Skewed target range strategy for multiperiod portfolio optimization using a two-stage least squares Monte Carlo method

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 return, 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 multi-period portfolio optimization problem with transaction costs, and develop a two-stage regression approach that improves the classical least squares Monte Carlo algorithm when dealing with difficult payoffs such as highly concave, abruptly changing or discontinuous functions. Our numerical results show substantial improvements over the classical least squares Monte Carlo 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. Compared to the CRRA utility approach, the STRS achieves a similar mean-variance efficient frontier while delivering a better downside risk-return trade-off.

Rule-based strategies for dynamic life cycle investment

“…The cumulative target strategy that we consider here has similarities with the strategies studied in [20] and [11]: risk is reduced once wealth exceeds a pre-defined wealth target. Contrary to [20] and [11], however, our investor saves for retirement and we relate the wealth target to the price of a bond with payoff equal to the desired pension.…”

“…The wealth target then allows the investor to identify a surplus: wealth up to the target may be invested in stocks, any remainder is invested in the risk-free rate. Zhang et al [20] solved a similar problem, although utility-based, and combined dynamic programming with the least squares Monte Carlo method. Upper and lower bounds for the wealth were prescribed in that paper, showing that upward potential comes with downside risk.…”

“…In addition to mean-variance that balances the mean and variance of returns, they studied a problem with a fixed wealth target. To reduce risk, both [11] and [20] proposed to invest excess wealth in a risk-free asset.…”

A Comprehensive Methodology for Investment Project Assessment Based on Monte Carlo Simulation

“…Optimization in investment decision-making is the subject of other research papers. We selected the following: authors of [18] who proposed an investment strategy for portfolio optimization problems that maximized the expected portfolio value bounded within a targeted range. Research in [19] surveyed the application of Monte Carlo sampling-based methods for stochastic optimization problems.…”