Sparse Mean-Reverting Portfolio Selection Methods

Summary

This code module outlines methods for constructing sparse portfolios intended to exhibit mean reversion. It includes Box–Tiao canonical decomposition, greedy support selection, semidefinite optimization under volatility constraints, and sparsity methods based on graphical LASSO and LASSO estimates of covariance or VAR(1) relationships. It also provides tools to calculate autocovariance matrices, fit a VAR(1), and estimate an Ornstein–Uhlenbeck mean-reversion coefficient and half-life for a weighted portfolio.

The methods frame portfolio selection as choosing asset weights and, in sparse approaches, limiting how many assets are used. The code description names objectives involving predictability, portmanteau statistics, and crossing statistics, but the supplied excerpt is incomplete and does not show every method’s assumptions or implementation. It presents no dataset, backtest, trading costs, or empirical comparison, so it cannot establish that selected portfolios will remain mean reverting or profitable. Estimated relationships can be sensitive to the sample, preprocessing, and optimization choices; results require validation and careful treatment of stability and execution risk.

Key ideas

• The module implements several approaches for selecting sparse portfolios with mean-reverting characteristics.
• Box–Tiao decomposition and greedy search use VAR and covariance estimates to derive portfolio weights.
• LASSO-based methods seek sparse covariance or VAR relationships among assets.
• Semidefinite formulations include objectives constrained by a minimum volatility level.
• The excerpt supplies methods but no empirical results or evidence of out-of-sample profitability.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.