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How Tick Size Affects the High Frequency Scaling of Stock Return Distributions

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Financial Econometrics and Empirical Market Microstructure

Abstract

We study the high frequency scaling of the distributions of returns for stocks traded at NASDAQ market as a function of the tick-to-price ratio. The tick-to-price ratio is a measure of an effective tick size. We find dramatic differences between distributions for assets with large and small tick-to-price ratio. The presence of returns clustering is evident for large tick size assets. The statistical differences between large and small tick size assets appear to reduce at higher time scales of observation. A possible way to explain returns dynamics for large tick size assets is the coupling of returns with bid-ask spread dynamics. A simple Markov-switching model is able to reproduce the properties of the distribution of returns for large tick size assets.

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Notes

  1. 1.

    Notice that for returns the discretization effect is different from clustering: discretization is a consequence of the fact that price is defined on a grid, while clustering denotes the preference for some price variations over others.

  2. 2.

    Hereafter we use \(\varDelta p\left (i\right )\) or Δ p instead of \(\varDelta p\left (i,n = 1\right )\).

References

  • Ahn, H. J., Cai, J., Chan, K., & Hamao, Y. (2007). Tick size change and liquidity provision on the Tokyo Stock Exchange. Journal of Japanese and International Economies, 21, 173–194.

    Article  Google Scholar 

  • Ane, T., & Geman, H. (2000). Order flow, transaction clock and normality of asset returns. The Journal of Finance, 55, 2259–2284.

    Article  Google Scholar 

  • Ascioglu, A., Comerton-Forde, C., & McInish, T. H. (2010). An examination of minimum tick sizes on the Tokyo Stock Exchange. Japan and the World Economy, 22, 40–48.

    Article  Google Scholar 

  • Bera, A. K., & Higgins, M. L. (1993). Arch models: properties, estimation and testing. Journal of Economic Surveys, 7(4), 305–366.

    Article  Google Scholar 

  • Berchtold, A. (1999). The double chain Markov model. Communications in Statistics - Theory and Methods, 28(11), 2569–2589.

    Article  Google Scholar 

  • Bessembinder, H. (2000). Tick size, spreads, and liquidity: An analysis of Nasdaq Securities Trading near Ten Dollars. Journal of Financial Intermediation, 9, 213–239.

    Article  Google Scholar 

  • Bessembinder, H. (1997). The degree of price resolution and equity trading costs. Journal of Financial Economics, 45, 9–34.

    Article  Google Scholar 

  • Bessembinder, H. (1999). Trade execution costs on NASDAQ and the NYSE: A post-reform comparison. The Journal of Financial and Quantitative Analysis, 34(3), 387–407.

    Article  Google Scholar 

  • Bessembinder, H. (2003). Trade execution costs and market quality after decimalization. The Journal of Financial and Quantitative Analysis, 38(4), 747–777.

    Article  Google Scholar 

  • Bollen, N. P. B., & Busse, J. A. (2006). Tick size and institutional trading costs: evidence from mutual funds. The Journal of Financial and Quantitative Analysis, 41(4), 915–937.

    Article  Google Scholar 

  • Bouchaud, J. P., & Potters, M. (2009). Theory of financial risk and derivative pricing: from statistical physics to risk management, (2nd ed.). Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • Christie, W. G., & Schultz, P. H. (1994). Why do NASDAQ market makers avoid odd-eighth quotes? The Journal of Finance, 49(5), 1813–1840.

    Article  Google Scholar 

  • Christie, W. G., Harris, J. H., & Schultz, P. H. (1994). Why did NASDAQ market makers stop avoiding odd-eighth quotes? The Journal of Finance, 49(5), 1841–1860.

    Article  Google Scholar 

  • Chung, K. H., Chuwonganant, C., & McCormick, D. T. (2004). Order preferencing and market quality on NASDAQ before and after decimalization. Journal of Financial Economics, 71, 581–612.

    Article  Google Scholar 

  • Clark, P. K. (1973a). A subordinated stochastic process model with finite variance for speculative prices. Econometrica, 41(1), 135–155.

    Article  Google Scholar 

  • Clark, P. K. (1973b). Comments on: a subordinated stochastic process model with finite variance for speculative prices. Econometrica, 41(1), 157–159.

    Article  Google Scholar 

  • Clauset, A., Shalizi, C. R., & Newman, M. E. J.(2009). Power-law distributions in empirical data. SIAM Review, 51(4), 661–703.

    Article  Google Scholar 

  • Cont, R. (2001). Empirical properties of asset returns: stylized facts and statistical issues. Quantitative Finance, 1, 223–236.

    Article  Google Scholar 

  • Curato, G., & Lillo, F. (2013). Modeling the coupled return-spread high frequency dynamics of large tick assets. Retrieved from http://arxiv.org/abs/1310.4539.

  • Dacorogna, M. M., Gençay, R., Müller, U. A., Olsen, R. B., & Pictet, O. V. (2001). An introduction to high-frequency finance. San Diego, California, USA: Academic Press.

    Google Scholar 

  • Dayri, K., & Rosenbaum, M. (2013). Large tick assets: implicit spread and optimal tick size. Retrieved from http://arxiv.org/abs/1207.6325.

  • Dayri, K. A., Bacry, E., & Muzy, J. F. (2011). The nature of price returns during periods of high market activity. In F. Abergel, B. K. Chakrabarti, A. Chakraborti & M. Mitra (Eds.), Econophysics of order-driven markets (pp. 155–172). Milano, Italy: Springer-Verlag Italia.

    Chapter  Google Scholar 

  • Eisler, Z., Bouchaud, J. P., & Kockelkoren, J. (2012). The price impact of order book events: market orders, limit orders and cancellations. Quantitative Finance, 12(9), 1395–1419.

    Article  Google Scholar 

  • Engle, R. F., Focardi, S. M., & Fabozzi, F. J. (2008). ARCH/GARCH models in applied financial econometrics. In F. J. Fabozzi (Ed.), Handbook of Finance. New York, NY: John Wiley & Sons.

    Google Scholar 

  • Gibson, S., Singh, R., & Yerramilli, V. (2003). The effect of decimalization on the components of the bid-ask spread. Journal of Financial Intermediation, 12, 121–148.

    Article  Google Scholar 

  • Gillemot, L., Farmer, J. D., & Lillo, F. (2006). There’s more to volatility than volume. Quantitative Finance, 6, 371–384.

    Article  Google Scholar 

  • Goldstein, M. A., & Kavajecz, K. A. (2000). Eights, sixteenths, and market depth: changes in tick size and liquidity provision on the NYSE. Journal of Financial Economics, 56, 125–149.

    Article  Google Scholar 

  • Gopikrishnan, P., Plerou, V., Amaral, L. A. N., Meyer, M., & Stanley, H. E. (1999). Scaling of the distribution of fluctuations of financial market indices. Physical Review E, 60(5), 5305–5316.

    Article  Google Scholar 

  • Hamilton, J. D. (2008). Regime-Switching models. In S. N. Durlauf, & L. E. Blume (Eds.), The new palgrave dictionary of economics, 2nd edn. Basingstoke, UK: Palgrave Macmillan.

    Google Scholar 

  • Harris, L. (1991). Stock price clustering and discreteness. The Review of Financial Studies, 4(3), 389–415.

    Article  Google Scholar 

  • Hautsch, N. (2012). Econometrics of financial high-frequency data. Berlin: Springer-Verlag.

    Book  Google Scholar 

  • He, Y., & Wu, C. (2004). Price rounding and bid-ask spreads before and after decimalization. International Review of Economics and Finance, 13, 19–41.

    Article  Google Scholar 

  • Huang, R. D., & Stoll, H. R. (2001). Tick size, bid-ask spreads, and market structure. The Journal of Financial and Quantitative Analysis, 36(4), 503–522.

    Article  Google Scholar 

  • La Spada, G., Farmer, J. D., & Lillo, F. (2011). Tick size and price diffusion. In F. Abergel, B. K. Chakrabarti, A. Chakraborti & M. Mitra (Eds.), Econophysics of order-driven markets (pp. 173–187). Milano, Italy: Springer-Verlag Italia.

    Chapter  Google Scholar 

  • Loistl, O., Schossmann, B., & Veverka, A. (2004). Tick size and spreads: The case of Nasdaq’s decimalization. European Journal of Operational Research, 155, 317–334.

    Article  Google Scholar 

  • MacKinnon, G., & Nemiroff, H. (2004). Tick size and the returns to providing liquidity. International Review of Economics and Finance, 13, 57–73.

    Article  Google Scholar 

  • Mandelbrot, B., & Taylor, H. M. (1967). On the distributions of stock price differences. Operations Research, 15(6), 1057–1062.

    Article  Google Scholar 

  • Münnix, M. C., Schäfer, R., & Guhr, T. (2010). Impact of the tick-size on financial returns and correlations. Physica A, 389, 4828–4843.

    Article  Google Scholar 

  • Onnela J. P., Töyli, J., Kaski, K. (2009). Tick size and stock returns. Physica A, 388, 441–454.

    Article  Google Scholar 

  • Osborne, M. F. M. (1962). Periodic structure in the Brownian Motion of stock prices. Operations Research, 10(3), 345–379.

    Article  Google Scholar 

  • Plerou, V., Gopikrishnan, P., Amaral, L. A. N., Meyer, M., & Stanley, H. E. (1999). Scaling of the distribution of price fluctuations of individual companies. Physical Review E, 60(6), 6519–6529.

    Article  Google Scholar 

  • Plerou, V., Gopikrishnan, P., & Stanley, H. E. (2005). Quantifying fluctuations in market liquidity: Analysis of the bid-ask spread. Physical Review E, 71, 046131-1/046131-8.

    Google Scholar 

  • Plerou, V., & Stanley, H. E. (2007). Test of scaling and universality of the distributions of trade size and share volume: Evidence from three distinct markets. Physical Review E, 76, 046109-1/046109-10.

    Google Scholar 

  • Ponzi, A., Lillo, F., & Mantegna, R. N. (2009). Market reaction to a bid-ask spread change: A power-law relaxation dynamics. Physical Review E, 80, 016112-1/016112-12.

    Google Scholar 

  • U.S. Securities and Exchange Commission. (2012). Report to Congress on Decimalization. Retrieved from http://www.sec.gov/news/studies/2012/decimalization-072012.pdf.

  • Robert, C. Y., & Rosenbaum, M. (2011). A new approach for the dynamics of ultra-high-frequency data: the model with uncertainty zones. Journal of Financial Econometrics, 9(2), 344–366.

    Article  Google Scholar 

  • Wyart, M., Bouchaud, J. P., Kockelkoren, J., Potters, M., & Vettorazzo, M. (2008). Relation between bid-ask spread, impact and volatility in order driven markets. Quantitative Finance, 8(1), 41–57.

    Article  Google Scholar 

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Acknowledgements

Authors acknowledge partial support by the grant SNS11LILLB Price formation, agents heterogeneity, and market efficiency.

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Authors and Affiliations

  1. Scuola Normale Superiore, Pisa, Italy

    Gianbiagio Curato & Fabrizio Lillo

  2. Dipartimento di Fisica e Chimica, University of Palermo, Palermo, Italy

    Fabrizio Lillo

Authors
  1. Gianbiagio Curato
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  2. Fabrizio Lillo
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Correspondence to Fabrizio Lillo .

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Editors and Affiliations

  1. Department of Economics, University of Illinois, Urbana, Illinois, USA

    Anil K. Bera

  2. Perm State University, Perm, Russia

    Sergey Ivliev

  3. Scuola Normale Superiore, Pisa, Italy

    Fabrizio Lillo

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Curato, G., Lillo, F. (2015). How Tick Size Affects the High Frequency Scaling of Stock Return Distributions. In: Bera, A., Ivliev, S., Lillo, F. (eds) Financial Econometrics and Empirical Market Microstructure. Springer, Cham. https://doi.org/10.1007/978-3-319-09946-0_6

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