Monthly Discussion



The Bubble Indicator


This month's discussion topic takes up once more the bubble indicator described in An S-Shaped trail to Wall Street (pp 75-79).



The approach in brief


Using the notion of relative price one can objectively understand whether the market is overvalued or undervalued and estimate how close we may be to bursting a bubble or to bottoming out from a major dip.

The DJIA that we study and forecast in this Newsletter is calculated from the average DOW price weighted by the share volume. This price is calculated as the ratio of the DJIA痴 dollar value over the DJIA痴 share volume and is expressed in dollars. The same ratio, but with dollar value and share volume expressed as percentages of the NYSE totals, defines a relative price. Relative price is nothing else but the DOW's average price divided by the NYSE's average price.* The relative price gives a more realistic description of how DOW moves. It may reveal, for example, that DOW痴 poor performance is not so poor after all, or that a good performance is not that good.

It is true that DOW's performance and NYSE's performance are strongly correlated (that's why we use the DOW as an index!) But in a particular day it may be that the average NYSE stock gains 15%, while the average DOW stock only 3%. In this case DOW's performance must be considered rather poor. In contrast, if some day the average NYSE stock drops by 5% while the DOW remains unchanged, the latter's performance should be considered as rather good.

Large-capitalization stocks present more resistance to the whims of the market (small-capitalization stocks are know to be more "fickle"). We can therefore use the relative price as a barometer for detecting exaggerated market moves, be it in the direction of overstating or understating. This is a dynamic detection process, i.e., it can only be done on the move, as things change with time. For example, if DOW's price increases between two dates more than the DOW's relative price between the same dates, the DOW is overstating the market and we are having a bubble situation. If DOW's price decreases faster than its relative price, we have an under-valued market most likely to be followed by a bull market. Large bubbles can burst with a crash. Following a crash, the total NYSE value generally finds itself below the real value, and a bull market is likely to follow.

During an overstated market both the NYSE and the DOW may form bubbles, but the two bubbles do not generally grow at the same rate. The difference between the percentage change of the DJIA average price and its relative price is proportional to the size of the bubble. Therefore a null difference is evidence that there is no bubble.



The bubble indicator updated


Exhibit 3 shows that the average price and the average relative price of the 30 industrials moved hand in hand for most of the last 32 years (most of the points are close to the zero line). Occasionally we see important excursions upward with price increasing faster than relative price, or downward with relative price increasing faster. Let us look more closely at some large excursions in each direction. From the three bubbles (in 1971, 1975 and 1987) only the last one burst. An undervalued market preceded the first two bubbles, which is what may have caused the formation of these bubbles in the first place. If it is true that a bubble sometimes forms as a reaction to an undervalued market, it may be reasonable to conclude that such a bubble is not likely to burst via a crash but rather diffuse via a more gentle mechanism (soft landing). After all, the amplitude of the 1975 bubble exceeded that of 1987, and yet it did not burst.

Conversely among the largest market undershoots that we see in Exhibit 3, only the one in 1987 should be interpreted as a reaction to the bubble that preceded it. In that light, we can say that the other four market dips not preceded by bubbles were caused by more deeply seeded phenomena. All the same, they were followed by bubbles, which can now be seen as reactions to the dips.

To summarize, a bubble or a dip of the market can be viewed as action or reaction, depending on whether it initiates a deviation from zero, or follows a deviation from zero. The relative-price indicator obviously enhances our ability to predict reactions more than actions.

Let me point out here that over-shoots and undershoots of the market often coincide with bull markets and bear markets respectively. But for the bear markets of 1977 and of spring 1997 there is neither significant overshoot nor undershoot. We must therefore conclude that the poor performance of the DJIA in these two cases was not a correction but was simply real.



Exhibit 3. Based on the last 32 years (points every six months), we can say that bubbles and dips of the market do not extend beyond 25 percentage points in the difference between the average DJIA price and its relative price. On October 31, 2002 we are in a situation of a dip.


We also see in Exhibit 3 that in October 31, 2002, the market was on the dip side, which can be interpreted to some extent as a reaction since some sort of overvalued market preceded it. However, the bubble indicator was at -17% on October 31, 2002. This value is large enough so that even if part of is due to a reactive correction there is reason to trigger a bull market, as it happened following the dip of October 30, 1998. Bubbles burst and dips trigger bull markets when the amplitude of our bubble indicator approaches 20 percentage points or more.

Exhibit 4 shows a study with variable sampling and finer time resolution. We are looking at daily data to detect a bubble with respect to October 8, 1998. This date was chosen for two reasons. First because it corresponds to a time period when the DJIA was again at present levels, and second because it also was a time of an undervalued market. We see in Exhibit 4 that the DJIA kept building a bubble until early 2001, then went through a dip, corrected itself, and then fell again to a negative level, thus corroborating an undervalued market at present time.

Exhibit 4 demonstrates better than Exhibit 3 the classic by now bursting of 典he bubble because six-month sampling is too rapid to describe a process spread over a whole year. But whether we look at the market from one semester to the next, or with respect to October 8, 1998, the conclusion is that the market today is undervalued. Reaction or not, some further recovery should still take place.


Exhibit 4. Daily data indicate the existence of an undervalued market with respect to October 8, 1998.



* Because of the way it is calculated (value over volume) this average is weighted by the share volume, as it should be.