@article {15788, title = {Portfolio Selection Using Tikhonov Filtering to Estimate the Covariance Matrix}, journal = {SIAM Journal on Financial Mathematics}, volume = {1}, year = {2010}, month = {2010///}, pages = {932 - 961}, abstract = {Markowitz{\textquoteright}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.}, keywords = {covariance matrix estimate, Markowitz portfolio selection, ridge regression, Tikhonov regularization}, doi = {10.1137/090749372}, url = {http://link.aip.org/link/?SJF/1/932/1}, author = {Park,Sungwoo and O{\textquoteright}Leary, Dianne P.} }