Which Trend Is Your Friend?

Managed futures funds and commodity trading advisers (CTAs) use heuristics or statistical measures often called “filters” to trade on price trends. Two key statistical measures of trends are “time-series momentum” and “moving-average crossovers.” We show, empirically and theoretically, that these trend indicators are closely related. In fact, they are equivalent representations in their most general forms. They also capture many other types of filters, such as the Hodrick–Prescott (HP) filter, the Kalman filter, and all other linear filters. We show how these filters can be represented through “trend signature plots,” demonstrating their dependence on past prices and returns by horizon.The summary was prepared by Pamela G. Yang, CFA.What’s Inside?The trend-following investment strategy is a widely practiced investment style, especially for futures, commodities, and hedge fund traders. Trend indicators rely on past prices and returns. On an empirical and a theoretical basis, generalized forms of different trend-based investment strategies are closely related. The authors use two key statistical measures to capture trends: the time-series momentum (TSMOM) method, which shows the return over some recent time period, and the moving-average crossover (MACROSS) method, which shows different price levels over different time periods. The academic literature and practitioners have put forth a host of strategies that, on the surface, appear unique but are all related to trend following at a high level. The authors seek to unify many of these seemingly disparate strategies in a simple, robust, and intuitive framework.How Is This Research Useful to Practitioners?Momentum investors like to follow trends. Trend strategy is intuitive and based on the belief that trends are likely to continue. Understanding how to identify a price trend is essential for investors. Day-to-day price changes can be noisy, and the random walk hypothesis suggests that future price moves are completely unpredictable and that trend-following strategies should not work. Nevertheless, trend-following investors believe that markets are not completely efficient and that risk premiums change over time; thus, under certain circumstances, trend following may add value.A TSMOM signal, on one hand, shows the return over some recent time period. To simplify with an example, assume that investing in gold has resulted in a positive return over the past 12 months. The trend is assessed to be upward, and the TSMOM signals to buy gold. On the other hand, a MACROSS signal shows the crossover of two moving averages, a fast-moving average that puts more weight on recent prices and a slow-moving average that puts more weight on past prices. In our example, assume that the moving average of gold prices over the past 20 days crosses over the moving average of gold prices over the past 260 days. As recent prices are above where prices used to be, the trend is assessed to be upward, and MACROSS signals to buy gold.The authors examine both methods packaged in various ways and demonstrate that the most general form of MACROSS can be viewed as a special case of the most general form of TSMOM, and vice versa. They further demonstrate that a large set of linear filters—for example, the Hodrick–Prescott filter, the Kalman filter, or any other trend estimation using an ordinary least-squares trend regression—are equivalent to a generalized TSMOM or MACROSS signal. In conclusion, TSMOM and MACROSS filters capture prominently all of the other filters and features in applications.How Did the Authors Conduct This Research?The authors show, via detailed mathematical formulas with variations and different combinations of coefficients, how TSMOM and MACROSS work. They illustrate how each trend signal can be represented graphically using trend signature plots based on either past prices (MACROSS) or past returns (TSMOM). The conclusion is that TSMOM and MACROSS are essentially equivalent.To support this conclusion, the authors perform an empirical study that relies on 58 instruments ranging from currency pairs to commodity futures and covers prices from 1985 to 2015. They calculate signals from a return index rather than from prices by rolling futures and forward prices. They construct three standard TSMOM strategies and three standard MACROSS strategies that are relatively comparable. To put the trading signals on an equal footing, the authors use the same portfolio construction methodology for signals related to both strategies. The result is that both strategies perform similarly for all horizons, including in terms of annual returns (excess of cash), annualized volatility, and Sharpe ratios. However, some deviations are observed. For example, the authors note the positive significance in the alphas of some of the TSMOM signals when they are regressed on the MACROSS signals, which may simply mean that MACROSS signals have a harder time mimicking a TSMOM signal. The reverse is not true because the shape of TSMOM signals more easily fit an arbitrary MACROSS signal.Abstractor’s ViewpointTrend or momentum trading versus valuation trading has always separated investors into two camps. Over the long run, both strategies may deliver similar results, although each may add value at different stages. This study focuses on momentum trading and may not generate much interest from valuation investors. However, for those who are trend followers, this research shows that various measures to capture trends are, in essence, merely variations of one another and do not affect outcomes materially. Although common implementations of these trend signals may not be exactly the same in practice, the authors’ findings confirm that no matter what methodology investors use to identify trends, they will not stray far from the trend as long as they have a robust and disciplined implementation.Editor’s note: This article was reviewed and accepted by Executive Editor Stephen J. Brown.Editor’s note: Both authors are affiliated with AQR, a global investment management firm running long-only and alternative investment products, including managed futures funds.