You can't direct the wind, but you can adjust your sails.

Transcription

1 You can't direct the wind, but you can adjust your sails. German Proverb WESCAP proprietary model evolved around ideas of motion which are fundamentally different from those of classical mechanics. In quantum mechanics, there is no such concept as a path of a particle. The fact that an electron has no definite path means that it also, of itself, has no other dynamic characteristics. The possibility of quantitative description of motion of an electron requires the interaction with physical objects which obey classical mechanics to a measurable degree of accuracy. If an electron interacts with such a classical object, the state of that object is generally altered and the nature and magnitude of this change depends on the state of the electron, and therefore serves to characterize it quantitatively. The basis of a mathematical formalism of quantum mechanics lies in the proposition that the state of the system can be defined by some function Ф(q) where q is the set of coordinates in a quantum system. The square of the modulus of Ф(q) determines the probability distribution of the values of the system coordinates. Ф 2 dq is the probability that a measurement performed on the system will find the values of the coordinates to be in the element dq of configuration space. dq is the product of the differentials of coordinates q, however, it is nothing other than a representation of an element of volume in configuration space of the system. For one particle, dq = element of volume dv in ordinary space (x,y,z). The function Ф is called the wave function of the system. And now we have arrived at the very core of any quantum mechanical system and its solution. If we are able to solve the wave function Ф in any coordinate system q, we will be able to calculate the probability of any measurable occurrence. Early in our developmental work we opted to redefine the largely unsolvable Quantum model to a series of solvable configuration spaces. In a nutshell, we redefined the Quantum configuration space to a mathematically solvable configuration space. Thus, at the core of the WESCAP proprietary model is a probability driven discipline which measures the momentum and energy of a measurable classical state resulting from a probabilistic interaction in a redefined configuration space.

2 Slide 1 shows a probability driven momentum trace (in red) generated by our model for the S&P500. Several things are immediately evident momentum is dynamic it moves around as it adjusts to the market s interaction resulting in a measurable price output. But the purpose here is to show the forecasting capabilities of the time independent QM model. Slide 1 Slide 2 displays the same momentum curve for the S&P500 with potential states V() defined. Nomenclature of the states is not significant but for our purposes we follow a T4 system and reset our Potential s beginning with each cycle as we can see (Blue Box) starting in Aug 2004 with V*1 to V*5. A simple transformation gets us back to a discrete Hermitian eigenstate designation. Typically, the model closes positions at V4. Lets walk through the physics of the QM system. As the occurrence probability of any system changes, it generates a discrete series of theoretical less excited to more excited momentum potential V() states. The interaction of any such state with any classical system (for example, with configuration space such as volume, price, earnings, and time)

3 has a resulting measurable influence on that classical system. In fact, as price/volume approaches any of such excited potentials, energy is defused, such that more and more threshold energy is required to push through each higher excited state while less and less is available. Finally, an excited state is reached where the system s energy is not sufficient to exceed the threshold energy of that state, and the dynamic system(price/volume) collapses to a less excited state. Typically, this occurs at V(4) in our nomenclature. Slide 2 Slide 3 displays the same momentum curve and potential states V() (Slide 2), with daily price action (in black) inserted for the period in question. The prognosticating capabilities of the QM discipline are readily visible. Starting in March 04, led by a sharp decline in the Momentum (more on this later), the INX displays a late cycle sell down. As the momentum leads the decline, eigenstate potentials V(-1) to V(-5) are generated below and ahead of the declining price action. Negative V s designate support states. V(-4) is generated at arrow A on March 22 nd, a level which price action will not achieve until Aug 13 th, coincidentally defining the very bottom of that cycle. Starting with Aug 13 th, price action lacks sufficient momentum to penetrate through the V(-4) state at which point it reversed. Again led by a rising momentum, positive

4 potentials V*(1) to V*(5) are generated above and ahead of the rising price action. These connote overhangs or resistance nodes, each one fully capable of stopping further price appreciation. Intersect B on Nov. 12 th generates state V*(4) which typically defines the top of the cycle. Despite that subsequent price action exceeds V*(3) threshold, and decays to the next lower excited state V*(2) (this typically occurs), it returns to test V*(4) on March 7, It exceeds state V(3 7/8) threshold potential but lacks sufficient excitement to reach V*(4) and decays. The failure is followed by a steep decline to V*(2) highlighted with arrow C. Thus we see that cycles are bound by discrete and measurable eigenstates which are identifiable and predicted by the QM model. Slide 3 In slide 4 we are now in virgin territory, to the right of the blue box, and would like to know where the price action is heading next. Based on the discipline we have learned so far, we don t know. But, we do know that the reversal nodes (tops and bottoms) will play out between the stated potentials. Lets roll the slide forward to see what happens next.

5 Slide 4 In fact they do. Next true reversal occurs at V*(+3/4) and next top at V*(5) which coincidentally is V*(-4) and V**(4) in an overlapping cycle. You can identify these new overlapping states for yourself. But the QM model offers a great deal more, in particular the solution to the above asked question where is the price action heading next. It is in the very nature of the wave function Ф that its solution is separable as a product Ψ(q 1 )θ(q 2 ) resulting in one wave function Ψ(q 1 ) ( which solution yields discrete momentum, energy, eigenstate potentials), and some other wave function θ(q 2 ) which solution results in what we choose to call Probability Pressure or Pressure Wave β of a normalized amplitude (+/-)1 and a pressure gradient ( / q)ω. For those who still believe that markets are random, take a look at the harmonics of the pressure wave (Slide 5). The Pressure wave is in blue and its gradient is in black below the Momentum curve. Because of input variables required, a much better representation of the harmonics may be seen on individual stocks, not an index which Slide 5 represents. Since the Momentum Wave function is one part of a discrete solution of a collapsed wave function Ф, one would expect the momentum function to lead the price action and offer a

6 high degree of predictability. In fact that is the case. If we look at Slide 5, the momentum function is in red, price action is in black. Focusing on the shaded areas, the trading discipline immediately becomes evident since the momentum function leads price and price follows, when momentum falls below the price leading the price to a lower excited state (as in the shaded ellipse) a sell is generated. When momentum crosses above the price a buy is generated. Thus in the ellipse a sell is generated on July A buy is generated o Aug.2 nd On a long only or long/short discipline this would have saved or picked up 22 points. The following shaded rectangle shows a Buy on Aug 18 th 2004, at That long position would have been closed on Sept 22 nd at for a pick up of 18 points. The 3 rd shaded rectangle shows a buy on Oct 27 th at which position probably would have been closed on Nov 30 th at 1173 for a 48 point pickup. Slide 5 Slide 6 moves forward in time, showing the ability to avoid steep declines, to project high probability supports and resistances, but above all, in combination with Slide 5, to avoid low probability buy and sell signals. As the momentum function interacts tick by tick, it generates numerous signals, some of which are coincidental, others are just plain noise.

7 So far we have mentioned the Pressure Wave function only by reference. This is the other wave function θ. Because a major QM tenet, called a principle of superposition of states, leads us to the result that the probability distribution of the whole system must be equal to the product of the probabilities of its parts, a wave function Ф of a system can be represented in the form of a product of the wave functions Ψ(q 1 )θ(q 2 ) of its parts. The solution of Equation Ф(q 1, q 2 ) = Ψ(q 1 )θ(q 2 ) for θ then gives birth to a Pressure Wave function β. And because, the sum of all probabilities of all possible values of coordinates of the system must be equal to unity, Ψ(q 1 ) and θ(q 2 ) are related by Ψ(q 1 ) θ(q 2 ) d q 1 d q 2 = 1 Slide 6 The Probability Wave function β in Slides 5 and 6 (shown in blue) for the sake of enhanced visualization is actually inverted. At its peak, Probability is low for price appreciation. At its trough probability is high for price appreciation. But since it is a probability pressure wave oscillating between +1 and -1, it is easier to visualize as declining or rising with the price action. For purposes here, one can visualize it as a high probability for price decline at its peak and at its trough a high probability for price appreciation.

8 Slides 5 and 6 demonstrate the Probability Wave functions ability to avoid noise and or coincidental signals. In Slide 5, we mentioned the short position opened July 1 st was closed Aug 2 nd. We could have re-opened it subsequently on Aug 3 rd when a fresh sell signal was generated, but for purposes here this is academic. The issue here being that a buy was generated on Aug 2 nd and, would the discipline have necessarily put on a long position with the Aug 2 nd buy at the same time it closed the short? In Slide 6 would the model have followed a generated buy on Apr 6 th (occurring just to the upper left of the large ellipse), ie. would it have put on a long position, other than just closing the short? In all probability not. The answer lies in the Probability Wave function. At each such occurrence, the Probability Pressure is at its peak meaning the probability is high for price decline, suggesting the Momentum Buy signal is suspect or at a minimum, indicating a low probability for gain. The discipline then puts on buy/sell positions at the most probability opportune times. For example, only when a momentum generated buy signal is in phase with the most probability opportune time for price appreciation, is a long position taken. Positions are not applied when the two signals are out of phase. SUMMATION We have demonstrated that the QM model Is capable of forecasting up and down trends and generating timely buy and sell signals; Is capable of predicting price action and price break levels; Is capable of identifying low probability trends; Is capable of identifying and forecasting cycle tops, cycle bottoms, reversals and targets. Finally, the QM model does not predict result efficiency of any investment, ie., which stock will be most efficient or profitable. It is not a filter for best performing stocks. It is a filter for maximizing returns. It does not replace fundamentals it merely maximizes its efficiencies. Thus, we continue to employ a top down selection approach and then based on those fundamentals select an investment universe on which the QM model operates. The rule of thumb is the better the fundamentals the better the trade. Fundamentals provide the vehicle and its horsepower the QM model tells us when to hitch a ride, its destination, and when to get off and, when to do it over and over again.