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Shiller's PE ratio valuation model states that expected stock returns over the next 10 years have an inverse relationship to the PE ratio based on the real (inflation-adjusted) level of stock prices and the 10-year average of real earnings. As I indicated in my commentary on Bill Gross' piece, I believe that earnings are a better and simpler indicator of expected returns than dividends. In a very long discussion several months ago, I argued that the long-run return on equities ought to be approximately equal to the long-run "return on equity," with equity represented by the fair market value of the company. This is sometimes called the "earnings yield." Actually, this is a relatively simple and obvious expectation. Since reported earnings represent, almost precisely, the increase in the common shareholder equity, it should be the principal driver of the value of the company.

It should be noted that the earnings yield is simply the inverse of the PE ratio. An earnings yield of 6.7% represents a PE ratio of 15. As Jeremy Siegel pointed out, 15 has been the average PE ratio of the US stock market, and the fact that real stock market returns have been 6.7% over that time period is not a coincidence, but a virtual necessity. Siegel also estimates that normal earnings on the S&P 500 today imply a PE ratio of 20, and an earnings yield of 5%, so that stocks should only be expected to provide a real (inflation-adjusted) return of 5% in the foreseeable future. If inflation averages around 3% (the average inflation rate over the 20th century), stocks will return approximately 8%. While I have some quibbles with Siegel's approach, I think it essentially sound, which suggests I also believe a period of lower stock returns may be on the horizon. So why on earth do I reject Shiller? Well, the truth is, I don't: I only reject the popular interpretations of the meaning of his research. I do have some difficulties with his analysis, though, which I will lay out for you, gentle reader [g]. There are three, and the third is far and away the most important. Let's begin:

(1) STATISTICAL SIGNIFICANCE OF HIS RESULTS

The calculations performed by Shiller go back to 1871, representing 130 years of data. This sounds like a considerable amount of time, but since he is estimating 10-year returns from 10-year PE ratios, the first 10 years of the database are needed to calculate the PE ratio to apply to predicting the next 10, and there can be no 10-year periods beginning less than 10 years from the end of the database. As a result, the spread from the start of the earliest period of calculated returns to the start of the latest is only 110 years. He shows the results on a year-by-year scatter chart in IRRATIONAL EXUBERANCE, with 110 different data points plotted. But since overlapping periods do not represent different periods, 110 years of 10-year predicted earnings only represent a total of 11 observations, and anything can happen in a mere 11 observations. If a coin is flipped 11 times, it should come up heads 5.5 of them (presumably landing on its tip one of those times [g]), but it wouldn't at all be surprising to see it only come up heads 4 times and tails 7 times, and this is about how much Shiller's results vary from a random one. For those who think that 110 year-by-year observations of 10-year results within 110 years is more meaningful than 11 observations of 10 years at a time, why not report the results by day-by-day, instead of year-by-year? With 250 days in a year, Shiller could have taken the same time period and claimed that it represented 27,500 observations of 10-year returns [g].

As proof of this, take a look at the scatter chart on page 11 of his book (I'm afraid I don't know a comparable online source, so for those not interested in picking up a copy of his book, I'll describe it). Starting from the decade beginning on 1/1/1882, and going year-by-year ending with the decade beginning 1/1/1991, I calculated the real stock returns over each of those periods, just as Shiller did. I identified 13 time periods in which stocks failed to outperform the rate of inflation, while it appears Shiller calculated 14 of them. We agreed that the decades beginning 1909, 1910, 1911, 1912, 1937, 1965, 1966, 1968, 1969, 1970, 1972, and 1973 were negative. I had 1913 fractionally negative, and his scatter chart appeared to calculate a fractional positive. I had 1967 and 1971 as fractionally positive, and his scatter chart appeared to calculate a fractional negative.

Different databases often have minor disagreements on stock returns or inflation rates, but it is clear that the data I have to analyze is the same as his: perhaps my database has some trivial errors in it (since I obtained the data from popular sources and he has access to the Cowles database that is considered the most authoritative). Since I want to do some further calculations, and only have precise numbers of my own (he didn't provide a numerical table to accompany his scatter diagram), we will use my calculations for the later posting in this discussion, but for this first I want to take his 14 negative years: 1909, 1910, 1911, 1912, 1937, 1965, 1966, 1967, 1968, 1969, 1970, 1971, 1972, and 1973.

Now, I could simply note that only 14 out of 110 periods failed to beat inflation, which means stocks were winners, even after inflation, nearly 90% of all decades. But is there anyone who thinks the above represents 14 different periods? Of course not! The first 4 negative decades started in consecutive years, and the last 9 negative decades started in consecutive years. At most, these represent 3 periods: the first 4 losses were the result of the runaway inflation during World War I, and the last 9 observations represented every 10-year period that included the "stagflation" bear market of 1973-4. The 1937-1946 decade stands by itself, starting from the peak of the first bull market after the crash, and ending at the end of a year of massive postwar inflation once wartime price controls were lifted (the fact that every single negative observation was related to bursts of hyperinflation will be addressed later).

So any conclusions based on this study are based on very little evidence. Since PE ratios weren't even above average at the start of 1909, 1910, 1911, and 1912, Shiller's model didn't predict these periods. In effect, the entire success of his model depends on the 1973-4 bear market.

More generally, the correlation between PE ratios and future returns in his model was only -0.3. Two perfectly correlated items (one predicts the other perfectly) would be 1.0 if the correlation was direct, and -1.0 if the correlation was inverse (whether positive or negative, the correlation has the same strength). A correlation of 0.0 means there is no relationship between the two. Thus, a correlation of -0.3 means there is a relatively small negative correlation between the PE based on the last 10 years of earnings and the expected returns over the next 10. I was just reading a book the other day touting investments in REITs, and one of the advantages cited was the extremely low correlation between REITs and the S&P 500. This "extremely low" correlation was the same 0.3 one would calculate from Shiller's data. The predictive power of PEs is, thus, weak. And if you eye the scatter diagram, though you can see a tendency for it to slope down (higher PE ratios predicting lower returns), it is by no means a straight line: the points on the scatter diagram are quite scattered [g].

In fact, the correlation between Shiller's historical PEs and future returns is considerably weaker than the so-called Super Bowl model, which says the market will fall in any year that a team from the old AFL wins the Super Bowl. This one has a 0.7 correlation, so the stock losses of the past year are far less likely to be the result of high 10-year PEs then they are the fault of the New England Patriots' victory in Super Bowl XXXVI, and the only thing that could produce a 4th down year is a victory this month by the Oakland Disciples of Satan [g]. Anyone with sense knows that the 0.7 correlation must be a coincidence, and this indicator actually had XXXVI observations (36 for people who don't count like Roman Gladiators). By the way, this clearly bogus correlation doesn't necessarily hold for some other clever predictors such as the hemline indicator, which says the market moves up and down with the fashion in ladies' skirts: the argument is that there is a real correlation between people making lots of money and more playful styles in clothing. Being a sincere student of market research, I keep my eye on this indicator all the time.

I remember a trading technique that was promoted a few years ago based on being in the market only on certain days that were historically best, such as the last day of the month and the first four days, the two days before holidays, and other dates on which history showed unusually positive results. I saw a summary of results once that showed this strategy outperformed the stock market over a 20-year time period. Impressive. But it turned out that the entire advantage over a buy-and-hold market approach would have been wiped out, and more, if October 19, 1987 had been one of the investment days. A method whose entire success required that it get one day right is not statistically verified, and a model to warn of negative stock returns that depends in its entirety on the ability to call a single bear market in 1973 is similarly unproven.

Shiller, by the way, has acknowledged this criticism (I want to make sure I am not accused of originality in my commentary, since most of my observations were undoubtedly made by others before me). He points out that some confirming evidence comes from the examination of other countries, and I believe him, even though I haven't seen the evidence. As I said, I do believe that real stock returns ultimately depend on earnings, so there is some plausibility of this model even in the absence of conclusive evidence. The problem, of course, is that earnings over the past 10 years are not earnings over the next 10: they are simply being used in the hopes they come close. As we can see from 5 of the 14 negative observations, world wars have a way of messing up expectations [g].

In fact, it isn't at all clear that the correlation that WAS found in Shiller's model was the result of any particular importance in historical earnings (especially since there isn't any particularly exciting correlation between earnings of the past 10 years and earnings of the next 10). Since he averages earnings over such a long time period, current year earnings are only one-tenth of the total: the high PE readings are basically the result of periods of runaway stock prices, when prices get ahead of earnings and everything else, and a model that simply looked at the movement of the stock market over the past 5 years would have identified the same high points as Shiller's model without all the effort of calculating earnings. The highs in his model are pretty much impossible without a runaway bull market lasting at least 5 years, and pretty much inevitable with it. A drop in earnings, while it theoretically could cause the high readings, rarely does, since the market has a tendency to anticipate earnings and drop before the reports come out, and in any event a single year of earnings only represents one-tenth of the denominator in the calculation, and the numerator (price) moves much, much faster.

Thus, whatever vague relationship exists in his model may not be the result of the importance of past earnings at all, but of the principle of mean reversion in prices that I mentioned in my last message. Nonetheless, I will concede at this point that the relationship between 10-year PE ratios and returns over the next decade does not appear to be random: even if past PEs are not the cause for the lower future returns, they may still be related in having a different, common cause (rapid increases in the market lasting 5 or more years), and they do appear to have a slightly negative relationship to each other.

SO IS LESS SAYING THE SHILLER MODEL IS VALID, OR IS HE SAYING IT ISN'T?

Patience: installment 3 comes up shortly. Right now, I need to do more research on the hemline indicator [g].

I said it was nearly impossible to document such a result for any period EXCEEDING 20 years, which is why I limited the calculations to periods of 20 years or less. Glad you're paying attention, though [g].

Dear Randy:

Let's be fair to S&F. They went out to 10 years because Shiller did: you have to go out that far before you'll see anything remotely interesting. Jeremy Siegel looked at 5 year returns based on PE and they were pretty much as dull as 1 and 2. So did Shiller, which is why he doesn't provide any charts over periods shorter or longer than 10. More on that in my third installment.

I want to point out, however, that a boom-and-bust cycle that lasts 4 years (I assume we're talking about the presidential cycle) would not show up in projections of 4-year returns at all, since over that length of time we would have had both the boom AND the bust. It would show up the most in data that projected returns over the next half-cycle, which is the 2-year returns. If Shiller's 10-year returns are the best he can do (and I suspect they are, or he wouldn't limit his chart presentations to them), the implied valuation cycle is 20 years in length (which might be why there are virtually no periods in which stocks fail to beat bonds and bills once you go over 20 years).

I haven't died, but the argument section was designed for pieces that would take me a long time to write, and I have many urgent professional and personal matters to attend to, so it will be a few more days before I continue this thread. I'll address several interesting points that are in your last two postings as soon as I get the chance (separately from my final installment, but as part of this thread). Not promising when that will be, though: as an apology, I'm extending everybody's right to use the board another month at no additional charge [g].

(3) PRACTICAL USAGE

My final objection to the Shiller model is that it is of no practical benefit in making real investing decisions. Once again, Shiller shows his good character and thoughtfulness in his own book: if you search for his recommendations, you will find only the mildest recommendation of the conclusion drawn by so many people who cite Shiller but have never bothered to purchase a copy of IRRATIONAL EXHUBERANCE. Yes, he does suggest that an individual investor might, based on his model, lighten their equity holdings for a time. But then he notes, in the true spirit of a social scientist with a broader perspective than most, that it is IMPOSSIBLE for all of us to get out of the stock market at the same time, or even to lighten up. SOMEBODY must be holding every share at all times. Our system cannot survive without people being willing to hold stocks in good times AND bad.

Shiller's overall recommendation was pretty mild: that stock investors anticipate lower future returns on their investments and adjust their savings or expectations of future wealth accordingly. Which, by the way, is in total agreement with Jeremy Siegel, author of STOCKS IN THE LONG RUN, who still pushes for equity allocations of 100% (OR MORE) for long-term investors. The notion that one should move to bonds or bills, even if stock expectations over the next 10 years or so are below average, is flawed. Badly flawed.

For the sake of argument, let's say that you were able to identify every period in the Shiller database in which 10 year returns on equities were going to be negative. During those 13 years, the average annualized real loss in equities was 2.2%. What you would have done, knowing this in advance, was retreat to the safety of bonds: academics have said the bond maturity should match the time period, so you'd choose 10 year government bonds. And LOST an average of 2.8% per year [g]. WITHOUT A SINGLE POSITIVE TIME PERIOD.

Siegel noted that, had you invested $100 at every stock market peak of the 20th century, you would have, on average, still turned it into $125 in stocks. In bonds, it would have only grown to $107. And in the ultimate safety of Treasury bills? A drop to $99.

AND ALL OF THIS IS BEFORE TAXES. Since every dollar of interest is immediately taxed, and only dividends are taxed in stock holdings until sale, the advantage of stocks, even in bad time periods, is substantially increased (and don't forget that every attempt to exit the stock market realizes all gains to that point). But taxable or tax-favored: bad decades for stocks are always bad decades for fixed income investments.

So that I am not guilty of intentional blindness, let me point out that ALL of the decades of negative equity returns were periods in which inflation accelerated: that is why bonds and bills suffered as well. TIPS would have made real positive returns in those periods, had they existed, if they were held in tax-favored accounts. So anyone who simply refuses to acknowledge the case against timing should at least not kid themselves into thinking that fixed income investments are the safe haven. They should put their tax-favored investments in TIPS or TIPS funds. But their taxable investments should be left in equities all the time. All the time.

Many questions have been raised in this thread, and I will try to address them in due course. I must remind everyone, however, that my time to devote to the board is limited, and I always give highest priority to the questions that appear to be of immediate practical importance. As bbttpp so beautifully implied, this argument probably isn't relevant anymore, since we are 3 years past the peak, and the next bubble in stocks is a long way off. But my bet is still that stocks will end up better than bonds over the full decade of the naughties (2000-2009), even if it is limited to US stocks. And since when have I EVER suggested an investor should be limited to US stocks? [g]