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

31 Pages Posted: 6 Jun 2019

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

CSIRO

Fima Klebaner

Monash University - School of Mathematical Sciences

Kais Hamza

Monash University

Date Written: May 30, 2019

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

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 (May 30, 2019). Journal of Computational Finance, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3395258

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

CSIRO ( email )

Black Mountain
Canberra
Australia

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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