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Value at Risk: A Comparative Analysis

  • Filip Iorgulescu

    (Faculty of Finance and Banking, Bucharest University of Economics)

study develops a comparative analysis concerning Value at Risk measure for a portfolio consisting of three stocks traded at Bucharest Stock Exchange. The analysis set out from 1-day, 1% VaR and has been extended in two directions: the volatility models and the distributions which are used when computing VaR. Thus, the historical volatility, the EWMA volatility model, GARCHtype models for the volatility of the stocks and of the portfolio and a dynamic conditional correlation (DCC) model were considered while VaR was computed using, apart from the standard normal distribution, different approaches for taking into account the non-normality of the returns (such as the Cornish-Fisher approximation, the modeling of the empirical distribution of the standardized returns and the Extreme Value Theory approach). The results indicate that using conditional volatility models and distributional tools that account for the non-normality of the returns leads to a better VaR-based risk management. For the considered portfolio VaR computed on the basis of a GARCH (1,1) model for the volatility of the portfolio returns where the standardized returns are modeled using the generalized hyperbolic distribution seems to be the best compromise between precision, capital coverage levels and the required amount of calculations. Moreover, the Expected Shortfall risk measure offers very good precision results in all approaches, but at the cost of rather high capital coverage levels.

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File URL: http://www.dofin.ase.ro/Working%20papers/Iorgulescu%20Filip/iorgulescu.filip.dissertation.pdf
File Function: First version, 2009
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Paper provided by Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB in its series Advances in Economic and Financial Research - DOFIN Working Paper Series with number 25.

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Date of creation: Jan 2009
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Handle: RePEc:cab:wpaefr:25
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  1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  2. Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH," NBER Working Papers 8554, National Bureau of Economic Research, Inc.
  3. Suleyman Basak & Alexander Shapiro, 1999. "Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-032, New York University, Leonard N. Stern School of Business-.
  4. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
  5. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
  6. R. F. Engle & A. J. Patton, 2001. "What good is a volatility model?," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 237-245.
  7. Engle, Robert F, 2000. "Dynamic Conditional Correlation - A Simple Class of Multivariate GARCH Models," University of California at San Diego, Economics Working Paper Series qt56j4143f, Department of Economics, UC San Diego.
  8. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
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