A note on return distribution of UK stock indices

Abstract

The aim of this paper is to provide empirical evidence on the statistical distributions of returns on 32 UK sector indices as well as the FTSE-All and the FTSE-100 indices. These data are modelled for several holding periods, ranging from one day to one quarter, using symmetric stable Paretian distributions and their characteristic exponents are estimated. Numerical results suggest that both short and long horizon returns are non-normal and that deviation from normality is stronger for short horizon returns, with the exception of few sectors. In sum, these results suggest that asset pricing and risk management models, among others, should be modified to take into account departures form normality.

Notes

 The earliest evidence is provided by Mandelbrot (1963), Fama (1965), Officer (1972) and Rachev and Mittnik (1989), among others.

 See McCulloh (1996), McDonald (1996) and Rachev and Mittnik (2002) for financial applications of stable distributions.

 We do not provide summary statistics for different return horizons to save space. However, all results are available upon request.

 Various procedures for estimating the parameters α, β, δ, and c have been proposed in the literature such as the maximum likelihood approach (DuMouchel, 1971, 1973; Chen, 1991), Hill estimator (Hill, 1975), the method-of-moments approach (Press, 1972), the regression-type estimation approach (Koutrouvelis, 1980, 1981), tail estimation (Rachev and Mittnik, 1996), and the quantile approach (Fama and Roll, 1968, 1971; McCulloch, 1986), among others. See also de Haan and Perreira (1999). However, for f ∈ [0.95, 0.97], the estimator we use is robust against variations in the value of α (Fama and Roll, 1968, 1971).