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## 73-Year Chart Comparing Estimated Shiller PE Returns to Actual Returns

In The Siren’s Song of the Unfinished Half-Cycle John Hussman has a great annotated chart comparing the ten-year returns estimated by the Shiller PE to the actual market returns that emerged over the following ten years from each estimate (from 1940 to present):

Hussman estimates the ten-year return using a simple formula:

Shorthand 10-year total return estimate = 1.06 * (15/ShillerPE)^(1/10) – 1 + dividend yield(decimal)

He justifies his inputs to the simple formula as follows:

Historically, nominal GDP growth, corporate revenues, and even cyclically-adjusted earnings (filtering out short-run variations in profit margins) have grown at about 6% annually over time. Excluding the bubble period since mid-1995, the average historical Shiller P/E has actually been less than 15. Therefore, it is simple to estimate the 10-year market return by combining three components: 6% growth in fundamentals, reversion in the Shiller P/E toward 15 over a 10-year period, and the current dividend yield. It’s not an ideal model of 10-year returns, but it’s as simple as one should get, and it still has a correlation of more than 80% with actual subsequent total returns for the S&P 500.

Here is Hussman’s application of the simple formula to several notable points on the chart and comparison to the subsequent returns:

For example, at the 1942 market low, the Shiller P/E was 7.5 and the dividend yield was 8.7%. The shorthand estimate of 10-year nominal returns works out to 1.06*(15/7.5)^(1/10)-1+.087 = 22% annually. In fact, the S&P 500 went on to achieve a total return over the following decade of about 23% annually.

Conversely, at the 1965 valuation peak that is typically used to mark the beginning of the 1965-1982 secular bear market, the Shiller P/E reached 24, with a dividend yield of 2.9%. The shorthand 10-year return estimate would be 1.06*(15/24)^(1/10)+.029 = 4%, which was followed by an actual 10-year total return on the S&P 500 of … 4%.

Let’s keep this up. At the 1982 secular bear low, the Shiller P/E was 6.5 and the dividend yield was 6.6%. The shorthand estimate of 10-year returns works out to 22%, which was followed by an actual 10-year total return on the S&P 500 of … 22%. Not every point works out so precisely, but hopefully the relationship between valuations and subsequent returns is clear.

Now take the 2000 secular bull market peak. The Shiller P/E reached a stunning 43, with a dividend yield of just 1.1%. The shorthand estimate of 10-year returns would have been -3% at the time, and anybody suggesting a negative return on stocks over the decade ahead would have been mercilessly ridiculed (ah, memories). But that’s exactly what investors experienced.

The problem today is that the recent half-cycle has taken valuations back to historically rich levels. Presently, the Shiller P/E is 22.7, with a dividend yield of 2.2%. Do the math. A plausible, and historically reliable estimate of 10-year nominal total returns here works out to only 1.06*(15/22.7)^(.10)-1+.022 = 3.9% annually, which is roughly the same estimate that we obtain from a much more robust set of fundamental measures and methods.

Simply put, secular bull markets begin at valuations that are associated with subsequent 10-year market returns near 20% annually. By contrast, secular bear markets begin at valuations like we observe at present. It may seem implausible that stocks could have gone this long with near-zero returns, and yet still be at valuations where other secular bear markets have started – but that is the unfortunate result of the extreme valuations that stocks achieved in 2000. It is lunacy to view those extreme valuations as some benchmark that should be recovered before investors need to worry.

The actual return deviates from the estimated return at several points, including the most recent ten-year period from 2002. Hussman comments:

Note that there are a few points where the estimate of prospective market returns would have differed from the actual market returns achieved by the S&P 500 over the following decade. These deviations happen to be very informative. When actual returns undershoot the estimate from a decade earlier, it is almost always because stocks have moved to significant undervaluation. When actual returns overshoot the estimate from a decade earlier, it is almost always because stocks have moved to significant overvaluation. Note the overshoot of actual market returns (versus expected) in the decade since 2002. The reason for this temporary overshoot is clear from the chart at the beginning of this weekly comment: the most recent 10-year period captures a trough-to-peak move: one full cycle plus an unfinished bull half-cycle.

While Hussman’s formula is exceedingly simple, with a correlation of more than 0.8 it’s also highly predictive. It’s currently estimating very attenuated returns, and investors should take note.

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### 21 Responses

1. Any chance you have access to Hussman’s data set he used to create this chart? I tried using the excel spreadsheet from Shiller’s website (Irrational Exuberance) but mine came out looking differently. My correlation between the two data sets came out at .71, not over .8 like he claims.

If interested, I loaded up the spreadsheet to Google Drive. Let me know if access is needed.

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2. […] the Shiller PE and Buffett’s total market capitalization-to-gross national product measure, […]

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3. Tobias, regarding mean reversion, do you believe the following will revert to mean?

– GDP Gap

– Housing Prices

– Unemployment Rate

– Effective Tax Rates

– Wages

– Foreign Earnings

– Interest Rates

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4. I dont understand why current dividend yields are used to estimate yearly nominal yields.

Dividends are already factored into price & earnings. Companies have been using stock buy backs as an alternative to dividends for years. It seems like you are trying to factor in moments of high inflation or high growth which historically drove up dividends.

I would have thought a more accurate formula would be something like

Shorthand 10-year total return estimate = 1.06 * (15/ShillerPE)^(1/10) – 1 + (GNP Percent Change from a year ago – .06)

For 1965, that yields 5.73%

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5. […] « 73-Year Chart Comparing Estimated Shiller PE Returns to Actual Returns […]

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6. Hi Tobias, have you seen similar data for the Japanese stock market. By the way, I really like your blog, please keep up the good work!

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7. Given the above estimates for 10 year market returns, might it be possible to extrapolate out and plot a route for the market from here?

That is, if the market was at ‘x’ in 2003, and the short hand predicted an average annual return of ‘y%’, then at 2013, the market should be at x*(1+y/100)^10. One could do the same for each subsequent period to get a 10 year trajectory.

Granted, such a prediction would be entirely pinned on the assumptions of mean reversion (to 6% growth p/a, and to a CAPE of 15), but it might provide an alternative (or at least discussion worthy) means of testing the predictions of the model.

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• on April 5, 2013 at 8:54 am | Reply Tobias Carlisle

Yes. The formula is 1.06*(15/23.3)^(.10)-1+.02 = 0.034, so it estimates 3.4 percent compound for ten years.

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• I think you may be missing my point. Sure, the expected 10 year return from here might be 3.4% pa, but what about the trajectory? Does the model suggest the market goes down immediately from here? for how long? When would it expect to go back up? If we look at the expected 10 year returns from say 9 years ago, or 8, or 7, etc., and compare with the actual returns generated so far, we might get an idea.

Let me illustrate what I mean. Yesterday in another thread, you mentioned the expected return from the peak in 2007 was 0.5% compounded for the decade (approximately a 5% total return), but we currently have a total return of 14.4% – so from here to 2017, there’s a reasonable chance that we might get a -10% total return over the next 4 years. Similarly, from the 2009 low, we should expect a return of 9.1% p.a. by 2019 (cumulative return of 139%), but given we are at 138% total return today, over the next 6 years, we might expect no additional return. However, given that we expect a cumulative increase of about 40% between now and 2023 (3.4% compounded for 10 years), there are grounds to think that will all come between 2019 and 2023.

So piecing these three bits of information together, we might predict that between now and 2017 the market heads down (nearly 10%), but would then recover that loss by 2019, and from there gain at ~9% p.a. until 2023.

If we repeat this exercise for each year since 2003 (that is comparing predicted vs actual returns), we could get a finer grain prediction, not just giving a 10-year predicted return, but one for 1-year, 2-years, 3-years, etc all the way out to 10 years. You could even plot out where the S&P500 would be expected to be for each year (or even each 3 months) between now and 2023.

I’m sure if one includes st dev, these numbers would have no significant predictive basis, and that predicting whether the market goes up or down is a mugs game (we should just be buying cheap things), but I’m interested in the implications of the seemingly strong predictive power of this simple metric – how far can it be pushed?

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• on April 5, 2013 at 11:13 am | Reply Tobias Carlisle

You’ve lost me. The estimated trajectory is a positive 3.4 percent per annum compound for ten years from the date of calculation. You can’t use it to forecast what the market will do in between now and a decade from now by including past estimates. The model assumes constant mean reversion. When it over-or under- shoots it accounts for this with the assumption of mean reversion to 15x.

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• Hmm… I think I get it now, just had to see it the right way.

The problem I had was that I didn’t get why you couldn’t combine predictions – The above figure argues that the CAPE-derived predictions for subsequent 10-year returns match fairly well with the actual returns, therefore, a prediction made today should be just as valid as a prediction made 3 or 9 years ago.

But as you point out, the implicit mean reversion assumption implies that at t+10 the CAPE=15. That may be a reasonable assumption ‘in the long run’, but by combining predictions, you force it to happen in the short run. So comparing the prediction made back in 2004 (of x%) to the subsequent 9 year return (y%) and then saying that ‘in the next year, we should expect to see an (x-y)% return’ would be false because that would force the mean reversion to occur in a single year, which is not what the model was expected to do.

Having seen that, is there not a little hindsight bias introduced in the back-test (by using the 6% growth rate and the average CAPE of 15)?

On reflection, i suspect then that the above graph doesn’t just capture mean-reversion in CAPE, but also mean reversion in the other factors contributing to total return – inflation, dividends, and growth rates.

Regardless of the methodology nitpicking, I think the thrust of the argument is correct, stocks ain’t that cheap anymore, and it would be dangerous to convince yourself (or others) otherwise.

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• on April 5, 2013 at 1:13 pm | Reply Tobias Carlisle

It explicitly captures mean reversion in the multiple – it’s one of the inputs (15). Hussman uses those historical inputs for the reasons he outlines. You can substitute your own if you think Hussman’s are dictated by hindsight bias. For example, PIMCO’s Bill Gross thinks 6 percent is too high for the market, suggesting 3.5 percent is more likely in the future, which would shift returns down. You could also make an argument that the multiple to which the model should mean revert should be the current long-run average of 16.5x, and not 15x, which is the average excluding the last bubble years. That change would shift returns up. Together those two changes get you to 2 percent annually from here (1.035*(16.5/23.3)^(.10)-1+0.02), which is lower than Hussman’s estimate because the growth has such a huge impact. I think Hussman’s inputs are conservative enough, and have support both logically and, given the tight correlation, empirically.

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8. 1) Using nominal PEs instead of real earnings yields to forecast your Real Return over 10 years is bizarre & nonsensical. Re-run your screens according to real earnings yields and you’ll see that the market is cheaper than normal.

After all, in Fall 2011 when the market was at 1075, Shiller was saying ‘Stay Away!’ while Tepper and several other buy-siders correctly were calling a bottom. Shiller CAPErs have missed out on the 500-pt gain in 18 months.

2) You didn’t need anything other than the normal PE ratio to identify stocks as cheap at a PE of 7 in 1974 or 7-8 in 1981, anymore than you needed something else to notice stocks were a sell at a PE of 33x in late 1999-early 2000.

3) Using mean reversion to make ‘bullish’ data lower, but not to equally make ‘bearish’ data higher is intellectually bankrupt. The Oper/Reported EPS ratio needs to be normalized to take out things like the \$59 Billion FNM writedown a few years back – which they may write back up in the near future!

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• For what it’s worth, Warren Buffett said in a recent letter to shareholders, “Operating earnings, despite having some shortcomings, are in general a reasonable guide as to how our businesses are doing. Ignore our net income figure, however.”

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• on April 4, 2013 at 4:16 pm | Reply Tobias Carlisle

The CAPE is cyclically adjusted (Cyclically Adjusted Price Earnings). It uses real earnings. Are you proposing the Fed Model, or some variation of it? If you are, may god have mercy on your soul.

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• Do you honestly not understand the difference between using 10-yr adjusted real earnings and 10-yr adjusted nominal PE ratios? This is Finance 101.

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• Wait – are you confusing the mythical 10-yr business cycle assumed here with the varying inflation rates in history throughout various actual business cycles?

You don’t really think that inflation from 1972-1982 was the same level and had the same impact on stock prices and business and earnings as inflation did from 2002-2012?

If you think valuing the S+P at 14% inflation should be the same as at 1.4% inflation may God and the devil have mercy on your confused soul.

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9. This method roughly represents my first go at figuring out investing.

when I first starting caring about my investments back in 1999 I knew absolutely nothing about finance. But my returns for the previous 5 years seemed crazy. So I dug up some DJIA info from 1895 to 1999 and charted it against a 9% return line adding in 4.5% for dividends (that was what the website said average dividends were over that period. I used 9% because I had read that was the expected rate of return over the past 30 years for stocks). I found that the DJIA was way out of whack with that 9% return and moved heavily into bonds and cash while firing my adviser who thought I was nuts.

I’ve subsequently educated myself and actually try to incorporate Graham type principles when investing, but the fact that I understood the market will revert to a norm is still the most important understanding I have.

I don’t know why I figured that was the case. It just seems logical to me. I have no math background beyond High School. Perhaps it developed when I created a pricing system for baseball players in an effort to win my rotisserie league. I called my system Surplus Value. It was essentially a value investing strategy for rotisserie baseball – I just never heard of Warren Buffett or Benjamin Graham or value or growth investing. I was quite successful in my pool that ran for 12 years – because most everyone else in the pool was pretty much a growth investor and too enamored by recent results.

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• on April 4, 2013 at 1:10 pm | Reply Tobias Carlisle

Mean reversion is central (pardon the pun) to value investment. As you no doubt know, Graham and Dodd regarded it as such an important force that in the preface to the 1934 edition of Security Analysis they extract this quote from Horace’s Ars Poetica:

Many shall be restored that now are fallen
and many shall fall that now are in honor.

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