Optimizing Sparse Mean-Reverting Portfolio

TL;DR

This paper develops an optimization method for constructing sparse mean-reverting portfolios with the fastest mean reversion, demonstrating improved trading performance over non-sparse portfolios after accounting for transaction costs.

Contribution

It introduces a semidefinite programming approach to find optimal sparse portfolios with enhanced mean reversion properties for trading strategies.

Findings

Sparse portfolios outperform non-sparse ones after transaction costs.

The SDP formulation effectively incorporates sparsity and variance constraints.

Optimal weights lead to faster mean reversion in constructed portfolios.

Abstract

Mean-reverting behavior of individuals assets is widely known in financial markets. In fact, we can construct a portfolio that has mean-reverting behavior and use it in trading strategies to extract profits. In this paper, we show that we are able to find the optimal weights of stocks to construct portfolio that has the fastest mean-reverting behavior. We further add minimum variance and sparsity constraints to the optimization problem and transform into Semidefinite Programming (SDP) problem to find the optimal weights. Using the optimal weights, we empirically compare the performance of contrarian strategies between non-sparse mean-reverting portfolio and sparse mean-reverting portfolio to argue that the latter provides higher returns when we take into account of transaction costs.