Title: Estimation of Covariance Matrices for Portfolio Optimization using Gaussian Processes,
Abstract: Estimating covariances between financial assets plays an important role in
risk management and optimal portfolio allocation. In practice, when the sample
size is small compared to the number of variables, i.e. when considering a wide
universe of assets over just a few years, this poses considerable challenges
and the empirical estimate is known to be very unstable.
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 Bayesian treatment naturally
shrinks the sample covariance matrix towards a more structured matrix given by
the prior and thereby systematically reduces estimation errors.