Dynamic Portfolio Optimization with Liquidity Cost and Market Impact: A Simulation-and-Regression Approach

Accepted by Quantitative Finance

27 Pages Posted: 1 Dec 2015 Last revised: 21 Sep 2018

See all articles by Rongju Zhang

Rongju Zhang

Commonwealth Scientific and Industrial Research Organization (CSIRO); Monash University - Monash Centre for Quantitative Finance and Investment Strategies

Nicolas Langrené

Government of the Commonwealth of Australia - CSIRO (Commonwealth Scientific and Industrial Research Organisation)

Yu Tian

Monash University

Zili Zhu

Government of the Commonwealth of Australia - CSIRO (Commonwealth Scientific and Industrial Research Organisation)

Fima Klebaner

Monash University - School of Mathematical Sciences

Kais Hamza

Monash University

Date Written: September 5, 2018

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

JEL Classification: G11, C61, C15

Suggested Citation

Zhang, Rongju and Langrené, Nicolas and Tian, Yu and Zhu, Zili and Klebaner, Fima and Hamza, Kais, Dynamic Portfolio Optimization with Liquidity Cost and Market Impact: A Simulation-and-Regression Approach (September 5, 2018). Accepted by Quantitative Finance, Available at SSRN: https://ssrn.com/abstract=2696968 or http://dx.doi.org/10.2139/ssrn.2696968

Rongju Zhang (Contact Author)

Commonwealth Scientific and Industrial Research Organization (CSIRO) ( email )

Door 34, Goods Shed, Village Street
Docklands, VIC 3008
Australia
452204105 (Phone)

Monash University - Monash Centre for Quantitative Finance and Investment Strategies ( email )

9 Rainforest Walk
Clayton Campus
Monash University, Victoria 3800
Australia

Nicolas Langrené

Government of the Commonwealth of Australia - CSIRO (Commonwealth Scientific and Industrial Research Organisation) ( email )

Melbourne
Australia

Yu Tian

Monash University ( email )

Melbourne, Victoria VIC 3800
Australia

Zili Zhu

Government of the Commonwealth of Australia - CSIRO (Commonwealth Scientific and Industrial Research Organisation) ( email )

Gate 5 Normanby Road
Clayton
Melbourne, Australian Capital Territory 3168
Australia
61 3 95458003 (Phone)
61 3 9545 8080 (Fax)

Fima Klebaner

Monash University - School of Mathematical Sciences ( email )

Clayton Campus
Victoria, 3800
Australia

Kais Hamza

Monash University ( email )

23 Innovation Walk
Wellington Road
Clayton, Victoria 3800
Australia

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
193
Abstract Views
1,252
rank
180,254
PlumX Metrics