Modelling Ghana Stock Exchange Indicies and Exchange Rates with Stable Distributions

Abstract

Most of the concepts in theoretical and empirical finance that have been developed over the last 50 years rest upon the assumption that the return or price distribution for financial data follows a normal distribution. But this assumption is not justified by empirical data. Rather, the empirical observations (financial returns) exhibit excess kurtosis, more colloquially known as fat tails or heavy tails. This research first described the stable distribution family -   stable, Levy stable, Cauchy and Gaussian or Normal distributions. The study presented three methods of estimating parameters of   stable distributions, namely Maximum Likelihood estimation, Empirical Characteristic function and Sample Quantile methods, and goodness of fit tests- K-S and Chi-square, were used to quantitatively assess the quality performance of their respective estimates. A sample of weekly financial data (GSE All-Shares index, USD/GHC, GBP/GHC and EUR/GHC exchange rates) covering the period of 02/01/2000 − 31/12/2011 was analysed, and fitted to   stable, Cauchy and Normal distributions. Diagnostic tests such as P-P and Q-Q plots and goodness of fit tests (K-S, Chi-square, Anderson-Darling and Shapiro-Wilk) were graphically and quantitatively used to assess fitness to the returns of the data respectively. The study concludes that the weekly return distributions of Ghana financial data are heavy tailed and asymmetry and the maximum likelihood estimation method produce the most accurate and efficient estimates for the   stable fit to the data. The weekly financial data considered were modelled with   stable distribution and recommends that for efficient risk and assets returns management, analysts should explore and discover actual return distributions of financial data and not desist from speculative assumptions.