As far as stock markets are concerned there is often a tendency to over-emphasize the importance of crashes, by which we understand a rapid fall occurring within one or two weeks, at the expense of the long and steady declines that (in some cases) follow the crash. Crashes are impressive because of their suddenness, but it is not obvious and probably not even true, that crashes have a determining influence on the medium-term (i.e. yearly) evolution of markets. A slide that continues for over two or three years may have more significance for the stock market and for the rest of the economy than the crash itself.

A case in point is the parallel between the crashes of October 1929 and October 1987 on the NYSE (Fig.2). The price paths were very similar during the crashes and the six subsequent months; but, as one knows, the ultimate outcomes were very different. This observation suggests that steady slides (which are the topic of this paper) and abrupt crashes are two different phenomena. Applying the procedure delineated above, we obtain the results given in Table 1.

Note that the downturn in Paris occurred in February 1929 and cannot therefore be considered as a consequence of the Wall Street crash; incidentally, in Germany the downturn took place in June 1928 that is to say more than one year before the downturn on the NYSE. The analysis for the NYSE is based on the behavior of 85 individual stocks. The correlation is 0.87 for equation (1) and the distribution of sample points in the (A,B) plane is shown in Fig.3; it displays the range of both amplitudes and permits to verify that there is no non-linear effect.

Since this is the largest sample considered in Table 1, it can can be of interest to take a closer look at the statistical distribution of the amplitudes: A and B have an average of 5.6 and 2.0 respectively and the standard deviations are 5.0 and 2.3. Moreover it turns out that both A and B are distributed according to a log-normal density. This could have been expected; indeed, stock prices follow a lognormal law, at least in first approximation that is to say for time-samples of moderate size and time intervals larger than one day, and one knows that the ratio of two log-normal random variables is also a log-normal random variable.

The analysis of the Paris stock market is not based on individual stocks but on a set of indexes corresponding to 19 different economic sectors, e.g. banks, coal mines, railroads, electricity, chemicals, etc. Some indexes comprise more individual stocks than others, for instance the bank index comprises 20 banks while the electricity index has only 11; on average there are about 14 companies per sector. The results for the B versus A regression are given in Table 1: the a estimate is fairly close to the one obtained for the NYSE. The analysis of the 1989 peak on the Tokyo market is also based on indexes corresponding to different economic sectors. With as many as 26 different sectors the classification given in the Japan Statistical Yearbook is even more detailed than the previous one. It is not obvious whether that peak began in 1985 or in 1980.

It is true that the increase between 1980 and 1985 was not monotonic, but one can argue with good reason that these fluctuations were rather circumstantial. It is reassuring to observe that by taking t1 = 1980 one is lead to estimates which are fairly similar to those obtained for t1 = 1985; the fact that the correlation is higher in the first case in fact suggests that t1 = 1980 is the most “natural” starting point.

On the basis of the resilience pattern it could seem that one can invest in high-growth companies without much risk. This is not completely true however for that rule only concerns the medium-term behavior in the vicinity of a given peak; it does not guarantee that in the long-run the price of a stock which has experienced a huge peak will continue to increase. A spectacular counter-example is shown in Fig.4. Not only did the price of Columbia Gas System never again reach the level it had attained in 1929 but it remained far below.

By Dr B.M. Roehner

Next: Other speculative markets

Summary: Index