Noise Reducing Methods for Correlation Matrices - Improved Return and Risk Possible in Portfolio Management?

Abstract: The importance of the alluring goal of having the “perfect” or “true” information is more than visible in the financial world. In portfolio management financial correlation matrices measure the unsystematic correlations between assets e.g. stocks. Finding the true correlations between stocks would enable the creation of portfolios with less risk. In reality this information is more than hard to come by, partly since the correlations are buried under noise that effectively hides the precious, true correlations. If this noise could be reduced or even eliminated one would be able to unveil the true correlations, a powerful “weapon of knowledge” in portfolio management. Furthermore if patterns could be found in how the correlations change over time even further possibilities would emerge enabling faster adaptation to critical market trends. In the thesis we focus on evaluations of two different methods for noise reduction; Power Mapping, and RMT-filtering (a technique bases upon Random Matrix Theory). Both noise reduction methods are the offspring of Econophysics, a new scientific field combining Economics, Business Administration, and Physics. We also studied a new “hybrid method” previously created by the authors that merges Power Mapping and RMT-filtering. We came to the conclusion that all methods reduce risk for most of the portfolios, sometimes very strongly. Several aspects and behaviors of the methods were examined, with the aim to increase the understanding of these new, complex methods and the correlation structure in general. With a better understanding of the correlation matrices, we might indeed come one step closer to the shining promise of investments with less risk and even perhaps higher return.