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Abstract Asset market experiments are analyzed by distinguishing participants who are net bidders versus net offerers when the trading price is above fundamental value. We find evidence that the cash supply of the bidders diminishes and the cash supply of the offerers increases as the bubble forms. This suggests that the bubble is fueled by the cash of the momentum players and the reversal is caused by inadequate cash in their possession. The experimental data is also analyzed using asset flow difference equations with the result that both bidders are strongly influenced and offerers (surprisingly) are moderately influenced by price trend

Financial bubbles such as the high-tech/internet bubble of the late 1990s have posed a significant challenge to the efficient market hypothesis (EMH). At the later stages of this bubble, stock prices were so far removed from valuation that they appeared to be completely disjoint from the classical expected return models. Yet there have been only modest efforts in the academic community to understand the mechanisms that underlie this tremendous deviation from realistic value, even though a large segment of the population lost trillions of dollars as a consequence. Several years after this bubble we have little more knowledge about the strategies and motivations of individuals than we did at the time. Of course, this bubble is only the latest of many such episodes that include the 1980s bubble of Japanese stocks, the 1920s in US stocks, as well as historical bubbles of previous centuries. The 1990s bubble presented perhaps the biggest surprise in that it occurred at a time when information was so readily available from a variety of sources, thereby eliminating a key hypothesis that incomplete information alone is to blame. Market bubbles have been studied extensively from one perspective, namely, experimental economics (see Davis and Holt, 1993 for a review). Since the 1980s researchers have produced hundreds of bubbles in asset market experiments in which traders can buy or sell an asset through a computer network (see, e.g., Sunder, 1995, Sonnemans et al., 2004 and Hommes et al., 2005). At first, experimenters sought conditions under which a bubble could be created. Surprisingly, bubbles arose without any specific mechanisms to create them. As in the world markets, the initial bubbles results were met with denial, with critics claiming that a number of elements missing in these experiments could account for the large deviations from fundamentals. These included the absence of short selling, margin buying, a futures market, and so on. However, experiments showed that bubbles persisted when any of these were introduced (Porter and Smith, 1994). Only experience as a group tended to reduce the size of the bubble (Smith et al., 1988). Of course, in world markets there are always some newcomers with little or no experience, so this discovery is only limited consolation for EMH. One approach that has provided an explanation for the motivations that underlie bubbles was presented in mathematical models that incorporated a preference function that depended not only on deviation from fundamental value but on the price trend as well (see, e.g. Caginalp and Ermentrout, 1990 and Caginalp and Balenovich, 1999 and references therein). These models incorporated the conservation of cash and asset, and made the predictions that (i) a larger cash supply would result in a larger bubble and (ii) a lower initial price would yield a larger bubble, both contrary to the expectations of EMH. Both of these predictions were confirmed by experiment (Caginalp et al., 2001). These experiments also demonstrated a role, though limited, for the open book, whereby all traders can see the full set of orders, in mitigating the size of the bubble. There are two main advantages in using experiments: (i) conditions can be adjusted and experiments repeated, and (ii) detailed data sets about the actions of particular traders are available. In this work, we utilize the latter feature, as we distinguish the behaviors of different traders and test hypotheses with this information. The first step is to define a criterion for separating traders who trade on fundamentals (net offerers above fundamental value) from those who trade on momentum (net bidders above fundamental value). Some traders who do not fit either criterion are in a third group. We can then test a basic hypothesis that the peak of the bubble occurs when the momentum traders have depleted much of their cash. This hypothesis is confirmed. With the price being far above the actual value at this point, the fundamentalists are not interested in buying, and consequently the trading price drops precipitously. Beyond this result we seek to utilize a discretized version of the differential equations discussed above to evaluate the coefficients related to each of the two groups. In particular, we use the data in terms of cash and asset supply for each trader and the trading prices to see if the coefficients are of the correct sign and statistically significant. If so, it provides a confirmation of the model using two distinct groups. Furthermore, we would like to determine whether the momentum traders are influenced by fundamentals, and vice versa. Also of interest is whether the presence of an open book tends to diminish momentum trading.

Experimental asset markets contain much more data than just the trading prices. In this paper, we have utilized detailed data for individual traders. This has allowed us to classify the traders in terms of net bidders (momentum traders) or net offerers (fundamental traders) when the trading price is above the fundamental value. The asset flow difference equations confirm that the net bidders are using a momentum strategy while the net offerers are using a fundamentalist strategy. We find that the momentum traders have gradually diminishing cash (both as a group and per trader) and have cash levels near the lows when the bubble peaks. The opposite is true of the fundamental traders. This suggests that the bubble is fueled by the cash of the momentum traders, even though they are consistently outnumbered by the fundamentalists. The bubble seems to reverse due to the diminished buying power of the momentum players. The cash of fundamentalists increases as the peak is approached, but they are not interested in buying at this point. Thus one might summarize the buying at the peak as “Those who would, could not; those who could, would not.” The question arises as to how the price can move above the fundamental value so easily despite the fact that there are more fundamentalists than momentum traders. The price dynamics equations appear to provide an answer to this puzzle. Even those traders who are net sellers when the price exceeds fundamental value are strongly influenced by the trend, according to our statistical analysis of the difference equations. When the price is initially moving past the fundamental value, the premium is relatively small but the price derivative is often large. Thus, it seems that the fundamentalists are not selling very aggressively at this point. The statistics indicate that they are more likely to sell as the deviation from fundamental value increases and the price change is more muted. Hence, an asset whose price is considerably higher than fundamental value and beginning to stall becomes very risky to own. This analysis offers some insight into the high-tech bubble of the late 1990s, when a huge amount of cash poured into the market from recent investors who had little experience and were largely influenced by price movements. Part of the rationale for ignoring fundamentals was based on the idea that these benchmarks were antiquated metrics. As the market moved into the stratosphere in comparison with fundamentals, one might assume that more seasoned investors would be selling. If one were to extrapolate from the experimental analysis, one could conjecture that the fundamentalists during the high-tech bubble were also somewhat reluctant to sell as they observed sharply rising prices. As prices began to stall, however, one expects that the fundamentalists with stock are the first to sell. This may explain the fairly rapid turn in the market (in the absence of much new and negative information) in early 2000, when stocks which had been rising rapidly for some time stalled briefly before moving decisively lower. When prices are no longer rising, the value buyers could not be expected to step in until the prices were a tiny fraction of the peak trading price. Of course, once the trend is clearly downward, the momentum traders sell in force. Without any significant group with interest in buying and many interested in selling, prices fall precipitously. Our analysis displays the interaction between the strategies of different types of traders with their cash/asset position. Understanding this relationship is the key to the dynamics of financial markets. Contrary to the efficient market idealization, there are different motivations behind trades, and it would be impossible to predict where these motivations would lead without having a quantitative basis for assessing the impact of these traders. In gauging the effect of a particular group the sentiment and strategy must be combined with their cash and asset positions within some set of price dynamics equations. The equations we present do not have any a priori bias toward behavioral finance. If there were no significant tendency for traders to buy on rising prices, that particular coefficient would simply be estimated as zero by the statistical procedure. Hence this hybrid approach (statistical combined with difference equations) has the advantage of minimizing any bias in modeling. As noted earlier, traders are classified during each period, and we now examine the transition rates between the momentum and fundamental groups during the periods T − 4 to T + 2. The details are presented in the Appendix. In general we find that the transition from momentum to fundamental is reasonably low (about 12 percent) through period T − 2. Near the peak of the bubble, in periods T − 1 through T + 1 the transition probability triples to 36 percent. This is consistent with a simple learning process (i.e., participants are learning to focus on the realistic value) though it does not appear to be a linear function of time (see Appendix). When we examine the transition from fundamental to momentum, the same learning hypothesis would suggest fewer such transitions with increasing time. However, we find a more complex picture. Only 9 percent make the transition from fundamental to momentum during periods T − 4 and T − 3. Later, against a backdrop of soaring prices (and declining fundamental value), the transition probability jumps to 37 percent in period T − 2, suggesting that traders are not simply learning to focus on valuation. Rather, even some of those who started with a sound valuation strategy (i.e., not bidding on the asset at prices that are clearly more than the expected return) are swept into momentum trading with rapidly rising prices. This is a further indication that the cause of the bubble is not simply inexperience and confusion with trading strategy. A key cause is the abandonment of value based investing by the value traders. After the bubble has peaked, the transition probabilities (fundamental to momentum) also decline. In summary, the trading strategies of both groups appear to be very stable (under 11 percent in either direction during the early periods (T − 4 and T − 3)) until prices begin to rise rapidly above the fundamental value. It is only after a large rise in prices that a significant fraction of fundamentalists become momentum traders. Momentum traders change strategy in significant numbers only near the peak (T − 1, T and T + 1) as the soaring prices plateau. Thus, the traders appear to understand the trading strategy options available to them from the outset. Through adaptive learning they respond to the changing environment created by their fellow traders. For some, the value based investing appears to be a good strategy, but by period T − 2 they observe that a momentum strategy would have served their interests better. Through adaptive learning they switch to a momentum strategy. Soon after this point, however, trading prices begin to level off since much of the available cash for buying so far above fundamental value has already been used. Once prices are no longer soaring, there is continued adaptive learning, particularly on the part of the momentum traders, as they switch in much larger numbers during T − 1 and later periods to a value strategy. Thus there is a complex adaptive learning process that is intertwined with the basic conservation laws of cash and asset. From the perspective of these experiments, a good forecaster of the peak is the sharp spike in the transition rate from fundamental to momentum strategies that occurs approximately two periods prior to the peak and about two or three periods after prices have moved above fundamental value. World market bubbles often exhibit a stage when long-time value investors relinquish their strategy and join the bubble. With the insight gained from this analysis of experiments, the question arises as to how one can extract some of the relevant information in ordinary markets to utilize this approach. The necessary information consists of (i) an estimate of the motivations of different groups, and (ii) the asset sizes of the various groups. A key step in this direction would be to examine the data of the late stages of the high-tech bubble of the late 1990s and attempt to classify traders based upon the trade size, from 100 shares to block trades. One can then examine the nature of the trades, such as the fraction of these trades that are on the “uptick” (i.e., when the trade occurs on the high end of the spread) and the fraction of trades that occur when prices are rising within a specified small time period. If the information is available, one can determine whether the orders are limit orders or market orders. In previous studies, it has been shown that parameters estimated in experiments were close to those of the NYSE data for closed-end funds. Thus, the experimental parameters could be used as an approximation for the true values in the market until optimization methods offer more accurate values. Surveys and brokerage data on the trading of individuals could also provide the useful information. Within our approach one needs only an average value for a group so that is possible to utilize aggregate cash/asset data for a group analogous to our experimental data.