Mean Reversion and the Distribution of United Kingdom Stock Index Returns

24 Pages Posted: 7 Dec 2006

See all articles by David J. Ashton

David J. Ashton

University of Bristol - Department of Economics

Mark J. Tippett

Loughborough University - Business School; University of Exeter Business School


Our purpose here is to develop the Pearson Type IV distribution as a candidate for modelling the evolution of short period stock index returns. Here, early work by Praetz (1972 and 1978) and Blattberg and Gonedes (1974) has shown that the scaled "t" distribution, which is a particular (symmetric) interpretation of the Pearson Type IV, provides a reasonable description of the way stock index returns evolve over time. Our analysis shows this is certainly not the case for the daily stock index returns on which our empirical analysis is based. There is significant skewness in the data and this cannot be captured by symmetric distributions like the scaled "t" and normal distributions. However, the Pearson Type IV, which is a skewed generalisation of the scaled "t," is capable of modelling the skewness inherent in our data and in such a way that it satisfies asymptotically efficient goodness of fit criteria. Furthermore, the Pearson Type IV can be derived from a stochastic differential equation with standard Markov properties. This enables one to integrate the distributional and time series properties of the returns process and thereby, facilitates both the interpretation and understanding of the role played by the distribution's parameters in the generation of the underlying stock index returns.

Suggested Citation

Ashton, David John and Tippett, Mark J., Mean Reversion and the Distribution of United Kingdom Stock Index Returns. Journal of Business Finance & Accounting, Vol. 33, No. 9-10, pp. 1586-1609, November/December 2006. Available at SSRN: or

David John Ashton

University of Bristol - Department of Economics ( email )

8 Woodland Road
Bristol BS8 ITN
United Kingdom
+44 (0)117 928 8423 (Phone)

Mark J. Tippett (Contact Author)

Loughborough University - Business School ( email )

Ashby Road
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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