Application of Regime Switching and Random Matrix Theory for Portfolio Optimization

Market economies have been characterized by boom and bust cycles. Since the seminal work of Hamilton (1989), these large scale fluctuations have been referred to as regime switches. Ang and Bekaert (2002) were the first to consider the role of regime switches for stock market returns and portfolio optimisation. The key stylized facts regarding regime switching for stock index returns is that boom periods with positive mean stock returns are associated with low volatility, while bear markets with negative mean returns have high volatility. The correlation of asset returns also show asymmetry with greater correlation being found during stock market downturns. In view of the large portfolio losses from correlated negative movements in asset returns during the recent 2007 financial crisis, it has become imperative to incorporate regime sensitivity in portfolio management. This thesis forms an extensive application of regime sensitive statistics for stock returns in the management of equity portfolios for different markets. Starting with the application to a small 3 asset portfolio for UK stocks (in Chapter 4), the methodology is extended to large scale portfolio for the FTSE-100. In chapters 5 and 6, respectively, using stock index data from the subcontinent (India, Pakistan and Bangladesh) and for the Asia Pacific, optimal regime sensitive portfolios have been analysed with the MSCI AC Index (for Emerging and Asia Pacific Markets) being taken as the benchmark index. Portfolio performance has been studied using a dynamic end of month rebalancing of the portfolio on the basis of regime indicators given by market index and relevant regime dependent portfolio statistics. The cumulative end of period returns and risk adjusted Sharpe Ratio from this exercise is compared to the simple Markowitz mean-variance portfolio and market value portfolio. The regime switching optimal portfolio strategy has been found to dominate non-regime sensitive portfolio strategies in Asia Pacific and 3 asset portfolio for UK stocks cases but not in Subcontinent case (for the first half of out-sample period). In the case of the relationship of the sub-continental indexes vis-à-vis the MSCI benchmark index, the latter has negligible explanatory power for the former especially for the first half of out-sample period. Hence, the regime indicators based on MSCI emerging market index have detrimental effects on portfolio selection based on the sub-continental indexes. As regime sensitive variance–covariance matrices have implications for the selection of optimal portfolio weights, the final Chapter 7 uses the FTSE-100 and its constituent company data to compare and contrast the implications for optimal portfolio management of filtering the covariance matrix using Random Matrix Theory (RMT). While it is found that filtering the variance-covariance matrix using Marchenko-Pasteur bounds of RMT improves optimal portfolio choice in both non-regime and regime dependent cases, remarkably in the latter case for Regime 2 determined variance-covariance matrix, the RMT filter was least needed. This result is given in Chapter 7, Table 7.5-1. This confirms the significance of using Hamilton (1989) regime sensitive statistics for stock returns in identifying the ‘true’ non-noisy variance-covariance relationships. The RMT methodology is also useful for identifying the centrality, based on eigenvector analysis, of the constituent stocks in their role in driving crisis and non-crisis market conditions. A fully automated suite of programs in MATLAB have been developed for regime switching portfolio optimization with RMT filtering of the variance-covariance matrix.