Selecting Sparse Mean-Reverting Portfolios with Statistical Proxies
Summary
This document describes methods for selecting long-short portfolios that aim to mean-revert while holding only a small subset of assets. Sparsity can reduce trading costs and make portfolio exposures easier to interpret than dense portfolios that include the full universe. The methods include screening assets with covariance selection or penalized regression, then using greedy search or semidefinite optimization to find sparse weights. Dense Box-Tiao portfolios and Ornstein-Uhlenbeck fitting are also presented as comparison tools.
Portfolio quality is assessed through proxies for mean-reversion strength. Under a VAR(1) assumption, Box-Tiao predictability is minimized through a generalized eigenvalue problem; lower predictability indicates a more noise-like, mean-reverting portfolio. The portmanteau statistic aggregates autocorrelations without requiring that model, at higher computational cost. A crossing statistic measures sign changes and is extended using autocovariances. These are selection criteria rather than guarantees of profitable trading: results depend on estimation choices, data, and assumptions, and the supplied text is incomplete before detailing all procedures.
Key ideas
- Sparse portfolios seek mean-reversion while limiting the number of assets traded.
- Box-Tiao selection minimizes forecastability under a VAR(1) model using a generalized eigenvalue formulation.
- Portmanteau statistics assess autocorrelation without a specific time-series model, but require more computation.
- Crossing frequency provides another mean-reversion proxy related to first-order autocorrelation.
- Ornstein-Uhlenbeck speed can compare selected portfolios, though it is not directly optimized as a function of weights.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.