Corrections for Trading Frictions in Multivariate Returns.

When observed stock returns are obtained from trades subject to friction, it is known that an individual stock's beta and covariance are measured with error. Univariate models of additive error adjustment are available and are often applied simultaneously to more than one stock. Unfortunately, these multivariate adjustments produce nonpositive definite covariance and correlation matrices, unless the return sample sizes are very large. To prevent this, restriction on the adjustment matrix are developed and a correction is proposed, which dominates the corrected estimator. The estimators are illustrated with asset opportunity set estimates where daily returns have trading frictions. Copyright 1989 by American Finance Association.