Berlin 2018 – wissenschaftliches Programm
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 10: Financial Markets and Risk Management II
SOE 10.4: Vortrag
Dienstag, 13. März 2018, 12:15–12:30, MA 001
Estimation of Covariance Matrices using Gaussian Processes — •Rajbir-Singh Nirwan1 and Nils Bertschinger1,2 — 1Frankfurt Institute for Advanced Studies — 2Goethe University, Frankfurt am Main
Estimating covariances between financial assets plays an important role in risk management and optimal portfolio allocation. Especially if the number of assets is large compared to the number of observations, the sample estimators of covariance and correlation are very unstable or can even become singular. To cope with this problem, a wide range of estimators, e.g. factor models such as the CAPM or shrinkage estimators, have been developed and employed in portfolio optimization.
Here, we propose a novel covariance estimator based on the Gaussian Process Latent Variable Model (GP-LVM). Our estimator can be considered as a non-linear extension of standard factor models with readily interpretable parameters reminiscent of market betas. Furthermore, our fully Bayesian treatment naturally shrinks the sample covariance matrix (which maximizes the likelihood function) towards a more structured matrix given by the prior and thereby systematically reduces estimation errors.
We evaluated our model on the stocks of S&P500 from 1990 to 2017 and found significant improvements in terms of model fit as well as portfolio performance compared to the current state-of-the-art covariance estimators.