A copula-based scenario tree generation algorithm for multiperiod portfolio selection problems
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A copula-based scenario tree generation algorithm for multiperiod portfolio selection problems Zhe Yan1 · Zhiping Chen1
· Giorgio Consigli2 · Jia Liu1 · Ming Jin1
© Springer Science+Business Media, LLC, part of Springer Nature 2019
Abstract Global financial investors have been confronted in recent years with an increasing frequency of market shocks and returns’ outliers, until the unprecedented surge of financial risk observed in 2008. From a statistical viewpoint, those market dynamics have shown not only asymmetric returns and fat tails but also a time-varying tail dependence, stimulating the formulation of portfolio selection models based on such assumptions. The concept of tail dependence on upper or lower tails, roughly speaking, focuses on the risk that tail events may occur jointly in different markets. This notion can be given a rigorous probabilistic definition, and it turns out that a distinction between upper and lower tails is relevant in portfolio management. In this paper, relying on a discrete modeling framework, we present a scenario generation algorithm able to capture this time-varying asymmetric tail dependence, and evaluate resulting optimal investment policies based on 4-stages 1-month planning horizons. The scenario tree aims at approximating a stochastic process combining an ARMA-GARCH model and a dynamic Student-t-Clayton copula. From a methodological viewpoint, scenario trees are generated from this model by stage-wisely sampling and clustering and to improve tail fitting with original data, the scenarios’ nodal probabilities are calibrated on the returns’ lower tails for a set of equity indices. The resulting scenario trees are then applied to solve a multiperiod
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Zhiping Chen [email protected] Zhe Yan [email protected] Giorgio Consigli [email protected] Jia Liu [email protected] Ming Jin [email protected]
1
Department of Computing Science, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, Shaanxi, People’s Republic of China
2
Department of Management, Economics and Quantitative Methods, University of Bergamo, via dei Caniana, 2, 24127 Bergamo, Italy
123
Annals of Operations Research
portfolio selection problem. We present a set of empirical results to validate the adopted statistical approach and the optimal portfolio strategies able to capture asymmetric tail returns. Keywords Copula · Scenario tree generation · Tail of the distribution · Portfolio selection
1 Introduction We consider a multiperiod portfolio selection problem for a global equity investor based on a complex underlying return model with a stochastic volatility process and a dynamic copula function to capture markets’ co-movements. The problem is formulated as a discrete multistage stochastic program (MSP) (Birge and Louveaux 2011; Pflug and Pichler 2014; Shapiro et al. 2009) with recourse over a short planning horizon of just 1 month with weekly rebalancing. From a methodological viewpoint, we first consider the appropriateness of a copula-based return mode
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