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