Optimal Portfolio Selection with Regime-Switching Hamilton-Jacobi-Bellman (HJB) Equation and Maximum Value-at-Risk (MVaR) Constraint

Recently portfolio optimization has become widely popular in risk management, and the common practice is to use mean-variance or Value-at-Risk (VaR), despite the VaR being incoherent risk measure because of the lack of subadditivity. This has led to the emergence of the conditional value-at-risk (CVaR) approach, consequently, a gradual development of mean-CVaR portfolio optimization. To seek an optimal portfolio selection strategy and increase the robustness of the result, the paper studies the performance of portfolio optimization in Asian markets using a Monte-Carlo simulation tool, creates a variety of randomly selected portfolios that consists of Asian ADRs listed in NYSE from 2011 to 2016, and applies both optimization frameworks with different skewed fat-tailed distributions, including the Generalized Hyperbolic (GH) and skewed-T distribution. The main result shows that the Generalized Hyperbolic distribution produces the lowest risk under a given rate of return, while the skewed-T distribution creates a diversification allocation outcome similar to that of historical simulation.

Download Full-text

Simulation-Based Optimal Portfolio Selection Strategy—Evidence from Asian Markets

Applied Economics and Finance ◽

10.11114/aef.v5i4.3376 ◽

2018 ◽

Vol 5 (5) ◽

pp. 1

Author(s):

Longqing Li

Keyword(s):

At Risk ◽

Portfolio Optimization ◽

Portfolio Selection ◽

Value At Risk ◽

Optimal Portfolio ◽

Conditional Value At Risk ◽

Selection Strategy ◽

Optimal Portfolio Selection ◽

T Distribution ◽

Skewed T Distribution

Recently portfolio optimization has become widely popular in risk management, and the common practice is to use mean-variance or Value-at-Risk (VaR), despite the VaR being incoherent risk measure because of the lack of subadditivity. This has led to the emergence of the conditional value-at-risk (CVaR) approach, consequently, a gradual development of mean-CVaR portfolio optimization. To seek an optimal portfolio selection strategy and increase the robustness of the result, the paper studies the performance of portfolio optimization in Asian markets using a Monte-Carlo simulation tool, creates a variety of randomly selected portfolios that consists of Asian ADRs listed in NYSE from 2011 to 2016, and applies both optimization frameworks with different skewed fat-tailed distributions, including the Generalized Hyperbolic (GH) and skewed-T distribution. The main result shows that the Generalized Hyperbolic distribution produces the lowest risk under a given rate of return, while the skewed-T distribution creates a diversification allocation outcome similar to that of historical simulation.

Download Full-text

On the structure of multifactor optimal portfolio strategies

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2017013 ◽

2018 ◽

Vol 24 (3) ◽

pp. 1043-1058

Author(s):

Nikolai Dokuchaev

Keyword(s):

Mutual Funds ◽

Portfolio Selection ◽

Optimal Strategies ◽

Optimal Portfolio ◽

Performance Criteria ◽

Value Functions ◽

Portfolio Strategies ◽

Optimal Portfolio Selection ◽

Admissible Strategies ◽

Hamilton Jacobi Bellman

The paper studies problem of optimal portfolio selection. It is shown that, under some mild conditions, near optimal strategies for investors with different performance criteria can be constructed using a limited number of fixed processes (mutual funds), for a market with a larger number of available risky stocks. This implies dimension reduction for the optimal portfolio selection problem: all rational investors may achieve optimality using the same mutual funds plus a saving account. This result is obtained under mild restrictions for the utility functions without any assumptions on regularity of the value function. The proof is based on the method of dynamic programming applied indirectly to some convenient approximations of the original problem that ensure certain regularity of the value functions. To overcome technical difficulties, we use special time dependent and random constraints for admissible strategies such that the corresponding HJB (Hamilton–Jacobi–Bellman) equation admits “almost explicit” solutions generating near optimal admissible strategies featuring sufficient regularity and integrability.

Download Full-text

Optimal portfolios with maximum Value-at-Risk constraint under a hidden Markovian regime-switching model

Automatica ◽

10.1016/j.automatica.2016.07.032 ◽

2016 ◽

Vol 74 ◽

pp. 194-205 ◽

Cited By ~ 8

Author(s):

Dong-Mei Zhu ◽

Yue Xie ◽

Wai-Ki Ching ◽

Tak-Kuen Siu

Keyword(s):

At Risk ◽

Regime Switching ◽

Value At Risk ◽

Optimal Portfolios ◽

Regime Switching Model ◽

Switching Model ◽

Maximum Value ◽

Risk Constraint ◽

Markovian Regime Switching ◽

Markovian Regime

Download Full-text

Quantile-based optimal portfolio selection

Computational Management Science ◽

10.1007/s10287-021-00395-8 ◽

2021 ◽

Author(s):

Taras Bodnar ◽

Mathias Lindholm ◽

Erik Thorsén ◽

Joanna Tyrcha

Keyword(s):

Portfolio Selection ◽

Value At Risk ◽

Risk Measure ◽

Optimal Portfolio ◽

Conditional Value At Risk ◽

Closed Form Expression ◽

Selection Strategy ◽

Optimal Portfolio Selection ◽

Sufficient And Necessary Conditions ◽

Elliptically Contoured

AbstractIn this paper the concept of quantile-based optimal portfolio selection is introduced and a specific portfolio connected to it, the conditional value-of-return (CVoR) portfolio, is proposed. The CVoR is defined as the mean excess return or the conditional value-at-risk (CVaR) of the return distribution. The portfolio selection consists solely of quantile-based risk and return measures. Financial institutions that work in the context of Basel 4 use CVaR as a risk measure. In this regulatory framework sufficient and necessary conditions for optimality of the CVoR portfolio are provided under a general distributional assumption. Moreover, it is shown that the CVoR portfolio is mean-variance efficient when the returns are assumed to follow an elliptically contoured distribution. Under this assumption the closed-form expression for the weights and characteristics of the CVoR portfolio are obtained. Finally, the introduced methods are illustrated in an empirical study based on monthly data of returns on stocks included in the S&P index. It is shown that the new portfolio selection strategy outperforms several alternatives in terms of the final investor wealth.

Download Full-text