Normalitetsanalyse af aktieafkast og implikationer af normalitetsbrud for den moderne porteføljeteori

Lars Rytter Jensen

Student thesis: Master thesis


This thesis deals with the modern portfolio theory and the key assumption that asset returns are normally distributed. The purpose of the thesis is to examine whether realized stock returns are normally distributed and what implications non-normality might have for the modern portfolio theory. An examination of the returns of several stock indices indicates that stock returns do not seem to be normally distributed. This is consistent with numerous empirical studies of stock returns. By examining different return frequencies, normality in the distribution of daily, weekly and monthly returns are rejected. Especially the distribution of daily and weekly returns exhibit abnormal high levels of kurtosis which means that the distribution of returns have much fatter tails than the normal distribution. It is also shown that the financial crisis in 2008 have a great impact on my results as an exclusion of the period means that monthly returns seem to be approximately normally distributed. This highlights the fact that research of normality in stock returns is sensitive to the period chosen, as volatility seems to cluster. The rejection of the assumption of normally distributed returns has practical importance for most institutional investors. The fatter tails of returns indicate that the risk of portfolios may be greater than expected when using normally distributed returns. Therefore the risk of portfolios seems to be underestimated and makes the mean-variance approach insufficient in describing the real risk of portfolios. Other measures of risk need to be included in a modified portfolio theory that focuses on more than just the standard deviation. Inclusion of the third and fourth distribution moment might give a better description of risk but has not yet been fully tested. Several other adjustments to the modern portfolio have been suggested. But optimization of portfolios with stable distributions or models that allow time varying variance does not seem to solve the problem concerning normality completely. From this thesis it is clear that the modern portfolio theory is an insufficient risk model. While using a wider spectrum of distribution moments to describe risk seems more accurate, it will never be possible to fully describe the risk of investing in portfolios. For lack of a complete description of risk we have to settle for the current models. However, the importance of understanding the weaknesses of the models and theories are crucial.

EducationsMSc in Finance and Accounting, (Graduate Programme) Final Thesis
Publication date2009
Number of pages153