Objects in Motion: Momentum Trading Strategies
You may remember from your primary school days that objects in motion tend to stay in motion unless acted upon by an equal or opposite force. It has been suggested that financial markets behave similarly to the physical world– in fact, there is an entire field of study relating to this idea (sometimes referred to as econo-physics, much to the chagrin of economists and physicists). One particularly well-known concept borrowed from physics and applied to financial markets is momentum. Non-physicists need not run for the back button– momentum is an easy-to-understand concept that has been heavily researched and well-documented. In this article, we will review what the research says about momentum and consider how we can use that information to construct a trading strategy.
Price momentum is the tendency for the price of an asset to continue moving in the direction of an existing trend. The momentum phenomenon, while in direct contrast with efficient market theory, has been observed across asset classes and is used by many traders and CTAs. Researchers have attributed the momentum effect to the behavioral inefficiencies of market participants—specifically the tendency for investors to under-react initially to new information and overreact in the long term 1. Examining the conclusions of existing research on price momentum is a useful exercise for traders planning to use principles of price momentum to construct a trading strategy.
Cross-Sectional and Time-Series Momentum
In one of the first and most widely-cited studies of the momentum phenomenon, Jegadeesh and Titman (1993) propose a methodology for buying well-performing assets and selling poor-performing assets, and find evidence of significant positive returns. The strategy selects assets on the basis of their returns over the past J periods and holds them for K months. Known as the J-month/K-month strategy, it is created as follows 2:
1. At the beginning of each month t , rank a group of assets in ascending order based on their returns over the past J months
2. Then, split the list into 10 portfolios
3. Go long the best-performing portfolios and short the worst-performing portfolios
4. Hold the positions for K months
This type of strategy is known as cross-sectional momentum, and has been replicated by many traders and researchers. Cross-sectional momentum compares the returns of a group of assets over a selected period of time to pick winners/losers, and predicts that those winners/losers will continue to win/lose in the future, creating a strategy that is long historically outperforming assets and short historically under-performing assets.
Unlike cross-sectional momentum, time-series momentum uses only the recent historical performance of an asset to predict its future returns without consideration of other assets. The main difference between cross-sectional and time-series momentum strategies is whether you are calculating the returns of an asset relative to other assets or relative to its own historical performance. As cross-sectional momentum is relative, strategies can be made to be market-neutral by balancing the long and short exposure, adapting to varying market conditions. On the other hand, time-series strategies are absolute performance strategies as profit is generated solely based on whether you are long a rising asset or short a falling asset, so they are by definition not market-neutral. Research suggests time-series momentum significantly outperforms during extreme periods in the market so it could be used as a hedge for extreme events 1.
Regressing the returns of time-series momentum and cross-sectional momentum, Moskovitz et al. (2011) find that time-series momentum is able to “explain some of the prominent factors in asset pricing, namely cross-sectional momentum.” Further, they regress the returns of time-series momentum strategies over different lookback and holding periods and identify the “existence and significance of time series momentum is robust across horizons and asset classes, particularly when the look-back and holding periods are 12 months or less.” They conclude the time-series momentum strategy is profitable for each of the 58 instruments considered in their study.
In their 2017 study, Bird et al. (2017) test both cross-sectional and time-series momentum strategies on a portfolio of stocks over time period f. In the cross-sectional strategy, stocks are selected based on their relative performance over formation period f in relation to other stocks. Similar to the model employed by Jegadeesh and Titman (1993) , the stocks generating returns in the top 20% are assigned to the winner portfolio while the bottom 20% are assigned to the loser portfolio. For the time-series portfolio, stocks are selected according to their absolute performance over the same period, assigning stocks with a return above 5% to the winner portfolio and below 3% to the loser portfolio. Both strategies are measured against a zero-investment strategy, taking a long position in the winner portfolio and a short position in the loser portfolio 3. The results of the Bird et al. (2017) research show that while both time-series and cross-sectional momentum strategies produced profits, “time-series momentum is superior” particularly in up-trending markets. They find that the average winning stock chosen using time-series momentum outperforms the average winning stock under cross-sectional momentum. The full results of the study can be found here.
Baltas and Kosowski (2012) conduct a test of time-series momentum portfolios to explore profitability of time-series momentum strategies used by CTAs. Their strategy is constructed by taking a long/short position in a single asset for holding period h based on the sign of its return over lookback period J. Several time periods in increments of days, weeks and months are tested against the inverse-volatility weighted average returns of all available univariate strategies. They report the results of their study “represent strong evidence that the historical out-performance of the CTA funds is statistically significantly related to their employment of time-series momentum strategies using futures contracts over multiple frequencies”4.
Formation and Holding Periods
Moskovitz et al. (2011) conclude that the time-series momentum effect partially reverses after one year, which appears to be a common conclusion among research of both cross-sectional and time-series momentum strategies, many of which find the best performance when employing a formation period of approximately 9-12 months and a holding period of approximately 1-3 months 1,3,5,6. In a follow up to their 1993 study, Jagadeesh and Titman (2001) conclude that performance of a momentum portfolio reverses to the downside in the 13th to 60th month following the formation month 6. Bird et al. (2017) found the best implementation of their time-series momentum strategy was a 12-month formation period with a 3-month holding period, using “inverse volatility to weight the stocks and to re-balance the portfolios monthly with no lag in implementation.”
Menkhoff et al. (2011) analyze a cross-section of currency pairs, the returns of which by nature follow a time series. Interestingly, the results of this study are similar to those of other momentum studies in terms of the optimal formation and holding period. Using a cross-section of eight currencies over twenty years, they form portfolios based on the best and worst lagged returns over the formation period f, (where f = 1, 3, 6, 9, 12 months) with h as the holding period in months that a position is held (where h = 1, 3, 6, 9, 12 months). They find excess returns are dependent on the formation period f and tend to be strongest for a holding period h=1 month.
Creating a Momentum Strategy
To build your own momentum strategy, consider the points outlined in our examination of the existing research:
1. Determine whether you will be using a time-series or cross-sectional model
2. Determine a formation period
3. Identify the holding period
It is shown that momentum returns decay over time, so be sure to factor that into your decision and test several combinations of formation and holding periods. Or, construct multiple portfolios of varying formation and holding periods and diversify across them. Remember, past performance cannot predict future returns with certainty, and effective risk management should always be utilized.
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1 | Moskowitz, T.J., Ooi, Y.H., & Pedersen, L.H. (2011). Time Series Momentum. Chicago Booth Research Paper No. 12-21; Fama-Miller Working Paper. http://dx.doi.org/10.2139/ssrn.2089463
2 | Jegadeesh, N., & Titman, S. (1993). Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. The Journal of Finance, 48(1), 65-91. doi: 10.2307/2328882
3 | Bird, R., Gao, X., & Yeung, D. (2017). Time-series and cross-sectional momentum strategies under alternative implementation strategies. Australian Journal of Management, 42(2), 230–251. https://doi.org/10.1177/0312896215619965
4 | Baltas, N., & Kosowski, R. (2012). Momentum Strategies in Futures Markets and Trend-following Funds (January 5, 2013). Paris December 2012 Finance Meeting EUROFIDAI-AFFI Paper. http://dx.doi.org/10.2139/ssrn.1968996
5 | Jegadeesh, N., & Titman, S. (2001). Profitability of Momentum Strategies: An Evaluation of Alternative Explanations. The Journal of Finance, 56(1), 699-720. doi: 10.3386/w7159
6 | Menkhoff, Lukas and Sarno, Lucio and Schmeling, Maik and Schrimpf, Andreas, Currency Momentum Strategies (November 7, 2011). Available at SSRN: https://ssrn.com/abstract=1809776 or http://dx.doi.org/10.2139/ssrn.1809776
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