## The Shiller P/E Ratio

Robert J. Shiller, an American academic, made waves in the economic community when he correctly anticipated the sharp decline in equities in 2000 in his book “Irrational Exuberance.” In the book, one of Shiller’s basic tools for thinking about equity values is the market’s cyclically adjusted P/E ratio. We wanted to take a look at Shiller’s famous ratio today, with the hope that it might assist us in assessing current market conditions. We will walk through Turnkey’s calculation of Shiller’s famous ratio, review how we present it on our site, and then see what kind of signals it is sending us today.

**How is the ratio calculated?**

The first step in calculating the cyclically adjusted P/E is to determine the nominator, which is the real price of equity markets. For example, on 9/30/11, the S&P closed at a nominal value of 1,131. In our model, we express all values in terms of 2010 dollars (10/31/10), so we take today’s nominal S&P value of 1,131, and adjust it for inflation. The CPI was 218.7 on 10/31/10, but on 9/31/11 it stood at 227.2. Therefore in real terms, the S&P is at 1,089:

We can then use this methodology to calculate a real S&P close for every month going back to 1/31/1871.

The next step in calculating the cyclically adjusted P/E is to determine the denominator. First, we look at nominal earnings figures for the S&P. While the numbers have not been finalized, S&P currently estimates that on 9/30/11 the index’s trailing twelve months earnings per share for the overall S&P index were $88. That is to say, if you owned today’s index at $1,131, the earnings associated with that equity ownership interest would equate to $88, for a twelve month trailing nominal P/E of 12.9x earnings. You can go back in time and, for any given month in the history of the S&P, determine the trailing 12-months earnings figure for the overall index. Now we adjust these figures for inflation, using the same methodology discussed above. So for example, for 9/30/11, we see the real earning for the S&P are:

We can look at a stream of such monthly figures, each representing the 12-month trailing average real earnings for the S&P. Below is a graph showing this calculation for each month over the past 10 years:

Note that the average is $58. This is the “cyclical adjustment” in the calculation, which normalizes the gyrations in earnings figures apparent in the graph above. It is saying that, on average, the market has had real earnings of 58 per year in each of the past ten years.

Now we can see that the cyclically adjusted real P/E for the market is about 19:

**How we think about Shiller’s Ratio**

We hate to admit it, but bond folks are typically smarter than their equity counterparts. We may never reach their IQ level, but we can always borrow their ideas.

Here at Turnkey Analyst we prefer to look at earnings yield, or the reciprocal of the P/E, because it allows a more direct comparison with yields in other asset classes (real estate, fixed income, CDs, etc.). Looking at yields is also a more intuitive way of thinking about what you get when you purchase an asset. For example, I buy a popsicle stand at a 12% yield; I get 12$ for every $100 I invest. Whereas, “I buy a popsicle stand for a P/E of 8.33x” is less intuitive. Especially when I have to compare the popsicle stand to the treasury bonds paying a 5% yield.

12% vs. 5%. Got it. **8.33x compared to 5%? **What the heck is that supposed to mean? Anyway, I digress…

**How we create a predicted 10-year return figure**

Taking the reciprocal of the cyclically adjusted real P/E, above, we get a yield of 5.28%. Next, we go back and calculate a cyclically adjusted real yield for the market, using the methodology outlined above, for every month when 10 years of trailing data was available, which turns out to be back to 1/31/1881.

Then we added one more piece of data. On the date of each calculation, we asked “what was the real return of the S&P, per year, over the subsequent 10 year period?” This is an geometric average calculation. The latest period for which we know the full 10-year real return subsequent to an observation of the cyclically adjusted real yield of the market is 9/30/01. On that date, the S&P closed at 1,281 in real terms, and as we know on 9/30/11, the S&P closed at 1,089 in real terms. So in the equation below, we want to solve for r.

So we divide both sides by 1,281, take the 10^{th} root of both sides, and subtract 1 from both sides:

We can see that the average yearly real return of the S&P from 9/30/01 to 9/30/11 was -1.6%. Now we have two variables: 1) the cyclically adjusted real yield for any given point in time, and 2) the subsequent 10 year real returns from that date.

Now we want to see in what way the first variable is predictive of the second variable, so we run a regression on these two variables, using input from every year data is available (from 1/31/1881 through 9/30/2001), and solve for an intercept, A, and a slope, B, in the regression equation (Y) = A + BX. Below is the output for the regression:

The regression returns an intercept value of A=-3.54, and a slope coefficient of B=0.75. This means that for every 1.0 percentage point move in cyclically adjusted real yield, we see, on average, a 75bp move in predicted real S&P returns over the subsequent 10-year period.

Now we are ready to take the final step and see what the regression model predicts for the S&P for the next 10 years. Recall that we have already calculated the current (9/31/11) cyclically adjusted real yield for the S&P above, and came up with 5.28%. Now we take: Y = -3.54 + 0.75 * 5.28, and solve for Y. In this case, Y = 0.43 (or if you take the regression inputs out several decimal places, 0.425146). This suggests that, based on our regression model, the stock market will see real returns of 0.4% per year for the next 10 years. Kind of makes TIPS look a little more appealing, no?

Reviewing the data above, in our Predicted 10-Year Real Return (Based on Estimated Linear Regression Model) screen, we can see the Most Recent Value of 0.425146, as discussed above. This predicted return falls in the 28.2%ile of the predicted universe. You can also see minimum, median, and maximum predicted values, as well as several %ile breakpoints, for comparative purposes.

At the end of the day, the current cyclically adjust real yield of 5.28% is telling us that the stock market is expensive, at least by historical standards. This yield falls in the lower third of predicted states for the market’s value. So it’s possible that the stock market is not an especially good place to invest your money, at least at today’s prices.

**Sure the predicted market returns sucks, but investing is about opportunity costs, right?**

Investing, and life, are all about opportunity costs. Sure, we all want a college degree, but what if we spend 4 years getting a degree in basket-weaving, end up with $200,000 in debt, and can’t get a job? Perhaps going to work at the local lumber mill at $15/hr was a better choice? Who knows. Similarly, we all want 20% inflation-adjusted CAGR on our stock market investments, but what if the market is only offering up 43bp? Well, maybe that isn’t that bad if bonds are offering up -5% inflation-adjusted CAGR?

We’ve got a tool to help you address these concerns. One of the metrics we like to look at is the inflation-adjusted spread between the 10-year earnings yield of the stock market compared to the 10-year Treasury Bond yield. Currently, the **inflation-adjusted** 10-year earnings yield sits at 5.276% (previously discussed above) and the **nominal **10-year treasury bond (as of 9/30/2011) sits at 1.98%. To adjust the nominal 10-year bond into real terms we simply take [(1+1.98%)/(1+CPI%)]-1. The 1-year CPI change from 9/30/2010 to 9/30/2011 was 3.99%, which implies the real bond yield is -1.94%. Putting this information all together, we identify that the real spread between earnings yield and bond yields is 7.21%, which is actually the 71%ile based on history.

**Conclusions**

1) We’ve identified that predicted real stock returns are projected to be 43bp a year for the next 10 years according to a very simple linear regression model. **STOCKS SEEM EXPENSIVE**

2) We’ve also identified that relative to bonds, the real spread between stocks and bonds is 7.2% in terms of yields. **STOCKS RELATIVE TO BONDS SEEM CHEAP.**

3) So if stocks are expensive, and stocks relative to bonds seem cheap, this implies that bonds are also expensive. **EVERYTHING IS EXPENSIVE!**

**4) The Fed is accomplishing their desired mission: keep interest rates low and force people into overpriced risky assets.**

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[...] What the Shiller P/E ratio tells us about stocks, bonds and the Fed. (Turnkey Analyst) [...]

Exactly!

Thanks for some good work. But what about dividends? I’ve seen dividends added to the inverse of the PE, meaning that as of 10/6/11, a PE of 12.652 was 7.90%, to which one would add a dividend yield of 2.28%, for a (per this method) earnings yield of 10.2%…?

And then I’ve seen people further back something else OUT of this – tbils or bonds, or something. Plus don’t forget, dividends would materially affect your total return calculation too – perhaps not much over the last 20 years or so, but very much so prior to that. I recall seeing a Pimco piece (about 10 years ago I think) which suggested that fully half of the equity market’s purported “long term return of 7%” was from dividends (the point of which was, per the article, that dividend payouts were then at an all-time low so this had to be factored into return expectations).

Consideration of dividends may not significantly impact your ultimate conclusion here, that US equities are expensive. And right now we’re seeing dividends of 4-6% in Europe, which really reinforces your point about Europe. However, looking at Malaysia, say, it has one of the highest PE’s (12.3) and thus earnings yield in emerging markets. But it also has one of the highest dividend yields, of 4.2%. Maybe it’s not so expensive after all….

Finally, I’d love to see somebody do something similar related to the PB. I’ve read a lot of stuff saying that PB is a more reliable indicator of valuation than PE, and if you look globally, PB values are the cheapest in at least 12 years in certain markets (Germany, Brazil, Austria, small cap India, etc…). Best

Frank,

We’ll look into all of this and put something together for you. We’ll also add price/book on our turnkey analyst platform for our next release.

[...] Here is an interesting, if a little wonkish, piece on what the Shiller P/E ratio is telling us about market pricing at the moment. [...]

I did a similar analysis of the Schiller data. A few points.

- I came to an expected real annualized price return of about 1%. Maybe we did the regression differently. For one thing, I used the median 10 year cyclically adjusted earnings yield rather than the mean as Schiller does.

- The calculated expected return is real rather than nominal. There’s nothing wrong with that but something to keep in mind.

- Dividends are not included in this analysis. At just over 2%, IMHO the dividend yield should not to be ignored when the expected price return is only 0.4% per year real. I get an expected annualized real return of 79% of earnings yield minus 2.2% when dividends are included.

- One standard deviation of error is about 5%, which is huge IMHO.

Please don’t interpret this as bullish. Based on the Schiller data, I got an expected real annualized total return of around 2.5% +/- 5% for the S&P when dividends are included based on the September data; you won’t see me buying and holding that for the next decade.

Since you have the spreadsheet set up, for fun, I suggest looking into whether the market is efficient in the sense that low earnings yields have historically been predictive of high subsequent earnings growth. They haven’t. It’s like someone fired a shotgun at the scatter plot.

acamus

We are working a post that discusses a lot of the things you’ve mentioned–stay tuned.

I agree with you 100% regarding predictability–the analysis presented is extremely rough, but that’s life. There are some other models out there that predict long term market returns, but for the extra complication and brain damage involved with trying to understand them brings very little value-add above and beyond the basic Shiller concept.

[...] What the Shiller P/E ratio tells us about stocks, bonds and the Fed. (Turnkey Analyst) [...]

That’s some interesting calcs you got there!

Please note that Shiller has moved on from the PE10 work contained in “Irrational Exuberance”. If you go to his website, you’ll see that he has updated his earlier work and it now includes an analysis on whether the adjusted PE10 figure can predict future returns and also an historical comparison between equity and bond yields.

I haven’t looked at that new work for several months now, but your calcs don’t seem to add a lot to Schiller’s latest analysis.

I’m not suggesting that you have plagiarised Schiller’s latest work, but you could have saved yourself some number crunching by just linking to Schiller’s website.

Shiller does have some work that was last updated in 1996 at http://www.econ.yale.edu/~shiller/data/peratio.html.

We updated the results to the present day and do a different prediction regression. We also tie all the results and analysis and put them in the context of today’s markets, which is helpful to those who are interested in learning how to apply various tools.

This is Prof Shiller’s latest set of numbers.

http://www.econ.yale.edu/~shiller/data/ie_data.xls

Hey Turnkey,

First of all, I absolutely love your blog and your approach. Aside from CXO, there are very few sites geared to testing the validity of the myriad ideas expressed in the financial sphere, most of which is bunk.

On the topic of returns, we have performed a similar analysis of market valuations and likely forward returns over horizons of 5 through 30 years, and based on myriad valuation metrics related to aggregate earnings, balance sheets, profit margins, GDP, and price. I would be quite keen to hear your thoughts on our analysis when you have a moment. Please find the most recent update (as of September 23rd) at:

http://www.butlerphilbrick.com/papers/estimating_future_returns_September_update.pdf

Thanks in advance, and keep up the great work.

Adam

[...] unless you are familiar with “predictive regressions.” (see an old post we have on the Shiller P/E, which is the same sort of analysis [...]

[...] http://turnkeyanalyst.com/2011/10/the-shiller-pe-ratio/ The model is predicting a 3.31% 10-Year CAGR. [...]

[...] As Brett Arends mentioned last week in Why a ‘Balanced’ Portfolio May Not Work, three valuation measures with a decent track record of predicting long term returns are stock prices in relation to dividends (dividend yield), the replacement cost of company assets (Q Ratio or Tobin’s Q), and the past 10 years’ earnings (Schiller P/E). [...]