Risk Separation from Correlation Matrices in Portfolio Optimization

Oliver Laybourn & Christopher Joseph Kurish

Student thesis: Master thesis


In this master thesis we use statistical methods to clean noise from large correlation matrices and then apply these cleaned correlation matrices to improve risk management. Using covariance matrices to optimize a portfolio has been a powerful tool to assess risk, since Markowitz introduced the concept of minimum variance portfolios. By minimizing risk, we are able to decide what the optimal weights would be for a large portfolio of stocks. We are interested in interpreting what kind of risk is inherent in this portfolio. We do so by applying an orthogonal factor model to our approximation. Here we analyze risk as being either systematic or idiosyncratic. We present another cleaning method from the theory of Random Matrix Theory, which compares the eigenvalues of an empirical correlation matrix with the distribution of eigenvalues of a random correlation matrix generated from i.i.d normal distributed returns. Risk is then seen as either genuine or random. We consider the FTSE 100 on the London Stock Exchange, which is a market that consists of the 100 stocks with the largest market capitalization on the London Stock Exchange. We make a thorough analysis of the eigenvalues and eigenvectors for one fiscal year and find resemblance of random behavior in the eigenvalues-eigenvector pairs we observe as random. Afterwards we clean our correlation matrices using methods from Factor analysis and Random Matrix Theory, where two cleaning methods are applied. We compare our cleaned models with the empirical correlation matrix to see if we are able to make better risk predictions. When we estimate risk over one-year periods the results are ambiguous, but the overall impression is that cleaning methods have a positive effect. Finally, we see that using shorter periods of time gives the best performances for improving risk management.

EducationsMSc in Business Administration and Mathematical Business Economics, (Graduate Programme) Final Thesis
Publication date2019
Number of pages113
SupervisorsPeter Dalgaard