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

Claeson, Martin LU (2017) STAM01 20171
Department 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 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... (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 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. (Less)
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author
Claeson, Martin LU
supervisor
organization
course
STAM01 20171
year
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
2018-01-23 09:28:30
date last changed
2018-01-23 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 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.},
  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},
}