چکیده:
This paper presents an optimal portfolio selection approach based on value at risk (VaR), conditional value at risk (CVaR), worst-case value at risk (WVaR) and partitioned value at risk (PVaR) measures as well as calculating these risk measures. Mathematical solution methods for solving these optimization problems are inadequate and very complex for a portfolio with high number of assets. For these reasons, a combination of particle swarm optimization (PSO) and genetic algorithm (GA) is used to determine optimized weights of assets. Stocks’ Optimized weight results show that proposed algorithm gives more accurate outcomes in comparison with GA algorithm. According to back-testing analysis, PVaR and WVaR overestimate risk value while VaR and CVaR give a rather accurate estimation. A set of companies in Tehran Stock Exchange are considered as a case study for empirical analysis.
خلاصه ماشینی:
"Optimal Portfolio Selection for Tehran Stock Exchange Using Conditional, Partitioned and Worst-case Value at Risk Measures Adabi, Bagher Mehrara, Mohsen and Mohammadi, Shapour 1 Received: 1/21/2015 Approved: 5/24/2015 Abstract This paper presents an optimal portfolio selection approach based on value at risk (VaR), conditional value at risk (CVaR), worst-case value at risk (WVaR) and partitioned value at risk (PVaR) measures as well as calculating these risk measures.
In fact, considering a given mean and variance-covariance of risky assets returns, they offered a new conservative risk measure with a pessimistic approximation of VaR named as worst-case value at risk (WVaR).
Empirical Results This study concentrates on finding optimum portfolio based on VaR, CVaR, WVaR and PVaR optimization approaches using GA and HGAPSO algorithms and calculation of these mentioned risk measures.
Back-testing As it is shown in pervious section, in addition to extraction of companies‟ optimized weights, four risk measures including VaR, CVaR, WVaR and PVaR are calculated for mentioned portfolio at 0.
Evaluation of computed risk measures of VaR family is based on the fact that the value of calculated back-testing statistics should be lower than standard distribution ones.
5. Conclusion Unlike the classic portfolio optimization problem in which variance is considered as a risk measure, this study employed optimization approaches based on VaR, CVaR, WVaR and PVaR to find optimized portfolio and calculate four mentioned risk measures.
"Portfolio value-at-risk optimization for asymmetrically distributed asset returns", European Journal of Operational Research, 221, 397–406."