Smoothing Updates to Factor Orthogonalization Regressions

Summary

The document considers how to update the regression coefficients used to orthogonalize a climate exposure factor in a Fama–French–Carhart style return model. The factor is constructed by regressing returns from two exchange traded funds on interest rate variables. Since periodic coefficient changes can create abrupt shifts in the resulting factor series, the question is how to refresh those estimates smoothly.

One proposed approach is to estimate the regression each month using a rolling five year history, then average the most recent half-year or year of coefficient estimates. This is presented as a question for discussion rather than a tested recommendation: no performance analysis or comparison with alternatives is included. The note highlights the tradeoff between adapting coefficients as relationships evolve and avoiding discontinuities in the factor, but leaves the appropriate window, averaging scheme, and validation method unresolved.

Key ideas

• The factor is orthogonalized by regressing two exchange traded fund returns on interest rate variables.
• Periodic coefficient changes can cause abrupt shifts in the calculated factor series.
• The proposed smoothing method uses monthly rolling regressions and averages recent coefficient estimates.
• The document does not test the proposal or establish the best estimation window.

Tags

# how should I update a return factor's orthogonalization parameters?


# how should I update a return factor's orthogonalization parameters?












We have constructed a return factor for a Fama-French-Carhart type factor model which adds a "BMG" factor for climate risk exposure (see open-climate-investing)

This BMG factor is orthogonalized based on regression of returns of 2 ETF's against interest rate variables. Periodically the regression coefficients should be updated, but how should we do it so that it's not "jerky"--ie, a sudden change in the factor series when we decide to update the variables every year?

One idea is to run the regression for the previous 60 months of returns every month, and then set use the rolling average of the last 6 or 12 month regressions, so that we smooth out the change in the orthogonalization.

Does this sound reasonable? Have you seen other ways to do this?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.