Predicting the Global Minimum Variance Portfolio

53 Pages Posted: 21 Nov 2019 Last revised: 21 Sep 2021

See all articles by Laura Reh

Laura Reh

University of Cologne - Department of Economics

Fabian Krüger

Karlsruhe Institute of Technology

Roman Liesenfeld

University of Cologne, Department of Economics

Date Written: August 18, 2021

Abstract

We propose a novel dynamic approach to forecast the weights of the global minimum variance portfolio (GMVP) for the conditional covariance matrix of asset returns. The GMVP weights are the population coefficients of a linear regression of a benchmark return on a vector of return differences. This representation enables us to derive a consistent loss function from which we can infer the GMVP weights without imposing any distributional assumptions on the returns. In order to capture time variation in the returns' conditional covariance structure, we model the portfolio weights through a recursive least squares (RLS) scheme as well as by generalized autoregressive score (GAS) type dynamics. Sparse parameterizations and targeting towards the weights of the equally weighted portfolio ensure scalability with respect to the number of assets. We apply these models to daily stock returns, and find that they perform well compared to existing static and dynamic approaches in terms of both the expected loss and unconditional portfolio variance.

Keywords: Consistent loss function; Elicitability; Forecasting; Generalized autoregressive score; Recursive least squares; Shrinkage.

JEL Classification: C14, C32, C51, C53, C58, G11, G17

Suggested Citation

Reh, Laura and Krüger, Fabian and Liesenfeld, Roman, Predicting the Global Minimum Variance Portfolio (August 18, 2021). Available at SSRN: https://ssrn.com/abstract=3471216 or http://dx.doi.org/10.2139/ssrn.3471216

Laura Reh (Contact Author)

University of Cologne - Department of Economics ( email )

Cologne, 50923
Germany

Fabian Krüger

Karlsruhe Institute of Technology ( email )

Kaiserstraße 12
Karlsruhe, Baden Württemberg 76131
Germany

Roman Liesenfeld

University of Cologne, Department of Economics ( email )

Albertus-Magnus-Platz
D-50931 Köln
Germany

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
193
Abstract Views
1,109
rank
200,403
PlumX Metrics