Many Wall Street strategists are calling the stock market "undervalued" today based largely on how far and fast it has fallen over the last two years, and the coming prospects for economic recovery. The truth is very different. The fact that stocks could have fallen so much since March 2000 and still be so expensive today is a statement about how silly we all got in 1999-2000 and about the disingenuousness or error of those who did not sound the alarm then and, with some notable exceptions, are generally not doing so now. It is not a statement that stocks are cheap today. After 1999-2000, investors might, with some justification, feel they were duped into buying into a bubble. However, this time, if the bubble re-inflates much further, and investors are fooled again, they will have no one to blame but themselves.

Let's look at one very common, and very intuitive, measure of how "cheap" or "expensive" the stock market is, the price-to-earnings ratio of the S&P 500, based on trailing one-year earnings.

On this scale (as of December 31, 2001), the P/E of the S&P 500 is the highest in all of recorded U.S. history back to 1871. Stocks cheap? I think not.

Now, the bearish implications of the above paragraph go too far. Optimists say you should not worry about the very high P/Es prevailing now (of course, optimists always say that!). The reason is this P/E is exaggerated by temporarily depressed earnings (an extreme example would be the Nasdaq, which today has negative trailing earnings and thus no P/E ratio on this basis).

This argument is valid. It is often misleading to base a P/E ratio on any single year's earnings if that year represents a temporary aberration. Rather, our calculation of the market's P/E should be based on a more "normal" or sustainable level of earnings (curiously, while it is the bulls who are saying this now, this is exactly what the bears said in 1999 when earnings were at a cyclical high and one-year P/Es were thus biased to look misleadingly low). To account for this, I borrow a technique used by Yale economist Robert Shiller. Instead of using last year's earnings to calculate P/E, I use an average of inflation-adjusted earnings from the previous 10 years to smooth out the peaks and troughs (thus, P/E now represents the price of the S&P 500 today divided by the average of earnings over the last 10 years, rather than earnings over just the last year). This P/E is usually slightly higher than the traditional one-year P/E (because earnings tend to grow over time, the 10-year average is usually less than the last year), but that doesn't matter as we are only comparing with itself through time.

The 10-year P/Es are more reasonable, and unlike one-year P/Es, are down since March 2000's dizzying heights. However, by this measure the S&P 500 is still extraordinarily expensive. Equities today are just a tad cheaper than before Black Monday in 1929. Excluding the 1999-2000 bubble, and the period right before October 1929, today we are still witness to the most expensive stock market in recorded history. Even including these bubble periods, the S&P 500 P/E today is in the 92nd percentile over the modern era (post 1950), and the 96th percentile going back to 1881. Unlike what some market apologists will tell you, stocks do not look expensive today solely because earnings are temporarily depressed due to recession. Rather, they look exceptionally expensive on any reasonable measure. This, of course, should make us all wonder why many Wall Street strategists continue to tout stocks, often daringly calling them "undervalued." Can you imagine yelling: "Buy, buy, we're a bit cheaper than right before the crash of 1929!"?

Of course, all of the above analysis assumes that the "E" in today's P/E is accurate. If, as now seems very possible, the bull market of the 1990s has witnessed an erosion of accounting standards such that today's "E" is overstated vs. the past, the situation is potentially worse.

Interest Rates To The Rescue?

Now, to be fair, many strategists do not base their statements about "undervaluation" solely on the analysis above, but rather on the correct observation that historically, when inflation and interest rates are low, P/Es tend to be high (i.e, a version of the so-called "Fed model"). There are various ad hoc stories for why low inflation would make a high P/E acceptable, with varying degrees of validity. However, the most common explanation is that stocks are the discounted present value of future cash flows. In other words, stock prices today should reflect the future cash flows you'll receive from owning stocks, adjusted for the fact that a dollar today is worth more than the expectation of a dollar in the future. The logic then follows that when interest rates and inflation are low, like today, the present value of the stock market's future cash flow is high, and thus a high price should be paid today.

Unfortunately, while reasonable, this ignores another sobering reality. Over long periods, nominal earnings growth moves with the level of inflation. This means that when forecasted inflation is lower, so too is prospective nominal earnings growth (perhaps because, like now, pricing power is nil in such times). Lower discount rates alone are indeed good for stocks, but they come with lower expected future earnings growth, which is, of course, bad for stocks. In fact, historically, these effects are pretty much offsetting. However, investors, and many famous "strategists" still mistakenly think that low inflation means super high P/Es are acceptable. This mistake is often called "money illusion," comparing a nominal number like interest rates with a "real" number like P/E. By Wall Street citing the good effects of falling inflation and ignoring the bad, it is trying to have its cake and eat it too (actually, it is trying to have and eat your cake).

Essentially, what the strategists tell you is that times of low inflation and interest rates have tended to coincide with times of high stock market P/Es. And they are right. Historically they do come together. The obvious intended implication is to make you comfortable buying stocks at high P/Es because inflation and interest rates are currently low, because this is "normal." However, rather amazingly, they don't show you what "normally" happens next! What the strategists forget to tell you, or possibly don't know, is that rather than justifying high stock market P/Es, low inflation and interest rates seem only to be the hook that gets investors to mistakenly accept them (again, historically the hook does work, high P/Es often come during times of low inflation). Regardless of starting inflation or interest rates, high P/Es more often than not lead to low long-term stock returns going forward. That's the part they leave out.

Forecasting The Future

How strong is the link between starting P/E and subsequent long-term returns? As part of my analysis, I place every 10-year period (measuring from the start of each month) from 1926 to 2001 into one of six buckets, based on the starting P/E of the S&P 500 (Shiller's 10-year method). I then look at the set of decade-long stock market returns in each bucket (i.e., the set of all decade-long stock market returns that began with P/Es in a certain range). I examine the median inflation-adjusted return (the stock market's return minus inflation-also called the real return) for each range of starting P/Es, as well as the worst total return ever achieved (because so many focus on the infallibility of equities over long periods). In other words, I look at what happens historically (median and worst case) over the next 10 years if you buy the S&P 500 when its P/E is in a certain range.

Looking at all decades that began with P/Es in the cheapest range of 5.2 to 10.1, the median inflation-adjusted annual return was 10.6% (so if inflation averaged 5%, the total annual return to investors would have been about 15%), and the worst 10-year real return ever achieved was a respectable 45.1%. However, buying equities when their P/Es started in the most expensive range of 19.0 to 31.7 was not so attractive. The median decade-long annual return was actually less than inflation (a slightly negative inflation-adjusted return), and the worst decade was devastating (stocks losing 36.1% of their purchasing power over 10 years). This relationship is strong throughout the sample. Quite simply, the higher the price you pay for stocks, the worse you have done on average over the next decade, including actually losing to inflation if you buy when stocks are very expensive. Looking at worst cases, equities are historically infallible over decades if purchased on the cheap, but very fallible, and in fact quite dangerous over decades when purchased at high prices.

Adjusting P/Es for starting interest rates, again the so-called "Fed Model" favored by many strategists, doesn't do nearly as good a job at forecasting 10-year returns as does simple P/E. Simply put, for forecasting long-horizon returns, while nothing is infallible, basic P/E (unadjusted for inflation or interest rates) seems to be king. Interestingly, as of March 2000, the Shiller P/E was 44.7, a P/E never observed through history so we don't know what "usually" happens in the next decade. Of course, we need to wait until 10 years after March 2000 to add that data to our analysis, but so far, with stocks down substantially since this peak, it appears distinctly possible that this next entry will continue the historical pattern (that's not good). Today's prices are, of course, substantially below the insane peak of March 2000. But, this is only slight cause for comfort. The Shiller P/E for the S&P 500 is "only" about 31 at the end of December 2001. This P/E still puts us firmly at the very upper end of the most expensive range observed in history, with zero to negative real returns forecast for the next 10 years from here if history repeats, and with bad luck, the possibility of a decade of returns that would be devastating to investor wealth.

It Might Not Be Quite That Bleak

Now, admittedly, the analysis above might be too pessimistic (hopefully!). Part of the historical relation between starting P/E and stock returns over the next decade comes from the fact that when P/Es are high, historically they have fallen, and vice versa. This is often called "mean reversion." Some argue that unlike the past, today's high P/Es are sustainable. Of course, that is what "some" always argue in times of high P/Es, but such optimism cannot be dismissed out of hand. Perhaps mean reversion will not occur this time, and P/Es will remain high. Unfortunately, even without mean reversion in P/Es, while not as gloomy, the forecast for stocks is not pretty in relation to history. Even if the optimists are correct and P/Es stay at today's level, buying in at a very high price means your investment dollar is commanding less earnings and dividends, and subsequently being reinvested at higher prices, than if P/Es were more reasonable. Thus, all else being equal, investing at high and stable P/Es still leads to lower returns going forward, even if the P/Es themselves do not come down.

This is not arguable, it's just math (while not arguable, it is quite clearly often ignorable!). As of today, if P/Es stay at their current lofty levels, the stock market is priced to deliver about 0% to 2% returns over bonds. If we get historically average earnings growth, it will be 0%-1%. You can get to a 2% forecast over bonds by being extra-optimistic about future long-term sustainable earnings growth. In a rare show of mercy and decorum, I've politely left out the third possibility of less than average long-term earnings growth going forward, which would leave the future risk premium negative, even without P/E reversion.

"Say No To Three In A Row"

Despite today's extremely high prices, many anxious investors are waiting for any sign the recession is turning, assuming that such a turn presages a return to partying like it was 1999. Every day that the market is up, we are told it is on "profit optimism" and that investors are "looking over the valley," to a recovery in 2002. Given the level of prices, investors are indeed looking over the valley but perhaps discounting an arrival in la-la-land. Well, maybe those forecasting a huge new bull on signs of economic recovery are right, but if so, they are simply forecasting a return to mania. When stocks are as expensive as they are today, it is entirely possible, and indeed rational, for the economy to recover (as we all hope) and not to have a huge bubble re-inflation.

In 2001, the clichÈ of choice for the "in platitudes we trust" crowd of bulls was "don't fight the Fed." Well, it now seems that this clichÈ does not always work. Going into 2002, the platitude sweeping the sound-bite world (paraphrasing) is "say no to three in a row." The observation is that the stock market has not dropped three years in a row since the Great Depression, and the last two times it dropped two years in a row (1940-41 and 1973-74), we saw strong market recoveries the next year. Unfortunately, the marketing geniuses behind this slogan once again forgot (or ignored) valuation. At the end of 1940-41, the S&P 500's P/E based on 10-year prior earnings was about 10, and at the end of 1973-74 it was about 8. Today, this P/E is about 31. A belief that some event cannot happen again just because it has happened already is a form of what's called the "gambler's fallacy." It is the sad belief that just because you have lost most of your life savings already, you have to win on the next throw of the dice. Of course, nobody knows what will happen this year (notice, I judiciously stick to 10-year forecasts as the market has proved many times it can do whatever it wants in the short-term!). But, if stocks rise, it will be because people are willing to accept permanently low long-term returns, or because the bubble re-inflates, not because the gambler's fallacy is suddenly promoted to fact.

Nowadays, of course, one cannot discuss short-term stock market behavior without discussing technology stocks. That investors are still enamored of the same small set of technology stocks that led the last bubble, and they seem to fear missing the "freight train leaving the station" on these stocks more than they fear paying prices that still make the S&P 500 look cheap, only makes the worry of returning mania more acute. Repeatedly we hear that investors (largely professionals in this case) are terrified of missing a tech rally because of what this will do to their relative performance. In many cases, they explicitly or tacitly admit that they know they are buying overpriced nonsense, but they feel they have to do so once the momentum starts again (as it did for the 4th quarter of last year). This might be in their short-term best interest, but if that is the case, we have collectively designed this aspect of our financial system to be quite destructive to long-term prosperity, as it encourages bubbles and their ugly aftermaths. Let me end with a final note on the subject of tech stocks. Whenever prices rise for a few days, we hear "tech stocks rally on economic optimism" because "tech tends to lead in a recovery." Journalists, pundits, strategists, etc., should be barred from ever writing this unless they simultaneously mention that the precise rational for buying these exact same stocks in 1999 was that they offered noncyclical steady long-term growth independent of the business cycle. In 1999, it was "buy tech as it is immune to an economic slowdown or rate increase"; now it's "buy tech for the recovery." The recommendation seems to be to buy any tech stock in any storm. Investors seemingly have not learned that buying the technology of the future does not automatically lead to strong returns if you are buying high-priced stocks in very competitive businesses (despite being taught this by countless "technology" bubbles throughout the ages, including the most recent one). Despite the experience of 2000-2001, on many days they seem only to have learned to worry about missing the freight train.

The Lady Or The Tiger?

I should conclude by noting that today's exceptionally high P/Es, and the low future expected returns that come with them, do not necessarily mean the stock market has to fall sharply from here. As previously noted, optimists believe that today's high P/Es are sustainable. One scenario might be that investors believe that stocks are less risky today, and perhaps offered "too good" of a deal from 1926 to 2001. Thus, investors today might require lower returns on stocks than was realized historically and thus will now accept higher P/Es permanently. If so, no crash or extended fall in prices is necessary, but we are simply in for permanently low average stock returns going forward (vs. bonds and inflation). Indeed, some of the more honest market observers acknowledge that stock returns will be low going forward, but make eloquent cases why such low returns still should be acceptable to investors. This link is crucial to understand. If high P/Es are acceptable, it is only because investors now find low long-term returns on the stock market acceptable. It is very possible that this is the scenario that comes to pass.

While this is plausible, and perhaps even rational, we must also give credence to the opposite, more pessimistic (at least for the short-term) scenario. Investors hear ubiquitous discussion of the wonderful long-term properties of stock returns, repeated to them from source after source. Perhaps, strangely enough, they actually believe the legion of experts telling them to expect these historical results to repeat going forward if only they keep their long-term focus. Perhaps they are indeed counting on this in their financial planning. Perhaps, again shockingly, investors (including not just individuals but many pension funds and financial planners) blithely plugging the historically wonderful stock results into their retirement calculators and making life decisions based on the output, actually believe these numbers! If so, we have a problem.

This question is crucial because investors are rationally and calmly accepting low stock returns (the scenario described earlier), then P/Es don't have to fall. But if investors are living in a fantasy land expecting 1926 to 2001 type stock returns (e.g., stocks beat bonds by 5% or more per year, they never lost to bonds over any long-term period, etc.) going forward, we might be in for the "mother of all mean reversions" as reality eventually meets wishful thinking.

To offer my opinion, the reoccuring rush back into (and then out of) the mania stocks that led the 1999-2000 bubble on any evidence of economic recovery, despite the incredible valuations still given these stocks, argues against broad rational acceptance of low stock returns going forward. Rather, it tells of an investing public either terrified of falling behind benchmarks they know to be overpriced, or still looking for the next winning lottery ticket. To be blunt, despite widespread brainwashing to the contrary, if investors really do understand that the ubiquitously quoted 1926 to 2001 stock market experience no longer applies going forward at today's prices, but are calmly and soberly buying stocks (and tech-bubble stocks in particular) anyway to get their 0% to 2% per year over bonds, then I missed it on PowerLunch.

Cliff Asness is managing principal at AQR Capital Management, LLC, and before that was a managing director at Goldman, Sachs & Co. This article is based on a more exhaustive essay entitled "The Bubble Has Not Popped" and a book draft from June 2000 called "Bubble Logic" available for download at