We consider the problem of optimal asset allocation for portfolio with a large number of shares. The numerical solution relies on the estimation of the covariance matrix between the assets. Such estimation, typically obtained with maximum likelihood, is aected be the so-called \maximization estimation error", which grows with the dimension of the covariance matrix. The use of a robust estimator of the covariance matrix can reduce such estimation error considerably, even when data are outlier free and outperform the standard approaches when data have marked heavy tails or aected by the presence of outliers. The performance of our new robust estimator is studied with simulations, and real data.
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