Shiller’s Folly

Robert Shiller‘s most famous (or infamous) book, is Irrational Exuberance (2000). According to the Wikipedia article about the book,

the text put forth several arguments demonstrating how the stock markets were overvalued at the time. The stock market collapse of 2000 happened the exact month of the book’s publication.

The second edition of Irrational Exuberance was published in 2005 and was updated to cover the housing bubble. Shiller wrote that the real estate bubble might soon burst, and he supported his claim by showing that median home prices were six to nine times greater than median income in some areas of the country. He also showed that home prices, when adjusted for inflation, have produced very modest returns of less than 1% per year. Housing prices peaked in 2006 and the housing bubble burst in 2007 and 2008, an event partially responsible for the Worldwide recession of 2008-2009.

However, as the Wikipedia article notes,

some economists … challenge the predictive power of Shiller’s publication. Eugene Fama, the Robert R. McCormick Distinguished Service Professor of Finance at The University of Chicago and co-recipient with Shiller of the 2013 Nobel Prize in Economics, has written that Shiller “has been consistently pessimistic about prices,”[ so given a long enough horizon, Shiller is bound to be able to claim that he has foreseen any given crisis.

(A stopped watch is right twice a day, but wrong 99.9 percent of the time if read to the nearest minute. I also predicted the collapse of 2000, but four years too soon.)

One of the tools used by Shiller is a cyclically-adjusted price-to-earnings ratio known as  CAPE-10 . It is

a valuation measure usually applied to the US S&P 500 equity market. It is defined as price divided by the average of ten [previous] years of earnings … , adjusted for inflation. As such, it is principally used to assess likely future returns from equities over timescales of 10 to 20 years, with higher than average CAPE values implying lower than average long-term annual average returns.

CAPE-10, like other economic indicators of which I know, is a crude tool:

For example, the annualized real rate of price growth for the S&P Composite Index from October 2003 to October 2018 was 4.6 percent. The value of CAPE-10 in October 2003 was 25.68. According to the equation in the graph (which includes the period from October 2003 through October 2018), the real rate of price growth should have been -0.6 percent. The actual rate is at the upper end of the wide range of uncertainty around the estimate.

Even a seemingly more robust relationship yields poor results. Consider this one:

The equation in this graph produces a slightly better but still terrible estimate: price growth of -0.2 percent over the 15 years ending in October 2018.

If you put stock (pun intended) in the kinds of relationships depicted above, you should expect real growth in the S&P Composite Index to be zero for the next 15 years — plus or minus about 6 percentage points. It’s the plus or minus that matters — a lot — and the equations don’t help you one bit.

As the Danish proverb says, it is difficult to make predictions, especially about the future.

Whither the Stock Market?

Drawing on the database maintained by Robert Shiller, author of Irrational Exuberance, I estimated the constant-dollar value of the S&P Composite Index (S&P) with dividends reinvested. The validity of my estimate is confirmed by comparing it with the Wilshire 5000 Total Return Index (WLX), which is based on the reinvestment of dividends in the underlying stocks:


“Real” means that the underlying values are inflation-adjusted. The indices are equated to 1 in December 1970 because that is the first month of the WLX.

Shiller uses a cyclically adjusted price-earnings ratio (CAPE) based on the inflation-adjusted value of S&P and earnings on the constituent stocks. Specifically, he uses the current inflation-adjusted price divided by the average of inflation-adjusted earnings for the preceding 10 years. Accordingly, he calls it CAPE-10:


What is the relationship between the value of CAPE-10 for a particular month and the total return on the S&P over an extended period? Shiller’s database (which is reconstructed, of course) goes back to January 1871. January 1881 is therefore the date of his earliest CAPE-10 value. This graph shows the relationship between CAPE-10 and total returns for all 15-year periods beginning January 1881 and ending June 2018:


There’s an inverse relationship, as you would expect. But it’s a loose one because of marked shifts in the value of CAPE-10.

There’s a much tighter relationship for the “modern” financial era. I trace the beginning of this era to about 1982, when the stock market bottomed (see Figures 1 and 2) while inflation was receding from its post-World War II peak in 1980:


Here’s the relationship between CAPE-10 and real, annualized 15-year returns on the S&P since 1982:


The current value of CAPE-10 is about 32. If the relationship in Figure 5 holds true for the next 15 years, investors can expect real, annualized returns (with dividends reinvested) of 2 percent to 4 percent on broadly diversified mutual funds and stock portfolios.

Not great, you say? Well, the current real return on Baa-rated corporate bonds is about 1.5 percent. It’s less than that for Aaa-rated bonds, Treasury issues, most CDs, money-market funds, and deposit accounts. So if you’re into buy-and-hold, the stock market isn’t a bad bet. Alternatively, you can try to pick the next “big thing” — Tesla, for example.

Busting the Bubble-Predictors


Scott Sumner has some thoughts on the subject. Sumner debunks the bubble-prediction prowess of Robert J. Shiller, and concludes with this:

[Shiller’s] stock market model has done very poorly since 2010, when his model suggested the S&P500 was 20% overvalued. At the time it was at 1070! [It closed on Friday, August 30, at 2003.]

We all make either implicit or explicit forecasts about the markets. If we later notice market movements that seem to align with our initial forecasts we tend the pat ourselves on the back and assume the forecasts were correct. This is just one of many cognitive biases that we human beings are prone to. My suggestion is to pay no attention to bubble forecasts. They are useless. Indeed the entire bubble concept is useless.

Shiller’s model relies heavily on an indicator that he devised: CAPE-10 (10-year cyclically adjusted price-earnings ratio). A current graph and the underlying data can be found here.

One problem with CAPE-10 — though not the only problem — is knowing when the market is “too high.” What is the norm against which current stock prices should be evaluated? It seems that a lot of weight is given to the trend since January 1871, which is how far back Shiller has reconstructed the value of the S&P 500 Index. (He calls it the S&P Composite, which is a broader index of 1,500 stocks — but he uses values for the S&P 500.)

January 1871 is an arbitrary date, of course. There have been many trends in the intervening 143 years. Consider some of the trends that began in January 1871:

Cyclically adjusted price-earnings ratio

Of the trends shown in the graph, only the trend through 1901 and the trends through 1999 and the present have been positive. The current trend (heavy black line) is the longest. Does that make it “normal”? Well, “normal” will shift up and down as the series extends into the future.

Many other trends can be concocted; for example 1901-1920 (negative); 1920-1929 (positive); 1929-1932 (negative); 1932-1937 (positive); 1937-1942 (negative); 1942-1966 (positive); 1966-1982 (negative); 1982-1999-positive; and 1999-March 2014 (negative). Take your pick, or concoct your own.

When it comes to stock prices, a trend is a useless concept. It’s manufactured from hindsight, and has no predictive value.

What about the relationship between CAPE-10 and price growth in subsequent years? Shiller made much of this in his non-prediction of 1996. (See his “Valuation Ratios and the Long-Run Stock Market Outlook.”) There is, as you might expect, a generally negative relationship between CAPE-10 and subsequent stock-price returns.

Real price growth in 15 years vs CAPE-10

But the relationship for 1871-2014 (shown above) is so loose as to be useless as a predictor. One might, as Shiller did, select a subset of the data and focus on the relationship for that subset, which is almost certain to be tighter than the relationship for the entire data set. But which subset should one choose? The correct answer — if there is one — becomes obvious only in hindsight. And by the time hindsight comes into play, the relationship will no longer hold.

I said it more than 30 years ago, and I stand by it: Trends were made to broken.

And we never know when they will break.

ADDENDUM (09/03/14):

The focus on stock prices is much ado about relatively little. The rate of real growth in the S&P index since January 1871 is 1.8 percent a year. For the same period, he rate of real growth in the S&P index with dividends reinvested is 6.6 percent a year. Huge difference:

S&P index - real price growth and returns

As of June 2014, the green line had increased 12,750-fold; the blue line, only 23-fold.

Buy and hold” should be: Buy, reinvest dividends, and hold.