Can random matrix theory resolve Markowitz optimization enigma?

TL;DRAbstract

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

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