Yes, There Is Such a Thing as a Rational Bubble -- We're in One Now

By Aaron Brown  OCT 17, 2012 3:45 PM

Double, double, toil and trouble, fire burn and caldron bubble. Why financial bubbles are not as crazy as they seem.

 


MINYANVILLE ORIGINAL When I got interested in finance in the late 1970s, the economy was in the midst of a real asset bubble. Financial assets—stocks and bonds—were hammered during that decade while real assets—real estate and commodities—soared. From 1976 to early 1980, the price of gold rose from $100 to $850 per ounce. Two years later, gold was under $300.

Jonathan Swift in 1721 was the first writer to use “bubble” to mean a public delusion that inflates the price of something without economic justification. But calling something a “delusion” or “the madness of crowds” is not helpful for prediction or explanation. While bubble investors as a group seem to be irrational, individually they can hope to sell at an even more inflated price than they buy, and in fact many people do make money investing in bubbles. The trick is to take out more money than you put in before the bubble pops.
This notion is the germ of the idea that bubbles might be explained without positing irrational actions. If so, not only would that deepen our understanding of bubbles, but it might point to ways to predict them, or perhaps to prevent them, or best of all, to modify them in ways that preserved their benefits while avoiding their costs.

There was a lot of work on rational bubbles from 1978 to 1987, but the stock market crash on October 19, 1987 pretty much ended it. The crash refocused most academic interest to behavioral explanations. There are several well-documented psychological mechanisms that can support irrational bubbles: Overconfidence, recency bias, confirmation bias, information cascades, reputational herding, and envy, among others.

Of course, all these mechanisms are real, and illuminate some aspects of bubbles. But despite years of efforts, behavioral work failed to generate non-obvious insights about historical bubbles. Individuals have biases, but that doesn’t explain why other individuals don’t figure this out and offset those biases, or why institutions do not develop to control the effect of individual biases.

The same behavioral theories that explain bubbles are also used to explain fashions, but fashion seems to revolve steadily rather than generating booms and busts. Behavioral theorists had no trouble explaining why interest in a financial idea might expand rapidly and then decline even more rapidly, just as clothing or music fads rise and fall. But going from this to a plausible and useful explanation of the economic effects of bubbles proved more difficult. In particular, behavioral models produced nothing but Monday morning quarterbacking regarding the Internet bubble that popped in 2000 and the housing bubble that popped in 2007. Therefore, rational bubble models from the 1980s are coming back into fashion, including one of mine. I like it because it’s mine, of course, but also because I think it’s the simplest one. In my opinion, the basic logical argument is the same for all rational bubble models, and more elaborate mathematical structures don’t add insight. The key to applying these models is the empirical methods used to investigate them, and the quality of data, not the sophistication of the underlying mathematics.

To understand the sense in which a bubble can be rational, consider an asset whose price each quarter either doubles or goes to $2 with equal probability. I’m not telling you why the price does this for now; just assume that it does. If the price of the asset today is P, its expected price in one quarter is (2P + 2)/2 = P + 1. So buying the asset at any price has a positive expected value, and therefore is arguably rational.

On the other hand, the price of this asset must eventually go to $2, so buying it at any price above $2 will lead to certain loss.

If you simulated this price path and graphed it on a computer, you would see bubble-like behavior. The price would go up steadily for a while, sometimes to relatively high values like $64 or more, but always fall back to $2 at some point.

Think about buying this asset at $16 and holding it for 25 years. Since its expected value increases $1 per quarter, the expected value at the end of the period is $116, or an expected compounded annual return of 8.25%. That is all true, and all misleading. For 0.01% of the time, you end up with over $10,000; in those cases, you have an average of $843,776. The other 99.99% of the time when you end up with less than $10,000, your average terminal value is $13. $16 of the $116 expected value comes from the one in nonillion (one followed by 30 zeros) chance of getting over $16 nonillion by having all 100 coin flips come up in your favor. This kind of distribution, with a high expected value driven by microscopic chances of astronomical payouts, even meaningless payouts, was discussed in Whodunit?

This feels like a bubble. Every investor rationally expects a return greater than his or her investment, yet also knows that the price must eventually crash below his or her purchase price. Before resolving this dilemma, we have to discuss why a price might follow this kind of process. I’ll tackle that next week.
No positions in stocks mentioned.

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