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Measuring downside risk — realised semivariance

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  • Ole E. Barndorff-Nielsen
  • Silja Kinnebrock
  • Neil Shephard

    ()
    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

We propose a new measure of risk, based entirely on downwards moves measured using high frequency data. Realised semivariances are shown to have important predictive qualities for future market volatility. The theory of these new measures is spelt out, drawing on some new results from probability theory.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-42.

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Length: 22
Date of creation: 02 Sep 2008
Date of revision:
Handle: RePEc:aah:create:2008-42

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Market frictions; Quadratic variation; Realised variance; Semimartingale; Semivariance;

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References

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  1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility," CREATES Research Papers, School of Economics and Management, University of Aarhus 2007-18, School of Economics and Management, University of Aarhus.
  2. Neil Shephard, 2004. "A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales," Economics Series Working Papers, University of Oxford, Department of Economics 2004-FE-21, University of Oxford, Department of Economics.
  3. Mao, James C T, 1970. "Survey of Capital Budgeting: Theory and Practice," Journal of Finance, American Finance Association, American Finance Association, vol. 25(2), pages 349-60, May.
  4. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, Econometric Society, vol. 76(6), pages 1481-1536, November.
  5. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
  6. Babsiri, Mohamed El & Zakoian, Jean-Michel, 2001. "Contemporaneous asymmetry in GARCH processes," Journal of Econometrics, Elsevier, Elsevier, vol. 101(2), pages 257-294, April.
  7. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Power and bipower variation with stochastic volatility and jumps," Economics Papers, Economics Group, Nuffield College, University of Oxford 2003-W17, Economics Group, Nuffield College, University of Oxford.
  8. Jacod, Jean & Li, Yingying & Mykland, Per A. & Podolskij, Mark & Vetter, Mathias, 2009. "Microstructure noise in the continuous case: The pre-averaging approach," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 119(7), pages 2249-2276, July.
  9. Barndorff-Nielsen, Ole E. & Graversen, Svend Erik & Jacod, Jean & Shephard, Neil, 2006. "Limit Theorems For Bipower Variation In Financial Econometrics," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 22(04), pages 677-719, August.
  10. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers, Economics Group, Nuffield College, University of Oxford 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
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  13. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometrics of testing for jumps in financial economics using bipower variation ," OFRC Working Papers Series, Oxford Financial Research Centre 2004fe01, Oxford Financial Research Centre.
  14. Hogan, William W. & Warren, James M., 1974. "Toward the Development of an Equilibrium Capital-Market Model Based on Semivariance," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 9(01), pages 1-11, January.
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  16. Barndorff-Nielsen, Ole Eiler & Graversen, Svend Erik & Jacod, Jean & Podolskij, Mark, 2004. "A central limit theorem for realised power and bipower variations of continuous semimartingales," Technical Reports, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen 2004,51, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  17. Andrew Ang & Joseph Chen & Yuhang Xing, 2005. "Downside risk," Proceedings, Board of Governors of the Federal Reserve System (U.S.), Board of Governors of the Federal Reserve System (U.S.).
  18. Silja Kinnebrock & Mark Podolskij, 2007. "A Note on the Central Limit Theorem for Bipower Variation of General Functions," OFRC Working Papers Series, Oxford Financial Research Centre 2007fe03, Oxford Financial Research Centre.
  19. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2004. "Analytical Evaluation Of Volatility Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(4), pages 1079-1110, November.
  20. S»bastien Laurent and Jean-Philippe Peters, 2001. "G@RCH 2.0: An Ox Package for Estimating and Forecasting Various ARCH Models," Computing in Economics and Finance 2001, Society for Computational Economics 123, Society for Computational Economics.
  21. Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
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  23. Christian Pedersen & Stephen Satchell, 2002. "On the foundation of performance measures under asymmetric returns," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 2(3), pages 217-223.
  24. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 14(1), pages 45-52, January.
  25. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, American Economic Association, vol. 67(2), pages 116-26, March.
  26. Suzanne S. Lee & Per A. Mykland, 2008. "Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 21(6), pages 2535-2563, November.
  27. Nelson, Daniel B., 1992. "Filtering and forecasting with misspecified ARCH models I : Getting the right variance with the wrong model," Journal of Econometrics, Elsevier, Elsevier, vol. 52(1-2), pages 61-90.
  28. Hogan, William W. & Warren, James M., 1972. "Computation of the Efficient Boundary in the E-S Portfolio Selection Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 7(04), pages 1881-1896, September.
  29. Jean Jacod & Yingying Li & Per A. Mykland & Mark Podolskij & Mathias Vetter, 2007. "Microstructure Noise in the Continuous Case: The Pre-Averaging Approach - JLMPV-9," CREATES Research Papers, School of Economics and Management, University of Aarhus 2007-43, School of Economics and Management, University of Aarhus.
  30. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(3), pages 339-50, July.
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Cited by:
  1. Julien Chevallier & Benoît Sévi, 2011. "On the volatility-volume relationship in energy futures markets using intraday data," EconomiX Working Papers, University of Paris West - Nanterre la Défense, EconomiX 2011-16, University of Paris West - Nanterre la Défense, EconomiX.

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