real interest rates (part 3)

Just to round out the thoughts on real interest rates, I've run a simplistic multi-variable linear regression in Excel to try isolating the effect of real interest rates on the S&P 500. The idea is to re-test the association between real interest rates and the S&P while controlling for the aforementioned effects of inflation on those real interest rates. The reason I say it's a simplistic analysis is because there is some obvious multi-collinearity involved whereby our two explanatory variables (real interest rates and inflation) are not totally independent of each other. Therefore, you can't trust the co-efficients derived by the analysis (i.e. "how much"), but I think perhaps it's at least helpful to suggest whether or not the S&P tends to go up or down when real rates increase. I'm sure there are more sophisticated statistical techniques capable of overcoming this multi-collinearity amongst the explanatory variables, but if so, they are beyond my knowledge.

As shown in the charts above, the results suggest there is in fact an inverse relationship between real interest rates and the S&P 500. The co-efficient for inflation is -5.98, meaning when inflation increases 1%, the S&P tends to decrease on average -5.98% that year. The co-efficient for real interest rates is -4.25, meaning when real interest rates increase 1%, the S&P tends to decrease on average -4.25% that year. Like I said, you can't trust the exact value of these co-efficients, but I believe at least the signs are correct, such that increasing real interest rates are associated with a decreasing S&P 500.

Considering that inflation is currently low by historical standards, one might reasonably conclude the probability of an increase in inflation is greater than the probability of a decrease. By extension, one might reasonably conclude the probability of a decrease in the S&P 500 is greater than the probability of an increase. On the other hand, since real rates are not low by historical standards, one could reasonably expect an increase in inflation to be accompanied by a decrease in real interest rates, which would counteract some of the negative influence upon the S&P.