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Beta Stationarity and Estimation Period: Some Analytical Results

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  • Theobald, Michael

Abstract

The stationarity of beta factors has received considerable attention in the financial economics literature. One particular area of study has been to investigate how the measured stationarity of beta factors changes over data sets of varying lengths. By increasing the length of the estimation period, sampling fluctuations may be reduced; however, the probability of beta factors having changed will increase. The optimal data set length, then, involves a trade-off between these two opposing phenomena. Baesel [2] reported the empirical finding that the stationarity of beta was, indeed, dependent upon the estimation period length over which beta factors were estimated. He found, using transition matrices that beta stationarity was an increasing function of the calendar period used for beta estimation. In this paper, analytic expressions will be derived to explain how and when this empirical phenomenon arises. Conditions will be presented for beta stationarity to increase with calendar period length, and it will be demonstrated that beta stationarity will not increase indefinitely with estimation period length. An identical condition is required for beta stationarity to be an increasing function of the subsequent calendar period length. This phenomenon was empirically investigated by Roenfeldt, Griepentrog, and Pflaum [6], and the analysis presented here explains, in part, their findings.

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  • Theobald, Michael, 1981. "Beta Stationarity and Estimation Period: Some Analytical Results," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 16(5), pages 747-757, December.
    • Handle: RePEc:cup:jfinqa:v:16:y:1981:i:05:p:747-757_01
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    Cited by:

    1. Yan Zeng & Josie McLaren, 2015. "The impact of large public sales of Government assets: empirical evidence from the Chinese stock markets on a gradual and offer-to-get approach," Review of Quantitative Finance and Accounting, Springer, vol. 45(1), pages 137-173, July.
    2. Deepak Chawla, 2003. "Stability of Alphas and Betas over Bull and Bear Markets: An Empirical Examination," Vision, , vol. 7(2), pages 57-77, July.
    3. Jonathan Ross, 2023. "Does prior stock return correlation predict future stock return correlation?," SN Business & Economics, Springer, vol. 3(9), pages 1-15, September.
    4. J. Andrew Coutts & Terence Mills & Jennifer Roberts, 1997. "Time series and cross-section parameter stability in the market model: the implications for event studies," The European Journal of Finance, Taylor & Francis Journals, vol. 3(3), pages 243-259.
    5. Vintilă Georgeta & Păunescu Radu Alin, 2015. "Econometric Tests of the CAPM Model for a Portfolio Composed of Companies Listed on Nasdaq and Dow Jones Components," Scientific Annals of Economics and Business, Sciendo, vol. 62(3), pages 453-480, November.
    6. Kayo, Eduardo K. & Martelanc, Roy & Brunaldi, Eduardo O. & da Silva, Walter E., 2020. "Capital asset pricing model, beta stability, and the pricing puzzle of electricity transmission in Brazil," Energy Policy, Elsevier, vol. 142(C).
    7. Prabhdeep Kaur & Jaspal Singh & Sidharath Seth, 2021. "Investigating the Dynamics of Exchange Traded Funds Across the Bear and Bull Markets: Evidence from Indian Equity ETFs," Vision, , vol. 25(3), pages 350-360, September.
    8. Maik Eisenbeiss & Goran Kauermann & Willi Semmler, 2007. "Estimating Beta-Coefficients of German Stock Data: A Non-Parametric Approach," The European Journal of Finance, Taylor & Francis Journals, vol. 13(6), pages 503-522.
    9. Cornelis Los, 2004. "Measuring the Degree of Efficiency of Financial Market," Finance 0411003, University Library of Munich, Germany.
    10. Dimitrios Dadakas & Christos Karpetis & Athanasios Fassas & Erotokritos Varelas, 2016. "Sectoral Differences in the Choice of the Time Horizon during Estimation of the Unconditional Stock Beta," IJFS, MDPI, vol. 4(4), pages 1-13, December.

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