Trend vs. Mean Reversion: A Statistical Physics Approach to Financial Markets

Trend and mean reversion are two prevalent forces in financial markets. Studying their interplay is important, as it provides clues for developing accurate timing models. Reference [1] formally examines the relationship between trend and mean reversion in financial markets, across timeframes ranging from intraday to monthly, and spanning over 300 years.

The authors propose a lattice gas model of financial markets, where the lattice represents the social network of investors, and the gas molecules represent shares of an asset. Mathematically, for a given market and time horizon, they define the strength ϕ of a trend using its t-statistic. They find that tomorrow’s return, 𝑅(𝑡+1) (normalized to have variance 1), is well modeled by a cubic polynomial of today’s trend strength,

R(t + 1) = a + b · ϕ(t) + c · ϕ(t)^3 + ϵ(t)

• …trends tend to revert before they become statistically strongly significant. In other words, by the time a trend has become so obvious that everybody can see it in a price chart, it is already over. This is consistent with the hypothesis that any obvious market inefficiency is quickly eliminated by investors.

• The parameters b, c are universal in the sense that they seem to be the same for all assets within the limits of statistical significance. This is in line with the fact that many successful trend-followers use the same systematic trading strategy for all assets.

• c is negative and does not seem to depend much on the trend’s time horizon T. However, b depends on the horizon: it peaks at T ∼ 3-12 months, which is in line with the time scales on which trend followers typically operate. b decays for longer or shorter horizons and appears to become negative for T < 1 day or T > several years.

• While c has been fairly stable over time, b appears to have vanished over the decades. This is in line with the fact that trend following no longer works as well today as it did in the 1990’s. Markets seem to have become quite efficient with respect to trends.

In short, the authors develop an interesting model of the financial market and conclude that markets tend to be in a trending regime over time scales from a few hours to a few years while exhibiting mean reversion over shorter and longer horizons. In the trending regime, weak trends tend to persist, whereas in the reversion regime, weak trends tend to reverse.

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References

[1] Sara A. Safari, Christof Schmidhuber, Trends and Reversion in Financial Markets on Time Scales from Minutes to Decades, https://arxiv.org/abs/2501.16772