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

Abstract

We present a simulation-and-regression method for solving dynamic portfolio optimization problems in the presence of general transaction costs, liquidity costs and market impact. 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 impact. To handle endogenous state variables, we adapt a control randomization approach to portfolio optimization problems and further improve the numerical accuracy of this technique for the case of discrete controls. We validate our modified numerical method by solving a realistic cash-and-stock portfolio with a power-law liquidity model. We identify the certainty equivalent losses associated with ignoring liquidity effects, and illustrate how our dynamic optimization method 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.

Keywords:

• Dynamic portfolio optimization
• Multi-period asset allocation
• Transaction cost
• Liquidity cost
• Permanent market impact
• Least squares Monte Carlo

MSC Classification:

• 91G10
• 93E20
• 91B24
• 65C05
• 91G60
• 91B06
• 90C39
• 93E24

Acknowledgments

The authors gratefully thank Wen Chen for her helpful remarks. The authors are also grateful to the two anonymous referees for their insightful comments and suggestions which have helped to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 These data are obtained from Yahoo Finance.