Bubbles in financial markets have been studied not only through historical evidence, but also through experiments, mathematical and statistical works. Smith, Suchanek and Williams designed a set of experiments in which an asset that gave a dividend with expected value 24 cents at the end of each of 15 periods (and were subsequently worthless) was traded through a computer network. Classical economics would predict that the asset would start trading near $3.60 (15 times $0.24) and decline by 24 cents each period. They found instead that prices started well below this fundamental value and rose far above the expected return in dividends. The bubble subsequently crashed before the end of the experiment. This laboratory bubble has been repeated hundreds of times in many economics laboratories in the world, with similar results.
The existence of bubbles and crashes in such a simple context was unsettling for the economics community that tried to resolve the paradox on various features of the experiments. To address these issues Porter and Smith and others performed a series of experiments in which short selling, margin trading, professional traders all led to bubbles a fortiori.
Much of the puzzle has been resolved through mathematical modeling and additional experiments. In particular, starting in 1989, Gunduz Caginalp and collaborators modeled the trading with two concepts that are generally missing in classical economics and finance. First, they assumed that supply and demand of an asset depended not only on valuation, but on factors such as the price trend. Second, they assumed that the available cash and asset are finite (as they are in the laboratory). This is contrary to the “infinite arbitrage” that is generally assumed to exist, and to eliminate deviations from fundamental value. Utilizing these assumptions together with differential equations, they predicted the following: (a) The bubble would be larger if there was initial undervaluation. Initially, “value-based” traders would buy the undervalued asset creating an uptrend, which would then attract the “momentum” traders and a bubble would be created. (b) When the initial ratio of cash to asset value in a given experiment was increased, they predicted that the bubble would be larger.
An epistemological difference between most microeconomic modeling and these works is that the latter offer an opportunity to test implications of their theory in a quantitative manner. This opens up the possibility of comparison between experiments and world markets.
These predictions were confirmed in experiments that showed the importance of “excess cash” (also called liquidity, though this term has other meanings), and trend-based investing in creating bubbles. When price collars were used to keep prices low in the initial time periods, the bubble became larger. In experiments in which L= (total cash)/(total initial value of asset) were doubled, the price at the peak of the bubble nearly doubled. This provided valuable evidence for the argument that “cheap money fuels markets.”
Caginalp’s asset flow differential equations provide a link between the laboratory experiments and world market data. Since the parameters can be calibrated with either market, one can compare the lab data with the world market data.
The asset flow equations stipulate that price trend is a factor in the supply and demand for an asset that is a key ingredient in the formation of a bubble. While many studies of market data have shown a rather minimal trend effect, the work of Caginalp and DeSantis on large scale data adjusts for changes in valuation, thereby illuminating a strong role for trend, and providing the empirical justification for the modeling.
The asset flow equations have been used to study the formation of bubbles from a different standpoint in where it was shown that a stable equilibrium could become unstable with the influx of additional cash or the change to a shorter time scale on the part of the momentum investors. Thus a stable equilibrium could be pushed into an unstable one, leading to a trajectory in price that exhibits a large “excursion” from either the initial stable point or the final stable point. This phenomenon on a short time scale may be the explanation for flash crashes.
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