An alternative approach for solving the problem of close to singular covariance matrices in modern portfolio theory
(2017) STAM01 20171Department of Statistics
 Abstract
 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 outofsample is misleading and inadequate.
To solve this shortcoming an alternative approach is presented. By grouping similar stocks together, utilizing sector indices, the dimension... (More)  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 outofsample 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 outofsample. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/8931835
 author
 Claeson, Martin ^{LU}
 supervisor

 Krzysztof Podgorski ^{LU}
 organization
 course
 STAM01 20171
 year
 2017
 type
 H1  Master's Degree (One Year)
 subject
 keywords
 global minimum variance portfolio, singular covariance matrix, sector index portfolio
 language
 English
 id
 8931835
 date added to LUP
 20180123 09:28:30
 date last changed
 20180123 09:28:30
@misc{8931835, abstract = {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 outofsample 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 outofsample.}, author = {Claeson, Martin}, keyword = {global minimum variance portfolio,singular covariance matrix,sector index portfolio}, language = {eng}, note = {Student Paper}, title = {An alternative approach for solving the problem of close to singular covariance matrices in modern portfolio theory}, year = {2017}, }