Applications of Random Matrix Theory to Portfolio Management and Financial Networks

This thesis is an application of Random Matrix Theory (RMT) to portfolio management and financial networks. From a portfolio management perspective, we apply the RMT approach to clean measurement noise from correlation matrices constructed for large portfolios of stocks of the FTSE 100. We apply this methodology to a number of correlation estimators, i.e., the sample correlation matrix, the Constant Conditional Correlation Model (CCC) of Bollerslev (1990), the Dynamic Conditional Correlation (DCC) Model of Engle (2002) and the Regime-Switching Beta CAPM Correlation Model, based on Ang and Bekaert (2004). For these estimators, we find that the RMT- filtering delivers portfolios with the lowest realised risk, the best prediction accuracy and also the highest cumulated returns and Sharpe Ratios. The gains from using the RMT-filtering, in terms of cumulated wealth, range from 65%, for the sample correlation matrix to 30%, for the regime-dependent correlation estimator. In the case of regime switching CAPM models, we find that the regime switching correlation matrices, in the high volatility regime are found to be a good filter which makes further RMT- filtering to be redundant. This establishes the validity of using regime sensitive portfolio management to deal with asymmetric asset correlations during high and low volatility regimes. From a financial network perspective, we assess the stability of a global banking network built from bilateral exposures of 18 BIS reporting banking systems to net debtor countries. For this, we applied the eigen-pair method of Markose (2012), which is based on the work of May (1972, 1974) for random networks. We use a stability condition based on the maximum eigenvalue (λmax) of a matrix of net bilateral exposures relative to equity capital as a systemic risk index (SRI). We provide evidence of the early warning capabilities of λmax, when this surpasses a prespecified threshold. We use the right and left associated eigenvectors as a gauge for systemic importance and systemic vulnerability, respectively. The λmax SRI was found to be superior in terms of early warning when compared to the standard SRIs based on market price data, viz. the DCC-MES of Acharya et al. (2010), the SRISK of Acharya et al. (2012) and the DCC-ΔCoVaR of Adrian and Brunnermeier (2011).