The Truth About the Shiller PE

Is now a good time to invest in stocks?NYSE floor Old - Crop

Like the weather, the market outlook is a topic that can always be discussed, whatever the circumstances, and generally without much in the way of a definitive conclusion. It is often reduced to a question of whether or not the market is expensive or cheap just now.

Lately, the most popular measure of market valuation appears to be the current market price divided by the last ten years average earnings. This is variously known as PE10, the cyclically adjusted PE (CAPE), or Shiller’s PE, in honor of the Yale economist Robert Shiller who has popularized it. (But would never claim to have invented it. He calls it CAPE and so shall I.)

In just the past week, CAPE was sagely mentioned in both The New York Times and The Wall Street Journal. The Times called it “a conservative method” and used it to make the case that stocks are not particularly cheap at the moment. The Journal used it to make the argument that the market can be effectively timed, but left it to the reader to draw his own short-term conclusions.

I do not know that Prof. Shiller has ever gone so far as to advocate that people use CAPE to make investment decisions. In the context of his book Irrational Exuberance he uses it to make the smaller point that the market was objectively expensive at certain times just before it went down a lot, for example in 1929 and 1999. That may seem like a small issue to belabor, but academics feel a great burden to demonstrate that price movements are not entirely random. In other places (e.g. in this paper from 1996) Shiller does his best to warn people off relying on CAPE, saying that it “has to be interpreted with great caution” and that its observed predictive power could be “a chance relation with no significance.”

That predictive power is generally demonstrated by showing a high (negative) correlation between CAPE and subsequent 10 year stock market returns. In other words, when the market is more expensive as measured by CAPE than it has typically been in the past, it tends to do less well over the following decade. And when it is cheaper it tends to do better.

I have several objections to this, from both philosophical/theoretical and empirical/statistical points of view. Conceptually, I have difficulty with the idea of valuing any asset (or asset class) in a vacuum. Cheap or expensive is an inherently relative statement. A scheme that will tell us if stocks are a good or bad buy without any reference to the relative prices of other potential investments is more than a little suspect.

Moreover, valuing the market relative to its own history, that is, comparing the current price to the long-run average, implicitly makes the assumption that there exists some kind of true or natural price level for the stock market. That very well might be the case, but it is an awfully big assumption to bake into the analysis without further ado.

Moving on to the empirical arena within which I am always more comfortable, I downloaded the stock market data helpfully provided on Shiller’s website. Using monthly observations of CAPE and the 10 year forward real stock market return from January 1881 to January 2000, I get a correlation of –0.44. That corresponds to an R squared of 0.19, which is impressively strong in the world of finance. Okay.

By far my biggest issue with this is the use of ten year forward returns instead of, for example, one year forward returns. In the 1996 paper Shiller defends this by arguing, essentially, that ten years works better as it is easier to predict. That may be so, but things get weird fast if you suppose that CAPE works on ten year but not one year horizons. Are we to make only ten year stock market commitments? If we are a little more short-term oriented, would it make sense to look at the CAPE readings from two or three years ago? (Sell now because the market was expensive in 2008?)

More to the point, the combination of a ten year earnings average going into CAPE and a ten year average return as the dependent variable has a drastic impact on the effective sample size for the calculation. The spreadsheet may have 1440 monthly observations in each column but they are very far from being independent. For example, in any year the May CAPE and subsequent 10 year return pairing is nearly identical to the June one.

Taken to the opposite extreme, it is worth pointing out that in the 120 year period 1881 to 2000, we have only 12 completely independent (non-overlapping) paired CAPE and 10 year return observations. Statistically speaking, the situation is not quite that bad, but the practical sample size is a lot closer to 12 than it is to 1440. Which raises the specter that this could be just “a chance relation with no significance.”

The predictive effect of CAPE does not disappear if you use one year forward returns, but it is considerably muted. For the same 1881 to 2000 period I get a correlation between CAPE and one year returns of –0.15. That is not nearly as powerful as the ten year prediction, but it is still not too shabby. And, as Shiller tells us, one year return numbers are more noisy so our expectations need to be lower.

Alas, I have a few more quibbles. As constructed, this test of CAPE has a significant look-ahead bias. That Shiller (apparently) missed this is further evidence that he was thinking of the exercise as an interesting description of historical behavior rather than a practical scheme for investing.

Essentially, the CAPE measure of valuation compares the current CAPE reading to the long-run average reading to find out if the stock market is cheap or not. Problem is, that assumes that an investor knows what the long-run average is. It is one thing for us to say that back in 1932 the market was very cheap, but quite another for somebody back then to realize it. We, after all, know that 1932 would turn out to be a low never to be seen again. To effectively test this as an investment strategy we need to restrict the inputs to just data that could have been available to an investor at the time.

To adjust for this, I hereby christen the Growing CAPE or GCAPE. This statistic is the same as CAPE, but for each month I divide the value by the average CAPE from January 1881 through to that particular month. In other words, it is the CAPE relative to the long-run average as it was known at that time. The correlation between GCAPE and forward one year returns is –0.12.

A correlation of –0.12 not a total disaster, but we are still making an epic assumption about how clever we could have been in decades long past. It is not just that there was no internet to allow us to download a spreadsheet of numbers back in 1932, modern cap-weighed indexes as we know them, with accessible figures on such things as composite earnings, did not then exist. Which means that although investing on GCAPE was conceptually possible, as a practical matter it was not really an option.

That is important because one of the great principles of financial economics is that anomalies such as simple and effective ways to time the market do not persist for long because investors will spot them and price them out of existence. But, for most of the 120 years that we are talking about, investors would have had a lot of difficulty doing that.

What if we look at a smaller sample, for example the last third of the full time period, the 40 years from 1960 to 2000? By 1960 the rudiments of modern portfolio theory were being worked out and data services and indexes that we would recognize were available, at least to the most sophisticated investors. Also, it’s a few years before I was born.

The correlation between GCAPE and forward one year returns from 1960 to 2000 is +0.0024. In other words, since the end of the Eisenhower Administration GCAPE has been throwing darts. (1950 to 2000 is –0.06 and 1970 to 2000 is +0.05.) It may be a fair statement that, on average, over 120 years GCAPE (and CAPE) has been somewhat predictive of stock market returns, but most or possibly all of that predictive success happened long long ago. During my lifetime, it has not been much of a help.

So as a simple market timing rule, GCAPE does not work. Is this really a surprise? Would I ruffle many feathers if I asserted that there are no such simple rules? I believe that a model that timed the market is possible, although I personally do not know how to build one. I am sure it would be far from simple.

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