Dynamic portfolio optimization with liquidity cost and market impact: a simulation-and-regression approach

TL;DR

This paper introduces a simulation-and-regression method to optimize dynamic portfolio allocation considering transaction, liquidity costs, and market impacts, improving accuracy and robustness over classical methods.

Contribution

It extends the least squares Monte Carlo algorithm to include switching costs and multiple state variables, with a global iteration procedure for better allocation estimates.

Findings

Quantifies losses from ignoring liquidity effects.

Demonstrates protection of capital in illiquid markets.

Analyzes sensitivities of returns and allocations under different liquidity conditions.

Abstract

We present a simulation-and-regression method for solving dynamic portfolio allocation problems in the presence of general transaction costs, liquidity costs and market impacts. This method extends the classical least squares Monte Carlo algorithm to incorporate switching costs, corresponding to transaction costs and transient liquidity costs, as well as multiple endogenous state variables, namely the portfolio value and the asset prices subject to permanent market impacts. To do so, we improve the accuracy of the control randomization approach in the case of discrete controls, and propose a global iteration procedure to further improve the allocation estimates. We validate our numerical method by solving a realistic cash-and-stock portfolio with a power-law liquidity model. We quantify the certainty equivalent losses associated with ignoring liquidity effects, and illustrate how our dynamic allocation protects the investor's capital under illiquid market conditions. Lastly, we analyze, under different liquidity conditions, the sensitivities of certainty equivalent returns and optimal allocations with respect to trading volume, stock price volatility, initial investment amount, risk-aversion level and investment horizon.