Folio Lab/Documentation

Maximum Decorrelation

The portfolio that minimises the quadratic form of the correlation matrix — choosing weights so that the average pairwise correlation, weighted by the portfolio, is as small as possible.

Overview

Maximum Decorrelation is the minimum-variance portfolio computed on the correlation matrix instead of the covariance matrix. It allocates weight to assets that are minimally correlated with the rest of the portfolio, ignoring their absolute volatility scales. When all assets have identical volatility it coincides with min-vol; when volatilities differ markedly, it differs.

This method is useful when you want to isolate the diversification effect from volatility: it ranks pairs purely by correlation redundancy.

Mathematical Formulation

Let be the asset correlation matrix. The Maximum Decorrelation portfolio solves:

Folio Lab projects the correlation matrix onto the cone of positive semi-definite matrices before solving (clipping any negative eigenvalues to zero) and uses cvxpy with CLARABEL / OSQP / SCS as solver fallbacks.

Advantages & Limitations

Advantages

  • Pure diversification: Isolates the correlation effect.
  • Volatility-agnostic: Doesn't favour low-vol assets the way min-vol does.
  • Convex QP: Tractable and reliable.
  • No return estimates: Robust to forecast error.

Limitations

  • Ignores volatility: May load on highly volatile but uncorrelated names.
  • Estimation noise: Sample correlations are noisy in small samples.
  • No return view: Not designed for return-seeking strategies.
  • Sensitive to outliers: Pearson correlation is not robust to tail events.

References

  • Christoffersen, P., Errunza, V., Jacobs, K., & Langlois, H. (2012). "Is the potential for international diversification disappearing?" Review of Financial Studies, 25(12), 3711-3751.
  • Christofides, T. C., & Vrontos, I. D. (2010). "On the optimal portfolio for the exponential utility maximization." European Journal of Operational Research, 203(2), 461-470.
  • Choueifaty, Y., & Coignard, Y. (2008). "Toward Maximum Diversification." The Journal of Portfolio Management, 35(1), 40-51.