“Lower interest rates justify a higher than average price-earnings valuation”. – Pundit

You’ve heard the story before:

Equity valuations are high…

Interest rates are low…

Data sources for all charts/tables herein: Robert Shiller (http://www.econ.yale.edu/~shiller/data.htm)

Ergo, high valuations are “justified” by lower interest rates. Why?

Some argue that because stocks are the present value of future cash flows, lower interest rates should result in a higher present value, and vice versa (PV = FV / (1+i)^n, where i = interest rates).

Others argue that when bond yields are lower, earnings yields (Earnings/Price) should be lower as well. Investors are said to be choosing between stocks and bonds (they are “competing” asset classes), and if they are accepting a lower interest rate on bonds, they should also accept a lower yield on stocks. The corollary: they will accept a higher valuation (Price/Earnings).

Putting aside whether these arguments hold water, what does the data suggest? Is there a strong relationship between interest rates and valuations? Let’s take a look…

Going back to 1881, there is little evidence of a strong relationship. The R^2 between the two variables (CAPE Ratio and 10-Year Treasury Yield) is .025, which means that knowledge of interest rates accounts for only 2.50% of the variation in CAPE ratios. This would be essentially useless for predictive purposes, as 97.50% of the variation in CAPE ratios occurs for reasons unconnected to interest rates.

Breaking 10-year yields down into deciles, one can readily observe the lack of a linear relationship…

The lowest decile of interest rates (1.5% – 2.4%) actually has a median CAPE Ratio of 15, which is slightly below the overall median of 16.

The highest average CAPE ratios historically were found not in periods of extremely low interest rates, but in the 8th decile (range of 4.5% to 6% 10-Year Treasury yield).