Subtle Is the Lord, but Malicious He Is Not: The Calculation of Abnormal Stock Returns in Applied Research

48 Pages Posted: 13 Nov 2018

See all articles by Adrian Melia

Adrian Melia

University of Newcastle (Australia)

Xiaojing Song

Lecturer of Accounting & Finance

Mark J. Tippett

Loughborough University - Business School; University of Exeter Business School

Date Written: October 1, 2018

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.

Keywords: Abnormal Return; Feller Diffusion; Geometric Brownian Motion; Logarithmic Return

JEL Classification: C52, G14, G17

Suggested Citation

Melia, Adrian and Song, Xiaojing and Tippett, Mark J., Subtle Is the Lord, but Malicious He Is Not: The Calculation of Abnormal Stock Returns in Applied Research (October 1, 2018). Available at SSRN: https://ssrn.com/abstract=3270729 or http://dx.doi.org/10.2139/ssrn.3270729

Adrian Melia

University of Newcastle (Australia) ( email )

University Drive
Callaghan, NSW 2308
Australia

Xiaojing Song

Lecturer of Accounting & Finance ( email )

Norwich
NR4 7TJ
United Kingdom

Mark J. Tippett (Contact Author)

Loughborough University - Business School ( email )

Ashby Road
Loughborough
Nottingham NG1 4BU, LE11 3TU
Great Britain

University of Exeter Business School ( email )

Streatham Court
Xfi Building, Rennes Dr.
Exeter, EX4 4JH
United Kingdom

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