Methodology
Let us consider a typical price peak such as the one in Fig.1. While it is easy to identify the moment t2 when the price reaches its peak level p2, the determination of the initial moment t1 (corresponding to p1) and the end moment t3 (corresponding to p3) is not so easy. Fortunately, as will be seen subsequently, the relationship (1) does not depend upon the choice of t1 or t2 in a critical way. A peak will be delimited in two steps (i) At the global level of the whole market the price peak is identified by using a broad annual index; in that way one already gets a rough definition of t1, t2, t3 (ii) At the level of individual companies t1 will be selected as the first year for which the annual price change is positive, t2 as the peak year and t3 as the last year for which the annual price change is negative.
Let us illustrate the procedure on an example (Fig.1). As one knows there was a short bull market on the NYSE after World War I which culminated in 1920; thus, for the great majority of the stocks the first positive price change was 1921-1922, which leads us to t1 = 1921. At the end of 1929 the downturn occurred very abruptly which means that for almost all stocks t2 = 1929. By and large the market bottomed out in 1931; yet for some stocks such as for instance Consolidated Edison the fall continued until 1935; in that case one would take t3 = 1935.
Once the limits of the peak have been determined for each individual stock, the ratios p2/p1 and p3/p1 are computed for the deflated prices; then the correlation and regressions are carried out for the sample of stocks under consideration. We now apply this procedure to several case studies.
By Dr B.M. Roehner
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Summary: Index