Trend and mean reversion have been studied extensively. However, Reference [1] takes a refreshing approach by applying a lattice model borrowed from statistical mechanics to analyze market trends. In a follow-up paper [2], the authors extend the model and examine the relationship between trend, future volatility, and correlations.
The study utilizes 33 years of daily data across 24 futures markets, spanning equities, interest rates, foreign exchange, and commodities. Trend horizons range from 2 to 1,024 trading days, with trend strength measured using the t-statistic, as in the previous paper. The authors pointed out,
The e and f terms refine such models by also taking current trends into account. The positive value of f implies that the variance tends to grow day after day in times of strong trends, which explains why it is high after trends have built up, as shown in fig. 1, right. The negative value of e shows that the variance grows faster in times of strong down-trends as opposed to up-trends. We have found that this asymmetry is particularly strong for equities and mostly stems from short-term trends. Since trends measure cumulative recent returns, this can be interpreted as the “leverage effect”: strong negative returns tend to be followed by an increase of the variance.
… Since g < 1, the correlation tends to revert to the long-term correlation. The o-term refines such models by taking trends into account. It implies, e.g., that the next-day correlation of two assets is about 0.1 − 0.2 higher (lower) than their average correlation, when both trends are strong (ϕ, ψ ≥ 2) and point in the same (opposite) direction.
In short, the paper finds that,
- Future volatility depends on current trend strength, not just current volatility,
- Future cross-asset correlations depend on the trend strengths of both assets. Strong common trends imply higher future correlations, especially in downtrends,
- The leverage effect is strongest for equities.
This study provides another interesting perspective on market trends and volatility through the lens of statistical mechanics. It has implications not only in trading but also in risk management.
Let us know what you think in the comments below or in the discussion forum.
References
[1] Sara A. Safari, Christof Schmidhuber, Trends and Reversion in Financial Markets on Time Scales from Minutes to Decades, arXiv:2501.16772
[2] Sara A. Safari, Christoph Schmidhuber, Trends, Volatility, Correlations, and Critical Phenomena in Financial Markets, arXiv:2606.20145
Originally Published Here: A Statistical Mechanical Model of Trend, Volatility, and Correlation
source https://harbourfronts.com/statistical-mechanical-model-trend-volatility-correlation/
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