Skewed Target Range Strategy for Multiperiod Portfolio Optimization Using a Two-Stage Least Squares Monte Carlo Method

Journal of Computational Finance, Forthcoming

25 Pages Posted: 22 Aug 2016 Last revised: 14 Jun 2019

See all articles by Rongju Zhang

Rongju Zhang

Commonwealth Scientific and Industrial Research Organization (CSIRO)

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 10, 2018

Abstract

In this paper, we propose a novel investment strategy for portfolio optimization problems. The proposed strategy maximizes the expected portfolio value bounded within a targeted range, composed of a conservative lower target representing a need for capital protection and a desired upper target representing an investment goal. This strategy favorably shapes the entire probability distribution of returns, as it simultaneously seeks a desired expected return, cuts off downside risk and implicitly caps volatility and higher moments. To illustrate the effectiveness of this investment strategy, we study a multiperiod portfolio optimization problem with transaction costs and develop a two-stage regression approach that improves the classical least squares Monte Carlo (LSMC) algorithm when dealing with difficult payoffs, such as highly concave, abruptly changing or discontinuous functions. Our numerical results show substantial improvements over the classical LSMC algorithm for both the constant relative risk-aversion (CRRA) utility approach and the proposed skewed target range strategy (STRS). Our numerical results illustrate the ability of the STRS to contain the portfolio value within the targeted range. When compared with the CRRA utility approach, the STRS achieves a similar mean–variance efficient frontier while delivering a better downside risk–return trade-off.

Keywords: target-based portfolio optimization, alternative performance measure, multiperiod portfolio optimization, least squares Monte Carlo, two-stage regression

JEL Classification: G11, D81, C63, C34

Suggested Citation

Zhang, Rongju and Langrené, Nicolas and Tian, Yu and Zhu, Zili and Klebaner, Fima and Hamza, Kais, Skewed Target Range Strategy for Multiperiod Portfolio Optimization Using a Two-Stage Least Squares Monte Carlo Method (September 10, 2018). Journal of Computational Finance, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2826520 or http://dx.doi.org/10.2139/ssrn.2826520

Rongju Zhang (Contact Author)

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

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

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

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