# V.14:2 (55-62): Gauging Mobility with Price Distributions by Mel Widner, Ph.D.

Item# \V14\C02\GAUGING.PDF
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NEW TECHNIQUES

Gauging Mobility With Price Distributions

The price distribution function, which analyzes the distribution of prices over a lookback period, is useful for predicting price mobility. Here's a new method called the mobility oscillator that will allow you to do so. By Mel Widner Ph.D.

When prices remain about the same for a given period, that indicates that, essentially, buying and selling pressures are in balance. If this persists, then the area of price activity represents an area of congestion. Since traders often place stop orders, take profits and open new positions based on their entry or exit point, it is most likely market participants will make note of this congestion area. The more time the market spends in this area, the greater its significance, and the more recent the congestion is, the greater its significance.

Basically, all price histories have ranges where the price spends more time than in others, and so there is always some degree of congestion. For some data histories, there can be regions of large and small congestion and multiple regions of congestion. These regions of congestion can be measured by determining how prices are distributed. In fact, it is possible to construct a price distribution function (PDF) to identify areas of congestion for analysis.

A PDF can be developed from a recent history of prices by computing the frequency of occurrence of a price for each price within the price range. Large values of the distribution correspond to areas where the price history spend a long time and small values to areas where the price history spend a short time. The PDF is determined over the range from the minimum low to the maximum high for the period and may contain one or more peaks within the range.

So what does this mean? If the current price has moved from a region where the distribution function is small to a region where it is large, then it might be expected that the move started with a small number of traders and is moving to a region where there are a larger number of traders waiting to enter. It is possible the move will be stopped by the reaction of the larger number of traders or be absorbed by increased market activity. Conversely, if the move is from large to small, then it is plausible that there is less reaction and less activity and the move will go further. The hypothesis to be examined is that it is easier for prices to move in regions where the PDF is smaller (high mobility) and more difficult in regions where the PDF is larger (low mobility).

If the price move is significant, then the situation is different and other factors must be considered. There can be reversals corresponding to profit taking or entry of new traders. Such reversals result in peaks or troughs that are the basis for well-established support and resistance analysis. These peaks and troughs are implicitly included in the PDF analysis, since the PDF is bounded by the maximum high and minimum low for the period. It is possible to construct a mobility oscillator (MO) that captures reversals often occurring at the price extremes as well as reflections that occur from the mode of the PDF.

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