| Summary: | From option pricing using the Black and Scholes model, to determining the signi cance of regression coe cients in a capital asset pricing model (CAPM), the assumption of normality was pervasive throughout the eld of nance. This was despite evidence that nancial returns were non-normal, skewed and heavy- tailed. In addition to non-normality, there remained questions about the e ect of rm size on returns. Studies examining these di erences were limited to ex- amining the mean return, with respect to an asset pricing model, and did not consider higher moments. Janse van Rensburg, Sharp and Friskin (in press) attempted to address both the problem of non-normality and size simultaneously. They (Janse van Rens- burg et al in press) tted a mixture of two normal distributions, with common mean but di erent variances, to a small capitalisation portfolio and a large cap- italisation portfolio. Comparison of the mixture distributions yielded valuable insight into the di erences between the small and large capitalisation portfolios' risk. Janse van Rensburg et al (in press), however, identi ed several shortcom- ings within their work. These included data problems, such as survivorship bias and the exclusion of dividends, and the questionable use of standard statistical tests in the presence of non-normality. This study sought to correct the problems noted in the paper by Janse van Rensburg et al (in press) and to expand upon their research. To this end survivorship bias was eliminated and an e ective dividend was included into the return calculations. Weekly data were used, rather than the monthly data of Janse van Rensburg et al (in press). More portfolios, over shorter holding periods, were considered. This allowed the authors to test whether Janse van Rensburg et al's (in press) ndings remained valid under conditions di erent to their original study. Inference was also based on bootstrapped statistics, in order to circumvent problems associated with non-normality. Additionally, several di erent speci cations of the normal mixture distribution were considered, as opposed to only the two-component scale mixture. In the following, Chapter 2 provided a literature review of previous studies on return distributions and size e ects. The data, data preparation and portfolio formation were discussed in Chapter 3. Chapter 4 gave an overview of the statistical methods and tests used throughout the study. The empirical results of these tests, prior to risk adjustment, were presented in Chapter 5. The impact of risk adjustment on the distribution of returns was documented in Chapter 6. The study ended, Chapter 7, with a summary of the results and suggestions for future research.
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