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The limiting extremal behaviour of speculative returns: an analysis of intra-daily data from the Frankfurt Stock Exchange

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  • Thomas Lux

Abstract

This paper provides a statistical analysis of high-frequency recordings of the German share price index DAX. The data set extends from November 1988 to the end of the year 1995 and includes all minute-to-minute changes during trading hours at the Frankfurt Stock Exchange. The focus of this study is on the limiting behaviour characterizing the tail regions of the empirical distribution. Application of the popular Hill estimator for the tail shape yields results very similar to those of other analyses of speculative returns. However, since the reliability of tail index estimation rests on the appropriateness of the tail regions, the question of optimally choosing the sample fraction emerges. Exploiting recent advances in extreme value theory a couple of novel approaches are applied for determining the optimum cut-off value for the 'tail' of the empirical distribution. As it turns out, most algorithms suggest that one has to go out quite far into the tails for estimation of the extremal index. The findings obtained at the highest frequency (minute-to-minute returns) are confirmed when considering data at various levels of time-aggregation. A test for stability of extreme value behaviour over time gives no clear indication of changes of the limiting distribution. It is also illustrated how the approximation of the tails can be used to estimate the likelihood of large returns.

Suggested Citation

  • Thomas Lux, 2001. "The limiting extremal behaviour of speculative returns: an analysis of intra-daily data from the Frankfurt Stock Exchange," Applied Financial Economics, Taylor & Francis Journals, vol. 11(3), pages 299-315.
  • Handle: RePEc:taf:apfiec:v:11:y:2001:i:3:p:299-315 DOI: 10.1080/096031001300138708
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    1. Clare, A. D. & Priestley, R. & Thomas, S. H., 1998. "Reports of beta's death are premature: Evidence from the UK," Journal of Banking & Finance, Elsevier, vol. 22(9), pages 1207-1229, September.
    2. Leamer, Edward E, 1983. "Let's Take the Con Out of Econometrics," American Economic Review, American Economic Association, vol. 73(1), pages 31-43, March.
    3. Elton, Edwin J, et al, 1993. "Efficiency with Costly Information: A Reinterpretation of Evidence from Managed Portfolios," Review of Financial Studies, Society for Financial Studies, vol. 6(1), pages 1-22.
    4. Brown, Stephen J & Goetzmann, William N, 1995. " Performance Persistence," Journal of Finance, American Finance Association, vol. 50(2), pages 679-698, June.
    5. Grinblatt, Mark & Titman, Sheridan, 1992. " The Persistence of Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 47(5), pages 1977-1984, December.
    6. Lo, Andrew W & MacKinlay, A Craig, 1990. "Data-Snooping Biases in Tests of Financial Asset Pricing Models," Review of Financial Studies, Society for Financial Studies, vol. 3(3), pages 431-467.
    7. Ron Bird & Helen Chin & Michael McCrae, 1983. "The Performance of Australian Superannuation Funds," Australian Journal of Management, Australian School of Business, vol. 8(1), pages 49-69, June.
    8. Malkiel, Burton G, 1995. " Returns from Investing in Equity Mutual Funds 1971 to 1991," Journal of Finance, American Finance Association, vol. 50(2), pages 549-572, June.
    9. Andrew Clare & Richard Priestley & Stephen Thomas, 1997. "Is Beta dead? The role of alternative estimation methods," Applied Economics Letters, Taylor & Francis Journals, vol. 4(9), pages 559-562.
    10. Jagannathan, Ravi & Kubota, Keiichi & Takehara, Hitoshi, 1998. "Relationship between Labor-Income Risk and Average Return: Empirical Evidence from the Japanese Stock Market," The Journal of Business, University of Chicago Press, vol. 71(3), pages 319-347, July.
    11. Brown, Stephen J, et al, 1992. "Survivorship Bias in Performance Studies," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 553-580.
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    Cited by:

    1. Westerhoff, Frank H. & Dieci, Roberto, 2006. "The effectiveness of Keynes-Tobin transaction taxes when heterogeneous agents can trade in different markets: A behavioral finance approach," Journal of Economic Dynamics and Control, Elsevier, vol. 30(2), pages 293-322, February.
    2. repec:eee:respol:v:46:y:2017:i:7:p:1187-1197 is not listed on IDEAS
    3. Upper, Christian & Werner, Thomas, 2002. "Time Variation in the Tail Behaviour of Bund Futures Returns," Discussion Paper Series 1: Economic Studies 2002,25, Deutsche Bundesbank.
    4. Carolina Castaldi & Bart Los, 2008. "The identification of important innovations using tail estimators," Innovation Studies Utrecht (ISU) working paper series 08-07, Utrecht University, Department of Innovation Studies, revised Feb 2008.
    5. Chiarella, Carl & Iori, Giulia, 2009. "The impact of heterogeneous trading rules on the limit order book and order flows," Journal of Economic Dynamics and Control, Elsevier, pages 525-537.
    6. Grilli, Ruggero & Tedeschi, Gabriele & Gallegati, Mauro, 2014. "Bank interlinkages and macroeconomic stability," International Review of Economics & Finance, Elsevier, vol. 34(C), pages 72-88.
    7. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    8. Suárez-García, Pablo & Gómez-Ullate, David, 2013. "Scaling, stability and distribution of the high-frequency returns of the Ibex35 index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1409-1417.
    9. Segnon, Mawuli & Lux, Thomas, 2013. "Multifractal models in finance: Their origin, properties, and applications," Kiel Working Papers 1860, Kiel Institute for the World Economy (IfW).
    10. Giorgio Fagiolo & Mauro Napoletano & Andrea Roventini, 2008. "Are output growth-rate distributions fat-tailed? some evidence from OECD countries," Journal of Applied Econometrics, John Wiley & Sons, Ltd., pages 639-669.
    11. Lux, Thomas, 2008. "Stochastic behavioral asset pricing models and the stylized facts," Economics Working Papers 2008-08, Christian-Albrechts-University of Kiel, Department of Economics.
    12. Ryuichi Yamamoto, 2015. "Dynamic predictor selection and order splitting in a limit order market," Working Papers 1514, Waseda University, Faculty of Political Science and Economics.
    13. repec:eee:streco:v:42:y:2017:i:c:p:13-25 is not listed on IDEAS
    14. Thomas Werner & Christian Upper, 2004. "Time variation in the tail behavior of Bund future returns," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 24(4), pages 387-398, April.
    15. Castaldi, Carolina & Milakovic, Mishael, 2007. "Turnover activity in wealth portfolios," Journal of Economic Behavior & Organization, Elsevier, vol. 63(3), pages 537-552, July.
    16. Pan, Raj Kumar & Sinha, Sitabhra, 2008. "Inverse-cubic law of index fluctuation distribution in Indian markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2055-2065.
    17. Silverberg, Gerald & Verspagen, Bart, 2007. "The size distribution of innovations revisited: An application of extreme value statistics to citation and value measures of patent significance," Journal of Econometrics, Elsevier, pages 318-339.
    18. Lux, Thomas, 2008. "Stochastic behavioral asset pricing models and the stylized facts," Kiel Working Papers 1426, Kiel Institute for the World Economy (IfW).
    19. Niklas Wagner & Terry Marsh, 2004. "Tail index estimation in small smaples Simulation results for independent and ARCH-type financial return models," Statistical Papers, Springer, vol. 45(4), pages 545-561, October.

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