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Estimates of high dimensional covariance matrices suffer from great instability. In this paper a novel approach of robust covariance matrix estimation based on sparse factor modeling is presented. Sparsity is obtained by both factor modeling and
l1-regularization of the factor loadings matrix that shrinks single factor loadings to zero. The positive aspect of this framework is the ability to consider also weak factors that affect only a subset of the available time series. Hence, our sparse factor model enhances the modeling flexibility in contrast to the standard approximate factor model that allows only for strong factors, affecting the entire set of time series. In the theoretical part of the paper, we derive the consistency of the factors and factor loadings estimators and establish various risk bounds for the covariance matrix estimator based on our sparse factor model.
\indent The new approach applied to portfolio modeling shows superior properties compared to alternative shrinkage strategies that are commonly used in the literature. More specifically, our sparse factor model provides the lowest out-of-sample portfolio standard deviation across all considered portfolio sizes. Additionally, it offers the highest out-of-sample portfolio returns and hence is also superior in terms of certainty equivalent and sharpe ratio.
