In this seminar I will discuss some major areas of my thesis. The von Mises Fisher distribution, which is a kind of distribution on the sphere, and a method of hypothesis testing sparked by Chernoff in 1954, provide the most significant parts of my thesis. We model a financial portfolio by a mixture model containing von Mises Fisher distributions from lower subcomponents. We find the asymptotic distribution of the deviance statistic for the null hypothesis of whether the concentration parameters of the 2-dimensional portfolios are equal or not. The data are taken from the Yahoo Finance website and are historical prices of three different indices I use for making monthly portfolios.