A Fresh Look at Bubbles: Revising Assumptions

03-01-10 © OkeaBubble baths are good, but taking a bath because of a price bubble … not so good.

Robert A. Jarrow has taken a close theoretical look at the phenomenon of asset pricing bubbles. Everybody talks about them so frequently, and the talk occurs at so many different levels of both generality and sophistication, that one might think there is by now nothing more to say about bubbles! Still, Jarrow (who among much else is one of the three theorists behind the venerable Heath-Jarrow-Morton framework for the valuation of interest rate derivatives) takes a fresh look at the subject.

Jarrow starts with the assumption of “competitive and frictionless markets that contain no arbitrage opportunities.” When that sort of statement appears, as here, in the very first paragraph of an economist’s paper, it can cause a lot of wailing and gnashing of the teeth. People who don’t understand the significance of a counter-factual thought experiment will rage on, “But there is friction! But there is arbitrage! What good can come of such idealizing assumptions?”

The general answer is that one has to grant a modeler his/her assumptions, and then judge the model by its fertility.

There is a more specific answer here, though: many, perhaps most, theories about bubbles work from precisely the opposite premise. They deduce the bubbles from friction, or the sort of inefficiencies that allow for arbitrage. If it is possible for bubbles to arise in frictionless circumstances, then it follows that any theory that treats bubbles as the consequence of friction is, at very best, incomplete. And that is important to know especially if policy makers are busy drawing their own conclusions from those incomplete theories.

Grant Him His Assumptions

So … grant Jarrow his premises. What follows? First, he does develop a theory that rigorously allows for bubbles without the supposed causes posited by other theories. Specifically, his model allows for no free lunches with vanishing risk. Thus, unless some smart critic can find a flaw in his derivation, the onus is on advocates of those other theories to back up their assumptions.

Frankly, I can’t follow the math here. But my suspicion is that Jarrow is adding formality and rigor to the idea that incomplete markets are subject to bubbles. An “incomplete” market is one in which certain assets closely related to the assets under consideration are not available. It is intuitive, in particular, to suggest that an underlying asset without a range of associated futures, forwards, or options is more volatile than the same asset would be if the helper assets did exist.

A second point: Jarrow’s model in this paper is consistent with positive alpha. This second point follows directly from the first. Wherever there are bubbles, somebody is on the winning side, buying the affected assets early in the bubble and selling soon enough to record above-normal profit. Or maybe shorting the affected assets at the right moment. Either way, if bubbles are possible, then positive alpha is possible.

The third key point is that when a given asset “has a price bubble, bubble risk-factors exist, increasing an asset’s risk premium.” This might explain “pricing anomalies documented in the empirical literature.”

Remembering 2000-2002

If Jarrow’s underlying case is that the completeness of markets is a critical component for the efficiency of results, and that these consequences (bubbles, alpha, risk premia) follow from the absence of any assumption of completeness, even given the other assumptions mentioned above, then his point is one with a fascinating history of its own. For that was one of the key arguments behind the creation of a legal framework for the purchase and sale of single stock futures in the U.S. over the period 2000-2002.

The talk at that juncture was that the dotcom bubble and its burst was a consequence of incomplete markets, and that the creation of securities futures, by rendering markets more complete, could avert such run-ups.

It obviously didn’t avoid the next crisis. But then, nothing ever manages to avoid the next crisis. That’s why it’s always the next crisis. It doesn’t necessarily follow that the point wasn’t, or isn’t, a good one.

Is the best response to the more recent crises, too, “let’s look for the missing assets that might have avoided these?”



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