Most theoretical literature on bubbles and crashes focuses on establishing conditions under which a bubble can occur. Irrespective of whether a theoretical model can accommodate the presence of a bubble, the empirical evidence on bubbles and crashes so far in Kindleberger (2000) and Shiller (2000) compels further research. As the main purpose of this chapter we empirically investigate the hypothesis that the presence of a bubble increases the probability of a crash in the next period. We refrain from the theoretical debate on bubbles. However, the findings of the theoretical research can
help us steering our examination and set up the investor perspective that we take towards bubbles and crashes.
A bubble is commonly defined as a period during which the price of an asset ex-ceeds its fundamental value (see e.g. Brunnermeier, 2001; LeRoy, 2004). Asymmetric information is crucial for the occurrence of a bubble. Santos and Woodford (1997) show that a bubble can only exist under very strict conditions in a case with sym-metric information. Abreu and Brunnermeier (2003) and Conlon (2004) show that bubbles can exist in a setting where some investors know about the bubble while others do not, and investors do not know who is informed and who is not.
The start of a bubble is commonly related to displacement in a Minsky model (see Kindleberger, 2000, p. 14) or new-economy thinking (see Shiller, 2000). Improve-ments in the fundamentals of an industry increase its outlook, and consequently asset prices in that industry grow at a faster rate than before. However, uninformed market participants extrapolate this faster growth rate and expect it to hold in per-petuity.2 De Long et al. (1990) argue that the behavior of noise traders, who base their trades on such extrapolation (called feedback trading), can lead to the continu-ation of a bubble. Instead of trading against the bubble, the informed investors will try to ride the bubble at the expense of the noise traders. Abreu and Brunnermeier (2003) prove the optimality of this trading strategy for a setting where informed traders are unaware of the proportion of informed traders. Temin and Voth (2004) and Brunnermeier and Nagel (2004) provide empirical evidence of this behavior.
Most bubble models either explicitly state that a bubble ends with a crash (see for instance Blanchard and Watson, 1982; Abreu and Brunnermeier, 2003), or imply that a bubble ends with a crash, because the bubble becomes common knowledge.
Though likely, a bubble does not necessarily have to end with a crash. It can also deflate without a crash. In theoretical models like Abreu and Brunnermeier (2003) the noise traders are assumed to be fully unaware of a bubble taking place, contrary to the informed traders who are fully aware of it. In reality, investors cannot be char-acterized as fully aware or fully unaware, but will show varying degrees of awareness.
As a consequence, feedback trading may vary over time, and gradually decreasing feedback trading can lead to a soft landing of the bubble.
In our research we investigate whether bubble characteristics like its size and length help in determining the probability of a crash. We base two hypotheses mainly on the model of Abreu and Brunnermeier (2003). The investor perspective they use in their model makes it easy to relate their model to our empirical setting. In the model of Abreu and Brunnermeier a bubble has a maximum size. All traders start being
2This behavior is examined empirically by Frankel and Froot (1988) and experimentally by Andreassen and Kraus (1990).
uninformed, but per unit of time a fixed proportion of traders becomes fully aware of the bubble. Though they know its maximum, they do not know when it started, and consequently they do not know how long it will last before it bursts. Because traders do not know whom of the other traders are informed, a coordination problem arises.
Informed traders will ride the bubble and try to sell out before it bursts. A bubble always ends with a crash, when it reaches its maximum size. This maximum can be exogenously given or endogenously arise as the point where selling pressure of the informed traders exceeds the buying capacity of the noise traders. We hypothesize that a bubble with a stronger growth rate will burst sooner, because it reaches its maximum size sooner.3 Our hypothesis is in line with the hypothesis of Youssefmir et al. (1998) that larger bubbles are more susceptible to shocks, which they base on simulations. A crucial assumption in the model of Abreu and Brunnermeier (2003) is that the investors do not know the exact start date of the bubble, which makes it difficult to determine its length. Therefore, we test whether the length of the bubble that the investor infers does not help in predicting the probability of a crash.
The assumption that a crash happening after a bubble is related to it is implicit in our approach. While crashes may occur because of news reaching the market, crashes in the presence of a bubble are mostly too large to be explained by that news (see Shiller, 2000, Ch. 4). Abreu and Brunnermeier (2003) argue that news can act as a synchronizing event, leading to massive sell out by the informed investors.4 If selling pressure exceeds the buying capacity of the noise traders, the bubble will burst and the asset price will fall. However, if this coordinated attack fails, a temporary strengthening of the bubble will set in, followed by new crashes. We call these crashes aftershocks.
In the next section we investigate whether these theoretical aspects of bubbles and crashes are present in industries. We test the hypotheses, but we do not test whether a specific model describes bubbles and crashes accurately. However, since the investor perspective of Abreu and Brunnermeier (2003) can be easily related to our approach, our findings can be interpreted as support in favor or against their model.
3In the case that the maximum size of a bubble arises endogenously as selling pressure exceeding buying capacity, the effect of a larger growth rate in the model of Abreu and Brunnermeier (2003) is twofold. On the one hand, traders have a stronger incentive to ride the bubble. Consequently, the bubble will be larger when selling pressure bursts it. On the other hand, it will reach this size sooner.
4In broader sense, this argument can apply to ‘real’ news that has a serious impact on the outlook of a sector, but also to sunspots or lumpy information that has been held up by restricted investors as in Hong and Stein (2003) and Cao et al. (2002).