IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v10y2010i4p375-387.html
   My bibliography  Save this article

Robust estimation with flexible parametric distributions: estimation of utility stock betas

Author

Listed:
  • James Mcdonald
  • Richard Michelfelder
  • Panayiotis Theodossiou

Abstract

The distributions of stock returns and capital asset pricing model (CAPM) regression residuals are typically characterized by skewness and kurtosis. We apply four flexible probability density functions (pdfs) to model possible skewness and kurtosis in estimating the parameters of the CAPM and compare the corresponding estimates with ordinary least squares (OLS) and other symmetric distribution estimates. Estimation using the flexible pdfs provides more efficient results than OLS when the errors are non-normal and similar results when the errors are normal. Large estimation differences correspond to clear departures from normality. Our results show that OLS is not the best estimator of betas using this type of data. Our results suggest that the use of OLS CAPM betas may lead to erroneous estimates of the cost of capital for public utility stocks.

Suggested Citation

  • James Mcdonald & Richard Michelfelder & Panayiotis Theodossiou, 2010. "Robust estimation with flexible parametric distributions: estimation of utility stock betas," Quantitative Finance, Taylor & Francis Journals, vol. 10(4), pages 375-387.
    • Handle: RePEc:taf:quantf:v:10:y:2010:i:4:p:375-387
    DOI: 10.1080/14697680902814241
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/14697680902814241
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697680902814241?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    2. Klein, Roger W. & Bawa, Vijay S., 1976. "The effect of estimation risk on optimal portfolio choice," Journal of Financial Economics, Elsevier, vol. 3(3), pages 215-231, June.
    3. Fama, Eugene F. & MacBeth, James D., 1974. "Tests of the multiperiod two-parameter model," Journal of Financial Economics, Elsevier, vol. 1(1), pages 43-66, May.
    4. Bali, Turan G. & Weinbaum, David, 2007. "A conditional extreme value volatility estimator based on high-frequency returns," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 361-397, February.
    5. Blume, Marshall E & Friend, Irwin, 1973. "A New Look at the Capital Asset Pricing Model," Journal of Finance, American Finance Association, vol. 28(1), pages 19-33, March.
    6. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(4), pages 465-487, December.
    7. Newey, Whitney K., 1988. "Adaptive estimation of regression models via moment restrictions," Journal of Econometrics, Elsevier, vol. 38(3), pages 301-339, July.
    8. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
    9. Turan G. Bali, 2003. "An Extreme Value Approach to Estimating Volatility and Value at Risk," The Journal of Business, University of Chicago Press, vol. 76(1), pages 83-108, January.
    10. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(3), pages 428-457, December.
    11. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    12. Andrew F. Siegel & Artemiza Woodgate, 2007. "Performance of Portfolios Optimized with Estimation Error," Management Science, INFORMS, vol. 53(6), pages 1005-1015, June.
    13. Butler, Richard J, et al, 1990. "Robust and Partially Adaptive Estimation of Regression Models," The Review of Economics and Statistics, MIT Press, vol. 72(2), pages 321-327, May.
    14. Blume, Marshall E, 1975. "Betas and Their Regression Tendencies," Journal of Finance, American Finance Association, vol. 30(3), pages 785-795, June.
    15. Francis, Jack Clark, 1975. "Skewness and Investors' Decisions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 10(1), pages 163-172, March.
    16. Chan, Louis K. C. & Lakonishok, Josef, 1992. "Robust Measurement of Beta Risk," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(2), pages 265-282, June.
    17. Handa, Puneet & Kothari, S P & Wasley, Charles, 1993. "Sensitivity of Multivariate Tests of the Capital Asset-Pricing Model to the Return Measurement Interval," Journal of Finance, American Finance Association, vol. 48(4), pages 1543-1551, September.
    18. Akgiray, Vedat & Booth, G Geoffrey, 1988. "Mixed Diffusion-Jump Process Modeling of Exchange Rate Movements," The Review of Economics and Statistics, MIT Press, vol. 70(4), pages 631-637, November.
    19. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    20. Brian Boyer & James McDonald & Whitney Newey, 2003. "A Comparison of Partially Adaptive and Reweighted Least Squares Estimation," Econometric Reviews, Taylor & Francis Journals, vol. 22(2), pages 115-134.
    21. Sukant K. Misra & Jeannie Nelson, 2003. "Efficient Estimation of Agricultural Time Series Models with Nonnormal Dependent Variables," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 85(4), pages 1029-1040.
    22. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    23. Bey, Roger P., 1983. "Market Model Stationarity of Individual Public Utilities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(1), pages 67-85, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. BenSaïda, Ahmed & Slim, Skander, 2016. "Highly flexible distributions to fit multiple frequency financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 203-213.
    2. Scott Alan Carson & Wael M. Al-Sawai & Scott A. Carson, 2023. "Partially Adaptive Econometric Methods and Vertically Integrated Majors in the Oil and Gas Industry," CESifo Working Paper Series 10733, CESifo.
    3. Theodossiou, Alexandra K. & Theodossiou, Panayiotis, 2014. "Stock return outliers and beta estimation: The case of U.S. pharmaceutical companies," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 30(C), pages 153-171.
    4. Roger Buckland & Julian Williams & Janice Beecher, 2015. "Risk and regulation in water utilities: a cross-country comparison of evidence from the CAPM," Journal of Regulatory Economics, Springer, vol. 47(2), pages 117-145, April.
    5. Joe Hirschberg & Jenny Lye, 2021. "Estimating risk premiums for regulated firms when accounting for reference-day variation and high-order moments of return volatility," Environment Systems and Decisions, Springer, vol. 41(3), pages 455-467, September.
    6. Sikora, Grzegorz & Michalak, Anna & Bielak, Łukasz & Miśta, Paweł & Wyłomańska, Agnieszka, 2019. "Stochastic modeling of currency exchange rates with novel validation techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1202-1215.
    7. Szarek, Dawid & Bielak, Łukasz & Wyłomańska, Agnieszka, 2020. "Long-term prediction of the metals’ prices using non-Gaussian time-inhomogeneous stochastic process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. James B. McDonald & Richard A. Michelfelder & Panayiotis Theodossiou, 2009. "Robust Regression Estimation Methods and Intercept Bias: A Capital Asset Pricing Model Application," Multinational Finance Journal, Multinational Finance Journal, vol. 13(3-4), pages 293-321, September.
    2. Scott Alan Carson & Wael M. Al-Sawai & Scott A. Carson, 2023. "Partially Adaptive Econometric Methods and Vertically Integrated Majors in the Oil and Gas Industry," CESifo Working Paper Series 10733, CESifo.
    3. Bali, Turan G. & Mo, Hengyong & Tang, Yi, 2008. "The role of autoregressive conditional skewness and kurtosis in the estimation of conditional VaR," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 269-282, February.
    4. Hansen, James V. & McDonald, James B. & Turley, Robert S., 2006. "Partially adaptive robust estimation of regression models and applications," European Journal of Operational Research, Elsevier, vol. 170(1), pages 132-143, April.
    5. Mauleon, Ignacio, 2003. "Financial densities in emerging markets: an application of the multivariate ES density," Emerging Markets Review, Elsevier, vol. 4(2), pages 197-223, June.
    6. Delis, Manthos & Savva, Christos & Theodossiou, Panayiotis, 2020. "A Coronavirus Asset Pricing Model: The Role of Skewness," MPRA Paper 100877, University Library of Munich, Germany.
    7. James B. McDonald & Daniel B. Walton & Bryan Chia, 2020. "Distributional Assumptions and the Estimation of Contingent Valuation Models," Computational Economics, Springer;Society for Computational Economics, vol. 56(2), pages 431-460, August.
    8. Delis, Manthos D. & Savva, Christos S. & Theodossiou, Panayiotis, 2021. "The impact of the coronavirus crisis on the market price of risk," Journal of Financial Stability, Elsevier, vol. 53(C).
    9. Randall A. Lewis & James B. McDonald, 2014. "Partially Adaptive Estimation of the Censored Regression Model," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 732-750, October.
    10. Adcock, C.J. & Shutes, K., 2005. "An analysis of skewness and skewness persistence in three emerging markets," Emerging Markets Review, Elsevier, vol. 6(4), pages 396-418, December.
    11. Allen, Linda & Bali, Turan G., 2007. "Cyclicality in catastrophic and operational risk measurements," Journal of Banking & Finance, Elsevier, vol. 31(4), pages 1191-1235, April.
    12. James B. McDonald & Hieu Nguyen, 2012. "Heteroskedasticity and Distributional Assumptions in the Censored Regression Model," BYU Macroeconomics and Computational Laboratory Working Paper Series 2012-09, Brigham Young University, Department of Economics, BYU Macroeconomics and Computational Laboratory.
    13. Richard Harris & C. Coskun Kucukozmen, 2001. "The empirical distribution of stock returns: evidence from an emerging European market," Applied Economics Letters, Taylor & Francis Journals, vol. 8(6), pages 367-371.
    14. Adcock, C J & Meade, N, 2017. "Using parametric classification trees for model selection with applications to financial risk management," European Journal of Operational Research, Elsevier, vol. 259(2), pages 746-765.
    15. BenSaïda, Ahmed & Slim, Skander, 2016. "Highly flexible distributions to fit multiple frequency financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 203-213.
    16. Fong, Wai Mun, 1997. "Robust beta estimation: Some empirical evidence," Review of Financial Economics, Elsevier, vol. 6(2), pages 167-186.
    17. C. James Hueng & Ruey Yau, 2006. "Investor preferences and portfolio selection: is diversification an appropriate strategy?," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 255-271.
    18. Choi, Pilsun & Nam, Kiseok, 2008. "Asymmetric and leptokurtic distribution for heteroscedastic asset returns: The SU-normal distribution," Journal of Empirical Finance, Elsevier, vol. 15(1), pages 41-63, January.
    19. Lin, Chu-Hsiung & Changchien, Chang-Cheng & Kao, Tzu-Chuan & Kao, Wei-Shun, 2014. "High-order moments and extreme value approach for value-at-risk," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 421-434.
    20. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:quantf:v:10:y:2010:i:4:p:375-387. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.