IDEAS home Printed from https://ideas.repec.org/a/taf/eurjfi/v25y2019i9p835-855.html
   My bibliography  Save this article

Subtle is the Lord, but malicious He is not: the calculation of abnormal stock returns in applied research

Author

Listed:
  • Adrian Melia
  • Xiaojing Song
  • Mark Tippett

Abstract

We use the expected logarithmic returns formula for the Geometric Brownian Motion (GBM) in conjunction with the expected logarithmic returns formula for the Feller diffusion to illustrate the nature and magnitude of errors which arise in computed abnormal returns when one applies an expected logarithmic returns formula which is incompatible with the stochastic process that generates a stock’s returns. Empirical analysis based on FTSE 100 stock price data for the five year period ending in 2017 shows that the scale of the errors in computed abnormal returns will hinge on the volatility of the returns generating process but will be particularly pronounced for relatively low stock prices. Although our principal focus is with comparing abnormal returns on the GBM and Feller diffusion, we also simulate logarithmic returns for the Uhlenbeck and Ornstein (1930) process, several interpretations of the Constant Elasticity of Variance (CEV) process and the scaled ‘t’ process of Praetz (1972) and Blattberg and Gonedes (1974). Taken in conjunction with the GBM and the Feller diffusion, these processes underpin virtually every equilibrium based asset pricing model which appears in the literature. However, computing abnormal returns for any of these processes using the expected logarithmic returns formula for the GBM inevitably leads to errors in the abnormal returns. Hence, an important principle which emerges from our analysis is that it is crucially important for researchers and others to test the compatibility of empirically observed returns with the distributional assumptions on which the empirical analysis is based if the complications arising from mis-specified modelling procedures are to be avoided.

Suggested Citation

  • Adrian Melia & Xiaojing Song & Mark Tippett, 2019. "Subtle is the Lord, but malicious He is not: the calculation of abnormal stock returns in applied research," The European Journal of Finance, Taylor & Francis Journals, vol. 25(9), pages 835-855, June.
  • Handle: RePEc:taf:eurjfi:v:25:y:2019:i:9:p:835-855
    DOI: 10.1080/1351847X.2018.1537981
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/1351847X.2018.1537981
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/1351847X.2018.1537981?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.

    More about this item

    Statistics

    Access and download statistics

    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:eurjfi:v:25:y:2019:i:9:p:835-855. 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.

    We have no bibliographic references for this item. You can help adding them by using 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/REJF20 .

    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.