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points of trend reversal

In the preceding six articles, it has been shown that the support and resistance levels associated with points of trend reversal in the   price of a stock can be classified with respect to a hierarchy of theoretical curves. It is now appropriate to derive the simple   algorithm giving rise to these curves from a consideration of familiar aspects in the psychology of the market participants. After   all, it is precisely the dynamic interaction between the greed and fears of those who already hold the stock and those who wish to

become owners that determines the price at which supply and demand find at least temporary equilibrium.

One can approach the problem from both the supply side and the demand side with remarkably similar results. First consider   someone who already has a long position in a given stock. What will motivate this person (the "owner") to sell? If the stock is held   at a profit, the more substantial this profit is the greater the temptation to take it. If - not having taken such profit - the owner sees   the price has now dropped back almost to the purchase price, his propensity to sell is at a minimum because he is still in profit -   albeit small - and believes the stock will at least partially retrace the higher prices of recent memory.

On the other hand, if the owner has been holding the stock at a loss, his overriding desire is to "get out even". Thus, as the stock   price approaches from below the price at which he bought, his propensity to sell reaches a maximum. It is thus the purchase price   which becomes either a support or resistance level for that owner; he either dumps the stock on the market or witholds it   depending on the direction from which the market price is approaching his purchase price.

Now let's look at the demand side and consider the psychology of someone (we'll call him the "accumulator") wishing to take a   substantial long position. He starts his buying and the price starts to rise attracting other buyers. Not wishing to "chase the stock",   our accumulator holds off on future purchases until the price drops back to the average price at which he had assembled his   position thus far. He can then buy more without substantially changing his aggregate cost per share. Thus, as the market price   approaches from above towards his average cost, his propensity to buy reaches a maximum.

If his average cost happens to coincide with the average cost of the owner considered earlier, then it is little wonder that the price   trend reverses at this point since the accumulator now starts to buy again while the owner has lost interest in selling. Supply and   demand are maximally out of balance and the price must therefore rise sharply, i.e. "bounce".

In reality, of course, there are many "owners" with a corresponding spectrum of purchase prices. Similarly, while there may in fact   be only a single "accumulator" in the initial stages of a bull move (e.g. a group of insiders, or a large institutional investor), as the   move evolves distinctly different accumulators come on the scene (either traders attracted by the price action or other institutions   recognizing the same fundamental "value" spotted by the initial investors). Each has their own time horizon, price objective, risk   aversion, etc., and it is tempting to associate the hierarchal structure of S/R levels with such different groups of accumulators   coming into the market at successive times.

To model this situation mathematically is quite complex. While one can certainly construct a purchase price spectrum from price   and volume historical data, the decomposition of this spectrum into "owners" and "accumulators" would be tentative at best.   Furthermore, at some point the psychology of the accumulator transitions into that of the owner. Above all, even if these   complexities could be resolved, the modelling process would be multi-parametric (time horizon, risk aversion, profit objective, stop loss points, etc.)

As a first approximation, we can restrict consideration to just the first moment of the purchase price spectrum - the mean. That is,   we simply ask "What is the average price at which this stock has been bought?" during a specific interval of time. Once this   interval has been specified, the computation is trivial. One simply averages the daily prices ("price"=.5*(high+low)) weighted by   the ratio of the daily volume to the total cumulative volume over the interval in question. If we use brackets to denote a simple   arithmetic average, then the average price [P] is simply [PV]/[V].

We have not yet specified the interval over which the averages are to be taken. In fact, it is this CHOICE OF AVERAGING   INTERVAL WHICH UNIQUELY DISTINGUISHES THE MIDAS METHOD. While even a casual reader of the earlier articles   can already deduce the answer from the examples given, the rationale requires some discussion which is best left to the next article in the series.