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Analytical Portfolio Value-at-Risk

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  • Kaplanski, Guy

Abstract

The paper develops analytical tools used to calculate the VaR of a portfolio composed of generally distributed assets. Accordingly, the VaR of a portfolio is analytically constructed from the conditional returns of the individual assets. This analytical VaR can then be used to construct optimal portfolios of generally distributed assets for the case in which the target function and/or constraints are expressed in terms of VaR. The proposed method is applicable in a wide range of practical problems such as utility maximization under a VaR constraint. The article demonstrates this method by developing a minimal VaR rule that identifies the proportions that minimize the portfolio VaR. This rule is used to compare the minimal VaR portfolio with the minimal standard deviation portfolio in the case of the lognormal distribution. This example illustrates the importance of downside risk in optimal asset allocation even under modest deviations from the normal distribution such as in the case of the lognormal distribution.

Suggested Citation

  • Kaplanski, Guy, 2005. "Analytical Portfolio Value-at-Risk," MPRA Paper 80216, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:80216
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    References listed on IDEAS

    as
    1. Yiu, K. F. C., 2004. "Optimal portfolios under a value-at-risk constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1317-1334, April.
    2. Alexander, Gordon J. & Baptista, Alexandre M., 2002. "Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1159-1193, July.
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    5. Kaplanski, Guy & Kroll, Yoram, 2002. "VaR Risk Measures versus Traditional Risk Measures: an Analysis and Survey," MPRA Paper 80070, University Library of Munich, Germany.
    6. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
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    More about this item

    Keywords

    Value-at-Risk; Risk measurement; Portfolio Optimization; Downsize Risk;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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