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Markowitz's portfolio selection problem chooses weights for stocks in a portfolio based on an estimated covariance matrix of stock returns. Our study proposes reducing noise in the estimation by using a Tikhonov filter function. In addition, we prevent rank deficiency of the estimated covariance matrix and propose a method for effectively choosing the Tikhonov parameter, which determines the filtering intensity. We put previous estimators into a common framework and compare their filtering functions for eigenvalues of the correlation matrix. We demonstrate the effectiveness of our estimator using stock return data from 1958 through 2007.

Portfolio Selection Using Tikhonov Filtering to Estimate the Covariance Matrix