Folio Lab/Documentation

EWMA Mean-Variance

A RiskMetrics-style mean-variance optimisation that uses exponentially weighted moving averages of returns and covariances. Recent observations weigh more, so the portfolio adapts faster to regime changes.

Overview

Classical MVO uses equally weighted historical means and covariances, which implicitly assumes return generation is stationary. EWMA-MVO replaces those moments with their exponentially-weighted counterparts, following J.P. Morgan's RiskMetrics methodology. Recent observations dominate the estimate, so the optimiser reacts more quickly to changes in volatility and correlation regimes.

With the EWMA moments in hand, the portfolio is found by maximising the Sharpe ratio on the resulting efficient frontier — long-only with box bounds .

Mathematical Formulation

With decay parameter , the exponential weights are:

Folio Lab uses , the RiskMetrics default. The EWMA mean and covariance are:

Both are then annualised. The portfolio is the max-Sharpe point on the efficient frontier built from these moments:

Advantages & Limitations

Advantages

  • Adaptive: Responds quickly to changes in volatility regimes.
  • Industry standard: Same machinery as RiskMetrics.
  • Tunable horizon: Decay parameter encodes a memory length.
  • Compatible with frontier methods: Drop-in for any MVO objective.

Limitations

  • Inherits MVO sensitivity: Still hostage to noisy mean estimates.
  • Decay choice: Wrong can over- or under-react.
  • Higher turnover: Faster reaction means more rebalancing.
  • No structural change handling: Cannot detect regime breaks; only weights toward recent.

References

  • J.P. Morgan / Reuters (1996). RiskMetrics — Technical Document, 4th Edition.
  • Tsay, R. S. (2010). Analysis of Financial Time Series (3rd ed.). Wiley.
  • pypfopt documentation — EfficientFrontier.max_sharpe.