Daily Academic Alpha: Which Trend if Your Friend?

Daily Academic Alpha: Which Trend if Your Friend?

May 19, 2015 Uncategorized

Last updated on January 18th, 2017 at 02:43 pm

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Which Trend Is Your Friend?

Managed-futures funds (sometimes called 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 trend filters can be equivalently represented as functions of past prices vs. past returns. Our results unify and broaden a range of trend-following strategies and we discuss the implications for investors.

Uncovering Trend Rules

Trend rules are widely used to infer whether financial markets show an upward or downward trend. By taking suitable long or short positions, one can profit from a continuation of these trends. Conventionally, trend rules are based on moving averages (MAs) of prices rather than returns, which obscures how much weight is assigned to different historical time periods. In this paper, we show how to uncover the underlying historical weighting schemes of price MAs and combinations of price MAs. This leads to surprising and useful insights about popular trend rules, for example that some trend rules have inverted information decay (i.e., distant returns have more weight than recent ones) or hidden mean-reversion patterns. This opens the possibility for improving the trend rule by analyzing the added value of the mean reversion part. We advocate designing trend rules in terms of returns instead of prices, as they offer more flexibility and allow for adjusting trend rules to autocorrelation patterns in returns.


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About the Author

Wesley R. Gray, Ph.D.

After serving as a Captain in the United States Marine Corps, Dr. Gray received a PhD, and was a finance professor at Drexel University. Dr. Gray’s interest in entrepreneurship and behavioral finance led him to found Alpha Architect. Dr. Gray has published three books: EMBEDDED: A Marine Corps Adviser Inside the Iraqi Army, QUANTITATIVE VALUE: A Practitioner’s Guide to Automating Intelligent Investment and Eliminating Behavioral Errors, and DIY FINANCIAL ADVISOR: A Simple Solution to Build and Protect Your Wealth. His numerous published works has been highlighted on CBNC, CNN, NPR, Motley Fool, WSJ Market Watch, CFA Institute, Institutional Investor, and CBS News. Dr. Gray earned an MBA and a PhD in finance from the University of Chicago and graduated magna cum laude with a BS from The Wharton School of the University of Pennsylvania.