Mean-variance portfolio selection with estimation risk and transaction costs

There are many approaches that have been proposed to improve the empirical performance of the Markowitz mean-variance model. Designed to mitigate the impact of parameter uncertainty and estimation error, these approaches have delivered substantially better out-of-sample performance. In this paper, we consider the portfolio optimization problem for a single-period investor facing different types of transaction costs. By reformulating the rebalancing problem into a linear regression framework, we show analytically that considering different transaction costs is equivalent to imposing additional constraints on the portfolio weights, thus providing desired properties such as sparsity and stability in the trading strategy.