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Asymptotic behavior of the estimated weights and of the estimated performance measures of the minimum VaR and the minimum CVaR optimal portfolios for dependent data

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  • Taras Bodnar
  • Wolfgang Schmid
  • Taras Zabolotskyy

Abstract

In this paper we derive the asymptotic distributions of the estimated weights and of estimated performance measures of the minimum value-at-risk portfolio and of the minimum conditional value-at-risk portfolio assuming that the asset returns follow a strictly stationary process. It is proved that the estimated weights as well as the estimated performance measures are asymptotically multivariate normally distributed. We also present an asymptotic test for the weights and a joint test for the characteristics of both portfolios. Moreover, the asymptotic densities of the estimated performance measures are compared with the corresponding exact densities. It is shown that the asymptotic approximation performs well even for the moderate sample size. Copyright Springer-Verlag Berlin Heidelberg 2013

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  • Taras Bodnar & Wolfgang Schmid & Taras Zabolotskyy, 2013. "Asymptotic behavior of the estimated weights and of the estimated performance measures of the minimum VaR and the minimum CVaR optimal portfolios for dependent data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(8), pages 1105-1134, November.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:8:p:1105-1134
    DOI: 10.1007/s00184-013-0432-1
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    2. Zhongde Luo, 2020. "Nonparametric kernel estimation of CVaR under $$\alpha $$α-mixing sequences," Statistical Papers, Springer, vol. 61(2), pages 615-643, April.
    3. Taras Bodnar & Taras Zabolotskyy, 2017. "How risky is the optimal portfolio which maximizes the Sharpe ratio?," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(1), pages 1-28, January.

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