From the comments, on Bob Shiller and CAPE

For context, CAPE is the cyclically adjusted price-earnings ratio.  On that topic, 3rdMoment writes:

While I have great respect for Shiller, I don’t understand his confidence that the CAPE is likely to return to it’s historical average of around 16. There are several reasons why we might expect the average CAPE going forward to be higher than in the past:

1. The average levels of CAPE in most of the last century appear, with hindsight, to have been puzzlingly low. This is the well-known “equity premium puzzle.”

2. There has been a large shift in corporate payout mix, from virtually all dividends in the past, to a roughly equal mix of dividends and share repurchases today. This by itself will add a couple of points to CAPE even if nothing else changes, (as shown in this post by the anonymous blogger who tweets as “Jesse Livermore”):

3. Some other accounting changes to the definition of profits might raise the CAPE as well, again see the linked blog post above.

4. Lower information and transaction costs and the rise of index investing have dramatically lowered the cost of maintaining a globally diversified portfolio. This decreases the raw rate of return for any given required rate of realized returns. For example if the costs of investing in equities fall by just 50 basis points, this would allow the required raw earnings yield to fall from 5% to 4.5%, corresponding to a rise in CAPE from 20 to 22, without changing realized returns for investors.

5. The real “risk free” return on treasuries seems to be very low by historic standards. Real returns on other forms of debt also appear low. This lowers the return stocks need to be attractive by comparison.

6. Large corporate cash balances, a “global savings glut,” lower rates of real economic growth, possible “secular stagnation,” all seem to point to the idea that real returns are somewhat harder to get than the past.

Some of these reasons are more certain than others, but taken together they seem to show that we have good reason to expect CAPE levels significantly above the historical average going forward.

Are there any countervailing reasons offsetting the list above, factors that would tend to make CAPE lower than in the past? I can’t really think of any. And I haven’t seen anybody else offering any.


I agree with 3rdMoment and philosophicaleconomics.

I don't have a countervailing reason that it might be lower. I do have another reason that it would be higher. Firms are much less leveraged than they were in the 1970s and 1980s, which means that more profits go to the shareholders and profits are less volatile. That should translate into a higher PE ratio. In fact, the level of corporate leverage had tended to rise with higher interest rates decrease with lower interest rates, so that an inverted graph of corporate leverage matches up generally with the ups and downs of CAPE.

"Firms are much less leveraged than they were in the 1970s and 1980s,"

Not actually true of banks, which are more leveraged.

It's the financial sector which I think throws off nearly all the calculuations here...

That's a good point. I'm only talking about non-financial corporations. But, even within bank balance sheets you can see this effect. Commercial & Industrial loans have declined since the 1970s, relative to total bank assets. The additional assets are generally from real estate loans, which would naturally increase as interest rates decline.

All of the above is true, but first of all: Historical earnings figures (as old as ten years) carry no information about the current stock prices, whatsoever. Even current earnings may be totally irrelevant sometimes: remember 1Q2009.

Thank you. 10-year average earnings obscures almost everything one wants to know. I predict Shiller's ratio will suddenly look much better in 2019, when 2007-2008 fall out of his average. What does it mean? Nothing.

One reason using long windows for earnings can produce higher quality data is because the issue of accrual vs. cash earnings drops out over a long period. A sizable body of academic research has demonstrated that not all earnings are "made equal." A company with lower earnings, but higher cash flow tends to have higher returns. As you move up the chain of accounting abstractions, from cash to short term receivables to goodwill, the value of those profits diminishes. This is because the less concrete the form of profit the more prone it is to manipulation or even just the optimistic biases of management.

However as you extend longer, fake earnings that accumulate in the form of accruals will eventually get revealed. Bad accounts must eventually be written off. Bad receivable get written off. Expenses masquerading as capital expenditures get depreciated without generating ROI over their lifespan. So in some sense taking ten years of earnings helps smooth out some of the noise implicit in accrual accounting.

This seems like a long way around the block to unmask dubious earnings. Alternatively, one can learn to read through the PR that is financial statements.

What everyone wants to know, of course, is what FUTURE earnings will be. Ten years ago is ancient history. What possible value is there in using Google's 2005 earnings as part of the basis for future earnings estimates? Or, in the other direction, Sears?

I agree that using CAPE to value individual stocks is ludicrous. But if you want a simple, low-parameter (i.e. immune to data-mining bias) way to look at quality earnings for the *entire* market, then its hard to come up with a better metric. P/B largely suffers from the same accounting issues. FCF might work, but I'm not sure, and the historical data's probably harder to come by.

Fair enough. It seems to me, though, that the 'dodgy earnings' issue you raise as the reason for a 10-year average is much less of an issue when looking at a broad basket of stocks., unless you suspect some kind of systematic bias in current year numbers, but it still leaves you with oddities like a predictable drop in CAPE in 2018-2019 when the bad years fall out of the average.

I do think that the high CAPE indicates an overvalued market right now... but I think that's entirely due to one or two sectors being severely overvalued, while the rest are fine.

High CAPE can mean a lot of different things.

A couple of reasons we might expect CAPE to be lower in the future than historically; first firms are becoming more intangible and less capitally intense. Capital assets are worth something even if management are poor, so there is more downside risk. Second many newer companies, like say twitter, are one product based, fashions can change very fast.

Interesting. You are essentially saying, I believe, that accounting profits are less "real" than in the past. As far as intangibles, I'm not sure what the effect would be. If you make a bad capital investment, you put it on your balance sheet and it only comes out of profits slowly over years as it depreciates. If you make a bad R&D expenditure, you generally have to expense it up front, lowering your profits immediately. So increased intangibles might bias earnings downward rather than upward.

It seems your theory might predict a decreasing long-term relationship between earnings and cash-flows (at the aggregate level). The theory might also predicting an increased "dilution" effect, as new firms replace old firms so that the gap between the growth of index earnings and economy-wide growth in earnings should be larger than in the past.

I don't know if we can detect any changes like that in the data.

(Bernstein and Arnott write about the dilution effect here:)

No, I am not saying that accounting profits are less real. In the case of Twitter say, I would say that their profits for any one year are just as real as say GEs. But GE is a much more diversified business than Twitter, so GE is much less reliant on one business succeeding or failing. So you should be willing to pay more for GE's shares per unit of profit than Twitter. My second point is that, in a downside scenario where perhaps GE and Twitter both get some bad management and go into bankruptcy due to cash flow problems then GE will have a bunch a real assets to sell (factories, machinery, etc) that are going to be worth something, but the intangible assets of Twitter will be more difficult to sell. So again you should value a unit of profit at GE more than in Twitter. So as the stock market increases in Twitter like stocks we should expect the PE ratio to go down as the stock market is more risky for the same level of profit. You won't be able to see this risk in cash flows, it will only evidence itself during times of stress, which occur, by definition, only rarely. Its the Black Swan type problem.

No, this is a basic fallacy. If GE split into 100 firms each with a single business line, the overall risk of the assets as a whole would not rise - same assets, same risk in aggregate (there are some hairs you can split about this relating to deadweight losses in financial distress but let's not). Investors can do their own diversification so the PE does not go down in a specialized economy. Experience suggests, in fact, that the PE goes up because specialized firms grow faster.

Well who knew? A diversified company has the same risk as an undiversified one apparently. Are you sure? There is a Nobel out there for you if you can prove it.

They already gave Nobel prizes to Modigliani, Miller, Sharpe long ago, so I think it's too late.

Robert, you're wrong. The key point is that specialized firms are more likely to be private than diversified firms. So in a specialized economy, it's actually harder to have a diversified portfolio.


The first part of your Twitter/GE comparison you make goes against portfolio theory. For instance, it implies that if GE spun off its businesses, those new companies are worth less than because they are no longer diversified. Or that Twitter becomes more valuable because GE buys it because then Twitters profits would be a portion of a more diversified company. Which all leads to why the standard advice is to buy an index fund. It's easy for investors to make their own diversified portfolio. They don't need GE to do it for them.

I think there is some confusion here based on a misunderstanding of portfolio theory, Portfolio theory does not say that every stock has the same level of risk, that would be absurd. So GE, a diversified company, is lower risk (or less volatile) than a company which has a single source of revenue like Twitter. So the PE you should pay (assuming same expected discounted profit) for a diversified business should be less for the more volatile business - because your risk is higher.

Now portfolio theory says that you can improve your risk adjusted returns by holding a diversified portfolio. But it does not mean that all the stocks in your portfolio have the same risk. The point that you can simulate the effect of a diversified business by holding separate diversified stocks does not change the fact that a diversified business is lower risk than an undiversified one. It is just an alternative way by the investor to lower his investment risk. In fact portfolio theory relies on stocks with different levels of risk, with the higher risk ones being compensated by lower prices.

Look at the simplest case. You have a stock that earned $1 a share last year with a 10% chance of going bust next year and one that earns $1 per share last year with 50% chance of going bust next year. Which one is more valuable?

This is a good case of people reading business magazine summaries and thinking that they are experts.

Chris A, theoretically you would need to separate market risk from idiosyncratic risk. The market risk of the spun off firms wouldn't change, so, in theory their total value wouldn't change, all else equal.

Yup, this time it's different.

By the by, "the real “risk free” return on treasuries seems to be very low by historic standards" is quite striking in an era when it's possible that risk-free returns are riskier than usual.

Corporate leverage will rise with interest rates because many firms will roll over their debt. As rates rise, debt servicing costs rise, cutting into earnings. Re #2 above, cash dividends are money in the bank for the investor. For an investors staying the stock, stock repurchases are an indirect benefit. They are based upon the psychology of investors, valuation of the market, and future earnings. The full cost of these repurchases also has yet to be finalized. Should interest rates rise and cut into the profitability of firms, stock prices will fall and those debt laden balance sheets used to buy back stock will become an albatross. That is your low CAPE scenario, and it can be achieved either through debt deflation or high rates of inflation.

The U.S. market is currently expensive relative to world markets based on CAPE. The U.S. CAPE may or may not hit new lows, but it will come down in the coming years. The real return on stocks from current levels has a high probability of being negative, and that's going by historic valuation alone. Thanks to global markets, the U.S. doesn't have to do anything badly for CAPE to collapse. If Europe becomes more Greece than Germany, then EU equities will be headed in the direction of a Greek CAPE of 4. Consider geopolitical risk, rising Japan-China tensions, U.S. retiring as world policeman, political shift towards protectionism, etc. I see the argument for a higher CAPE, but I expect the world is going to become a messier place. Even if U.S. assets remain relatively expensive, their valuation will converge on the global mean.

Some good points here, but here's the part that's bullshit:

The real return on stocks from current levels has a high probability of being negative, and that’s going by historic valuation alone.

Just... no. Over the 10 year time frame that Delong was discussing the historical record shows a much higher probability of positive rather than negative returns at this CAFE, even before we get to the question of whether the historical CAFE average is something we should expect equities to anchor around.

I would like to again make the point that "stocks" (an index basket) can do very badly even while most stocks do well.

There was a paper a few years ago, and I cannot for the life of me find it, which demonstrated that bonds (broad indexes) actually outperformed stocks (broad indexes) right up to World War I. All previous studies saying the opposite were *wrong*... solely because they had misaccounted for bankruptcies. Bankruptcy losses have a much larger effect than most realize, and the standard indexes undercount them.

Shiller, known for his expertise in behavioral economics, attributed today's high level CAPE to, surprise, "the realm of sociology and social psychology". Is there an app for that? Sorry, some things in economics, as in life, can't be explained by mathematical models.

On short time horizons, investors may rationally believe US tail risk is historically low. On longer time horizons, there is no rational basis to have any belief about whether tail risk is higher or lower.

On a tangential note, I've been hearing about the equity premium puzzle for a long time and don't understand how it could remain a puzzle. Surely someone thought to interview bondholders and ask them why they decided to buy bonds. Why did this not constitute a solution to the puzzle?

Ask your financial adviser which part of your retirement mix should be in which types of investments. Perhaps that would explain many actions by major institutional investors.

At 63, for example, it is ill advised to hold a lot of stocks, unless you're filthy rich, in which case you probably have a few hundred k in precious metals to back you up in case the entire financial system collapses. Less stratospherically wealthy people probably demand lots of "safer" investments which includes mutual funds oriented to bonds, etc.

"At 63, for example, it is ill advised to hold a lot of stocks"

This is standard advice but is probably wrong. A middle class reasonably healthy sixty year old can quite reasonably expect to live another 25 years. Consider: My wife is 57. Her mother is 88 and going strong. Her paternal grandparents both lived to ninety. My wife could easily live another 35 years As a result, our investment horizon for part of our money is thirty or more years. Given that, it is rational to hold some significant percentage in stocks.

More accurately, stocks have wild fluctuations in price, so you never want to have them if you might actually need to SPEND the money soon.

Unfortunately, bonds can be like that too.

Dividends and interest payments, however, are much more reliable.

The problem is puzzling insofar as the stated behavior of bond buyers cannot be well modeled by macroeconomists. That is, if asked, bond holders would say they bought bonds because they regarded them as less risky than stocks. A macroeconomist would retort that - for any conceivable risk profile - it is never sensible to buy bonds. Therefore, something is wrong: either the mathematics of risk, or the survey of bond buyers. Which and why, is a puzzle.

" it is never sensible to buy bonds"

I bought long bonds years ago at a time when I thought inflation and interest rates would fall. I have done very well on them.

If one factors in rare events that totally wipe out shareholders, but leave bondholders with something more than zero, some allocation to bonds is sensible. Historically these events have involved being on the losing end of a war or revolution, and while this hasn't occurred in the United States in a long while, other countries have more recent bad experiences and/or longer memories.

"If one factors in rare events that totally wipe out shareholders, but leave bondholders with something more than zero, some allocation to bonds is sensible."

These were actually common, even in the US, in the 19th century. Most analyses which purported to show stocks doing better than bonds during that period fail to account for these properly.

The four most dangerous words in finance: this time it's different

This criticism really pisses me off. It's just a non-argument. Making investment decisions is always dangerous. You can always under perform compared to some other investment decision. The whole point of this kind of analysis is to figure out what the underlying dynamics and trends are. Shiller has a proposal: CAFE. There are plenty of reasons to think CAFE is garbage. If you tried to invest based on CAFE, you would get crushed. That's the historical reality. But it is sufficiently interesting an intuitive to be worth talking about. That doesn't mean it should be taken as a default assumption, representative of some golden underlying feature of equity valuation.

Focusing on point 5:

To think about this logically, one has to divide the expected real stock return into two components: Expected risk free real return and expected risk premium for holding stocks. The real risk free rate is very low right now. 30-year TIPS is under 1%. Cyclically adjusted (and otherwise cleaned) P/E of say 20 would give a 5% real return on stocks assuming corporate investment earns cost of capital, or 4% risk premium.

4% risk premium is a high risk premium. It's not as high as the historical average, but for someone saving for retirement, that 5% looks a whole lot more attractive than the sub-1% that the bonds are offering. Play with the numbers, you'll end up living very differently in retirement compounding at 5% than compounding at 1%.

I fail to see overpricing of stocks here, at least relative to bonds.

I fail to see overpricing of stocks here, at least relative to bonds

Yes, because both are richly priced today by historical standards.

Bonds are riskier than they were historically, for a number of reasons (but mostly because corporate bankruptcy courts don't honor order of priority any more). This has totally changed corporate bond risk and pricing.

There has long been a strategy of investing that advocates getting in and out of the stock market when the 50 day and 200 day moving averages cross. So, can an investor get a better return by buying and holding an S&P 500 index fund or by getting in and out of the fund at some points of over or under the media of the historical CAPE? There's probably an academic somewhere with no money and lotsa time who's investigated this don't ya think?

It all seems to be voodoo to me but, whatever works for ya.

I got no problem with CAPE being higher than it is historically, but here is my complaint about the stock optimists/pushers- they also want to assume the historical equity price growth rate in combination with the now higher CAPE regime. If you are buying into a higher CAPE regime today, then it is most probable that you are also buying into a lower total return regime tomorrow.

Equity premium puzzle is mostly focused on the USA. It doesn't consider that many international investors invest in US financial tools for stability/security as much as anything, while conversely US investors often have "too much" security facilitated USD role as global currency, leading them to seek higher returns overseas.

This is one of the greatest unanswered questions of the 20th century, and I doubt this is much more than a tiny part of the story.

I think it is more common to think through that low performing companies easily disappear from future data.
Meanwhile, many low performing companies never get listed in the first place. (Or perhaps the data fails to internalized other benefits that these companies offer to their owners which are more difficult to measure in the form of a price to earnings ratio.)

Also, perhaps many investors do not truly believe that there is such a thing as a "risk free" investment. While the "risk free" investments may have extraordinarily low risk, if many people have intuitively internalized black swan and tail-risk forms of thinking into their portfolio decisions, then "risk free" investments will be treated as "risk-free plus a wee bit of risk", which would explain some of the observed behaviour. I do not think it would be possible to uncover this in any form of data that I'm aware of. But if you talk to people, I do not think that very many people at all considered US treasuries to be a truly zero risk investment.

"I think it is more common to think through that low performing companies easily disappear from future data. "

With regard to the 19th century in the US, this was proven to be correct by a study a few years ago (which I still cannot for the life of me find, but it made a splash in the news at the time)

Points 1 and 5 are in tension.

I don't see why. Point 1 says the equity premium "P" should be low. Point five says the risk free rate "r" is low. The return on stocks is by definition equal to r + P. So that is two separate reasons expected returns on stocks should be lower going forward, implying high price-earnings ratios today and in the future.

(Of course maybe the risk free rate is only temporarily low. As I said, some of these reasons are more certain than others.)

"6. Large corporate cash balances ..."

Large corporate cash balances effect CAPE directly. If you have a company with a market cap of $600 Billion and surplus cash on hand over $150 billion (cough Apple cough) then all of that cash will justify a higher P/E ratio than if the cash was not on hand and you were just valuing the operating business. Same with CAPE.

The "Equity Premium Puzzle" is a myth.

The risk of equities is several times the risk of bonds (T-notes, Corporate bonds - investment grade or junk, MBS, etc.) The return above the risk free rate is not several times greater.

When we calculate the Sharpe ratios. IG fixed income is somewhere a little below 1, and may be above 1 for some asset classes, and is around 0.3 for equities. You really are not being paid for the risk you are taking.

The question is why are equity returns so low.

You need to match the measure of volatility to the holding period. Nobody is saying you should invest in equities for money you will be spending in a year.

Absent autocorrelation (which is negligible for liquid assets for any longer than a few days), Sharpe ratios are invariant across timespans.

How can Sharpe ratios be invariant across timespans when standard deviations rise with the square root of horizon? Can you share the math that supports your claim?

Without getting into all the math, it seems pretty clear to me just from looking at empirical data that there is a mean-reversion effect that applies to stock market returns. Isn't this what we see when we look at the late 90s surge followed by the 2000-2002 drop, or the 2008 cratering followed by the huge bounce back in 2009?

In other words, when Warren Buffet says he doesn't know where the market will be a year from now but he's reasonably confident where it will be in 20 years, is he talking like a sausage?

If you look at a random walk, you will see the patterns you want to see.

the 95 surge was followed by the 1996 surge, the irrational exuberance speech, and the biggest surges yet in 1998, and 1999.

the 2000 drop was followed by a 2001 drop...

Most of the analyses find that mean reversion does not exist.
Warren Buffet is talking like a sausage.
Part of the problem are the way we quote the numbers... over 30 years.

If in scenario A you have a 12% return over 30 years and scenario B you have a 9.5% return, how much better was scenario A?
In scenario A your 100,000 initial investment turned into $3 million. In scenario B your 100,000 investment turned into $1.5 million. How much better is scenario A than scenario B now? 1.5 million isn't bad but in is not 3!

Thanks Doug.

Kevin Erdmannn, if you're still around, what do you think?

Here's a post where I looked at the past 90 years.

bonds have not had much reversion to the mean over the course of an investors lifetime, but stocks do revert strongly. But, I think most of the serial correlation in bonds is nominal, mostly stemming from fed policy. So, homes have tended to be a decent hedge, since they are roughly an inflation adjusted investment, and now Tips bonds might provide a decent hedge. Mostly, since the way we buy real estate forces many people to short long term nominal bonds in the form of a mortgage, bonds can serve to hedge the mortgage, so having them in a portfolio isn't totally unreasonable.
If the persistence of bond returns is mostly a product of Fed policy, a regime shift to something like NGDP targeting could change their character compared to historical experience.

The equity premium puzzle doesn't come from the Sharpe ratio of one-year returns. It comes from these two facts:

1. Equity returns have been negatively autocorrelated at long horizons. The 10-year return volatility is less than sqrt(10) times the one-year return volatility.

2. For most people, the drops in stock prices aren't that correlated with their consumption. Therefore, they should either invest more in the stock market to get the correlation up or the market should priced higher to bring the premium down. Low correlation of stock returns and consumption AND the high risk premium TOGETHER is the puzzle.

For me personally, my consumption shocks are very correlated with global stock returns. But I am probably not close to the wealth weighted average investor out there.

Most of studies of auto-correlation find momentum rather than mean reversion. That means that 1 year volatility is grater than weekly or daily volatility annualized, and 10 year vol is greater than the square root 10 * annual vol.

Momentum effects are contained within a few years. Mean reversion dominates at mid to long term.

We shouldn't underestimate our abilities to come up with reasons for anything. An interesting exercise would be to do your best to place yourself sometime back in time (say 1990s), and try to come up with similar reasons why CAPE should be higher in the future only using what you could have know then as evidence. I would imagine that if you really tried, that argument would look pretty convincing too.

I'm not taking a stand on where CAPE is going or saying anything is wrong with your analysis, but in a world where causation does not imply causation (about the future) anything is possible.

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At least for me, CAPE is a way to look at the earnings capacity of the economy. Over time GDP can only grow so fast and does only grow so fast. Over time earnings can grow no faster than GDP. Over time both profit margins and PE ratios mean revert. So, at any point in time fair value for the market should be based upon the long term growth rate of GDP, the average profit margin level (which is the earnings capacity of the economy), and the median PE. All CAPE does is simplify getting to the earnings capacity of the economy.

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