.
Any good explanation for momentum has to take into account the efficient-market hypothesis which is a very good theory for explaining asset prices that works most of the time but not all the time. Drawing from behavioral economics, it has been suggested that there is a systematic underreaction to recent data due to the anchoring effect — market participants anchor their views to past data and are reluctant to adjust their views. This prevents prices from immediately reaching a level that would be suggested from the efficient-market hypothesis and instead prices trend toward their fair value over time.
Another behavioral bias that leads to an underreaction to recent data is the disposition effect — the tendency of investors to sell assets that have increased too early while holding on to assets that have decreased.
Recent positive performance also interacts with confirmation bias in which market participants look for information that confirms what they already believe. As an asset’s price increases, this may confirm a market participants prior beliefs about the asset and thus lead to continued buying and a continuation in price trends.
Herding and crowd-like behavior is inherent in our psychology. There is a certain deeply rooted fear of missing out when a market participant observes a continued increase in prices. This compels even greater interest and greater buying. An extreme example of this behavioral bias manifests itself in the formation of asset bubbles.
Seminal Papers in Momentum Research
Imagine your knowledge of various topics as trunks of a greater knowledge tree. When learning something new, it’s helpful to place this new leaf of knowledge in the proper place within your knowledge tree, otherwise the thing you are trying to learn is so foreign that it doesn’t make sense. In other words, one must learn the basics and principles of something first in order to learn more complex things.
The problem with published academic papers is that the papers themselves are by definition expanding the limits of human knowledge. Therefore, often what they are talking about is so far from a trunk you are familiar with, so what I like to do is go back and review the seminal papers of a topic first before reading other papers.
“Some A Posteriori Probabilities in Stock Market Action” by Cowles and Jones (1937) was the first published paper that examined momentum. The authors concluded that there is structure in stock prices by discovering an increased probability of a past rise in prices followed by a future rise, or a past decline in prices followed by a future decline, over several time periods.
The seminal paper in modern momentum research is “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency” by Jegadeesh and Titman (1993). The authors found that stocks that performed the best over the past 3 to 12 months continued to outperform over the next 3 to 12 months.
Eight years after this paper was published, Jagadeesh and Titman (2001) followed up their initial work by demonstrating that the momentum effect that they identified persisted over the following eight years. This out-of-sample test indicated that the original effect was not due to data mining.
“Time series momentum” by Moskowitz, Ooi, and Pedersen (2012) was one of the first papers to investigate time-series momentum (as referred to as absolute momentum). The authors found that the past 12 month excess return of an asset is a positive predictor for its future return and that this finding occurred across 58 assets, including equities, currencies, commodities, and sovereign bonds.
“A Century of Evidence on Trend-Following Investing” by Hurst, Ooi, and Pederson (2014) further examines time-series momentum by using data from 1880 across global markets, extending the evidence for momentum by over 100 years. This long period of out-of-sample testing strongly suggests that the momentum effect is not the product of statistical randomness or data mining.
For a more complete review of the literature, I recommend reading Dual Momentum Investing by Gary Antonacci. The synthesis of modern momentum research is that the momentum effect is strong and has been demonstrated to exist across assets, countries, and time periods.
Simple Implementation of Momentum
To reinforce the intuition behind momentum, I present a simple time-series momentum strategy on the S&P 500 using the SPY ETF. The strategy goes long when the past 12 month return is positive and is flat when the past 12 month return is negative. The signal is generated daily. To simplify and focus on the intuition, trading fees are not considered.
The following plot shows the closing price of SPY with the trading signal overlayed on top as a color gradient. Blue indicates that the strategy is long (the signal is +1) and black indicates the strategy is flat (the signal is 0).
This strategy achieves an annualized return of 10% with lower volatility versus the S&P 500 return of 9% over this time period. Due to the power of compounding, such a strategy achieves a cumulative return of 830% versus 690% for the S&P 500.
By examining both plots above, you can develop some intuition on how momentum works and what types of environments are good for momentum-based trading strategies.
First, momentum trading strategies are trend following by nature, so they participate in most of the upside while avoiding bear markets once they are firmly established. Most of the outperformance of momentum relative to buy-and-hold comes from its ability to avoid bear markets.
Second, while momentum strategies retain most of the upside, they miss out on some gains during the transitions from bear markets to bull markets. For example, due to the lag introduced by using a 12 month lookback period, momentum missed out on some of the recovery immediately after the financial crisis.
Third, when there is no clear trend and prices experience large declines with equally large rebounds, momentum strategies struggle. Under this type of market environment, momentum strategies can participate in all the downside but none of the upside. This can be clearly seen in late 2015 and early 2016 when the S&P 500 experienced high volatility but with no trend upwards or downwards.
For additional discussion of momentum, I strongly suggest reading Dual Momentum Investing by Gary Antonacci. He is a great writer and the book is extremely well researched. It’s one of my favorite investing-related books.
The code for this post can be found on my Github.
I have an email list where I occasionally send updates to readers on the trading systems that I’m developing. If you are interested, please enter your email below.