Managed-futures funds and CTAs trade predominantly on trends. There are several ways of identifying trends, either using heuristics or statistical measures often called “filters.” Two important statistical measures of price trends are time series momentum and moving average crossovers. We show both empirically and theoretically that these trend indicators are closely connected. In fact, they are equivalent representations in their most general forms, and they also capture many other types of filters such as the HP filter, the Kalman filter, and all other linear filters. Further, we show how these filters can be represented through “trend signature plots” showing their dependence on past prices and returns by horizon. Our results unify and broaden a range of trend-following strategies, and we discuss the implications for investors.

Keywords: trend-following investing, momentum, moving average crossover, filtering, managed futures, CTA

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