An alternative approach for solving the problem of close to singular covariance matrices in modern portfolio theory

Sammanfattning: In this thesis the effects of utilizing the sample covariance matrix in the estimation of the global minimum variance (GMV) portfolio are presented. When the number of assets, N, are close to the number of observations, T, the sample covariance matrix approaches singularity, leading to a lot of uncertainties in form of estimation error. Due to that the computations of the sample GMV portfolio are linear transformations of the sample co- variance matrix inverse, the error is transferred to the portfolio weights. As a consequence, the portfolio performance out-of-sample is misleading and inadequate. To solve this shortcoming an alternative approach is presented. By grouping similar stocks together, utilizing sector indices, the dimension of the sample covariance matrix is decreased and consequently the estimation error. As a result, the sample sector index portfolio displays a more stable structure than the sample GMV portfolio counterpart as N / T → 1. This leads to more accurate parameter estimates and less volatile portfolio performances out-of-sample.