A very common refrain among stock market bulls these days - and an objection some made to my remarks yesterday that markets are still not making sense - is that the low level of interest rates warrants a high multiple, since future earnings are being discounted at a lower interest rate.

My usual response, and the response from far more educated people than me, like Cliff Asness who published "Fight the Fed Model" back in 2003, is that low interest rates explain high multiples, but they do not justify high multiples. High multiples have always historically been followed - whether explained by low interest rates or not - by poor returns, so it does no good to say "multiples are high because rates are low." Either way, when multiples are high you are supposed to disinvest.

But I thought it would also be useful, for people who are not as familiar with the argument and only familiar with the sound bite, to see the actual data behind the proposition. So, below, I have a chart of year-end Shiller P/E ratios, since 1900, plotted against year-end 10-year nominal interest rates.

Note that it is generally true that lower nominal interest rates are associated with higher multiples, although it is far more clear that higher nominal interest rates are associated with lower multiples, whether we are talking about the long tail to the right (obviously from the early 1980s) or the smaller tail in the middle that dates from around 1920 (when 5% was thought to be a pretty high interest rate). But, either way, the current multiples represent high valuations whether you compare them to high-rate periods or low-rate periods. The exception is clearly from the late 1990s, when the long downtrend in interest rates helped spark a bubble, and incidentally spurred the first widespread discussion/excuse of the so-called "Fed model." If you take out that bubble, and you take out the 1980s high-rates tail, then there is left just a cloud of points although there does seem to be some mild slope to it from lower-right to upper-left.

But in short, the data is hardly crystal clear in suggesting that low interest rates can explain these multiples, never mind justify them.

More interesting is what you get if you compare P/E ratios to real rates. Because equities are real assets, you should technically use a real discount rate. Since real economic growth in earnings should be reflected in higher real interest rates generally, only the incremental real growth in earnings should be discounted into higher values today. This eliminates, in other words, some of the 'money illusion' aspect of the behavior of equity multiples.

I haven't seen a chart like this before, probably because the history of real interest rates in the U.S. only dates to 1997. However, using a model developed by Enduring Investments (and used as part of one of our investment strategies), we can translate those historical nominal rates into the real rates we would have expected to see, and that allows us to produce this chart of year-end Shiller P/E ratios, since 1900, plotted against year-end 10-year real interest rates - using Enduring's model until 1997, and actual 10-year real interest rates thereafter.

I find this picture much more interesting, because there seems to be almost no directionality to it at all. The 'tail' at upper right comes from the late 1990s, when again we had the equity bubble but we also had real rates that were higher than at equilibrium since the Treasury's TIPS program was still new and TIPS were very cheap. But other than that tail, there is simply no trend. The r-squared is 0.02 and the slope of the regression line is not statistically different from zero.

And, in that context, we can again see more clearly that the current point is simply at the high end of the cloud of historical points. The low level of real interest rates - actually quite a bit higher than they were last year - is of no help whatsoever.

None of that should be particularly surprising, except for the buy-and-hope crowd. But I thought it constructive to show the charts for your amusement and/or edification.

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