Over the past decade, investors have seen near-parabolic advances in a variety of assets, followed by crashes. These have included dot-com stocks (which peaked and crashed well before the general market peak in 2000), technology stocks, housing, commodities, and stocks in a variety of emerging markets. These experiences have made investors somewhat more attuned to the destructive potential for speculative bubbles in various assets, but has also created something of a "casino economy" where a great deal of resources are directed in hopes of participating in these bubbles.
What exactly is a "bubble?" Informally, we can think of a bubble as an advance in an asset’s price to levels that are "detached from fundamentals" – essentially, the primary motive for investing ceases to be the expectation of future cash flows or consumption, and instead centers on the expectation of further increases in price. From this perspective, a bubble emerges at the point where a continual increase in the ratio of prices to fundamentals is required in order for investors to achieve satisfactory returns.
Formally, a bubble can be defined as a "non-fundamental" component of price which grows exponentially. Think about stocks. Let "k" be the long-term return that investors expect stocks to achieve. If these expectations are correct, then next year’s price Pt+1 will just be (1+k) times today’s price Pt, minus whatever dividend Dt will be paid. The next year’s price is determined the same way. If you write this out and solve the difference equation, you’ll get a solution that looks like this: Pt = Vt + Bt, where Vt is just the discounted value of expected future dividends, and Bt is an arbitrary constant. It can be anything, so long as it obeys Bt+1 = (1+k)Bt.
Mathematically, Bt is a "bubble component" of prices. If that component Bt is not zero, the price will gradually "explode" away from any relationship with fundamentals. Moreover, the present discounted value of the future price will not tend toward zero no matter how far into the future you look. Ultimately, this sort of price path is ruled out by the fact that the value of stocks cannot grow infinitely larger than the economy, so bubbles ultimately crash. But over the short-run, there is little to prevent investors from putting a little bit of "B" into prices from time to time. This becomes pathological when the sustained price gains expected by investors diverge significantly from the growth rate of the overall economy.
In short, a bubble is an advance in prices that "substitutes" for fundamentals, in the sense that the realized return on the investment continues to be positive even after the asset is no longer priced to achieve satisfactory returns on the basis of expected future cash flows (or in the case of housing and commodities, future consumption value or other services).
Keep reading here: Hussman Funds – Weekly Market Comment: Anatomy of a Bubble – March 14, 2011.
Pic credit: Jr. Deputy Accountant
