Robust multi-period portfolio selection based on downside risk with asymmetrically distributed uncertainty set

Abstract

Motivated by the asymmetrical attitudes of investors towards downside losses and upside gains, this paper proposes a robust multi-period portfolio selection model based on downside risk with asymmetrically distributed uncertainty set, in which the downside losses of a portfolio are controlled by the lower partial moment (LPM). A computationally tractable approximation approach based on second-order cone optimization is used for solving the proposed model. We show in theory that the optimal solution of the robust model can generate a given probability guarantee for individual and joint stochastic constraints. The effect of the asymmetrically distributed uncertainty set on performance of the optimal solution is analyzed by the usual comparative static method. Comprehensive numerical comparisons with real market data are reported and indicate that the proposed model can obtain the smaller standard deviation and turnover ratios which reduce the Sharpe ratios of optimal portfolio, compared with some well-known models in the literature.

Robust Portfolio Selection Problems: A Comprehensive Review

“…The downside of losses also can be controlled by the lower partial moment (LPM) in the objective function, which is more perceivable by investors than loss functions. Ling et al (2019) proposed a multi-period PSP based on a downside risk (lower partial moment) with an asymmetrically distributed uncertainty set. The objective function includes the terminal wealth of the portfolio and LPM.…”

“…The inherent uncertainty about future asset returns, the abundance of public data available and the risk-averse nature of most investors make robust optimization an appealing approach in this area. As shown in this review paper, a wide range of robust PSP variants was studied, from a "plain vanilla" single-period, mean-variance PSP with a simple box uncertainty set (e.g., Tütüncü & Koenig (2004)) to formulations that consider advanced risk measures (e.g., , Huang et al (2010)), adaptive uncertainty sets (e.g., Yu (2016)), reallife investment strategies (e.g., Pflug et al (2012), Paç & Pınar (2018)) and dynamic portfolio balancing (e.g., Ling et al (2019), Cong & Oosterlee (2017)). This variety of modeling assumptions and approaches and the overlaps among them make it difficult to develop a unifying framework for robust PSPs, yet we adopted a multi-dimensional classification scheme that depends on the risk measure to be optimized, the type of uncertain parameters, the approach used to capture uncertainty and the the planning horizon (i.e., single-vs. multi-period).…”

Robust International Portfolio Optimization with Worst-Case Mean-LPM

“…Even if they acquire the actual distributions of future security returns, the computation of LPM is also a difficult task. To deal with these problems, some researchers employ robust optimization techniques to portfolio selection models using LPM as the risk measure [10][11][12][13][14]. eir researches focus on the portfolio selection problems in one country and do not consider the international portfolio selection problems with the risk of exchange rates.…”

Distributionally robust multi-period portfolio selection subject to bankruptcy constraints

“…Variance as a risk measure has been widely criticized by practitioners as it equally weights desirable positive returns and undesirable negative ones [15]. To circumvent this drawback, the semi-variance risk measure which only measures the variability of returns below the mean is introduced to replace variance [12]. Another typical kind of risk measures are Value-at-Risk (VaR) and Conditional-Value-at-Risk (CVaR).…”

“…For the multi-period optimization problem, it has been shown that the problem can still be solved analytically in [14]. In [12], a robust multi-period portfolio selection under downside risk LPM with asymmetrically distributed uncertainty set is studied. A computationally tractable approximation approach is proposed to solve the original problem.…”