Predicting the Global Minimum Variance Portfolio

43 Pages Posted: 21 Nov 2019 Last revised: 14 Sep 2020

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: July 5, 2020

Abstract

We propose a novel dynamic approach to forecast the weights of the global minimum variance portfolio (GMVP). 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 optimal 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 combined with targeting towards nonlinear shrinkage estimates of the long-run GMVP weights ensure scalability with respect to the number of assets. An empirical analysis of daily and monthly financial returns shows that the proposed models perform well in- and out-of-sample in comparison to existing approaches.

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

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 (July 5, 2020). 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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