Traffic jams are fairly unpredictable because they depend upon a large number of factors, e.g. timing in the traffic, weather conditions, highway maintenance, automobile accidents, some of which are completely random. However once begun, traffic jams display fairly recurrent patterns as to average duration, behavior of the drivers, and so on. This traffic jam parallel has been introduced by Charles Tilly (12) in the context of historical sociology in order to explain why revolutions can hardly be predicted. It also applies to the occurrence of speculative price peaks: the downturn of price peaks can hardly be predicted because they depend upon a number of (possibly) exogenous factors[1].
However, as is the case for traffic jams, once a price peak is under way it obeys some definite rules; accordingly its outcome can to some extent be predicted at the level of individual companies. More precisely we focus our attention on the relationship between the prices at the beginning of the peak, at the peak and at the end of the peak. We denote by p1 the price level at the start of the peak, by p2 the price at the peak and by p3 the bottom price at the end of the falling price path; we further introduce the peak amplitude A = p2/p1 and the bottom amplitude B = p3/p1.
A and B can be defined for any company in the market; for instance on the NASDAQ where there are currently more than 5,000 companies listed A and B can be seen as variables for which there are several thousand realizations. In the next section we show that A and B are closely correlated; with a correlation of the order of 0.75 the following regression holds:
B = aA + b (1)
where a is usually of the order of 0.4. The fact that a is positive means that the higher the peak amplitude, the larger the bottom amplitude; in other words the higher the price of a stock climbs during the rising phase (bull market) the better it resists during the falling phase (bear market). The regularity summarized by equation (1) will be referred to as the resilience pattern. The paper proceeds as follows.
In the second section the statisticalmethodology is explained, then the resilience pattern is established and illustrated through several case studies: we consider three stock market peaks, one price bubble for postage stamps and two real estate bubbles. In the conclusion we discuss the possible implications of the resilience pattern.
1 For instance it has been argued (Business Line 8 May 2000) that the spurt in the NASDAQ composite index that occurred in December 1999 and January 2000 was fueled by a Y2K-motivated injection of money into the banking system. Needless to say, no model will ever be able to take into account such circumstantial factors. However, the present paper suggests that when a market rallies or plummets there are some structural invariants which are independent of triggering factors.
By Dr B.M. Roehner
Next: The resilience pattern
Summary: Index