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On the Optimization of a Fund of Funds. The Search of an Improved Estimator for the Covariance Matrix.

This dissertation studies the Markowitz model and its main problems, presents different alternatives to overcome them, and compare its performance through an empirical test with the historical closing prices of a set of funds. The main concussions of the empirical analysis are: (1) All the improved covariance estimators outperform the 1/N diversification rule and the usual sample covariance matrix across all metrics (variance, Sharpe ratio and turnover). They also overcome the problems of high sampling error and unstable results. (2) The strategy that best performs in terms of variance is Shrinkage to Market, and it requires less calculation time. (3) Adding the no short selling constrain improves the performance of almost all methods.