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Sampling Interval and estimated Betas : Implications for the Presence of Transitory Components in Stock Prices

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  • PERRON, Pierre
  • VODOUNOU, Cosme

Abstract

We provide a theoretical framework to explain the empirical finding that the estimated betas are sensitive to the sampling interval even when using continuously compounded returns. We suppose that stock prices have both permanent and transitory components. The permanent component is a standard geometric Brownian motion while the transitory component is a stationary Ornstein-Uhlenbeck process. The discrete time representation of the beta depends on the sampling interval and two components labelled "permanent and transitory betas". We show that if no transitory component is present in stock prices, then no sampling interval effect occurs. However, the presence of a transitory component implies that the beta is an increasing (decreasing) function of the sampling interval for more (less) risky assets. In our framework, assets are labelled risky if their "permanent beta" is greater than their "transitory beta" and vice versa for less risky assets. Simulations show that our theoretical results provide good approximations for the means and standard deviations of estimated betas in small samples. Our results can be perceived as indirect evidence for the presence of a transitory component in stock prices, as proposed by Fama and French (1988) and Poterba and Summers (1988).

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  • PERRON, Pierre & VODOUNOU, Cosme, 1998. "Sampling Interval and estimated Betas : Implications for the Presence of Transitory Components in Stock Prices," Cahiers de recherche 9816, Universite de Montreal, Departement de sciences economiques.
    • Handle: RePEc:mtl:montde:9816
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    3. Conlon, Thomas & Cotter, John & Gençay, Ramazan, 2018. "Long-run wavelet-based correlation for financial time series," European Journal of Operational Research, Elsevier, vol. 271(2), pages 676-696.

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    More about this item

    Keywords

    stochastic differential equations; Wiener ocess; market efficiency; meanreversion; Ornstein-Uhlenbeck ocess;
    All these keywords.

    JEL classification:

    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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