Bubbles are rarer than you think And very hard to recognise until it is too late

BUBBLES put the fun into financial history. Who can resist stories about Dutch tulips that were worth more than country estates or the floating of an “undertaking of great advantage but no one to know what it is”?

Economists have long debated whether bubbles can be identified, or indeed stopped, before they can cause widespread damage, as the crisis of 2007-08 did. But spotting them is easier said than done: even tulipmania may have been caused by a quirk in the wording of contracts that meant speculators would, at worst, walk away with only a tiny loss.

For many investors, the more important question is whether it is possible to avoid being sucked into a bubble at the top, and suffering declines like the 80% drop experienced by the NASDAQ 100 index of technology stocks between March 2000 and August 2002. Two essays in a new book*, from the CFA Institute Research Foundation and the Cambridge Judge Business School, indicate just how difficult market timing can be.

The first, from William Goetzmann of Yale School of Management, looks at the history of 21 stockmarkets since 1900. Mr Goetzmann defines a bubble as a doubling in a market’s value, followed by a 50% fall. He found that a doubling in a single year occurred just 2% of the time (in 72 cases). On six occasions, the market also doubled over the next year, whereas a 50% fall in the subsequent year occurred on just three occasions; Argentina in 1976-77, Austria in 1923-24 and Poland in 1993-94. Even after a further five years, markets were more likely to double again than to fall by half.

There were many more occasions when markets doubled over three years; around 14% of the total. After such rises, the markets dropped by half in the following year on fewer than one in 20 occasions. The markets lost half their value over the next five years around one tenth of the time. But in a fifth of such episodes, the market doubled again. On this basis, a sharp rise in a market is more of a buy signal than a sell indicator. That helps explain why investors find it so difficult to get out at the peak.

You can argue whether Mr Goetzmann’s definition of a bubble is the right one. He looks at overall markets, rather than individual industries such as technology. GMO, a fund-management group, uses a different concept—namely, that a bubble occurs when the price of an asset rises by more than two standard deviations above its previous long-term trend.

Another approach is to look at fundamentals. Asset prices are supposed to reflect the current value of future cash flows. In theory, a doubling in a market could reflect a sudden improvement in the outlook for that asset class, and thus be entirely rational. One valuation approach, often referred to in this column, is the cyclically adjusted price-earnings ratio, or CAPE, which averages profits over ten years. Highs in the ratio coincided with market peaks like 1929 and 2000.

In another chapter of the book, Antti Ilmanen of AQR Capital Management looks at the CAPE ratio as a market-timing measure (see chart). At first sight, this seems very promising. Buying the American equity market when it was cheapest brought an annual real return of 13% over the ensuing decade; buying it when it was dearest earned a return of just 3.5%. (He inverted the ratio to get an earnings yield, but that does not affect the results.)

The problem, however, is that the full historical range of valuations is available only with hindsight. Investors in the 1930s did not know that they would be buying at the cheapest level the 20th century would see. And the ratio is of little use in the short term: the market looked overvalued on the CAPE measure for much of the 1990s, not just at the peak.

So Mr Ilmanen devises a simple approach to show whether investors using the range of CAPEs that would have been known at that point could have been used to time the markets since 1900. Over the full period this tactic mildly outperformed a “buy-and-hold” strategy, but all the outperformance occurred in the first half of the sample. It would have underperformed for the past 50 years.

This is not very encouraging. Neither a doubling of the market nor a historically high valuation are reliable sell signals. Of course, that shouldn’t be too surprising. If timing the market were easy, big swings in prices would not happen in the first place.

* “Financial Market History: Reflections on the Past for Investors Today”, edited by David Chambers and Elroy Dimson.

This article appeared in the Finance and economics section of the print edition under the headline "Time and tide"