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Risk management and dynamic portfolio selection with stable Paretian distributions

  • Ortobelli, Sergio
  • Rachev, Svetlozar T.
  • Fabozzi, Frank J.

Abstract This paper assesses stable Paretian models in portfolio theory and risk management. We describe an investor's optimal choices under the assumption of non-Gaussian distributed equity returns in the domain of attraction of a stable law. In particular, we examine dynamic portfolio strategies with and without transaction costs in order to compare the forecasting power of discrete-time optimal allocations obtained under different stable Paretian distributional assumptions. We also consider a conditional extension of the stable Paretian approach and compare the model with others that consider different distributional assumptions. Finally, we empirically evaluate the forecasting power of the model for predicting the value at risk of a heavy-tailed return series.

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Article provided by Elsevier in its journal Journal of Empirical Finance.

Volume (Year): 17 (2010)
Issue (Month): 2 (March)
Pages: 195-211

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Handle: RePEc:eee:empfin:v:17:y:2010:i:2:p:195-211
Contact details of provider: Web page: http://www.elsevier.com/locate/jempfin

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  1. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  2. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  3. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  4. Tokat, Yesim & Rachev, Svetlozar T. & Schwartz, Eduardo S., 2003. "The stable non-Gaussian asset allocation: a comparison with the classical Gaussian approach," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 937-969, April.
  5. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420.
  6. Benoit Mandelbrot, 1967. "The Variation of Some Other Speculative Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 393.
  7. Sergio Ortobelli & Svetlozar T. Rachev & Stoyan Stoyanov & Frank J. Fabozzi & Almira Biglova, 2005. "The Proper Use Of Risk Measures In Portfolio Theory," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(08), pages 1107-1133.
  8. Ross, Stephen A., 1978. "Mutual fund separation in financial theory--The separating distributions," Journal of Economic Theory, Elsevier, vol. 17(2), pages 254-286, April.
  9. Duan Li & Wan-Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406.
  10. Eugene F. Fama, 1965. "Portfolio Analysis in a Stable Paretian Market," Management Science, INFORMS, vol. 11(3), pages 404-419, January.
  11. Yusif Simaan, 1993. "Portfolio Selection and Asset Pricing---Three-Parameter Framework," Management Science, INFORMS, vol. 39(5), pages 568-577, May.
  12. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71, pages 421.
  13. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
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