CEPR - Center for Economic and Policy Research


En Español

Em Português

Other Languages

Home Publications Blogs Beat the Press Stock Returns: Between Shiller and DeLong

Stock Returns: Between Shiller and DeLong

Monday, 18 August 2014 06:51

Robert Shiller had a piece in the Sunday NYT noting that the S&P 500 was unusually high relative to his measure of trailing earnings. He calculated a ratio above 25, far above the historic average of 15. Shiller said that in the past, each time this ratio crossed 25 the market took a plunge shortly thereafter. He concludes his piece by seeing it as a mystery that the market remains as high as it does.

Brad DeLong picks up on Shiller's analysis and points out that in most cases in the past where Shiller's ratio had exceeded 25, people who held onto their stock over the next decade would still have seen a positive real return. He notes the examples in the 1960s when investors would have seen a negative ten-year return, even though Shiller's ratio was below the critical 25 level. He therefore concludes there is no issue.

I would argue there is an issue, although not quite as much as Shiller suggests. To get at the problem, we have to recognize that stock returns, at least over a long period, are not just random numbers. Both Shiller and DeLong treat this as a question of guessing whether an egg will turn into a lizard or chicken based on the distribution of past hatchings that we have witnessed.

That would be a reasonable strategy if that is the only information we have. But if we saw that one of the eggs was laid by a hen, then we may want to up our probability estimate that it will hatch into a chicken.

In the case of stock returns we can generate projections based on projections of GDP growth, profit growth, and future price to earnings ratios. For example, we may note that the ratio of stock prices to after-tax corporate profits for the economy as a whole was 22.3 at the end of 2013. (This takes the value of stock from the Financial Accounts of the United States, Table L.213, lines 2 plus 4 for market valuation. After-tax corporate profits are from the National Income and Product Accounts, Table 1.10, Line 17).

This means that earnings are roughly 4.5 percent of the share price. If companies pay out 70 percent of their earnings as dividends or share buybacks (roughly the average), this translates into a 3.1 percent real return in the current year.


The next question is where we would expect share prices to be in ten years. While we don't know exactly what the economy will do over the next decade, there are few analysts who would project an average growth rate of much below 2.0 percent nor above 2.6 percent. This means that if the profit share of GDP were to remain constant and the price to earnings ratio were to remain constant then we can expect real returns to be between 5.1 percent and 5.7 percent.

Of course neither the profit share nor the price to earnings ratio need remain constant. Suppose the profit share drops from its current 7.2 percent share of GDP to its post-war average of 5.1 percent. In that case, total profits ten years from now would be 13.7 percent lower in the 2.0 percent GDP growth scenario and 8.4 percent lower in the 2.6 percent growth scenario. If the price to earnings ratio stayed constant, the slow growth scenario would imply a real decline in prices of 1.5 percent annually, leading to a total real return of 1.6 percent (3.1 percent minus 1.5 percent). The more rapid growth scenario implies a decline in real prices of 0.9 percent annually for a total real return of 2.2 percent (3.2 percent minus 0.9 percent).

It is also possible that the price to earnings ratio will fall back toward its historic average of 15 to 1. This makes the picture worse, but not by quite as much as it might first appear. In the slow growth case we would see a decline in real share prices that averaged 5.3 percent annually. In the latter case the decline in real share prices would average 4.7 percent annually. However it is important to keep in mind that a drop in the price to earnings ratio will lead to a rise in the dividend yield. If our endpoint is a price to earnings ratio of 15, it implies that in year ten the dividend yield will be 4.7 percent. To simplify matters, if we say the average yield over the ten year period is 3.9 percent (the average of the end-points) then the average real return is minus 1.4 percent in the slow growth scenario and minus 0.8 percent in the fast growth scenario.

To decide whether this would be a disaster it is necessary to consider the alternative investment opportunities. At the moment, short-term money pays a real interest rate of around -1.5 percent. Thirty-year Treasury bonds pay a real interest rate of around 1.0 percent. At this point, Treasury bonds also carry a substantial risk of a capital loss if interest rates rise, as is generally predicted, so this is not a risk free return.(The late 1990s gave a very different picture since the real return on long-term Treasury bonds was over 3.0 percent at the time.)

Taking these comparisons into account, stocks still look like a pretty good deal since even if there is some decline in the profit share of income and also some reversion toward long-term trends in price to earnings ratios (my bet is that the ratio stays above 20), then the real returns are still likely to be well above 3.0 percent. In short, I can't see the basis for Shiller's big fears, on the other hand, the high price to earnings ratios in the stock market means returns will almost certainly be lower in the next decade or so than their long-term average.

(There actually is a very good paper on this topic, see Baker, Delong, and Krugman, 2005.)  



Comments (28)Add Comment
Thanks for getting my point across
written by Dave, August 18, 2014 8:27
I was trying to get this point across to BD a while back. You did it much better.

Brad has been contemplating Bayesian probabilities lately, and I think the place where he went off track is to assume that all events are random. Probabilities are only valid if the thing being measured is random. I think a lot of people get really confused by this, and here is what I think is behind it:

Probabilities are only valid for betting on the next occurrence if the event is random in nature. So what is the event? Is it the move of the market? Or is it your bet?

Probabilities come from nature through quantum mechanics. Probabilities work here. When we start looking at the probabilities of betting on human-created events, if probabilities work at all it is only because our bests are random, not the underlying events. The underlying events that drive a market are not remotely random.

If you can have success betting on investments using probabilities, it is because you are trowing darts. Your bets are random, therefore probabilities work. I would not invest with somebody that throws darts.

Probabilities are way over used by most people. I've come to realize that the reason is that people WANT probabilities to work for everything even when they aren't appropriate for the situation.
further support
written by Bill, August 18, 2014 8:43
Further support for your analysis is that the 10 year TIPS is currently paying only 17 bps over inflation.
written by Bloix, August 18, 2014 8:54
I frankly don’t understand the theory behind the Shiller PE, which is a trailing average of S&P 500 earnings over 10 years (adjusted for inflation) divided into the current S&P price. I do understand the goal of smoothing data in order to remove noisy short-term trends. But ten years is so long that it seems to give undue weight to events long past that can’t possibly affect future trends. The current Shiller PE includes the bizarre year of 2009, when earnings fell so much faster than prices that the PE exploded to over 70 for the year. That was six years ago - yet that one year alone, it appears from eyeballing the data, counts for perhaps 4 of the almost 6 points between the Shiller PE of 25.85 over the 12-month PE, which is at 19.39.

So, okay, smooth the data – use three years, or maybe five. But what is the justification for ten?
written by skeptonomist, August 18, 2014 9:12
If you don't like the idea of averaging returns over 10 years, or are just lazy or don't have easy access to the data, you can just take the current real value of the indices - DJIA or S&P or your choice - per capita - no earnings needed. This gives numbers which are very similar to the Shiller P/E (and different from the P/E calculated from one year trailing earnings, which doesn't appear to have much predictive value).
written by LTR, August 18, 2014 9:14
So the point is to set aside all the stock market data that Robert Shiller has collected since 1880, data that have proven remarkably useful. This is like setting aside all the data the Piketty and Saez have collected on income concentration.
Real stocks prices only grow at GDP per capita
written by Doug Rife, August 18, 2014 9:37
Historically, real stocks prices and real dividends have only grown at a rate slightly less than the rate of growth of GDP per capita. That's a small number, only about 1% per year. Why then have stocks returned much more than 1% per annum in real terms? The answer is reinvested dividends. Back in the early 20th century dividend yields were much higher than today which explains why long term stock returns are so high. But today's dividend yields are much smaller so those large historical returns can no longer be expected in the future even if stock valuations do not increase or fall butstay at the same elevated level as today. See the paper "What Risk Premium is Normal?" for the historical evidence.

Shiller has support from Tobin's q
written by Doug Rife, August 18, 2014 9:52
One other point about Shiller's CAPE ratio is that it tracks very closely another valuation measure know as q, which is the ratio of stock market capitalization to the replacement cost of the underlying corporations. This measure was developed by Andrew Smithers and there is a website showing both q and CAPE together here:


The high q ratio today is saying that stocks are much more expensive than the replacement cost of the capital stock they represent. Over time stock prices tend to mean revert such that on average they equal the replacement cost of the capital stock.
Misunderstanding probability
written by Squeezed Turnip, August 18, 2014 10:40
Dave, sorry, you're confused and conflating issues. But to stay on topic, Dean isn't saying probability is useless here; he is saying that conditional probability is appropriate to get a more educated estimate of what the market might do. 90% of eggs from chicken A fail to hatch, only 40% of those from chicken B fail to hatch. We get an egg from an unknown one of those two chickens. Will it hatch? A priori we have a 65% chance it won't. But suppose by keen observation we know the egg came from B. Then it's only a 40% chance it won't hatch. That provides a pretty hefty incentive to learn to identify B's eggs. Dean's point is that investors generally do enough research to be able to distinguish those eggs which came from chicken B.

And, note, probability is totally appropriate to use here, but the user needs to be well schooled in inductive logics.
written by skeptonomist, August 18, 2014 11:29
And for those who are too lazy to actually check out what I say, here is the diagram:

If the Shiller P/E of the indices is actually telling us something important about the stock market, then it seems that earnings are not adding much to our knowledge. It may be that over 10 years they are averaging out. And maybe the things in q are not adding much either. The real per capita values have become distinctly higher lately, but we may not know what that means until after the next crash, if ever.

These values are basically measures of how much of the money in the economy is being devoted to the stock market. Market capitalization over GDP is also similar.
@Squeezed Turnip
written by Dave, August 18, 2014 11:36
Whatever. Stay on topic? You comment proves you don't even know what the topic is, because you aren't following along. Probabilities and the meaning of such are fundamental to understanding this.

I guess I shot way over your head.
The Big Pivot?
written by Larry Signor, August 18, 2014 12:02
Unemployment, wealth and income inequality and the social safety net conversations seem to be falling by the wayside. Those problems must be already solved. Obviously the conversation must return to the interests of the rentiers. Good to know we are back to normal.
Put it this way:
written by Dave, August 18, 2014 12:06
If the sustainable PE ratio is significantly different than it was in the past, it means something. It isn't interesting to look at it as a probability.

Look a bit deeper and it should be clear that the only thing that prevents the stock market from being a casino is the possibility of losing your money due to an event that knocks the value of companies back to a fair valuation. In the aggregate, this can only happen and be sustainable if the chances of a company going out of business is significantly less than in the past. Going out of business is the only event guaranteed to put a definite lower valuation on the company.

So has the chances of a company going out of business changed in the aggregate? This is a question of probability only if you are determined to invest in the aggregate. In other words, it is only a relevant probability if you are throwing around dumb money.
Doug Rife
written by ltr, August 18, 2014 12:15
Doug, thank you for the comments. The point about dividends is especially important.
written by aintnorep, August 18, 2014 2:24
This whole discussion is, in parts, over my head, but the thing that's driving the current insane Bull Market given the obvious market and truemacro© fundamentals is not. For what its worth some professional investors are currently calling for the bull run to end but not before the S&P goes about 50-100 points higher . . .unless of course the Russians invade Ukraine, Ebola virus breaks out on Wall Street, a collapse of a bank in Italy or France, or Singapore, ISIS gets the bomb etc, in which case all bets are off.

You can call it a bubble or you can call it your grandmom's nightie but when the thing falls away the stampede for the exits will leave everybody breathless.

As to whether the market recovers over the next five years after the blood on the exchange floors is cleaned up, well, per DeLong- Krugman, it might. Personally, I think the coming market collapse will not be the end but more like the middle of the endgame for Neo-liberalism and Finance Capitalism generally.

For a topper here is . . .David Stockman, who I'm probably about 150 degrees away from politically but who puts about 85% percent of the real case for the bull market bubble pretty well. With the rest of course being typical libertarian cant . . .

The indices have always been "LIBORed", and there have been structural changes
written by Blissex, August 18, 2014 3:44
This discussion comes up periodically, and it is based on what seem to me ridiculous premises:

* The DJIA or S&P are reliable indices of stock market returns.

* There have been no structural changes in the economy

and therefore one ridiculous conclusion:

* It is possible to easily compute and compare returns over many decades.

The DJIA (which must be used the the decades before the SP500 was created) and the SP500 are heavily "LIBOR'ed" indices becauase no only they suffer from "survivor" bias, but also heavily from selection bias: quite often the stocks part of the index are changed and the change is essentially always that low performing stocks are replaced by high performing ones. It is a bit like the CPI where prices that are going up faster are underweighted and prices that go up slower are overweighted.

It is hard for me to estimate the effect over time, but I guess (conservatively!) that it is 1-3 points per year, which is big.

The other point is that even using the "LIBOR'ed" indices a P/E of 15 is not "historical": the historical average or better median PE was 10, perhaps 11-12, which makes sense, considering how risky stocks are (stock are a lot riskier than stock indices that are "LIBOR'ed").

The reason is that there are two sharply different periods in the stockmarket, before 1994-1995 and since 1994-1995 with two rarther different averages.

In 1994-1995 "something" happened that gave rise to the most extraordinary leverage boom on record, and stocks (and asset prices in general) just ballooned. In 2001 they started reverting to historical trend, but the Fed and other central banks pumped them back up, and this has happened another two times. Every time collateral prices went down, various governments and their central banks pumped up leverage to keep them up, and to keep the debt-collateral spiral expanding.

This is startlingly obvious in this graph, comparing SP500, Nasdaq and Procter&Gamble which is a decent, quality company, which should have have seen its stock price suddenly boom in 1994-1995:


As you can see from the graph up until 1994-1995 there was a fairly stable trend, but the trend afterwards is sharply steeper, and then there are convulsions. If you want fun, substitute "PG" with "AIG"...

The trading volume graph below is also interesting: volume tends to go up during periods of heavy *selling*.
The interests of the rentiers
written by Blissex, August 18, 2014 3:56
«Obviously the conversation must return to the interests of the rentiers»

That's what most people who read the "business" or economics news care for, because they are rentiers; the people who earn middle-range or lower incomes don't read them.

But more broadly the neoliberal social engineering to turn middle income, working class people into small scale stock speculators has largely worked because:

* Most collective pension funds, for example those backing defined benefits pension funds, which are still gigantic, have been made to invest in stocks instead of bonds, in order to push stocks up and to collect gigantic "management" fees.

* Most individual savings and pension funds, like 401ks, are also heavily invested in stocks, because the advice to savers has been to put them in "higher performing" riskier investments with heavy "management" fees.

Governments and central banks have been pushing up the prices of real and financial assets used as debt collateral, bailing out creditors and investors and banks alike, not just to fund the bonus pools of their sponsors, but also because if they fall most collective and individual pension accounts get wasted, destroying the retirements of a lot of voters, in particular middle aged and older women, who are critically important swing voters in many contestable seats and states.

Sometimes in unexpected ways: for example if AIG had not been fully bailed out most likely its life assurance policies would have been wasted, destroying the retirements of many voters. And perhaps those policies would have had to be bailed out anyhow.

The stakes are much higher than most "aligned" economists are prepared to discuss, so they dissemble on comparative trivialities...
the pivot
written by Peter K., August 18, 2014 4:05

Do you remember Baker's post about Feldstein and Rubin? The rentiers are getting nervous that activist monetary policy is causing financial instability. It's the reason why the BIS says they should raise rates now.

They have to cause a recession now to prevent a downturn (which effects unemployment, wealth and inequality). Just like they need to cut retirement benefits now to prevent future cuts. Like Alice in Wonderland.

Baker thinks the preemptive tapering wasn't a big deal one way or the other, but I believe things would be better now had the Fed not tapered. I agree with many that monetary policy isn't the optimal way to go about this. Government spending or trade/currency policy would be better.
The Point Is...
written by Larry Signor, August 18, 2014 9:34
Why is a conversation about stock returns relevant to the millions of people who have not experienced the "uptick"? We got better things to do. Like cut firewood.
written by Squeezed Onion, August 18, 2014 9:46
If price-to-earning ratios helped provide valuations with a sufficient degree of the noise filtered out, then portfolio managers would use it. For example, a low PE stock can have high expected returns but it will still have low actual returns for years. So, the fact that "the sustainable PE ratio is significantly different than it was in the past" does not necessarily mean anything, it could just be noise caused by a lot of activity by noisy traders who don't have any other attractive investment options left (which covers Dean's point that stocks are still attractive, overall, and skepto's point that there is a lot of per capita investment going into the stock market right now, propelled in part, perhaps, by the negative real returns on ten year inflation protected treasuries (-0.3% last week):

PE ratios can be modeled by geometric random walks with non-stationary means, but the (non-stationary) variance is too high for this to be useful information for managing risk. I think Dean makes a good case for his range of valuation estimations, while allowing for the uncertainties.

I would edit Skepto's next to last comment as follows: "The real per capita values prices have become distinctly higher lately, but we may not know what that means until after the next crash, if ever." Value is not observable (so price can be altered by events that have no information content (e.g. IPO inflations)) [Fischer Black in, for example, his paper "Noise"].
written by jim, August 18, 2014 11:43
dean baker actually wrote a good article on the stock market
Intelligent investor
written by david, August 19, 2014 2:03
Intelligent Investor is the book to read for stock, Buffet was this guy's student.

Buy and hold. Buy and hold.

I live in Korea and I walk around and see what US products are selling well - Korea is a mirror to China, a huge market.

Also, East Asians are addicted to the net but they don't use google much. The Koreans use Naver. I had this Chinese student in my class and I asked her what search engine they use. She said "Baidu". Next day I put in my money on Baidu. Gone up 120 percent.

You can't predict the stock market. You just try to find good companies that aren't super over-valued. And you buy and hold.
written by Mark, August 19, 2014 4:29
You don't mention in your first paragraph that Shiller asserts that the only other 3 times that the CAPE has exceeded 25 (as it does now) were 1929, 1999 and 2007. If that doesn't scare the living daylights out of you, nothing will.

I wasn't a great believer in Shiller's CAPE until I saw that fact this week; I am now.
Then what's better?
written by Richard H. Serlin, August 19, 2014 5:03
The big question I'd like to ask Shiller is that if stocks are overpriced, as he largely implies, then that's relative to the alternatives, so what's better? What investment(s) is it that is/are making stocks a bad deal right now by comparison?

Bonds? That's a scary thought, that that's the best we can do right now.

I grapple with this question all the time for our own money, as well as in my work in personal finance.

I've moved a lot of money to real estate, when I can find good deals that really show promising numbers long term, but I have expertise in that area that few have. Last I checked, REIT's were as overpriced, or moreso, than stocks.

Now paying off your mortgage faster, that's a great alternative that lots of people have, so I'll offer that, but don't go out and spend more for a house. A house you live in is an expense, not an investment. It's like a car, with a negative average real return after expenses. Spend more and you're poorer on average.
US GDP not as relevant anymore
written by Bruno V, August 20, 2014 8:22
Why should US GDP comparisons with US stock market be much relevant when US listed companies now derive much more of their income from outside the US than decades ago?
why are we talking about this
written by ezra abrams, August 20, 2014 9:02
Dear Prof Baker: is there any evidence that anyone can predict the stock market ?
If not, why on earth is any of this interesting, and why are you and Prof Schiller wasting your time ?
I read Prof Schiller's piece as typical stock stuff: there is a tendency for stocks to move in a generally upward direction in the near to mid term, with a possibility of some corrections...or not
I mean, why ????
Clever question: what's better than stocks?
written by Blissex, August 20, 2014 2:35
«What investment(s) is it that is/are making stocks a bad deal right now by comparison?»

That's a very good question. Another recent blog was remarking worriedly that *all* asset valuations are rising.

Well, my take is that all *passive* investment opportunities are becoming more expensive. There are lots of wealthy and not so wealthy investor who want to buy into opportunities to cash high yields on very safe assets without any personal involvement and effort.

So if you want to actually make money, go the other way: invest actively in businesses you run.

Or the other way: sell into this surge of demand for wholly passive, coupon-style, assets and realize immense capital gains.
written by Sukh Hayre, August 20, 2014 10:59
I can see the logic for the case Dean Baker makes in regards to the stock market not being overvalued, BUT....

In a world of overcapacity, why is it not possible that corporate profits will drop considerably? Especially when you take into account the fact that taxes will eventually have to be raised to pay for rising costs relating to providing social security and healthcare.

The U.S. will have to deal with the lose of the benefits that came with being the printer of the world's reserve currency.

The developed world will have to deal with no longer having the luxuries provided at the expense of the slave-labour and oil of developing nations.

The developing nations will have to deal with the social issues that arise from relatively large populations (limited natural resources on a per capita basis).

written by Sukh Hayre, August 20, 2014 11:04
Sorry, forgot to mention two additional things...

What will be the impact on stock markets when the Chinese credit bubble pops?

What happens to stock prices when globalization is no longer a win-win situation and developing nations like China decide to focus instead on bilateral trade agreements (maybe after the U.S. officially labels them a currency manipulator). This will also be the end of the excessive rentier profits earned by the developed nations multi-national corporations as their intellectual property will no longer be respected whatsoever.

Write comment

(Only one link allowed per comment)

This content has been locked. You can no longer post any comments.


Support this blog, donate
Combined Federal Campaign #79613

About Beat the Press

Dean Baker is co-director of the Center for Economic and Policy Research in Washington, D.C. He is the author of several books, his latest being The End of Loser Liberalism: Making Markets Progressive. Read more about Dean.