Corrections for Trading Frictions in Multivariate Returns



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    • Faculty of Business, University of Alberta. My thanks to S. Beveridge, D. Fowler, B. Hsu, J. D. Jobson, A. Karolyi, Y. Kim, and especially T. Sydoryk and H. Turtle.


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 non-positive definite covariance and correlation matrices, unless the return sample sizes are very large. To prevent this, restrictions on the adjustment matrix are developed and a correction is proposed, which dominates the uncorrected estimator. The estimators are illustrated with asset opportunity set estimates where daily returns have trading frictions.