Can random matrix theory resolve Markowitz optimization enigma?: the impact of "noise" filtered covariance matrix on portfolio selection

Modern finance theory is based on the simple concept of risk and return trade-off. Risk is based upon one holding a diversified portfolio to get the lowest level of risk for a given expected return. This is the foundation of Markowitz’s mean-variance (MV) efficient portfolio. For nearly six decades since Markowitz’s pioneering work, it is still a puzzle as to why there are persistent doubts about the performance of MV approach to portfolio selection and the lack of acceptance as a viable tool in the investment community. This puzzle is coined as the “Markowitz optimization enigma”. The major problem with MV optimization is its tendency to maximize the effects of estimation errors in the risk and return estimates. iii The latest attempt to reduce the noise in covariance estimates is a branch from physics that uses Random Matrix Theory (RMT) prediction. The prediction is that when the number of securities is large relative to the number of observations, the eigenvalues of the covariance matrix within a predicted band closely resemble the distribution as if they were generated from purely random returns. These studies believe that by modifying the eigenvalues within the predicted band, the “filtered” covariance matrix would contain better information than the raw sample matrix. One proprietary commercial product, called the Neutron QuantumApp which was released in mid-2013, based its filtration technique on RMT prediction. The motivation of this dissertation is to examine the effectiveness of the Neutron product in terms of risk measurement, mean-variance efficiency and portfolio performance. More specifically, does the filtered covariance contain superior information as compared to the raw covariance? The evidence shows that the efficient frontier, generated from filtered covariance, indeed dominates the raw efficient frontier for the unconstrained case. When short-sale constraint is imposed, the result is similar except for the minimum variance portfolio (MVP). The MVP from the raw matrix dominates the MVP from the filtered matrix. In general, the filtered covariance appears to be better for the purpose of risk measurement and risk management. The filtered correlation structure is considerably higher. iv However, more efficient portfolios do not translate into better performers. For the period 2006 to 2013, one cannot reject the null hypothesis that the filtered portfolios perform similarly to the raw portfolios. Therefore, my conclusion is that the Neutron product cannot resolve Markowitz optimization enigma.Ph. D.Includes bibliographical referencesby Kim Wah N