Dynamic Modeling of the Global Minimum Variance Portfolio

44 Pages Posted: 21 Nov 2019

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: October 17, 2019

Abstract

We propose a novel dynamic approach to forecast the weights of the global minimum variance portfolio (GMVP). We exploit that the GMVP weights can be obtained as the population coefficients of a linear regression of one benchmark return on a vector of return differences. This enables us to derive a consistent loss function from which we can infer the optimal GMVP weights without imposing any distributional assumptions on the returns. In order to capture time variation in the assets' 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 ensure scalability with respect to the number of assets. An empirical analysis of daily and monthly financial returns shows that the model performs well in- and out-of-sample in comparison to existing approaches.

Keywords: Consistent loss function, Elicitability, Generalized autoregressive score, Recursive least squares, Forecasting

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

Suggested Citation

Reh, Laura and Krüger, Fabian and Liesenfeld, Roman, Dynamic Modeling of the Global Minimum Variance Portfolio (October 17, 2019). 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

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