A Robust Perspective on Transaction Costs in Portfolio Optimization

We show how to use a transaction cost term in a portfolio optimization problem to compute portfolios that are both efficient in terms of transaction costs and robust to estimation error. Theoretically, we prove that the portfolio problem with transaction costs is equivalent to three different problems designed to alleviate the impact of estimation error: a robust portfolio optimization problem, a robust regression problem, and a Bayesian portfolio problem. Motivated by these results, we propose a data-driven approach to portfolio optimization that calibrates the transaction cost term taking into account both transaction costs and esti-mation error. Our empirical results demonstrate that the data-driven portfolios perform favorably because they strike an optimal trade-off between rebalancing the portfolio to capture the information in recent his-torical return data, and avoiding the large transaction costs and impact of estimation error associated with excessive trading. Key words: transaction costs; estimation error; robust optimization; robust regression; Bayesian portfolios; data-driven portfolios. 1