# Stock prices and fundamentals

How low can stock prices go, and how worried should you be?

Since 1946, in an average year the stocks in the S&P500 offered a 3.5% dividend and went up in price 2% faster than inflation, for a combined real yield of 5.5%. At that rate, if you reinvested your dividends, you might expect to double the real value of your portfolio in 13 years.

The recent volatility in stock prices has led me to think some more about an old paper by Robert Shiller titled Do stock prices move too much to be justified by subsequent changes in dividends? In that paper, Shiller introduced the concept of a “perfect foresight” stock price, denoted P*(t), which is defined as the present value of the actual subsequent dividends over future periods, D(t+j):

P*(t) = D(t) + (1+r)-1 D(t+1) + (1+r)-2 D(t+2) + (1+r)-3 D(t+3) + …

Here r denotes the rate of return, which from the numbers above we might take to be r = 0.055 at an annual rate.

Let’s consider what this formula would imply for stock prices under various scenarios for what dividends might do over the future. As a starting point, we can calculate the perfect foresight price P*(t) under a scenario in which real dividends simply grow at a constant 2% annual rate from their present values. The graph below plots 100 times the natural log of the actual dividends on the S&P500 through 2008:M12 and their future path from here on under this first scenario. Measuring the variable in this way (100 times the log) allows one to read approximate percentage changes off of the vertical axis; for example, a vertical drop of 10 units on this scale corresponds approximately to a 10% decrease in the inflation-adjusted value of total dividends paid on the index.

##### Figure 1. For 1871:M1 through 2008:M12, series plotted is 100 times the natural log of the dividend on Shiller’s extended S&P500 stock index as measured in 2008:M12 dollars. Data source:Shiller (2009). Values for 2009:M1 forward calculated recursively from ln(D(s)) = ln(D(s-1)) + 0.00172811989 for s indexing months.

The black line in the figure below plots the observed historical value for the S&P500, while the blue line is the perfect foresight price P*(t) calculated from the formula given above under the specified scenario. When the actual price P(t) is above P*(t), it means that an investor who bought stocks at that date and held onto them forever would have earned a flow of subsequent dividends whose present value was less than the price paid, or, to put it another way, would achieve a real rate of return less than 5.5%. If you bought at a time when P(t) was less than P*(t), you would have enjoyed a better than 5.5% return. The figure reveals that, under the hypothesized scenario, we have just come out of a 20-year episode during which stocks were “overvalued”, but got back to a situation where they were again undervalued when the S&P500 fell below 830.

##### Figure 2.For 1871:M1 through 2009:M2, series plotted is the actual value for the S&P500 measured in 2008:M12 dollars, from Shiller (2009). Blue line is the value for the perfect-foresight price P*(t) under scenario 1.

I don’t want to claim too much for these specific numbers. Different but equally defensible values for the discount rate and growth rate would give you a quite different value for the “fundamentals-justified” value for the S&P. The calculations I’m offering here are for illustrative purposes only. As they say, your mileage may vary.Now let’s ask how much the stock price should change if we switch to an alternative, very different scenario for what’s about to happen to dividends. As an example, I decided to ask what would be the consequences if we’re just about to repeat what happened during the Great Depression. For this scenario, I simply took the historical trajectory of real dividends between 1931:M1 and 1936:M12 and pasted it onto the series beginning in 2009:M1, and supposed that afterward (from 2015 onward) real dividends go back to growing at 2% annually, with the Great Depression II keeping us stuck permanently with a level of dividends well below that implied by scenario 1. Thus scenario 2 looks like this.

##### Figure 3.Blue line: identical to Figure 1 above. Black line: hypothetical path for dividends under Great Depression II.

The green line in Figure 4 below plots the behavior of P*(t) under this alternative scenario 2. If we’re about the enter Great Depression II, stocks are still overvalued, and the S&P500 would have to fall another 19% [all percent calculations reported here are logarithmic changes] to get down to 608, the value at which investors could again anticipate a 5.5% real rate of return given the horrible news ahead on dividends. This alternative path for P*(t) doesn’t get back to the current value for the actual S&P (which closed at 735 on Friday) until 2016.

##### Annual rate of return under depression scenario
Holding period

Return

1 year

-13.5%

2 years

-4.0%

3 years

-0.9%

4 years

+0.7%

5 years

+1.7%

6 years

+2.3%

7 years

+2.8%

8 years

+3.1%

9 years

+3.4%

10 years

+3.6%

But that doesn’t mean that if you buy stocks today you’d have to wait 7 years before you’re even, because in the mean time you’ll still collect dividends from your stocks. The typical stock will pay a significantly lower dividend in 2009 and 2010 than it did in 2008, if we’re about to repeat the depression, but you’ll still get something, and under the depression scenario, you get more shares per dividend as you reinvest the dividends at cheaper stock prices. Plus, the value of P*(t) isn’t going to stay put at 608. By construction, the value of P*(t) necessarily grows over time, even in a period when dividends are falling, because the date t value of P*(t) is by definition sufficiently low to ensure the 5.5% total return across a period of falling dividends. Between the reinvested dividends and expected increase (from 608) in P*(t), if you buy at 735 now you’ll only be down 13.5% by the end of the year. The table at the right reports your average annual return if you buy at 735, watch the market drop instantly to its depression-justified value, reinvest the dwindling dividends for the specified number of years, and then sell out assuming that stocks are valued at P*(t+j) at the date you sell. You’d break even after 4 years, and if you held tight until 2019, your average annual return would be 3.6%.

Of course, under this scenario you would do better waiting for the market to recognize the depression and wait to buy at 608 rather than now at 735. Moreover, given the historical tendency for over exuberance in upswings and excessive pessimism in downturns, you might expect the actual price to fall well below 600 in another depression, at which point there will be returns to be had well in excess of 5.5% if you time your moves just so.

But good luck with carrying out that particular scheme. After all, scenario 2 assumed we’re about to start another Great Depression, and hopefully it goes without saying that this need not necessarily happen. If it doesn’t, you may find yourself waiting for the S&P to fall below 600 until you’re both retired and dead. If the downside to investing now, even under the depression scenario, is better than a 3% average real rate of return over the next decade, I can live with that.

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## 75 thoughts on “Stock prices and fundamentals”

1. Ironman

The recent volatility in stock prices is almost entirely due to changes in the expected growth rate of dividends per share, as has been the case for most of the current decade.
Speaking of the Great Depression and worst case investing scenarios…. We have a couple of tools that can tell how much an investor would have in their retirement account if they either invested through the worst sustained period for stocks in the U.S. during the Great Depression, or a mathematical model of the absolute all-time worst-ever recorded returns for the S&P 500. The way I see it, if your retirement plan can accommodate either scenario, anything better is pure gravy!

2. CSTAR

Re “a scenario in which real dividends simply grow at a constant 2% annual rate from their present values”
current values maybe?

3. ReformerRay

These graphs are extremely useful, if a person has any lose change he can afford to commit to the future.
I am going to save this post, if I can. It may be useful some day. It certainly will be interesting to compare with events as they unfold.

4. Anarchus

Nice work.
Not trying to be a permabear, but it’s clear from the charts that valuations are the major determinants of share prices – just look at the wide variance of past share prices about either the blue line or the green line.
Now. After the crash of 1929 and the economic depression of the 1930s, stocks were meaningfully undervalued relative to the blue Shiller calculation from roughly 1930 until sometime in the early 1950s. That’s kind of the negative scenario we’re looking at, and unfortunately the dividend yield on the S&P 500 right now does not begin to support the current level.
If the professor would like to wager on the S&P 500 not reaching the the 608 level in the next 2-3 years, I’d be delighted to offer even odds.

5. Dave

I agree with (and appreciate) your analysis, however, we do not need a Great Depression II to experience P*(t). Debt service will take up the dividend/growth margin between P(t) and P*(t). The S&P will trend down from 700 as the debt siphons cash leading to a slow bleed on the S&P to the 608 of your P*(t). Ironically, this probably means we avert total collapse, a kind of “payment plan” for the macro economy.

6. John Lee

Hi folks around, dear Professor:
W. Buffett has a comment in his 2008 letter
to the Shareholders of Berkshire Hathaway Inc.
related to the calculations above :
“Investors should be skeptical of history-based models. Constructed by a nerdy-sounding priesthood
using esoteric terms such as beta, gamma, sigma and the like, these models tend to look impressive. Too often,
though, investors forget to examine the assumptions behind the symbols. Our advice: Beware of geeks bearing
formulas.”-look at http://www.berkshirehathaway.com/letters/2008ltr.pdf, too.
Well folks, what do we really learn from this :
1) W. Buffett is a rich man.
2) Others are poor.
3) I am rich too. As I have tried to forget that MBA stuff as soon as possible.
4) No one knows about the future.

7. Anarchus

I was underwhelmed by Buffett’s 2008 letter, and I thought his 100-year put price critique of Black Scholes was the weakness part of his letter.
If it’s not obvious now that capital markets and Gaussian distributions don’t mix it never will be; more importantly, Buffett’s century-long example highlights a problem with B-S that geeks were already very aware of while completely ignoring the problem with put option pricing that works against him: the fat tails.
I do not know what the odds are of a discontinuity event in U.S. capital markets over the next 100 years (see Germany and Japan in the mid-1940s for one example), but I’m sure that my estimate is much, much higher than Buffett’s or B-S’s. All that said, as unimpressed as I am these days with Mr. Buffett’s intellect, the width of his wallet never fails to impress.

8. Eagle

The actual stock prices consist of two parts: 1) intrinsic value and 2) variance from the human emotion and dynamic market environments.
How low can stock prices go depends on economy future, Fed said financial crisis will end this year. next yaer the price will be up. http://www.Trade4Rich.com

9. AJB

Just trying to understand your reasoning…first, why do you assume for the “perfect foresight” stock value that the growth rate into the future is constant for each future period, and likewise that each discount rate for each future period is constant? Second, even assuming a flat yield curve, why use a historic rate (and why exactly that time period)?
A lot of the volatility in the market right now is due to the uncertainty in the equity risk premium. Curious why your analysis doesn’t address that.

10. Tripp

While I appreciate where the professors are going with their analysis, I question whether dividends are the most appropriate measure for the construction of this model. I understand it is far easier to access information on dividends for an index like the S&P500 but I believe the payout ratio (dividends plus share buybacks over net income) would be more appropriate. I believe it was the tax reform act in 1986 that made investors prefer share buybacks versus dividends due to the difference in income tax both payouts were subjected to, even though economically they are equivalent.
This would make the period from ~’94 on not look so egregious, but it would be hard to pull out the data on which share buybacks are specifically a form of payment to the investors versus the purchase of treasury stock for other corporate functions.
Thanks for the food for thought though!

11. Anonymous

@John Lee: I don’t think Buffett was referring to the type of back-of-the-envelope analysis (in the best sense) that Prof. Hamilton posted here. Benjamin Graham’s writings are infused by strong adherence to empirical evidence and data wherever it is available. Buffett himself makes extensive study of what happened in the past and if you watch this clip, towards the end you get a nice outline of how it figures into his decision making. Rather, he refers to a very particular school of thought in financial economics, associated with so-called efficient market theory, and a certain type of inadmissible transfer of models to market, if you get my drift. Here is a nice alternative discussion of modeling in general.

IMHO these graphs are exactly the right starting point if one wants to get a sense of the situation. Then one can dig more deeply. For example, note that the market price seems to oscillate around the theoretical value but with different time scale in up and down regimes. It follows superexponential growth paths followed by abrupt declines, for which Prof. Sornette in Zurich has advanced a very nice theory. Other than taking the earnings substitution a bit further by actually simulating the paths under different assumptions, I have one minor quibble and one big question:

The quibble is that the index is biased in that the risk is not adequately accounted for due to index exclusion. This analysis makes per se much more sense (and is in fact eye popping in some cases) when done on company level.

The question is time. Suppose someone has to take into account finite T, i.e. cannot hold his portfolio forever. Even in this rough picture, one can see the immense risk one runs if one is forced to sell at some T, and perhaps random T, and the T is correlated to one’s general economic well-being or income, other than stock holdings. Then what? Even more than valuation uncertainty, we get Keynes’s beauty contest and have to take the foolishness of masses into account in the blue line. Also, there is an interesting relationship between fundamentals and prices which Soros called “reflexivity”, also discussed by Blanchard and Watson (1982).

12. JDH

AJB: Given a value for P(t) and a sequence for {D(t+j), j=0,1,2,…} one can define the rate of return r to be the value that makes the displayed equation true. If you like, you can interpret these calculations as rough measures of how much difference a depression event should make for stock prices if you hold the rate of return constant.

Scenario 1 assumes constant growth, scenario 2 assumes the specific changes in dividends observed over 1931-36.

Perhaps you’re looking for more here than I am claiming. I just propose these calculations as a helpful way to frame some of the issues.

13. squeezed

“you might expect the actual price to fall well below 600 in another depression”
the 608 scenarios seems extremely optimistic. if i’m not mistaken, extrapolating the decline in GDI gives an s&p500 bottom in the vicinity of 200.
these theoretical index models do not account for the granularity of the typical index or mutual fund. (many of the stocks traded in 1937 are now worth exactly zero)

14. Anonymous

@squeezed: you said “these theoretical index models do not account for the granularity of the typical index or mutual fund. (many of the stocks traded in 1937 are now worth exactly zero)”

Agree! That’s exactly what I meant earlier that the use of SPX hides risk by index exclusion. The exclusion is subjective (by committee) and places an effective put around the minimum market cap that is not there for real-time investors.

15. GK

But if the yield on the 10-Year is under 3%, doesn’t that support a P/E on the stock market of 16 or so?
When 10-year yields rise due to high inflation that we are about to experience, then it is another story.

16. GK

“the 608 scenarios seems extremely optimistic. if i’m not mistaken, extrapolating the decline in GDI gives an s&p500 bottom in the vicinity of 200.”
Wrong. Very wrong.
If you assume a 7% nominal return per year since the bottom of the GD (dividends reinvested, nominal return), then :
GD bottom : Dow at 42 in 1932
7% a year return for 77 years
= (42)*(1.07)^77
=Dow 7700, which is S&P500 at about 800

17. GK

Remember that the period from 1973-82 was effectively a depression for the stock market, where real returns were negative over the decade (even with dividends reinvested).
Separately, even under a GD II scenario, it would appear that Value stocks would weather the storm a lot better than growth stocks, no?
Lastly, a volatile market is the problematic one. A depressed, yet stable market still allows opportunities for covered calls, which enable improved returns if done properly.

18. GK

JDH wrote :
“with the Great Depression II keeping us stuck permanently with a level of dividends well below that implied by scenario 1. Thus scenario 2 looks like this”
Why would this be permanent, extending up to 2050 in your chart? A GD II would last another 8-10 years, after which more favorable valuations would return. The stock market years from 1945 to 1965 were very favorable.

19. toddleem

Simply a great post.
I think that Marge Flavin (Jim’s wife) made a substantial contribution to Shiller’s work when she allowed the discount rate to vary over the business cycle due to risk aversion.
One could argue that we could get to a 600 level without a depression scenario if market participants suddenly require a very high risk premium due to extraordinary wealth effects.
I also like that this analysis is based on dividends. Jeremy Seigel recently has made arguments that valuations based on earnings may be biased since S&P earnings doesn’t weight earnings according to market value-their measure of earnings may be inappropriate when small market value companies (fallen angels like Citigroup) have huge earnings losses.

20. GK

Well, as long as you are not on margin, the fall from 735 to 600 is a lot less scary than the fall from 1250 to 735.
Again, consider a restrained, conservative covered-call strategy. It is not asking much to gain an additional 3% return a year, thus lifting the total return from 3% to 6%, and bringing breakeven much closer.

21. Anarchus

Based on the futures overnight, it’s now a decline from 726 to 600 for the S&P 500 . . . . . .

22. Joseph

One shouldn’t make too much of reversion to mean trend on a set of data. By definition, when you draw the best fitting line to the data, the data will mean revert because that is the way you plotted the line. Mean reversion didn’t cause the line; the chosen line created mean reversion.
This means that the current trend line doesn’t necessary imply the future trend. Twenty years from now you can draw a new line that shows mean reversion and may not be coincident with the current line.

23. JDH

Joseph: the series for P* is not “fit to the data.” Data on stock prices were not used in any way to construct P*, other than insofar as they are related to the average dividend yield over the subsample 1946 to 2008.

24. Steve van Emmerik

Excellent post – loved the original Shiller work (although obviously it’s only part of the story as far as stocks go) and great to see an update.
As far as short to medium term dynamics of stock prices go when you get a really large overshoot on the upside like the one we’ve had you tend to get a 30-50% overshoot on the downside followed by at least a decade considerably under what the discount dividend suggests is “correct/normal” stock market price level. Looking at the SP500 and taking say 700 as a reasonable level at the moment that would mean the SP500 goes to somewhere from 350 to 490 somethime in the next few years then spends the next 10 years growing at something a few percent above the inflation rate on a p.a. basis before taking off again. Unless you’ve got a much greater than 10 year investment view that doesn’t make todays prices look a great bargin.
GK wrote that
“JDH wrote :
“with the Great Depression II keeping us stuck permanently with a level of dividends well below that implied by scenario 1. Thus scenario 2 looks like this”
Why would this be permanent, extending up to 2050 in your chart? A GD II would last another 8-10 years, after which more favorable valuations would return. The stock market years from 1945 to 1965 were very favorable. ”
My answer to this is that a great depression type scanario means that there has been substantial misaallocation of resources leading up to and during the depression and that the output loss from a great depression is permanent. i.e misallocation is too many houses, factories, commerical buildings in the wrong places/industries, too much training of finance related people etc in the boom time and then a long period where these investments fail to generate “normal” returns and where there are vast amount of capital and labor that are underutilized. In other words the change is permanet because capitalisim stuffs up for a period and a great deal of the potential output/profits/dividends that usually occurs are lost. They aren’t magically reclaimed when things get back to normal.
Great to see a mention for Soros and reflexivity! I blog on this stuff at http://reflexivityfinance.blogspot.com/

25. Patricia

What about the fact that many firms now do not even pay dividends?
“In today’s modern market many firms have decided not to pay dividends under the principle that their reinvestment strategies will, through stock price appreciation, lead to greater returns for the investor. Thus, investors who buy stocks that do not pay dividends prefer to see these companies reinvest their earnings to fund expansion and other projects which they hope will yield greater returns via rising stock price. Although these are generally small- to medium-cap companies, certain large caps (e.g. Microsoft)have also decided not to pay dividends in the hopes that management can provide greater returns to shareholders through reinvestment.”
As a whole, we can not consider stocks as simply the sum of expected future dividend streams. And the stochastic discount rate might change substantially over time, probably more so over the business cycle. And the assumption is perfect foresight??? Please.

26. DickF

In the 1930s we experienced the Great Contraction. In the 1970s we experienced the Great Inflation. It appears that here in the 2010s we will experience both.
To give you an indication of what that means the decline in asset values will be greater than 50% (stocks, homes, businesses, etc.), but then when assets have declined to their maximum and people smell inflation in the air it will begin with a vengence. If it is as bad as the 1970s we will have approximately a 90% loss in purchasing power of the dollar in 10 years(this is a conservative estimate using gold in 1970 at \$35 then in the 1980s avearage of \$350; recall gold went to \$850 in the early 1980s).
To make this personal, a person who has a 401(k) with \$500,000, planning on retirement, has or will lose \$250,000 in asset value. Then to make things worse in the following inflation a modest automobile that today costs \$15,000 will cost \$150,000. Now you could be able to offset some of the loss in purchasing power of the dollar by buying hard assets but you will lose liquidity. It is doubtful that you will be able to sell your hard asset for the inflated price of the asset.
The potential for economic disaster is worse than most imagine, but this is what happens when a nation removes the foundation of its currency leaving currency value subject to the inflationary bias of government, then combines this with destroying the free market by government Fascist central planning.
Oh, how I hope I am a reactionary but I predicted double digit unemployment by the fall. California announced 10% unemployment just last week. What makes me sick is that it could all have been avoided with sane economic policy.

27. Bob_in_MA

I don’t know squat about P*(t), but I can tell you this: at the bottom in 1932 the DJIA yielded (after lots of dividend cuts) 15%.
Your formula seems to “prove” that a yield now of 2-3% is somehow a reasonable equivalent of the average of 5% from the days when people expected a fair amount of market volatility.
Guess what? People have now developed an expectation of high volatility. A yield of 2-3%, no matter how elegant the formula, is going to cut the mustard.

28. MikeR

Patricia, whether a stock pays a dividend or not, the same principles can be used. Eventually, a firm runs out of positive NPV investment opportunities and it begins to pay a dividend (ie Microsoft) or it buys back stock, in which case a similar analysis can be built around cash flow per share.
On your point about discount rates being stochastic, while it is true the gordon dividend discount model oversimplifies the nature of the variables, the simplification allows shiller to prove his point so that the average investor can understand. No one uses these models to get precise estimates, only probability distrubutions.

29. VoiceFromTheWilderness

What your analysis says to me is the following: Under an assumption of a repeat of the great depression, any money invested in the stock market will be a loss until 4 years from now. Looking a little more widely this means that anyone investing in a T-bill yielding 0.5% per year, will beat the stock market for approximately 7 years. This is a buy signal? uh, sorry, that thar’d would be stock market uber ales thinking. This is clearly not a buy.
The above analysis could then be reformulated to ask the following question: how good do dividends and prices have to be to beat investing in T-bills using the Schiller value formula? If the answer is ‘better than current performance’, then your metric is managing to explain the stock market drop. Everything else, including in particular, guesses about future market performance, are really emotion laden wish fulfillment

30. VoiceFromTheWilderness

follow up: I was thinking of 3-month T-bill rates. If we use 10 year T-Bill rates then the analysis suggests that investing in the stock market is a wash for a decade — even less compelling reason to buy.

31. GK

It seems that an equal number of people are worried about deflation and hyperinflation. That is quite a paradox.

32. aml

Hi Hyun-U,
I like the part of the Q&A when she quotes: “the purpose of margin of safety renders forecast unnecessary”
I wonder how does that principle translate into actual investment criteria.
He can’t just pull a number out of thin air and demand that his portfolio company attain that revenue/income target within a specified time frame, even if the target comes with big safety margins.
So Buffet has to have at least a heuristic estimate in mind of the company’s expected, aka, forecasted growth rate.

33. Bob_in_MA

GK, the answer is to buy TIPS. You can get close to a real 2.5% on the 20-year.
Why is is people think share prices rise with inflation? The period of highest inflation in our history was about 1968-1982. The DJIA barely stayed flat, even in nominal terms. Dividends yielded maybe 4-5% during years inflation was over 10%.
This market might be a screaming buy at sub-500 on the SPX, but not if dividend cuts keep the yield below 4%. Foreign markets nearly all yield higher rates, some much higher.

34. Fred

>It seems that an equal number of people are worried about deflation and hyperinflation. That is quite a paradox.
No paradox at all. It depends on the choices that a small number of human beings make. In particular, whether the Fed responds to inflation or not, and whether Congress pressures the Fed to not respond. That is far more unpredictable than the real dividend rate.
The prudent investor, especially one who has no other source of income than his investments, has no choice but to prepare for hyperinflation by putting a large chunk of his money into stocks or income-producing real-estate whenever these produce a reasonable rate of return, and simultaneously prepare for deflation by keeping some money in high-quality nominal bonds whenever these produce a reasonable yield. If prices on stocks/real-state/bonds drop after you purchase them, so that the new yield is better than what you got originally, then too bad. No different from buying a pound of tomatoes at one store, at a reasonable price, and then seeing tomatoes priced much cheaper at another store on the way home. Holding out for prices that are not merely reasonable, but rather constitute bargains, is not investing, it is speculating.

35. DickF

GK,
My post was to explain why some economists see both inflation and deflation. The deflation is actually a contraction rather than an appreciation in the purchasing power of the currency. Because this is diagnosed incorrectly the medicine could kill the patient with inflation.

36. squeezed

@GK, My comment referred to an extrapolation of peak to trough decline during GDI (not returns from GDI). IMO, 608 would be a mild outcome for this type of balance-sheet/credit crisis.
710 and dropping like a stone.

37. jg

Very nice work, Professor. Neat to see someone (finally!) working in G.D. history/stats into their analysis.
Earnings for the S&P 500 in Q4 08 are, for the first time since records began in ’35 or so, negative in the aggregate. And, the economic unwind is accelerating, it appears.
So, I think you should view the ’31-’36 dividend history as ‘best case during a depression,’ because I think dividend performance during this Greater Depression has a real chance of being inferior to that during ’31-’36.
http://www2.standardandpoors.com/portal/site/sp/en/us/page.topic/indices_500/2,3,2,2,0,0,0,0,0,1,5,0,0,0,0,0.html
then
“S&P 500 Earnings (Operating, As Reported & Core) and Estimate Report, includes Divisors and Aggregates, Core Breakdown, and Dividends, click here”

38. Jon

Two questions:
Is it correct to use the figures starting in 1946 to construct the forecast? If you take the edge of a book and extend your forward projection backwards, I see where it hits the graph in 1946, but way underpredicts history prior to 1946. Second (and somewhat related), the blue line in the second graph is the predicted price based on perfect foresight of dividends. It predicts if you bought right where the blue and black lines were coincident in like 1886ish, it would take about a century until you quadrupled your money. Does that seem right?

39. GK

I would have said 660 was the bottom on the S&P500. Currently at 710 and falling every day. Time will tell.

40. JDH

Jon: Yes, if you take the entire 1871-2008 period, the average growth rate of dividends is 1.65% rather than the 2% you find over 1946-2008. On the other hand, for the entire 1871-2008 period, the average growth rate for the stock price is about 2%, the same as the average growth rate for stock prices over 1946-2008 and the same as the average growth rate of dividends over 1946-2008. There is a problem calibrating parameters for this framework if the average growth rate of the stock price differs from the average growth rate of dividends. As I became aware of this issue in trying to update Shiller’s calculations, I looked back at his original article and found that he hadn’t really addressed these trend issues head-on, though he must have noted their relevance. Note also to get the series back to 1871, he spliced some things together. The application is quite clean on the 1946-2008 subsample, and I think those are also the best numbers to use to interpret the pre-1946 data as well.

As to your second question, I’m not quite following. Any time you buy at a date when black intersects blue and sell at a later date when black intersects blue, you have made an annual rate of return of 5.5% which doubles your real wealth every 13 years. Remember that reinvested dividends are contributing 3.5% of this and price appreciation only 2%.

41. Turbo

Nice post JDH. Several different valuation approaches indicate that now is a good time to be a long-run investor, provided one can hold on through the potential further downside. A year ago, this type of analysis would have been dismissed out of hand as the work of a permabear, now it seems to be viewed as overly optimistic. Market psychology never ceases to amaze.

42. Bing

Fantastic post. Could you kindly explain what is the difference between your perfect foresight Price and a dividend disount model.
I did a similar calculation. Using a dividend discount model and assuming 5.5% nominal growth (3% real and 2.5% inflation) the market is currently pricing in ca10% cost of capital. This is high but nowhere near the peak implied cost of capital of June 1932.
http://great2cents.blogspot.com/2009/02/valuation-update.html

43. Jon

Thanks. First question answered, second is my fault. I don’t know why I had it in my head that the black line (S&P 500) included reinvested dividends; now that I know that it does not, the graph makes a lot more sense.

44. Fred

Another way to get a fix for value is to get the average ratio of nominal SP500 earnings (in dollars) to nominal GDP (in trillions of dollars). Using nominal rather than inflation adjusted avoids problems with changes to the CPI deflator. A chart of the 10 year smoothed average of this ratio shows that it has been declining from 1940 but seems to be holding steady at 4.0 since about 1990. Unless we truly have a saving glut, such that investors are willing to accept much lower rates of return in the future than in the past, I see no reason why this ratio should decline permanently in the future.
Assuming this ratio holds in the future, we should expect SP500 earnings to eventually return to the trend line, or 4.0 X 14.2646 = 57.06 for 2008. Then multiply this by your favorite average P/E ratio to get fair value for the SP500. I’ll use 13, which gives fair value at 741. The typical bear bottom low for the 10 year trailing average PE is about 10, which would give a bottom of 570 for the SP500.

45. KnotRP

Sigh. Go read this past posting, for one of several examples on why this blog is always a day late and more than a dollar short:
http://www.econbrowser.com/archives/2007/08/wheres_the_risk.html
at 2:14AM (this was August 2007, a long long
time ago): Posted by: KnotRP at August 21, 2007 02:14 AM
“What this means to me is that there is simply no good place to preserve wealth at the moment.”
The good professor is still, circa 2009, ignoring a structural change and keeps grasping for a cycle bottom. This isn’t a cyclic change, and there ain’t no cyclic bottom, professor. The ability to generate Income is adjusting to globalization, which will cascade into all other prices. The developed world wage chump is now adjusting, and won’t be buying S&P 608 because they need every dime they have left to ride out a long phase of unemployment, waiting for the dollar to devalue enough to equalize wage pressures.
The time to be dilligent with a parachute is when you pack it. The economics profession is a dismal failure, not science.

46. Steve

The market will return to growth, once Barak Hussein Obama is either neutured by a Republican House, or is run out of office. Not until! Look for the free fall to continue until then. We may see a dow jones avg. at 3000 to 3500, which would represent a 75% to 80% overall decline. The reason is simple, there is a big sucking sound coming out of Washington. The only good news, in a terrible situation, is this may finally be the end of Keynes based economic theory. You cannot have the have nots consuming more then can be produced and have a functional market or society. No historical trend will work to forecast this situation. However, produce a chart of the damage and keep it for future generations. I hope they will learn by this collossal folly that has befallen this great people!

47. Steve

I overlooked one last thing. Should the U.S. be attacked during Obama’s watch, look for market to hit 1500.

48. Moopheus

“If it doesn’t, you may find yourself waiting for the S&P to fall below 600 until you’re both retired and dead.”
At the rate things are going, we could be there in April. All of this math is nice, but what, exactly, in our economy is going to produce earnings in the future? I mean, our “growth” for the last couple of decades was based on spending a lot of money we didn’t have. We’ve lost huge swaths of our manufacturing capacity, and what we have left is under pressure. Nonessential goods became cheap while essential goods (food, medicine, housing) became expensive. Do we know how to do anything but gamble on bubbles?

49. KnotRP

“The Fed can always inflate” solution (with matching post by the good professor) will not help because rising goods prices won’t be affordable to downwardly adjusting developed world wage chumps and retirees.
It’ll be deck chair rearrangement on the Hindenberg.
The economics profession toolbox apparently
only consists of monkey wrenches, in a variety
of sizes.

50. ed

I would love to hear a response to Tripp’s question; how does this analysis change if we account for the shift in recent decades away from dividends towards stock repurchases?

51. Movie Guy

Jim – “How low can stock prices go, and how worried should you be?”
Well, at least this low (as evidenced today):
DOW 6763.29
S&P 700.82
RUSSELL 367.8
NASD100 1076.67
Twenty to twenty-five percent further drop from these levels will not surprise me.
Worried? Not now. I cashed out large last August.
Nice main post, by the way.

52. calmo

Could be more to worry about than your portfolio…Steve times a million would be a worry for me right now.
Can we review this market participation and register the ~1% that holds 2/3 of it…(2005 numbers prolly worse now as modestly wealthy have actually had to sell rather than do as instructed by their brokerages)?
Working people and their emaciated 401ks have less of a cushion…and might be less than convivial hosts if you’d like to stop by and share something to eat.
This coming unemployment of recently disenfranchised folks…could be the real worry.

53. Steve van Emmerik

A couple of good points above in terms of valuation in US stocks.
1. They don’t seem real cheap in the sense there are solid stocks with solid earnings outloosk at reaonabel PE ratios.
2. They don’t seem real cheap when you compare tham to stocks in other countries which have signicantly lower PE ratios and higher dividend yields. Not to mention these other economies often have financial systmes that are healthier, and consumers and governments who are not as financially stretched.
Having said that I did close my US market short today anticipating a possible short term bounce. But will be back on that short soon.

54. ROB

Mark this down on your calendar that you heard it here first. This particular DOW spiral bottom will be between 4000-4500.

55. Michael Krause

An interesting exercise in backtesting, forecasting, and modelling, all based on the ridiculously flawed assumption that history will repeat itself.
If you derived your r in October of 2007, when it seemed very justified considering a 14T GDP and actual earnings (versus what in 2000 was just a high multiple), your curve trajectory would be very different.
But in reality, the markets don’t work like this. We could have an upward revaluation overnight if some exogenous events occur which policymakers have control of: dollar devaluation and/or several trillion of money printing, repeal of current fair value accounting standards, some unforeseen technological breakthrough (which seems to happen frequently enough).
Your r is a result of of arbitrary dates you pick to evaluate past returns by, and again arbitrary causes of dividend to earnings ratios.
Here’s my analysis: No one can convince me on why the S&P deserves a 10 multiple versus a 30 multiple (when we see countercyclical policy and 3-3.5% 10-30 yr treasury yields), nor why S&P earnings should be estimated as operating (~\$50) or reported (\$28 or lower)? With that in mind, the S&P can rightly get a 1500 estimate just as easily as a 280 estimate.
With that said, it seems foolish to take any curve fit too seriously.

56. Josh Stern

The specific question is about the details of how Shiller, or the sources he relies on, calculates dividend return. For example, does a corporate buyout count as a big dividend if the acquirer pays cash but not if they pay stock?

The second questions is about what supporters of this model think is the best way to reconcile the valuation model based on dividends with investor behavior. Only a small portion of investors seemingly base their decisions primarily on a search for dividend yield. Clearly, there is an idea that some (most?) stocks which do not pay a dividend now, might do so sometime in the future. One *could* say that, e.g. the stock of Microsoft was much higher in the past when it didn’t pay any dividend than it is now when it does because investors buying that stock thought it would pay a higher dividend now than it does, even though it had never previously paid any dividend, and hadn’t announced any intention to do so. And one *could* say that traders following TA signals and momentum are simply piggybacking on the trades of fundamental investors who are really seeking future dividend yield. And one *could* say that the reason why apparently overvalued individual stocks and apparently undervalued individual stocks rise and fall together is either because a) market participants find it so much easier to predict overall future dividend yield than future dividend yield for individual securities that they don’t want to risk tracking error by holding a portfolio of apparently undervalued securities, or b) common factors for prospects for future dividend yields of all securities really do change more on a daily basis than prospects for the difference in future dividend yields of individual securities compared to the overall trend, or c) the market has some very smart way to evaluate relative future dividend prospects for individual securities, but its overall prediction for the market that unstable and sometimes out of whack for decades.

57. anon

Michael Krause is a fool for not reading the article or not understanding it (I don’t know which is worse) and then leaving such a caustic, arrogant comment.

58. Michael Krause

I re-read this, just to make sure. I see that r is derived from dividends, not stock performance. (When I wrote my original reply, I must have incorrectly considered the 2% margin which accounted for inflation instead reflected average returns) I stand corrected. But r is still an average dividend, which as Tripp points out may have changed: “I believe it was the tax reform act in 1986 that made investors prefer share buybacks versus dividends due to the difference in income tax both payouts were subjected to, even though economically they are equivalent.” One can see many profitable companies not paying out much in dividends this past 2 decades to substantiate this.
Furthermore, the 2% annual inflation is form fitting once again. The whole game changes if you tweak that rate up or down .5-1% annually. And as we’ve seen, policymakers can screw up enough where a few large jumps in either can largely unsettle the smoothness of these curves, limiting their usefulness.

59. JDH

Michael Krause: there was no assumption of a 2% inflation rate. Shiller’s data set converts the historical dividends into current dollars on the basis of the ratio of the CPI today to the value of the CPI at the time the dividend was paid.

60. Fred

The correct return R for stocks can be derived in a number of ways independently of stock returns:
a) if the 20 year TIPS rate is 2.5% and we assume a 3% risk premium for stocks versus TIPS, then we get 5.5%.
b) if the 10 year A corporate bond yield is 6.5% and we assume 2%/year inflation and a 1% risk premium for stock versus corporate bonds (stocks have more default risk but less inflation risk than corporate bonds, which is why the risk premium is only 1%), then that also gives 5.5%.
So the assumption of 5.5% returns on stocks, assuming you buy the stocks at a “fair price”, is quite reasonable. Having validated that 5.5% return assumption, you can then legitimately fit curves in order to determine what constitutes fair price in order to get that 5.5%.

61. Fred

Perhaps the reasoning is my previous post is not clear. Assuming there are strong fundamental causes why investors expect a 5.5% return for stock equity investments, then the stock market will tend to return to one of many parallel linest line (on a logarithmic chart) which give a 5.5% return. Only one of these parallel lines is the fair value line. If the future is similar to the past (there has been no fundamental change to the economy such as to knock down earnings and keep them down permanently, such as the original poster discussed might have happened), then the fair value line is the one which can be regression fitted to a chart of historical stock market values. Otherwise, the fair value line might be below or above this regression line.
It is also possible that the 5.5% number might have changed, though I doubt this, since this number is related to deep psychological factors and there is no good reason why these should have changed recently: (a) aggregate willingness to forego immediate gratification by spending, in favor of a higher amount of deferred gratification by saving, aka the risk-free rate; (b) aggregate risk aversion, or risk-premium above the risk-free rate.

62. dan

Michael Kraus, Fred, there is no curve fitting involved in the calculations! it’s just averaging and then applying the standard DCF formula to see what would have been the price if investors had been able to foresee the level of future dividends.

63. Fred

It’s true that I misued the term curve fitting, but it conveys the idea of what is involved in picking the starting point for future dividends. Any line parallel to the two lines shown in figure 3 is acceptable, based on the 5.5% return assumption. The only reason the black and blue lines (or something between these two) are prefereable to other possible lines, is because the black and blue lines tend to fit the curve of historical dividends, whereas parallel lines much below the blue line or much above the black line seem unreasonable based on historical dividends.

64. JDH

Fred: You perhaps are still missing the point. The two paths for dividends are as radically different as normal growth is from the Great Depression, but the implied blue and green paths for stock prices are not so different. As you’ll see from the graph, these radically different assumptions about what happens to dividends after 2009 make particularly little difference for the implied fundamentals valuation prior to about 1990. You could likewise change the projected dividend paths quite radically after 2030 and it would not make much difference for the implied fundamentals valuation for 2009.

65. deaf

the math model is very questionable, if u look at fig one and extend the prediction line backward, u realize the growth line is way steeper than the real data. plus the data has no 2008-2009 market drop, what the hell

66. JDH

spiffy: OK, then start with paragraph 5: “When the actual price P(t) is above P*(t), it means that an investor who bought stocks at that date and held onto them forever would … achieve a real rate of return less than 5.5%.