Yesterday I shared a chart from Crestmont Research that compared CPI inflation with P/E ratios. The “Y Curve” showed that in times of either deflation or hyper-inflation, P/E ratios decline. That is, each dollar of earnings is seen as worth much less than it would be under normal monetary conditions.

My curiosity was to see how inflation would impact changes in P/E. So using Prof. Shiller’s data, I plotted the change in annual CPI inflation (on a monthly basis) with the change in annual P/E ratios. The resulting scatter-plot for data, from 1900 to today, is presented below:

First, to orient you, let me explain the chart: anything above the horizontal axis is inflation – that is, the CPI was higher than it was a year ago. And anything below the horizontal axis represents deflation, when the CPI was lower than 12 months prior.

The vertical axis bifurcates multiple expansion and contraction. Data points to the right show multiple expansion – that is, the P/E ratio was higher by the percentage shown compared to the previous year’s P/E ratio. Data points to the left show contraction.

It isn’t as pretty as I would have liked it to have been but if you look carefully some of the same conclusions emerge. Most of the data is concentrated between the 0%-5% inflation rate. As inflation increases (we move higher on the vertical axis) we see there is a tendency for multiple contraction. That is, data points become scarce to the right of the vertical axis and plenty to the left of it.

Going the other way, as the economy slides into deflation, we initially see a mix of P/E multiple expansion and contraction occurring at seemingly equal intervals. We have much more instances of serious inflation than serious deflation but as we slide down further and further into deflation, multiples again begin to contract. The worst contractions in P/E multiples in fact occur when we see deflation hit appx. 10%. If we had just one or two data points here, we could dismiss it as an outlier. But we see too many to ignore.

Overall, I think this corroborates the “Y-curve” – but it definitely isn’t as clear-cut. Let me know if you see something different or if you have a better way to gain insight into this relationship.

EDIT: Ed Easterling of Crestmont Research contacted me about this and we had a very fruitful discussion. I’ve corrected the data to account for a transposition error that Ed caught. I’ve also added a linear trendline overlay for “best fit”. Ed pointed out that by looking at the derivative of CPI and P/E ratios, we are distancing the relationship between the two. As well, there is a difference if we look at the short term data and the long term data.

In the short term, the large variations in inflation and P/E can confuse us with a lot of ‘noise’. But long term trends in the series become apparent when we step back to get a complete picture. So by looking at the change in inflation (year over year) vs. the change in P/E (year over year) I inadvertently made it even harder to find a correlation between the two because I was asking the data to show me a correlation between the short term changes in the series.

By slicing the data to a monthly level, we lose a lot of the larger picture and can’t really see the trend develop. Ed used the example of inflation moving from a low of say 1% to a high of 7%. It won’t get there in a smooth gradual increase but will have volatility. By looking at monthly snapshots we can’t see that larger trend take place. In the short term psychology drives the market but as we look at longer and longer periods of time this ‘volatility noise’ gets muted and we see that inflation affects the discount rate, which in turn affects P/E ratios.

That is why at the basis of it all is inflation. It drives the rate at which future earnings are discounted at the present time. Over the long term, earnings grow at the same approximate rate as the economy. This is why inflation has an inverse relationship with P/E ratios. In the case of deflation, future earnings are discounted in nominal dollars because the discount rate is low.

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Thanks for working this up!

It would be neat to see some regressions on this. Just eyeballing it (always dangerous, of course), it looks like a negative slope, so increasing CPI leads to decreasing PE, so inflation drops stock prices

in the short term(which, incidentaly, was my hypothesis from a few days ago).Also, for regression-type analysis, I would consider dropping the -10% deflation points as a outliers. Those data points almost certainly are a related set of events (I assume a series of a few months in the ’30s). Thanks again.