The Annals of Applied Statistics

High frequency market microstructure noise estimates and liquidity measures

Yacine Aït-Sahalia and Jialin Yu

Full-text: Open access

Enhanced PDF (452 KB)

Abstract

Using recent advances in the econometrics literature, we disentangle from high frequency observations on the transaction prices of a large sample of NYSE stocks a fundamental component and a microstructure noise component. We then relate these statistical measurements of market microstructure noise to observable characteristics of the underlying stocks and, in particular, to different financial measures of their liquidity. We find that more liquid stocks based on financial characteristics have lower noise and noise-to-signal ratio measured from their high frequency returns. We then examine whether there exists a common, market-wide, factor in high frequency stock-level measurements of noise, and whether that factor is priced in asset returns.

Article information

Source
Ann. Appl. Stat., Volume 3, Number 1 (2009), 422-457.

Dates
First available in Project Euclid: 16 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1239888377

Digital Object Identifier
doi:10.1214/08-AOAS200

Mathematical Reviews number (MathSciNet)
MR2668714

Zentralblatt MATH identifier
1160.62089

Keywords
Market microstructure noise robust volatility estimation high frequency data liquidity stock returns

Citation

Aït-Sahalia, Yacine; Yu, Jialin. High frequency market microstructure noise estimates and liquidity measures. Ann. Appl. Stat. 3 (2009), no. 1, 422--457. doi:10.1214/08-AOAS200. https://projecteuclid.org/euclid.aoas/1239888377


Export citation

References

  • Aït-Sahalia, Y. and Kimmel, R. (2007). Maximum likelihood estimation of stochastic volatility models. Journal of Financial Economics 83 413–452.
  • Aït-Sahalia, Y., Mykland, P. A. and Zhang, L. (2005a). How often to sample a continuous-time process in the presence of market microstructure noise. Review of Financial Studies 18 351–416.
  • Aït-Sahalia, Y., Mykland, P. A. and Zhang, L. (2005b). Ultra high frequency volatility estimation with dependent microstructure noise. Discussion paper, Princeton Univ.
  • Aït-Sahalia, Y., Mykland, P. A. and Zhang, L. (2006). Comments on “Realized variance and market microstructure noise.” J. Bus. Econom. Statist. 24 162–167.
    Mathematical Reviews (MathSciNet): MR2234447
  • Aït-Sahalia, Y. and Yu, J. (2009). Supplement to “High frequency market microstructure noise estimates and liquidity measures.” DOI: 10.1214/08-AOAS200SUPP.
  • Amihud, Y., Mendelson, H. and Pedersen, L. H. (2005). Liquidity and asset prices. Foundations and Trends in Finance 1 269–364.
    Zentralblatt MATH: 1140.91006
  • Andersen, T. G., Bollerslev, T., Diebold, F. X. and Labys, P. (2001). The distribution of exchange rate realized volatility. J. Amer. Statist. Assoc. 96 42–55.
    Mathematical Reviews (MathSciNet): MR1952727
    Zentralblatt MATH: 1015.62107
    Digital Object Identifier: doi:10.1198/016214501750332965
  • Ang, A., Hodrick, R. J., Xing, Y. and Zhang, X. (2006). The cross-section of volatility and expected returns. Journal of Finance 51 259–299.
  • Bandi, F. M. and Russell, J. R. (2003). Microstructure noise, realized volatility and optimal sampling. Discussion paper, Univ. Chicago Graduate School of Business.
  • Barndorff-Nielsen, O. E. and Shephard, N. (2002). Econometric analysis of realized volatility and its use in estimating stochastic volatility models. J. Roy. Statist. Soc. Ser. B 64 253–280.
    Mathematical Reviews (MathSciNet): MR1904704
    Zentralblatt MATH: 1059.62107
    Digital Object Identifier: doi:10.1111/1467-9868.00336
  • Brennan, M. J. and Subrahmanyam, A. (2002). Market microstructure and asset pricing: On the compensation for illiquidity in stock returns. Journal of Financial Economics 41 441–464.
  • Cao, C., Choe, H. and Hatheway, F. (1997). Does the specialist matter? Differential execution costs and intersecurity subsidization on the New York stock exchange. Journal of Finance 52 1615–1640.
  • Chan, L. and Lakonishok, J. (1997). Institutional equity trading costs: NYSE versus Nasdaq. Journal of Finance 52 713–735.
  • Chordia, T., Roll, R. and Subrahmanyam, A. (2000). Commonality in liquidity. Journal of Financial Economics 56 3–28.
  • Chordia, T., Roll, R. and Subrahmanyam, A. (2001). Market liquidity and trading activity. Journal of Finance 56 501–530.
  • Delattre, S. and Jacod, J. (1997). A central limit theorem for normalized functions of the increments of a diffusion process, in the presence of round-off errors. Bernoulli 3 1–28.
    Mathematical Reviews (MathSciNet): MR1466543
    Digital Object Identifier: doi:10.2307/3318650
    Project Euclid: euclid.bj/1178291930
  • Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation. Econometrica 50 987–1007.
    Mathematical Reviews (MathSciNet): MR666121
    Digital Object Identifier: doi:10.2307/1912773
  • Fama, E. F. and French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics 33 3–56.
  • Fama, E. F. and French, K. R. (1997). Industry costs of equity. Journal of Financial Economics 43 143–193.
  • Gençay, R., Ballocchi, G., Dacorogna, M., Olsen, R. and Pictet, O. (2002). Real-time trading models and the statistical properties of foreign exchange rates. Internat. Econom. Rev. 43 463–491.
  • Glosten, L. R. (1987). Components of the bid–ask spread and the statistical properties of transaction prices. Journal of Finance 42 1293–1307.
    Mathematical Reviews (MathSciNet): MR919477
    Digital Object Identifier: doi:10.1111/j.1540-6261.1987.tb04367.x
  • Glosten, L. R. and Harris, L. E. (1988). Estimating the components of the bid/ask spread. Journal of Financial Economics 21 123–142.
  • Goncalves, S. and Meddahi, N. (2005). Bootstrapping realized volatility. Discussion paper, Univ. Montréal.
  • Gottlieb, G. and Kalay, A. (1985). Implications of the discreteness of observed stock prices. Journal of Finance 40 135–153.
  • Hansen, P. R. and Lunde, A. (2006). Realized variance and market microstructure noise. J. Bus. Econom. Statist. 24 127–161.
    Mathematical Reviews (MathSciNet): MR2234447
  • Härdle, W. and Linton, O. (1994). Applied nonparametric methods. In Handbook of Econometrics (R. F. Engle and D. L. McFadden, eds.) 4 2295–2339. Elsevier, Amsterdam.
    Mathematical Reviews (MathSciNet): MR1315973
  • Harris, L. (1990a). Estimation of stock price variances and serial covariances from discrete observations. Journal of Financial and Quantitative Analysis 25 291–306.
  • Harris, L. (1990b). Statistical properties of the roll serial covariance bid/ask spread estimator. Journal of Finance 45 579–590.
  • Hasbrouck, J. (1993). Assessing the quality of a security market: A new approach to transaction-cost measurement. Review of Financial Studies 6 191–212.
  • Hasbrouck, J. (2005). Trading costs and returns for US equities: Evidence from daily data. Discussion paper, New York Univ.
  • Hasbrouck, J. and Seppi, D. J. (2001). Common factors in prices, order flows, and liquidity. Journal of Financial Economics 59 383–411.
  • Huang, R. and Stoll, H. (1996). Dealer versus auction markets: A paired comparison of execution costs on NASDAQ and the NYSE. Journal of Financial Economics 41 313–357.
  • Huberman, G. and Halka, D. (2001). Systematic liquidity. Journal of Financial Research 24 161–178.
  • Jacod, J. (1994). Limit of random measures associated with the increments of a Brownian semimartingale. Discussion paper, Univ. Paris-6.
  • Jacod, J. (1996). La Variation Quadratique du Brownien en Présence d’Erreurs d’Arrondi. Astérisque 236 155–162.
    Mathematical Reviews (MathSciNet): MR1417980
  • Jacod, J. and Protter, P. (1998). Asymptotic error distributions for the Euler method for stochastic differential equations. Ann. Probab. 26 267–307.
    Mathematical Reviews (MathSciNet): MR1617049
    Zentralblatt MATH: 0937.60060
    Digital Object Identifier: doi:10.1214/aop/1022855419
    Project Euclid: euclid.aop/1022855419
  • Madhavan, A., Richardson, M. and Roomans, M. (1997). Why do security prices change? Review of Financial Studies 10 1035–1064.
  • Newey, W. K. and West, K. D. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55 703–708.
    Mathematical Reviews (MathSciNet): MR890864
    Digital Object Identifier: doi:10.2307/1913610
  • Oomen, R. C. (2006). Properties of realized variance under alternative sampling schemes. J. Bus. Econom. Statist. 24 219–237.
    Mathematical Reviews (MathSciNet): MR2234448
  • Pastor, L. and Stambaugh, R. F. (2003). Liquidity risk and expected stock returns. Journal of Political Economy 111 642–685.
  • Roll, R. (1984). A simple model of the implicit bid–ask spread in an efficient market. Journal of Finance 39 1127–1139.
  • Zhang, L. (2006). Efficient estimation of stochastic volatility using noisy observations: A multi-scale approach. Bernoulli 12 1019–1043.
    Mathematical Reviews (MathSciNet): MR2274854
    Digital Object Identifier: doi:10.3150/bj/1165269149
    Project Euclid: euclid.bj/1165269149
  • Zhang, L., Mykland, P. A. and Y. Aït-Sahalia (2005a). Edgeworth expansions for realized volatility and related estimators. Discussion paper, Princeton Univ.
  • Zhang, L., Mykland, P. A. and Y. Aït-Sahalia (2005b). A tale of two time scales: Determining integrated volatility with noisy high-frequency data. J. Amer. Statist. Assoc. 100 1394–1411.
  • Zhou, B. (1996). High-frequency data and volatility in foreign-exchange rates. J. Bus. & Econom. Statist. 14 45–52.
  • Zumbach, G., Corsi, F. and Trapletti, A. (2002). Efficient estimation of volatility using high frequency data. Discussion paper, Olsen & Associates.

Supplemental materials

The Institute of Mathematical Statistics

The Annals of Applied Statistics

New content alerts

Email RSS ToC RSS Article
  • You have access to this content.
  • You have partial access to this content.
  • You do not have access to this content.
Turn Off MathJax

What is MathJax?

More like this

+ See more