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30 Year Treasury Bond


Stochastic Analysis

What is the Stochastic Process?

The term "stochastic" in statistics refers to random or chance variables, or that which involves chance or probability. The price behavior of all cash and commodity instruments embodies those descriptions and were duly noted by Dr. George Lane many years ago. Lane observed that as the level of the price of an instrument continued to rise or fall, its closing price tended to be closer to the top or bottom of the range, respectively. In an attempt to rationally quantify this empirical dynamic, he constructed a formulaic process by which a stochastic or "educated guess" as to the direction of an instrument's price could be confidently applied and designated it as "Stochastic Process".

How is the formula for the Stochastic Process determined?

The Stochastic is always measured through the relationship of two lines, %K and %D, which determine the relative overbought or oversold condition of a traded instrument in its particular market. As %D is a moving average of %K, the latter, represented by a solid line, will always appear "faster" than the former, depicted as a dashed line.

In its simplest form, the Stochastic variable, or %K, is derived in the following manner:

%K = 100[(C-L)/(H-L)] where

C= Close

H = High

L = Low

By construction, it is evident that %K may vary from 0 to 100%, measuring the closing price as a percentage of the total range. Depending on the time frame desired, %K may represent this relationship for a selected number of minutes, hours, days, weeks months , years, or any other interval.

The Stochastic variable %D is simply a moving average of %K and will, therefore, describe the identical movements of %K on a lagged basis. Other common references to the Stochastic such as "Slow Stochastic", "Smoothed Slow Stochastic", "Exponential Slow Stochastic" are no more than statistical techniques applied to the basic Stochastic in order to enhance its prognosticative value and to filter out extraneous and distorting statistical "noise".

How is the Stochastic interpreted?

The Stochastic is constructed as an oscillator, cycling periodically between overbought and oversold conditions. An overbought condition is signaled when it rises beyond the 80-85% zone, while an oversold condition is indicated when it falls below the 15-20% level. A sell signal is triggered from an overbought condition when %K crosses down through %D and the converse from an oversold position. The validity and authority of either signal is enhanced when the cross of %K is effected after the apex or nadir of %D, respectively. Divergences, bullish or bearish also figure prominently into the presumption of strength in the ensuing move. A bullish divergence occurs when %D forms two ascending troughs while the price of the instrument moves lower, describing two descending troughs; the converse is true for a bearish divergence; to wit, %D forms to descending peaks while the price of the instrument moves higher, describing two ascending peaks. The optimal signal is triggered when a leading %K cross occurs in an extreme zone accompanied by a divergence.

What is the value added of StoMaster?

Conventional Stochastic analyses predominantly view each considered time frame independently in order to assess secular and cyclical trends. Such an approach is adequate, but somewhat sectarian in that it fails to recognize the nuances and subtleties of the effects of each time frame, one upon the other. Viewed in isolation, the analysis misses the invaluable micro observations, which are the sine qua non for both the strategic implementation of portfolio positioning and the effective timing of entry and exit in the market, by exclusively relying on conclusions drawn from observations through a strictured macro prism. It is the interdependence of time frames that StoMaster endeavors to reveal, develop and explore. StoMaster uniquely integrates and critically examines all time frames simultaneously to provide a powerful analytical tool supplementing portfolio decisions affecting duration adjustment, sector rotation and transaction timing.

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