Cost-aware Portfolios in a Large Universe of Assets

2024-12-16

AI Summary

This paper addresses the finite-horizon mean-variance portfolio rebalancing problem in high-dimensional settings (number of assets exceeding sample size), explicitly incorporating both proportional and quadratic transaction costs—both nonconvex—within a unified framework for the first time. We propose a solution methodology integrating nonconvex regularized optimization with high-dimensional statistical inference, and establish theoretical guarantees on algorithmic convergence and statistical consistency of parameter estimation. Monte Carlo simulations and empirical studies on S&P 500 and Russell 2000 datasets demonstrate that our approach significantly improves Sharpe ratios and net returns, confirming the critical performance gains from explicit modeling of nonlinear transaction costs. The core contribution lies in overcoming the small-sample, high-dimensionality barrier to enable joint modeling and provably optimal optimization of realistic, nonconvex transaction cost structures.

Technology Category

• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: The sharing economy
• Security and Privacy: Large-scale security measurements

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.

Problem

• Optimizing portfolios with transaction costs in high-dimensional settings
• Addressing mean-variance rebalancing when assets exceed sample size
• Incorporating proportional and quadratic transaction costs in portfolio construction

Innovation

• Integrates transaction costs in high-dimensional portfolios
• Uses nonconvex penalty for portfolio construction
• Applies proportional and quadratic cost models