Portfolio Optimization with Random Matrix Theory and Artificial Neural Networks

Financial market data from the German stock market is analyzed with respect to the question of optimal capital allocation. There are two fundamental concepts in Modern Portfolio Theory which serve as reference theories. In the framework of mean-variance analysis, historical data is used to estimate expected returns of individual assets and cross-correlations across different assets in the market. These estimations are required when attempting to optimize the risk and return of potential investment portfolios. The Efficient Market Hypothesis states that all available information about a security is already priced into its price at any point in time and that consequently, the best estimation of future prices are the current prices. In this thesis, a systematic, automated approach to choose investment portfolios is developed. The resulting portfolios show lower combined risk than the ones that are obtained by mean-variance analysis. This is achieved by applying results from econophysics and in particular from Random Matrix Theory to improve future volatility estimations in an in-depth analysis of correlations between price fluctuations in the market. Furthermore, a neural network architecture is trained to estimate expected returns of securities. The resulting predictions are compared to the predictions that are obtained by the traditional mean-variance and the Efficient Market Hypothesis approaches.