Orthogonalized Regressors and Spurious Precision

11 Pages Posted: 3 Sep 2012 Last revised: 11 Feb 2013

See all articles by Piet Sercu

Piet Sercu

FEB at KU Leuven

Martina L. Vandebroek

Katholieke Universiteit Leuven - Faculty of Business and Economics

Date Written: September 1, 2012


Regressions often use pre-orthogonalized regressors. For example, the exposure of a stock's return to exchange-rate changes is conventionally estimated by regression, and often, the market return is included as an additional regressor. By first orthogonalizing the market return on the exchange rate one seems to have the best of both worlds: the market factor cannot subsume part of the exposure present in a stock's return, and the SE of the estimate beats both the simple- and the multiple-regression SE's. This last effect is illusory: since the simple and the pseudo-multiple regression always produce the same exposure estimate, given the sample, their precision must be identical too. Technically, the source of the problem is that the uncertainty about the market's exposure estimate is left out of the calculated SE. In published work, the calculated error variances should be corrected upward by 20 to 100 percent.

Keywords: orthogonalised regressors, market model, currency, exposure

JEL Classification: C3, C58

Suggested Citation

Sercu, Piet M. F. A. and Vandebroek, Martina L., Orthogonalized Regressors and Spurious Precision (September 1, 2012). Midwest Finance Association 2013 Annual Meeting Paper, Available at SSRN: https://ssrn.com/abstract=2140191 or http://dx.doi.org/10.2139/ssrn.2140191

Piet M. F. A. Sercu (Contact Author)

FEB at KU Leuven ( email )

Naamsestraat 69
Faculty of Economics and Business
Leuven, 3000
+32 16 32 67 56 (Phone)
+32 16 32 67 32 (Fax)

Martina L. Vandebroek

Katholieke Universiteit Leuven - Faculty of Business and Economics ( email )

Naamsestraat 69
B-3000 Leuven

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