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Nonparametric test for a constant beta over a fixed time interval

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  • Reiß, Markus
  • Todorov, Viktor
  • Tauchen, George

Abstract

We derive a nonparametric test for constant (continuous) beta over a fixed interval of time. Continuous beta is defined as the ratio of the continuous covariation between an asset and observable risk factor (e.g., the market return) and the continuous variation of the latter. Our test is based on discrete observations of a bivariate It^o semimartingale with mesh of the observation grid shrinking to zero. We rst form a consistent and asymptotically mixed normal estimate of beta using all the observations within the time interval under the null hypothesis that beta is constant. Using it we form an estimate of the residual component of the asset returns that is orthogonal (in martingale sense) to the risk factor. Our test is then based on the distinctive asymptotic behavior, under the null and alternative hypothesis, of the sample covariation between the risk factor and the estimated residual component of the asset returns over blocks with asymptotically shrinking time span. Optimality of the test is considered as well. We document satisfactory finite sample properties of the test on simulated data. In an empirical application based on 10-minute data we analyze the time variation in market betas of four assets over the period 2006-2012. The results suggest that (for likely structural reasons) for one of the assets there is statistically nontrivial variation in market beta even for a period as short as a week. On the other hand, for the rest of the assets in our analysis we find evidence that a window of constant beta of one week to one month is statistically plausible.

Suggested Citation

  • Reiß, Markus & Todorov, Viktor & Tauchen, George, 2014. "Nonparametric test for a constant beta over a fixed time interval," SFB 649 Discussion Papers 2014-022, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
  • Handle: RePEc:zbw:sfb649:sfb649dp2014-022
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    References listed on IDEAS

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    1. Ang, Andrew & Kristensen, Dennis, 2012. "Testing conditional factor models," Journal of Financial Economics, Elsevier, vol. 106(1), pages 132-156.
    2. Mancini, Cecilia & Gobbi, Fabio, 2012. "Identifying The Brownian Covariation From The Co-Jumps Given Discrete Observations," Econometric Theory, Cambridge University Press, vol. 28(2), pages 249-273, April.
    3. Kejriwal, Mohitosh & Perron, Pierre & Zhou, Jing, 2013. "Wald Tests For Detecting Multiple Structural Changes In Persistence," Econometric Theory, Cambridge University Press, vol. 29(2), pages 289-323, April.
    4. Per A. Mykland & Lan Zhang, 2009. "Inference for Continuous Semimartingales Observed at High Frequency," Econometrica, Econometric Society, vol. 77(5), pages 1403-1445, September.
    5. Lewellen, Jonathan & Nagel, Stefan, 2006. "The conditional CAPM does not explain asset-pricing anomalies," Journal of Financial Economics, Elsevier, vol. 82(2), pages 289-314, November.
    6. Hansen, Lars Peter & Richard, Scott F, 1987. "The Role of Conditioning Information in Deducing Testable," Econometrica, Econometric Society, vol. 55(3), pages 587-613, May.
    7. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, May.
    8. Aue, Alexander & Hörmann, Siegfried & Horváth, Lajos & Hušková, Marie & Steinebach, Josef G., 2012. "Sequential Testing For The Stability Of High-Frequency Portfolio Betas," Econometric Theory, Cambridge University Press, vol. 28(4), pages 804-837, August.
    9. Todorov, Viktor & Bollerslev, Tim, 2010. "Jumps and betas: A new framework for disentangling and estimating systematic risks," Journal of Econometrics, Elsevier, vol. 157(2), pages 220-235, August.
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    More about this item

    Keywords

    nonparametric tests; time-varying beta; stochastic volatility; high-frequency data;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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