My Finance

My undergraduate student Ian Anderson did this research available on his GitHub repository. He continued his research on earnings growth from the previous post. In that research, Ian considers growth terms where are earnings during year These earnings might be nominal (not inflation-adjusted) or real (inflation-adjusted). These are NOT IID Gaussian.

Enter the annual realized volatility computed by another undergraduate student Angel Piotrowski. Denote it by and divide by it the growth terms. These normalized earnings growth terms are, in fact, IID Gaussian.

But are they dependent upon bond rates or spreads? Ian ran simple linear regression of upon where we take rate data for January of year He has data 1928-2023. All regression residuals have ACF and QQ plots which show they can be modeled by IID Gaussian. Not surprising since terms are also IID Gaussian. Results for real (inflation-adjusted) earnings are given below.

We see that the correlation is significant for 1 year Treasury rate and (to a less extent) for the spread.

It is easy to explain the first correlation: Lower short-term rates make borrowing cheaper and increase access to capital, so earnings grow faster.

What about the second correlation? Such spread is larger in periods of turbulence, with risk premium increasing. But it is not clear why the correlation must be positive.

Results for nominal earnings growth are not very different, except in this case no correlation is strong enough to be statistically significant. The strongest correlation is again with 1-year Treasury rate, which is -14%, and the p-value (the smallest among the four) is 16%.