Utilizing Machine Learning to Address Noise in Covariance and Correlation Matrices: An Application and Modification of Enhanced Portfolio Optimisation

Abstrakt

Portfolio Optimisation is at the core of Asset Management since the invention of the Mean Variance Portfolio Optimisation by Harry Markowitz (1952). Its theoretical usefulness as well as its practical flaws have been studied by several academics. The recent developments within the Machine Learning environment enabled researchers to use modern technologies to find solutions on how to make Mean Variance Optimisation work. Enhanced Portfolio Optimisation has been coined and termed by Pedersen et al. (2021). It makes use of Machine Learning through the unsupervised algorithm Principal Component Analysis to detect noise and structure in the underlying correlation matrices of portfolios. By shrinking the correlation matrix towards the identity matrix, they realise substantially higher Sharpe ratios than their benchmarks. In their study, they are able to effectively address the problem of estimation noise. This finding cannot be confirmed by this thesis. Instead, it shows that their strategy yields inferior Sharpe ratios than the classical Mean Variance Optimisation. A modified version of the Enhanced Portfolio Optimisation is proposed by shrinking towards the average correlations instead of the identity matrix. This approach appears to be superior to the original approach. However, the Mean Variance Portfolio as well as the equally weighted portfolio are tough benchmarks to beat. The main finding is displayed by the dependence of the shrinkage parameter on the prevailing economic cycle, as well as the dependence of Enhance Portfolio Optimisation on the estimation of the correlation matrix.