The Feller Diffusion, Filter Rules and Abnormal Stock Returns

European Journal of Finance (Forthcoming)

26 Pages Posted: 17 Mar 2017 Last revised: 29 Jul 2019

See all articles by Paul Docherty

Paul Docherty

Monash University

Yizhe Dong

University of Edinburgh Business School

Xiaojing Song

Lecturer of Accounting & Finance

Mark J. Tippett

Loughborough University - Business School; University of Exeter Business School

Date Written: March 10, 2017

Abstract

We determine the conditional expected logarithmic (that is, continuously compounded) return on a stock whose price evolves in terms of the Feller diffusion and then use it to demonstrate how one must know the exact probability density that describes a stock’s return before one can determine the correct way to calculate the abnormal returns that accrue on the stock. We show in particular that misspecification of the stochastic process which generates a stock’s price will lead to systematic biases in the abnormal returns calculated on the stock. We examine the implications this has for the proper conduct of empirical work and for the evaluation of stock and portfolio performance.

Keywords: Feller Diffusion, Fokker-Planck Equation, Geometric Brownian Motion, Logarithmic Return

JEL Classification: C52, G14, G17

Suggested Citation

Docherty, Paul and Dong, Yizhe and Song, Xiaojing and Tippett, Mark J., The Feller Diffusion, Filter Rules and Abnormal Stock Returns (March 10, 2017). European Journal of Finance (Forthcoming). Available at SSRN: https://ssrn.com/abstract=2932318

Paul Docherty

Monash University ( email )

23 Innovation Walk
Wellington Road
Clayton, Victoria 3800
Australia

Yizhe Dong

University of Edinburgh Business School ( email )

Old College
South Bridge
Edinburgh, Scotland EH8 9JY
United Kingdom

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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