Dynamic Modeling of the Global Minimum Variance Portfolio
44 Pages Posted: 21 Nov 2019
Date Written: October 17, 2019
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
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