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Directional entropy and tail uncertainty, with applications to financial hazard

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  • Roger Bowden

Abstract

“Mine is a long and sad tale”, said the Mouse, turning to Alice and sighing. “It is a long tail certainly,” said Alice, looking down with wonder at the Mouse's tail; “but why do you call it sad?” And she kept on puzzling about it while the mouse was speaking … Financial risk management metrics such as value at risk (VaR) can be illuminated by means of a regime-specific concept of directional entropy. This enables a change of measure via a rescaling function to an equivalent logistic distribution, one that has the same total and directional entropies at the chosen critical point. VaR rescaling adjusts the critical probability to capture the long tail entropy. The scaling function can be used as a comparative metric for tail length, or equivalent conditional value at risk, even where moments do not exist. Directional entropy can also be used to identify regions of maximal exposure to new information, which can actually increase entropy rather than collapse it.

Suggested Citation

  • Roger Bowden, 2010. "Directional entropy and tail uncertainty, with applications to financial hazard," Quantitative Finance, Taylor & Francis Journals, vol. 11(3), pages 437-446.
  • Handle: RePEc:taf:quantf:v:11:y:2010:i:3:p:437-446
    DOI: 10.1080/14697681003685548
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    References listed on IDEAS

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    1. Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
    2. Bertsimas, Dimitris & Lauprete, Geoffrey J. & Samarov, Alexander, 2004. "Shortfall as a risk measure: properties, optimization and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1353-1381, April.
    3. Roger Bowden, 2006. "The generalized value at risk admissible set: constraint consistency and portfolio outcomes," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 159-171.
    4. O. Scaillet, 2004. "Nonparametric Estimation and Sensitivity Analysis of Expected Shortfall," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 115-129, January.
    5. Roger J. Bowden, 2005. "Ordered Mean Difference Benchmarking, Utility Generators, and Capital Market Equilibrium," The Journal of Business, University of Chicago Press, vol. 78(2), pages 441-468, March.
    6. Ruhnka, John C. & Young, John E., 1991. "Some hypotheses about risk in venture capital investing," Journal of Business Venturing, Elsevier, vol. 6(2), pages 115-133, March.
    7. Alexander, Gordon J. & Baptista, Alexandre M., 2006. "Does the Basle Capital Accord reduce bank fragility? An assessment of the value-at-risk approach," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1631-1660, October.
    8. Jeremy Berkowitz & James O'Brien, 2002. "How Accurate Are Value‐at‐Risk Models at Commercial Banks?," Journal of Finance, American Finance Association, vol. 57(3), pages 1093-1111, June.
    9. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2002. "Portfolio Value‐at‐Risk with Heavy‐Tailed Risk Factors," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 239-269, July.
    10. Chiampou, Gregory F. & Kallett, Joel J., 1989. "Risk/return profile of venture capital," Journal of Business Venturing, Elsevier, vol. 4(1), pages 1-10, January.
    11. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    12. 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.
    13. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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