Portfolio optimization under transaction costs, turnover constraints, and regulatory requirements using robust stochastic optimization and probabilistic guarantees

Abstract

This paper addresses the problem of portfolio optimization under realistic institutional-investor conditions, simultaneously accounting for transaction costs, turnover constraints and regulatory requirements in the presence of parameter uncertainty. We propose a multi-period robust stochastic optimization framework in which the objective is to maximize risk-adjusted terminal wealth using Conditional Value-at-Risk (CVaR) at the 95% level as a tail-risk measure. Uncertainty in expected returns is captured by an ellipsoidal uncertainty set, ensuring solutions that remain efficient under misspecification of input parameters. Regulatory constraints on asset concentration and liquidity are formulated as chance constraints and complemented by an explicit cap on portfolio turnover and a V-shaped specification of transaction costs. The model is empirically validated on a broad historical dataset of equity and bond returns over 2010–2023 and benchmarked against the classical single-period Markowitz mean–variance formulation and a standard (non-robust) multi-period stochastic model. The robust stochastic approach delivers the highest Sharpe ratio by substantially reducing volatility and almost tripling the reduction in transaction costs, while at the same time providing superior control of extreme losses (significantly lower 99% CVaR) and strict compliance with turnover and concentration limits. Additional stress tests confirm that the resulting portfolios are markedly less sensitive to systematic errors in expected returns and correlations, highlighting the practical relevance of the proposed framework for long-term asset management in a tightly regulated environment.