I have a large time-series dataset, which I performed regression on in order to assess how the beta changes across the time period. To generalise the results I found the mean and the median values of the beta across each period and I now want to use this in the CAPM model to estimate the expected rate of return. I am unsure about what to do for the error term, however. Is it appropriate to use the mean value of the error term that would've been produced from these regressions to include it in the model? If not, what is a better alternative?
Hello Morgan,
In most regression methods (OLS models), the mean error will be zero. So, there's not much utility in computing it. Other variants, such as MSE (mean squared error), MAD (mean absolute deviation), and the like are often used, depending on whether you wish to quantify error as a linear (MAD) or squared (MSE) loss function statistic.
Good luck with your work.
Theoretically, it will not make sense to estimate/use the error term in further tests since the CAPM assumes that the error equals zero, mainly because we can diversify away idiosyncratic risk and Beta captures systematic risk, so in theory you should only be concerned with B. In some cases you are concerned with the error term but that will be explicitly indicated in your research question. In this case you are using the model to estimate the amount systematic risk. If your only goal is to calculate expected returns you could also consider a single index, three, four-factor model. See Appendix B in this paper. Good luck,Article The Effect of Government Contracts on Corporate Valuation
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