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Investment Volatility: A Critique of Standard Beta Estimation and a Simple Way Forward

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  • Chris Tofallis
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    Abstract

    Beta is a widely used quantity in investment analysis. We review the common interpretations that are applied to beta in finance and show that the standard method of estimation - least squares regression - is inconsistent with these interpretations. We present the case for an alternative beta estimator which is more appropriate, as well as being easier to understand and to calculate. Unlike regression, the line fit we propose treats both variables in the same way. Remarkably, it provides a slope that is precisely the ratio of the volatility of the investment's rate of return to the volatility of the market index rate of return (or the equivalent excess rates of returns). Hence, this line fitting method gives an alternative beta, which corresponds exactly to the relative volatility of an investment - which is one of the usual interpretations attached to beta.

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    File URL: http://arxiv.org/pdf/1109.4422
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    Paper provided by arXiv.org in its series Papers with number 1109.4422.

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    Date of creation: Sep 2011
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    Publication status: Published in European Journal of Operational Research 187 (2008) 1358-1367
    Handle: RePEc:arx:papers:1109.4422

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    1. Blume, Marshall E, 1975. "Betas and Their Regression Tendencies," Journal of Finance, American Finance Association, vol. 30(3), pages 785-95, June.
    2. Booth, James R. & Smith, Richard L., 1985. "The Application of Errors-in-Variables Methodology to Capital Market Research: Evidence on the Small-Firm Effect," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 20(04), pages 501-515, December.
    3. Francis, Jack Clark, 1979. "Statistical Analysis of Risk Surrogates for Nyse Stocks," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 14(05), pages 981-997, December.
    4. Robert W. Faff & David Hillier & Joseph Hillier, 2000. "Time Varying Beta Risk: An Analysis of Alternative Modelling Techniques," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 27(5&6), pages 523-554.
    5. Don U.A. Galagedera, 2004. "A Survey On Investment Performance Appraisal Methods With Special Reference To Data Envelopment Analysis," Finance 0406013, EconWPA.
    6. Daraio, Cinzia & Simar, Leopold, 2006. "A robust nonparametric approach to evaluate and explain the performance of mutual funds," European Journal of Operational Research, Elsevier, vol. 175(1), pages 516-542, November.
    7. Fama, Eugene F & French, Kenneth R, 1992. " The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-65, June.
    8. Fabozzi, Frank J. & Francis, Jack Clark, 1978. "Beta as a Random Coefficient," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(01), pages 101-116, March.
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