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Robust Structure without Predictability: The "Compass Rose" Pattern of the Stock Market

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  • Crack, Timothy Falcon
  • Ledoit, Olivier

Abstract

Plotting daily stock returns against themselves with one day's lag reveals a striking pattern. Evenly spaced lines radiate from the origin; the thickest lines point in the major directions of the compass. This 'compass rose' pattern appears in every stock. It is caused by discreteness. However, counterexamples demonstrate that the existence of exchange-imposed tick sizes (e.g., eighths) is neither necessary nor sufficient for the compass rose. The compass rose cannot be used to make abnormal profits: it is structure without predictability. Among other consequences, the compass rose may bias estimation of ARCH models and tests for chaos. Copyright 1996 by American Finance Association.

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  • Crack, Timothy Falcon & Ledoit, Olivier, 1996. "Robust Structure without Predictability: The "Compass Rose" Pattern of the Stock Market," Journal of Finance, American Finance Association, vol. 51(2), pages 751-762, June.
    • Handle: RePEc:bla:jfinan:v:51:y:1996:i:2:p:751-62
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    Citations

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    Cited by:

    1. Shin S. Ikeda, 2015. "Illiquidity in the Japanese Day-Ahead Electricity Market," GRIPS Discussion Papers 15-04, National Graduate Institute for Policy Studies.
    2. Antonios Antoniou & Constantinos E. Vorlow, 2004. "Price Clustering and Discreteness: Is there Chaos behind the Noise?," Papers cond-mat/0407471, arXiv.org.
    3. IKEDA Shin Suke, 2017. "Illiquidity in the Japan Electric Power Exchange," Discussion papers 17122, Research Institute of Economy, Trade and Industry (RIETI).
    4. Szpiro, George G., 1998. "Tick size, the compass rose and market nanostructure," Journal of Banking & Finance, Elsevier, vol. 22(12), pages 1559-1569, December.
    5. Wang, Huaiqing & Wang, Chen, 2002. "Visibility of the compass rose in financial asset returns: A quantitative study," Journal of Banking & Finance, Elsevier, vol. 26(6), pages 1099-1111, June.
    6. George D. Cashman & David M. Harrison & Hainan Sheng, 2021. "Option Trading and REIT Returns," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 49(1), pages 332-389, March.
    7. Katarzyna Bien & Ingmar Nolte & Winfried Pohlmeier, 2011. "An inflated multivariate integer count hurdle model: an application to bid and ask quote dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(4), pages 669-707, June.
    8. An-Sing Chen, 1997. "The square compass rose: the evidence from Taiwan," Journal of Multinational Financial Management, Elsevier, vol. 7(2), pages 127-144, June.
    9. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    10. Constantinos E. Vorlow, 2004. "Stock Price Clustering and Discreteness: The "Compass Rose" and Predictability," Papers cond-mat/0408013, arXiv.org.
    11. Small Michael & Tse Chi K., 2003. "Determinism in Financial Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 7(3), pages 1-31, October.
    12. Katarzyna Bien & Ingmar Nolte & Winfried Pohlmeier, 2008. "A multivariate integer count hurdle model: theory and application to exchange rate dynamics," Studies in Empirical Economics, in: Luc Bauwens & Winfried Pohlmeier & David Veredas (ed.), High Frequency Financial Econometrics, pages 31-48, Springer.
    13. Wang, Eliza & Hudson, Robert & Keasey, Kevin, 2000. "Tick size and the compass rose: further insights," Economics Letters, Elsevier, vol. 68(2), pages 119-125, August.
    14. Ikeda, Shin S., 2019. "Illiquidity in the Japan electric power exchange," Journal of Commodity Markets, Elsevier, vol. 14(C), pages 16-39.
    15. Fang, Yue, 2002. "The compass rose and random walk tests," Computational Statistics & Data Analysis, Elsevier, vol. 39(3), pages 299-310, May.
    16. Gleason, Kimberly C. & Lee, Chun I. & Mathur, Ike, 2000. "An explanation for the compass rose pattern," Economics Letters, Elsevier, vol. 68(2), pages 127-133, August.
    17. Shin S. Ikeda, 2013. "An Empirical Market Microstructure Analysis of the Implied Spread Cost in the Japanese Day-Ahead Electricity Market," GRIPS Discussion Papers 12-22, National Graduate Institute for Policy Studies.
    18. Lanius, Vivian & Gather, Ursula, 2010. "Robust online signal extraction from multivariate time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 966-975, April.
    19. Lanius, Vivian & Gather, Ursula, 2007. "Robust online signal extraction from multivariate time series," Technical Reports 2007,38, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    20. Henrik Amilon, 2002. "A Score Test for Discreteness in GARCH Models," Research Paper Series 76, Quantitative Finance Research Centre, University of Technology, Sydney.
    21. Kramer, Walter & Runde, Ralf, 1997. "Chaos and the compass rose," Economics Letters, Elsevier, vol. 54(2), pages 113-118, February.
    22. Amilon, Henrik, 2003. "GARCH estimation and discrete stock prices: an application to low-priced Australian stocks," Economics Letters, Elsevier, vol. 81(2), pages 215-222, November.
    23. Wing Lon Ng, 2006. "Overreaction and Multiple Tail Dependence at the High-frequency Level — The Copula Rose," SFB 649 Discussion Papers SFB649DP2006-086, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    24. Mitchell, Heather & McKenzie, Michael D., 2006. "A note on the Wang and Wang measure of the quality of the compass rose," Journal of Banking & Finance, Elsevier, vol. 30(12), pages 3519-3524, December.
    25. Chun Lee & Ike Mathur & Kimberly Gleason, 2005. "The tick/volatility ratio as a determinant of the compass rose pattern," The European Journal of Finance, Taylor & Francis Journals, vol. 11(2), pages 93-109.

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