Optimal Liquidation Strategies Regularize Portfolio Selection

TL;DR

This paper derives optimal liquidation strategies considering market impact, showing how impact regularizes portfolio optimization under Expected Shortfall and stabilizes large portfolio solutions.

Contribution

It introduces a regularized optimization framework for portfolio selection with market impact, addressing instability issues in Expected Shortfall-based methods.

Findings

Market impact leads to a natural regularization of portfolio optimization.

Optimal liquidation strategies exhibit predictable behavior in large portfolios.

Market impact stabilizes the Expected Shortfall optimization problem.

Abstract

We consider the problem of portfolio optimization in the presence of market impact, and derive optimal liquidation strategies. We discuss in detail the problem of finding the optimal portfolio under Expected Shortfall (ES) in the case of linear market impact. We show that, once market impact is taken into account, a regularized version of the usual optimization problem naturally emerges. We characterize the typical behavior of the optimal liquidation strategies, in the limit of large portfolio sizes, and show how the market impact removes the instability of ES in this context.