This article was written as an antidote to "early onset optimism" as investors looked for an equity market bottom in November, 2008.

It's not that we had a strong view that equities had not bottomed, it's just that it wasn't clear to us that they were clearly "cheap". Such a view requires a fairly short-term perspective on equity valuation, and the work of Robert Shiller provides a longer-term and much more sobering perspective.

Looking back four years later, this article still holds up. It shows how, even in the heat of market turmoil, you can use a framework to make judgements. The suggestion that markets could well head even lower was supported by subsequent market events, and the suggestion of a possible low, while not meant to be taken as more than a useful example, was actually quite accurate!

What’s going on? How far can markets fall? When should I get back in? (Should I get back in?) Will my portfolio ever recover? It’s all very confusing and troubling! Every day some pro says in the paper or on the internet that “we think it’s time to start buying”. The next day (or moments later) someone else says: “stay out, keep your powder dry, there’s more to come”. Of course the answer is: no one really knows.

I think it is important to go back to basics. Before you even begin thinking about what to do, take some time to figure out where we are. Obviously the people who recommend buying believe that stocks are cheap. People who recommend staying on the sideline think either that stocks are not cheap, or else that they’ll be cheaper soon!

The best way I know of to get a handle on the situation is to put things into an historical perspective, and the best perspective that I am aware of uses the data and methodology popularized by Robert J. Shiller.(1) Working back from current data, we can look at the history of the S&P 500 while adjusting for inflation --- that is, comparing “real” prices, “real” earnings, and “real Price/Earnings ratios.

The top line in Figure 1 (green line with right scale) shows the real price level from Nov. 2008 month end (at 896.24) back to January 1871. Note the market peak in August 2000 (the tech bubble), the market bottom in September 2003, and the most recent peak in July 2005. On November 20, 2008 the market hit its recent low at 752.44, and closed November 2008 with a sharp rally to end at 896.24.

The bottom lines in Figure 1 (left scale) represent real earnings for the index. The more volatile red line shows 12-month trailing real earnings measured at each month end, while the smooth blue line shows “normalized” real earnings, a moving 10-year average of the real earnings series. In the rest of this analysis, we focus on the normalized earnings, since they reflect the general trend in earnings growth, and avoid the wild short-term swings of the month-by-month earnings series.

The key to linking prices and earnings is, not surprisingly, the Price/Earnings ratio. In this case we focus on the Real Price to Real Normalized Earnings ratio, which sometimes will be abbreviated as “Real P/E-10” in the charts (Figure 2 below). The relationship seems trivial: Price = Price/Earnings x Earnings. What makes the P/E ratio more interesting is using long-run normalized (10-year moving average) earnings. The normalization or smoothing means that the earnings component generally reflects long run earnings growth, and the P/E ratio represents the current market view of **how valuable** those normalized earnings are.

Figure 2 shows this relationship based on the price and earnings data in Figure 1. Note that the peaks and troughs in this version of the Real P/E-10 ratio corresponds very closely to the peaks and troughs in the S&P price series:(2) In bull markets investors pay very high multiples for normalized earnings, while in bear markets they pay very low multiples. The average real normalized P/E over all reported history in Figure 2 is 16.41. This means that until November of 2008, with a closing P/E of 15.32, the P/E has been above the long-term average since December of 1990 (using month end values) --- a span of just under 18 years.

Just this fact alone gives us a clue about one source of investor bullishness --- for those who argue that stocks are now cheap. They are likely (and in some cases are explicitly) comparing current valuations with history back to the 1990’s, or in some cases to the 1980’s. For the record, the average Real P/E-10 from Jan 1992 to the present is 28.04, while the average Real P/E-10 from January 1982 to the present is 22.62. So, for example, if you think that the relevant comparison set going forward is the experience from 1992 to the present, you might indeed think that stocks trading at a multiple of 15.32 are “wildly attractive”, and might even speculate that we now are in a “negative bubble”, perhaps the mirror of the internet bubble of the late 1990’s.

However, a little caution is in order. Perhaps markets going forward will be priced differently, more aggressively, than markets from 1871 to 1982. Perhaps investors will be willing to pay much higher multiples for earnings, on average, than they did in the first 110 years of this history. But let us at least look at a few facts from this history, in the light of a few home truths about equity investment returns.

If I buy into the market at a point in time, my return over a subsequent period is based on (1) the income from dividends, and (2) the change in price of my investment. Prices can change because (2a) the P/E multiple changes or (2b) earnings change. Looking at the broad market, there is good reason to believe that generally both earnings and dividends will change over time roughly in step with growth in the economy. So if a broadly based equity portfolio return outstrips the underlying growth in the economy over a long period of time, it must be because the P/E multiple has expanded: investors are paying more for earnings than they were when I first bought the portfolio. Intuitively, this seems to imply that there is more likelihood to profit from an equity investment if it is purchased when the P/E is low --- more chance for the P/E multiple to expand (and less chance for it to decline) --- than when the P/E is high. Let’s call this our “value hypothesis:” there is a higher probability of experiencing positive returns over the long run if you are able to purchase equities at a relatively low Real P/E-10 ratio.

We can update a very simple test outlined by Shiller(3) to illustrate this idea. Figure 3 plots the Real P/E-10 ratio for all available dates between December 1880 to October 1998 on the horizontal axis, and the ** subsequent 10-year annualized total real return** on the vertical axis.(4) Note that we are still working with real returns, so inflation has been removed, and also that these are “total” returns in that they are composed of both price returns and dividends.

The line of best fit is plotted in red as a smooth curve through the data. Just “eyeballing” the data begins to show a confirmation of the “value hypothesis”: First, the line of best fit travels from top left to bottom right, so that generally higher subsequent returns are linked with lower Real P/E-10 ratios, while lower subsequent returns are linked with higher Real P/E-10 ratios. Since the data show a distinct tendency to cluster around the line of best fit, the relationship appears to be fairly strong.(5) In addition, almost all of the negative return episodes are related to starting Real P/E-10 ratios of more than 12.5. This means that there is more chance that following a high initial Real P/E-10, the subsequent 10-year return will be negative.

While this picture is highly suggestive, it might be easier to examine the results in a Table 1 below. Six “buckets” of Real P/E-10 levels have been created with roughly equal numbers of observations in each. In this sample, the average Real P/E-10 is 15.25, the breakpoint between buckets three and four.(6)

The average subsequent real return for starting Real P/E-10’s above 20 is just 2.62% per annum with 29.8% of cases having a negative return. The average return for starting Real P/E-10’s below 10 is 11.4% per annum, with no cases of negative returns. While the table confirms that the “value hypothesis” was apparently strong in the past, it does not in itself prove anything about the future. However, it should give pause for thought!

Let’s look at this in another way. The Real P/E-10 of 15.32 at November 30, 2008 is about average for the data in Table 1, and slightly lower than the average of 16.41 for all Real P/E-10 data up to the present day. According to this history, if you start with a Real PE-10 at this level there is a fairly high probability of positive returns over the next 10 years, but also some probability of negative returns. By contrast, if you are now very bullish, and think that there is a __very__ high probability of strong returns in the next 10 years (higher than Figure 3 or Table 1 suggest), then you have to come up with a thesis that suggests why this is so, why the next ten years will be different. This will have to happen in one or more of three ways: that earnings growth will be higher than in the past, that dividend growth will be higher than in the past, or that Real P/E-10’s will trend (and remain) higher than average. Why do you expect that one or more of these three conditions will hold?

Any or all of these points may be true, or at least you might have good arguments to justify your beliefs. However, in the interests of sober thought, remember that since the 1982 recession, from which the market went on an eighteen year bull run, the only subsequent recession in that bull market was a brief few quarters of negative growth in 1991. The U.S also experienced a few quarters of negative growth in 2001 during the bear market, which led to the earnings dip in Figure 1. But we are now once again in a recession, which economists think will be at least as severe as the deep recession in 1982, and probably worse. We will see further de-leveraging of the financial system, which in turn can be expected to hamper real growth. In addition the fiscal stimulus programs will take a considerable time to work their way into the real economy.

We could draw a very negative picture here, but that is not my intention. What I am looking for is a way of answering the question: what might the market look like if we get a downturn in earnings, reflective of the current recession? Rather than wrestle with the question of how bad the economy (hence real earnings) may be in the next few years, I made a very simple extrapolation for illustrative purposes. Suppose earnings follow the course they took during the short bear market in 2001-2002. This is shown in Figure 4 as a red dotted line, along with the related implied extension of the real normalized (10-year) earnings series (smooth red line). Given the current financial and economic environment, this may be a somewhat optimistic possible path for earnings, especially the quick recovery. But since we’ve already been through this exact same earnings pattern, no one can say it’s not a reasonable possibility!

Now in this scenario Real Normalized Earnings reach a low of 52.9. How low might the market go in response to this fall? To give an idea of the range of possibilities here, let’s lay out three possible levels for Real P/E-10 as the recession impacts earnings: (a) it stays at the level of November month end (15.32), (b) it returns to its November 20 low of 12.86, and (c) a “worst case” scenario that it falls to a cyclical low of 10 (not by any means a worst case historically, but a level not seen since 1982). Table 2 shows the results.

Any further pronouncement on this is fraught with danger.(7) However, I would expect a multiple of 10 would only be reached under a scenario of long-term deflation and very long recession/depression. On the other hand, having Real P/E-10 remaining at levels of over 15 with all the potential for poor earnings and other bad news, seems overly optimistic to me now. You can see where I am headed with this.

I want to be very clear that I am not reviewing these issues to provide a short term market timing suggestion. For perhaps the major theme of Shiller’s insightful book was to examine the factors (structural, cultural, psychological, and even efficient markets theory itself) that allow for, and even foster, “irrational exuberance” --- long term irrational market pricing in the face of this kind of rational analysis.

Rather, I view this analysis as an important “background evaluation” tool, a checkup on the state of the market, and perhaps the first step in making an informed allocation decision. It’s a check that can be updated on a frequent basis, and not just when you are thinking that markets may be stretched to one extreme or the other.

I tend to believe that before the dust finally settles, we should expect lower Real P/E-10 multiples and lower normalized earnings than current (November month end) levels. If this tentative belief turns out to be correct, then full-blown re-investment in equities will be implementable at that time at better levels than are available now. But this opinion isn’t a consequence of the Shiller analysis (which tells us that equities are slightly cheap on a long-term historical basis), but rather is a consequence of concerns about further deleveraging, economic contraction, and deflation.

__Appendix 1__

Here is a quick example of building multiple scenarios, as mentioned in footnote 7. Using the earnings scenario outlined in the text of the article as a base or central case, I explored four other earnings paths to come up with alternative lows for Real Normalized Earnings.

- I found it very difficult to bring the normalized earnings down to 45, and took that as a short-term low, with a probability of 5%.
- A low of 50 could be obtained if earnings fell as in the base case, but only recovered very slowly. I assigned this a probability of 20%.
- I assigned a probability of 40% to the central case.
- I assigned a probability of 30% to a low of 55, which assumes a less dramatic fall and fairly early recover.
- The final case is 58.5 with a probability of 5% --- the current level of earnings, which allows for some fall in earnings but a recover by early 2010

The three P/E ratios of 10, 12.86 and 15.32 are maintained, with probabilities of 5%, 55% and 40% respectively.(8) The following table shows the cases, multiplies the probabilities through, and calculated a weighted average index level. The result is a weighted average of 723.89, slightly below the November 20 market low.

For interest, the “Sub-Scenario” results are plotted on the following graph, along with the weighted average index level.

The point here is methodology, not the actual forecast. But you can see what your intuitions need to tell you if you expect to avoid such a low result: either earnings have to fall much less and probabilities of a fall have to be lower, or else you have to assume that Real P/E-10 ratios must be more likely to expand or stay high.

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(1) Robert J. Shiller.* Irrational Exuberance*, 2nd Edition. New York: Doubleday, 2005. Data from his website http://www.econ.yale.edu/~shiller/data.htm has been updated using current data sources. (Return to Text)

(2) By contrast, the P/E ratio based on simple 12-month trailing earnings does not correspond to peaks and valleys in the price series. For example, the peak market price level (month end data) was 1517.68 in 2000/08, with a real normalized P/E of 44.28, the second-highest real normalized P/E level. The P/E based on trailing 12-month earnings peaked 19 months later at 61.65, part way through the bear market, as earnings had plummeted more than prices. (Return to Text)

(3) Campbell, John Y., and Robert J. Shiller. “Valuation Rations and the Long-Run Stock Market Outlook,” *Journal of Portfolio Management*, 24 (1998): pp.11-26.(Return to Text)

(4) Writing this in December 2008, October 1998 is the last month end with a subsequent 10-year period. Thus the high P/E period from November 1998 through the present day is not represented in the data in figure 3 or Table 1 below. (Return to Text)

(5) The r-squared of the regression is 29.6% which is on the surface quite strong. However, there are questions about the statistics here because the data are drawn from overlapping samples. See the original Campbell-Shiller article for discussion of these issues. (Return to Text)

(6) The average Real P/E-10 is 16.4 for the full sample, including the data subsequent to October 1998. (Return to Text)

(7) A more thorough approach would be to make a range of earnings scenarios, reflective of different possible environments, and then to use a number of P/E multiples to calculate a more complex range of possibilities. A good further step is to try to assign your own estimates of probabilities to the alternatives, to help crystallize your intuitions about the current situation and how it might unfold into the future. See Appendix 1 for a brief example. (Return to Text)

(8) I have made no attempt to make the alternatives and their probabilities symmetrical. (Return to Text)

Structured Capital presents a book by Tim Appelt:

Learning and Playing the Long-term Investment Game

Historical analysis of long-term global equity and bond returns is used to develop an analytical framework for a historical attribution of returns. In turn this attribution approach is used to develop expectations of future returns that acknowledge the past but take into account current market conditions.

Further information: