The relationship between stock prices and interest rates

Building a portfolio

Excess CAPE Yield and other models

This post is about the relationship between stock prices and interest rates and whether we can learn something from that relationship.

On Nov 30, 2020, ROBERT J. SHILLER (a Nobel laureate), LAURENCE BLACK, and FAROUK JIVRAJ published a paper titled Making Sense of Sky-High Stock Prices. They tell us: “…the level of interest rates is an increasingly important element to consider when valuing equities. To capture these effects and compare investments in stocks versus bonds, we developed the [Excess CAPE Yield] ECY, which considers both equity valuation and interest-rate levels. To calculate the ECY, we simply invert the CAPE ratio to get a yield and then subtract the ten-year real interest rate.”

They explain: “This measure is somewhat like the equity market premium [Equity Risk Premium] and is a useful way to consider the interplay of long-term valuations and interest rates. A higher measure indicates that equities are more attractive. The ECY in the US, for example, is 4%, derived from a CAPE yield of 3% and then subtracting a ten-year real interest rate of -1.0% (adjusted using the preceding ten years’ average inflation rate of 2%).” (Emphasis added)

The authors state: “…a key takeaway of the ECY indicator is that it confirms the relative attractiveness of equities, particularly given a potentially protracted period of low interest rates.” (Emphasis added) See article here.

A little history

The so-called “Fed Model” appeared in 1997. It was called the ‘Fed Model’, although it was never formally adopted or used by the Federal Reserve. It compared the earnings yield on the stock market as a whole with the yield on ten year government bonds. The S&P 500’s earnings yield is simply the inverse of its price earnings ratio. Readers will appreciate that inverting the CAPE ratio to get a yield is exactly the same as inverting the price earnings ratio of the S&P 500 to get an earnings yield. The only difference is that CAPE uses ten years of earnings whereas the Fed Model uses one year.

In the 1980s and 1990s the Fed Model worked quite well. But, the correlation between the Fed Model and the stock market has broken down in the last twenty years.

Robert Shiller’s views on Fed Model

“Over the whole period [1880 to 2005], there was not a strong relation between interest rates and the price-earnings ratio. In the Great Depression, interest rates were unusually low, which, by the Fed Model, would imply that the stock market should have been very high relative to earnings. That was not the case. Interest rates continued to decrease after the peak in the market after 2000, and then we saw the opposite of the predictions of the Fed Model: both the price-earnings ratio and the interest rates were declining. Since this happened, one has heard a lot less about the Fed Model. Although interest rates must have some effect on the market, the behavior of the stock market is not just a predictable reaction to interest rates. There is a lot more going on in the stock market, and a lot more for us to try to understand about its behavior.” (Shiller, Irrational Exuberance. 2005 Second Edition) p.9.

I must confess this seems to contradict the usefulness of his new measure, the Excess CAPE Yield. As he wrote in 2005, “the stock market is not just a predictable reaction to interest rates”.

People are relying on Excess CAPE Yield

I just read an article which said: “Adam Slater, lead economist at Oxford Economics, used the excess CAPE yield model to look at what’s currently going on. As the chart shows — and remember, since we’re looking at yield, low numbers imply higher valuations — current valuations aren’t outrageous.” The article was written by Steve Goldstein and published September 1, 2021 in Marketwatch. See here.

It includes this chart of ECY over the last 25 years.

My take

a) No model can predict where stocks will be in short to medium term; that is, from a matter of months to ten years or more. All models reach conclusions as to whether the stock market is expensive or cheap at a point in time and posit from there that future returns will be less or more, respectively, as a result. The models variously use the stock market’s earnings yield compared to the yield on treasury bonds (Fed Model), the level of the market’s price to earnings ratio to average levels (traditional model), dividend models, market cap to GDP, depreciated replacement cost or the market’s Price/Earnings ratio to a multi-year moving average usually adjusted for inflation (CAPE and others) and now ECY. The reason for this is that any prediction based on models can be overwhelmed by what happens in the real world which includes things like the economy, geopolitical events, animal spirits, Mr. Market and inflation.

b) If an investor needs to know what returns to expect from the stock market, say over a twenty to sixty year period, no model is necessary. All one needs to know is that stocks are highly likely to outperform bonds. When real bond yields are negative, it seems pretty clear that stocks will outperform bonds. Some institutions such as pension plans and life insurance companies need such predictions; individual investors do not.

c) Investors seeking superior returns are investing in individual stocks rather the market in total or in an index. The real question for investors in individual stocks is how the current stock market price of an individual stock compares to intrinsic value. The only time one might ask if stocks, in general, are expensive, is in a bubble. In that case one is asking whether stock prices in general are truly irrationally overpriced. This is a subject I have written about elsewhere. See here.

d) Furthermore, I have seen no evidence from the actual experience of any investor that changing the proportions allocated between stocks and bonds “as the level of stock prices appears less or more attractive by value standards”(to quote Robert Shiller), actually works. Simply back testing an approach does not make it valid, let alone for the future.


I see little to be gained from using Excess CAPE Yield to assess whether stocks are expensive.


To read about Warren Buffett’s view on the relationship between stock values and bond yields, take a look at the Motherlode, Chapter 37. Stocks as disguised bonds

That Chapter continues with these Sections:

37.01 An aside – bonds should be bought if more attractive

37.02 Earnings yield on book value

37.03 Earnings yield on price

37.04 Fed model and earnings yield on price

37.05 Stocks vs bonds – more


As for CAPE itself, you might check out my critique in these posts:

Problems with CAPE – Part l

Problems with CAPE – Part ll

Problems with CAPE Part lll


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