Analysis of Aggregated Return Distributions for Stock Markets

A key factor of analysing the financial market are multivariate return time series which are gained by stock prices. The distributions of empiric data displays heavy tailed behaviour which cannot be characterised by a normal distribution. This fact also entails that we encounter non-stationarity when comparing different stocks and even different time intervals of the same stock. This makes an accurate estimation of moments such as volatility, also referred to as risk, almost impossible. We will propose a model to fit this empiric distributions to better understand their tail behaviour. We analyze 479 US stocks included in the S&P500 index during the trading year of 2014. We use the data of single day to fit an algebraic distribution. Continuing we use larger time intervals. To offset the random fluctuations occurring in the correlation matrices we introduce a random matrix model. The assumptions for the two appearing distributions in the model are either Gaussian or algebraic. This results in four different combinations. We are able to fit the distributions of different interval lengths and data points used per epoch for all results of the model