Bubbles are important for the country because there is nothing more dangerous and damaging to an economy than a great asset bubble that breaks. And this is something the Fed never seems to get. … We looked back as far as we could, [of the 34 bubbles we found over the years], 32 have moved all the way back down to the trend line that existed prior to the bubble forming. There were no exceptions. The two that are outstanding, the UK and Australian housing bubbles, form a unique and interesting subset caused by, I believe, floating rate mortgages. The mortgages came down so fast that they protected the bubble, and now we have to see what happens when interest rates rise. But if they do not, in both cases, go back to the old trend line multiple of family income, which is what should drive house prices, it will be the first time in history that such a bubble has not broken. This is not something that I would want to bet on if I was thinking of buying a house right now.
-Jeremy Grantham, Interview with the Financial Times, 19 Apr 2010
Grantham defines a bubble as a 40-year event. If he knows the price and volatility of an asset, he can work out what a 40-year event is.
My informal working definition for a bubble is a price rise that is at least two standard deviations above trend. My assumption is that prices never follow a random walk. Rather prices are influenced little enough by past price movements below two standard deviations that a Gaussian bell curve is a good approximation of price data.
Above two-standard deviations the psychology of prior price movements starts to dominate price activity and a bubble forms in which power law characteristics come into play. Mark Buchanan and Benoit Mandelbrot each wrote books on this phenomenon. Both are on my reading list on the site.
Buchanan’s concept of "the critical state," a point at which a system reaches a tipping point into instability, is key in understanding market dynamics and bubbles. The critical state is something I have long wanted to write about as I consider most VaR-type models for markets with two standard deviation movements to understate market risk. This is a central lesson of the housing bubble and credit crisis.
I will definitely explore this topic in depth in a later post. Some of the housing markets to think about in regards to the two-standard deviation rule include Canada and South Africa as well as the UK and Australia, which Grantham mentioned.