Cost-aware Portfolios in a Large Universe of Assets

TL;DR

This paper introduces a novel high-dimensional portfolio rebalancing approach that incorporates transaction costs directly into mean-variance optimization, demonstrating improved performance through simulations and empirical data.

Contribution

It develops new portfolio models with nonconvex penalties that effectively integrate transaction costs in large asset universes, with proven theoretical properties.

Findings

Models outperform traditional methods in simulations

Inclusion of transaction costs improves portfolio performance

Empirical results on S&P 500 and Russell 2000 stocks validate the approach

Abstract

This paper considers the finite horizon portfolio rebalancing problem in terms of mean-variance optimization, where decisions are made based on current information on asset returns and transaction costs. The study's novelty is that the transaction costs are integrated within the optimization problem in a high-dimensional portfolio setting where the number of assets is larger than the sample size. We propose portfolio construction and rebalancing models with nonconvex penalty considering two types of transaction cost, the proportional transaction cost and the quadratic transaction cost. We establish the desired theoretical properties under mild regularity conditions. Monte Carlo simulations and empirical studies using S&P 500 and Russell 2000 stocks show the satisfactory performance of the proposed portfolio and highlight the importance of involving the transaction costs when rebalancing a portfolio.