EMAzing Trends: When One Moving Average Beats a Basket of Signals

The latest research from Sebastien Valeyre delivers a surprise to the CTA world: a single exponential moving average (EMA) can match — or even beat — the performance of elaborate, multi-indicator trend-following systems.

This conclusion comes from an empirical validation of a 2014 theoretical model by Grebenkov & Serror, which predicted the optimal Sharpe ratio for an EMA-based trend strategy given market autocorrelation and trend strength. Unlike the industry’s love affair with blending MACDs, crossovers, momentum mixes, and Bollinger Bands, the data suggest that simplicity wins.

The Theory: One Scale to Rule Them All

Grebenkov & Serror’s model treats asset returns as having two components:

  1. A random, noise-like part.
  2. A small, autocorrelated bias (the “trend”) modeled as an AR(1) process with a single mean-reversion time scale.

From this, they derived a formula linking the EMA smoothing parameter (η), market autocorrelation (λ), and trend strength (β₀) to the theoretical Sharpe ratio. Crucially:

  • The optimal EMA is slightly faster than the market’s own autocorrelation decay.
  • Positions should depend linearly on the signal — aligning with Markowitz and Agnostic Risk Parity (ARP) frameworks.

The Test: Theory Meets 30+ Years of Markets

Valeyre put the model to the test with:

  • 70 futures markets (commodities, FX, equity indices, bonds).
  • Daily data from 1990–2023.
  • ARP portfolio construction: rotationally invariant, correlation-matrix adjusted.

Signals tested:

  • Single EMA (various lengths).
  • MACD-style three-scale EMA blends.
  • Bollinger Band mixtures (to mimic EMA shapes).

The goal: compare empirical Sharpe curves to Grebenkov’s theoretical prediction.

The Results: A Beautiful Fit

  • The empirical Sharpe curve matched the 2014 theory almost perfectly.
  • Optimal EMA length ≈ 112 days (η ≈ 1/112), Sharpe ≈ 1.24.
  • Multi-scale MACD variants showed no meaningful advantage: Sharpe changes were within statistical noise, and correlations with the EMA strategy exceeded 0.95.
  • Even complex Bollinger Band mixes could replicate the EMA almost exactly.

Key takeaway: a single-time-scale trend model describes reality well enough that adding more scales doesn’t improve performance.

Why This Matters for CTAs

Most CTA trend-following systems layer multiple indicators to “capture different horizons” and appear robust. This study suggests:

  • Much of that complexity is cosmetic — and risks cherry-picking.
  • In a diversified, volatility-targeted portfolio, a single EMA is sufficient.
  • The optimal horizon is stable across assets, and performance is flat near the optimum (100–150 days), making parameter risk low.

The Outliers: When Simplicity Might Break

The only notable theoretical challenge comes from Schmidhuber (2021), who finds that extreme trends may require nonlinear adjustments (e.g., subtracting a cubic term to dampen overextended moves). Valeyre tested this tweak — it didn’t improve Sharpe in the ARP framework.

For now, Grebenkov’s one-scale model holds firm.

Final Thoughts

For quants, this is liberating: you can spend less time on exotic indicator alchemy and more on robust portfolio construction and execution.

For investors, it’s a reminder: complexity is not the same as sophistication.

Sometimes, the cleanest line through the noise is the best trade in town.

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