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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. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Econometrics of testing for jumps in financial economics using bipower variation," Economics Papers 2003-W21, Economics Group, Nuffield College, University of Oxford.
  2. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Papers 2006-W03, Economics Group, Nuffield College, University of Oxford.
  3. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  4. 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, vol. 7(04), pages 1881-1896, September.
  5. Ole E. Barndorff-Nielsen & Sven Erik Graversen & Jean Jacod & Neil Shephard, 2005. "Limit theorems for bipower variation in financial econometrics," Economics Papers 2005-W06, Economics Group, Nuffield College, University of Oxford.
  6. 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 2007-43, School of Economics and Management, University of Aarhus.
  7. 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 123, Society for Computational Economics.
  8. Robert F. Engle & Giampiero M. Gallo, 2003. "A Multiple Indicators Model For Volatility Using Intra-Daily Data," Econometrics Working Papers Archive wp2003_07, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  9. 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 2007-18, School of Economics and Management, University of Aarhus.
  10. Andrew Ang & Joseph Chen & Yuhang Xing, 2006. "Downside Risk," Review of Financial Studies, Society for Financial Studies, vol. 19(4), pages 1191-1239.
    • Andrew Ang & Joseph Chen & Yuhang Xing, 2005. "Downside risk," Proceedings, Board of Governors of the Federal Reserve System (U.S.).
  11. 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.
  12. 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, vol. 100, pages 1394-1411, December.
  13. 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, vol. 119(7), pages 2249-2276, July.
  14. Ole BARNDORFF-NIELSEN & Svend Erik GRAVERSEN & Jean JACOD & Mark PODOLSKIJ & Neil SHEPHARD, 2004. "A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales," OFRC Working Papers Series 2004fe21, Oxford Financial Research Centre.
  15. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Power and bipower variation with stochastic volatility and jumps," Economics Papers 2003-W17, Economics Group, Nuffield College, University of Oxford.
  16. 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, vol. 9(01), pages 1-11, January.
  17. Christian Pedersen & Stephen Satchell, 2002. "On the foundation of performance measures under asymmetric returns," Quantitative Finance, Taylor & Francis Journals, vol. 2(3), pages 217-223.
  18. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  19. Mao, James C T, 1970. "Survey of Capital Budgeting: Theory and Practice," Journal of Finance, American Finance Association, vol. 25(2), pages 349-60, May.
  20. Nelson, Daniel B., 1992. "Filtering and forecasting with misspecified ARCH models I : Getting the right variance with the wrong model," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 61-90.
  21. M, El Babsiri & Jean-Michel Zakoïan, 1997. "Contemporaneous Asymmetry in GARCH Processes," Working Papers 97-03, Centre de Recherche en Economie et Statistique.
  22. 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, vol. 21(6), pages 2535-2563, November.
  23. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2002. "Analytic Evaluation of Volatility Forecasts," CIRANO Working Papers 2002s-90, CIRANO.
  24. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-50, July.
  25. Kinnebrock, Silja & Podolskij, Mark, 2008. "A note on the central limit theorem for bipower variation of general functions," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 1056-1070, June.
  26. Laurent, Sebastien & Peters, Jean-Philippe, 2002. " G@RCH 2.2: An Ox Package for Estimating and Forecasting Various ARCH Models," Journal of Economic Surveys, Wiley Blackwell, vol. 16(3), pages 447-85, July.
  27. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 45-52, January.
  28. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-26, March.
  29. Mao, James C. T., 1970. "Models of Capital Budgeting, E-V VS E-S," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 4(05), pages 657-675, January.
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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 2011-16, University of Paris West - Nanterre la Défense, EconomiX.

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