Orthogonalized Regressors and Spurious Precision
11 Pages Posted: 3 Sep 2012 Last revised: 11 Feb 2013
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: Suggested Citation