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Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model

Author

Listed:
  • Kim, Young Shin
  • Giacometti, Rosella
  • Rachev, Svetlozar T.
  • Fabozzi, Frank J.
  • Mignacca, Domenico

Abstract

In this paper, we propose a multivariate market model with returns assumed to follow a multivariate normal tempered stable distribution. This distribution, defined by a mixture of the multivariate normal distribution and the tempered stable subordinator, is consistent with two stylized facts that have been observed for asset distributions: fat-tails and an asymmetric dependence structure. Assuming infinitely divisible distributions, we derive closed-form solutions for two important measures used by portfolio managers in portfolio construction: the marginal VaR and the marginal AVaR. We illustrate the proposed model using stocks comprising the Dow Jones Industrial Average, first statistically validating the model based on goodness-of-fit tests and then demonstrating how the marginal VaR and marginal AVaR can be used for portfolio optimization using the model. Based on the empirical evidence presented in this paper, our framework offers more realistic portfolio risk measures and a more tractable method for portfolio optimization.

Suggested Citation

  • Kim, Young Shin & Giacometti, Rosella & Rachev, Svetlozar T. & Fabozzi, Frank J. & Mignacca, Domenico, 2012. "Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model," Working Paper Series in Economics 44, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  • Handle: RePEc:zbw:kitwps:44
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    File URL: https://www.econstor.eu/bitstream/10419/62001/1/721568815.pdf
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    References listed on IDEAS

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    1. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.
    2. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
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    Citations

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    Cited by:

    1. Babaei, Sadra & Sepehri, Mohammad Mehdi & Babaei, Edris, 2015. "Multi-objective portfolio optimization considering the dependence structure of asset returns," European Journal of Operational Research, Elsevier, vol. 244(2), pages 525-539.
    2. repec:spr:annopr:v:253:y:2017:i:1:d:10.1007_s10479-016-2309-y is not listed on IDEAS
    3. repec:eee:apmaco:v:282:y:2016:i:c:p:187-203 is not listed on IDEAS
    4. Kim, Young Shin & Lee, Jaesung & Mittnik, Stefan & Park, Jiho, 2015. "Quanto option pricing in the presence of fat tails and asymmetric dependence," Journal of Econometrics, Elsevier, vol. 187(2), pages 512-520.
    5. Anand, Abhinav & Li, Tiantian & Kurosaki, Tetsuo & Kim, Young Shin, 2016. "Foster–Hart optimal portfolios," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 117-130.
    6. Michele Leonardo Bianchi & Gian Luca Tassinari, 2018. "Forward-looking portfolio selection with multivariate non-Gaussian models and the Esscher transform," Papers 1805.05584, arXiv.org, revised May 2018.
    7. Shao, Barret Pengyuan & Rachev, Svetlozar T. & Mu, Yu, 2015. "Applied mean-ETL optimization in using earnings forecasts," International Journal of Forecasting, Elsevier, vol. 31(2), pages 561-567.
    8. Michele Leonardo Bianchi, 2014. "Are the log-returns of Italian open-end mutual funds normally distributed? A risk assessment perspective," Temi di discussione (Economic working papers) 957, Bank of Italy, Economic Research and International Relations Area.
    9. Hassan A. Fallahgoul & Young S. Kim, 2014. "Elliptical Tempered Stable Distribution and Fractional Calculus," Papers 1408.3387, arXiv.org, revised Aug 2014.
    10. Michele Leonardo Bianchi & Gian Luca Tassinari & Frank J. Fabozzi, 2016. "Riding With The Four Horsemen And The Multivariate Normal Tempered Stable Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-28, June.

    More about this item

    Keywords

    portfolio risk; portfolio optimization; portfolio budgeting; marginal contribution; fat-tailed distribution; multivariate normal tempered stable distribution;

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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