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7 - Modelling return distributions

Published online by Cambridge University Press:  05 June 2012

Terence C. Mills
Affiliation:
Loughborough University
Raphael N. Markellos
Affiliation:
Norwich Business School, University of East Anglia
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Summary

The choice of unconditional distribution is something that has always puzzled academics and practitioners in finance. The standard assumption since the 1960s has been that financial prices are geometric Brownian motions and, therefore, logarithmic returns follow a normal distribution. This assumption has profound implications for a variety of theoretical and practical problems in finance, as expected returns and risks in a multivariate normal financial world can be fully described probabilistically using just means, variances and covariances. Much of finance analysis, such as primary and derivative asset pricing, portfolio optimisation and risk management, is built upon the assumption of normally distributed returns. The normal distribution also has important implications for econometric and statistical analysis, since most of the underlying theory is parametric and has been developed on the basis of normality.

The popularity of the normal distribution is easily justifiable from a practical point of view because it offers tractability and computational simplicity. Furthermore, the normality assumption is supported theoretically by the central limit theorem (CLT), which states that the sum of iid random variables with finite mean and variance will asymptotically converge to a normal distribution. Under these assumptions, the normal distribution will offer the best approximation to empirical return distributions in samples of reasonable size.

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Publisher: Cambridge University Press
Print publication year: 2008

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