Testing a Low-High Beta Portfolio Spread with a Regression

Summary

The document asks how to calculate the t-statistic for the difference between low-beta and high-beta portfolio alphas in an analysis of the beta anomaly. The accepted answer describes forming a time series of portfolio returns by subtracting one portfolio’s returns from the other’s, then running the usual regression on that spread portfolio. The regression’s estimated alpha and its t-statistic provide the corresponding spread results.

This approach tests the long-short portfolio directly, rather than trying to infer the spread’s t-statistic by subtracting the two individual t-statistics. The document gives no sample data, regression specification, or details about standard error choices, so those design decisions remain unspecified. Its guidance is a concise procedure for producing a spread regression and should be applied with the same factor model and inference choices appropriate to the underlying study.

Key ideas

• Construct a return series for the low-high portfolio by subtracting one portfolio’s returns from the other’s.
• Run the chosen regression on the resulting spread return series.
• Use the regression output to obtain the spread alpha and its t-statistic.
• The document does not specify the factor model, sample, or standard error method.

Tags

# Beta anomaly (t statistics)


# Beta anomaly (t statistics)












I would like to analyze the beta anomaly following the method used in the following paper "The low-risk anomaly: A decomposition into micro and macro effects" by (Baker et al, 2018). (the link: https://www.tandfonline.com/doi/full/10.2469/faj.v70.n2.2?needAccess=true) I constructed the quintiles and ran the regressions, and subtracted the Low-High alphas as they have done in table 1 (panel A). However, in table 1 panel B they put the t statistics of the subtraction row (Low-High) which is something I did not understand how they compute it (the Low-High t statistics). Anyone can help with this?

## Answer by phdstudent (score 5, accepted)

https://quant.stackexchange.com/a/72078

Yes. That is pretty easy. You have the returns for the high portfolio and for and low portfolio. You subtract one from the other and you have a time-series of returns for the High-Low portfolio. Then you just run the usual regression on that portfolio.

Hope this is clear.

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