Introduction

The moment man stopped counting on his hands,
He became a slave of his own invention.

Abacus Road® is the embodiment of the mathematical construct that underpins virtually every investment transaction on the planet, to include interest rates. Origins of the construct are nestled in the supply and demand for the goods of commerce, the resultant crowd psychology of barter, purchase, and sale.

Intuitively, Abacus Road® must exist. How else are world governments to monitor and regulate the trading of stocks, commodities, real estate, and even their own currencies? There must be a law. How else can governments assure any semblance of free trade? How are policing bodies to catch the crooks that abound in our markets? How are the NYSE, the NASD, the CFTC, the Treasury, the Department of Justice to prove illicit behavior in a legal system that provides every conceivable protection to the criminal and seldom solace or recompense for the victim? There must exist a definitive rule of behavior against which to compare and verify, to the greatest degree possible, individual transactions as well as long-term price trends to assure that trade movements are executed in a fair and timely manner without prejudice, without unsavory outside influence. How are governments to regulate price fluctuation of gold (and they do) both near and long term as the investment soars into favor or plummets into disfavor? How is one to price the U.S. dollar on the eve of a trade deficit announcement, much less after the announcement is made?

Intuitively, there must be a rule to assure that the most highly traded stocks and commodities, as well as the most infrequently traded of such instruments, are treated with equal revere. How else are the DOW, the NASDAQ, the Commodity Futures Trading Commission, and other industry, quasi-governmental, and governmental bodies to monitor and regulate equitable trade?

Intuitively, there must be a way for high volume brokerage houses to create program trading software for their mainframes. It is common knowledge that these programs exist. How are these programs to be written so that they can buy and sell investments safely, blindly, and without constant human input? How are these programs to be written so they can make the most efficient use of investors’ dollars? Should brokerage houses place massive orders and let them stand until filled? Should they execute random purchases? In what quantities should automatic orders be placed — 10 percent of the position per trade, 15 percent, hourly, daily? Surely there must be a way to enter a market without causing undue disturbance.

Intuitively, there must be a means for market makers, those industry sleuths that promote individual corporate stocks, to assure that trades are executed at a fair price. In the absence of a rule, a mathematical law, how are market makers to set price for a thinly traded stock that trades fifty shares on Monday, 10,000 shares on Tuesday, no shares on Wednesday, 100,000 shares on Thursday, and one hundred shares on Friday? Should the 100, 000-share price be ten times the 10, 000-share price? Should trading be halted because no shares were traded on Wednesday? How should a market maker supply shares to the exchange when his client invents a new product that will revolutionize its industry? Should it dump all the shares in its reserve at once? Should price be randomly set by a group of fractious floor traders in some forgotten bullpen? What about the investment that doesn’t trade for a period of weeks? Surely, there must be a rule.

Intuitively, there must be a way for professional fund managers to time purchases so as to obtain a fair price in exchange for their members’ life savings. True, few fund managers are aware of Abacus Road®, else there would be a Warren Buffet on every street corner, but fund managers must sit at some counter, watch some river, meander some path similar to Abacus Road® to ascertain when to purchase or sell their investments. Price averaging, where numerous purchases are made over time, works to a degree, but there must be a means to assure that purchases are not made at the zenith of extreme peaks and that sales aren’t made at the nadir of extreme troughs. There must be a means to avoid making wild purchases as markets temporarily spike to unruly highs. There must be a way to guarantee that investors’ funds are not dumped in panic during major market downturns, that manager performance is not wanton but legal, if not prudent. “Shirley, there must be a way!”

For the way to be valid, the rule, the law, must take into consideration all the nuances of human behavior plied in our markets from the adrenaline-laden bolt of the panicked small investor to the savvy, calculating dash of the shrewd New York financier, from the skittish nibble of the smallest trade to the market-stopping, tsunami wave created from a massive scramble for shares, from individual impulse buy to crowd frenzied sale. Whenever an investment is traded, wherever the crowd rushes a counter, any time an order or group of orders is executed, the activity creates waves. The waves form patterns. The patterns ripple on a sea, a sea of activity that is mathematically verifiable, even predictable.

For the rule, the way, to be valid, the law should account for the history of a thing. Earnings are reported at set points in time. Sales recur from year to year. Shortages arise. Waves are set by fad, by season, by recurring or nonrecurring limits to supply, whatever, for any given investment. The law must be able to account for these recurring waves. From lark to shrewd buy, fad to fashion, vogue to trend, there is safety in numbers; people buy in droves. They flock to counters in waves. Certainly there must be a cadence, a rhythm, to the waves that repeat from day to day, quarter to quarter, season to season, year to year. Even where a one-time shortage drives price through the ceiling, the jolt must ripple through the markets. There ought to be some means to log this ripple mathematically, especially if there is any chance that the event might occur again and initiate its own cadence through time.

To be valid, the rule, the law, must also be customizable. It must be able to be molded, tailored, for each particular investment without intervention, without maintenance. Set in motion at investment beginnings, the rule, the law, should regulate price movement, the ratcheting up and down of price without intervention.

A theoretical example: Last year, the harvest of corn set a record, driving price to historical lows. This year, corn production is above normal, but the harvest does not drive price quite so low because this year the corn is in shorter supply relative to last year. Superimposed on a single-year graph of supply and demand, the initial waves created for the two years must coincide. They must be similar. The harvests occur at the same time of year. But the demand for corn this year is higher because there is less corn to go around. In the wave created for the current year, the demand for corn, the impetus, the initial impulse, is stronger. Things being equal, the wave generated in the current year will be higher (have a higher frequency) and be of shorter duration because demand is higher; therefore, it will propagate differently from the wave generated the preceding year.

When one then slide this year’s wave forward to place it in proper chronological order on a two-year graph, he notices that last year’s wave is dampened as it has been subject to one year’s worth of attenuation. One can justify the thought of attenuation as he observes recurring waves in nature. From general observation, when one jumps in the water, the initial wave created is higher than its recurring ripple. In the corn example, one can think of the ripple effect resident in the attenuation of last year’s buying wave as the remembrance of last year’s crop results through time. This year, the ripple effect will be visible as the remembrance of last year’s crop results relative to the anticipation of this year’s buying spree. Like the dissipating effect of friction on a body in motion, the attenuating wave of last year’s shockingly high corn production wanes as its remembrance and importance fade in memory. In forthcoming years, the importance of last year’s bumper crop will be dampened. Last year’s surge will have less and less influence on future buying decisions, unless, of course, the frequencies of the oscillations of two or more waves happen to coincide, happen to reinforce one another at some point in the future.

The wave set up by this year’s corn crop will be similar to that of last year’s bumper crop, but its phase will be different. The waves will be similar, but because their initial energies are different and because the first year wave has been subject to attenuation, the waves will not propagate in the same way moving forward. However, as they propagate forward, the differing oscillation rates for the two waves will reinforce, modify, or cancel one another from time to time.

Standard waves will overlap as varying period oscillations overtake one another from time to time. The two waves cited above are similar (year to year), so the two waves will tend to reinforce each other at certain points in time due to overlapping oscillations and the mechanical phenomenon of harmonics. Harmonic waves are found everywhere. They are encountered in music. The vibration of a guitar string when applying light pressure at certain octaves and then releasing the string while plucking one end will initiate sound waves that will cause the string to vibrate freely on both sides of the pressure point and create an overtone that is the sum of the propagation of both sides. At times these oscillations will reinforce one another as the crest of one wave overtakes that of another. At times the waves will cancel as the crest of one achieves the trough of a counterpart. The combined action creates overtones that are the sum of the propagation of the waves within their respective portions of the string. The pluck of the string, of course, is but one strike. A surge in demand at the investment counter stems from many such strikes, in sum, a cacophony where each and every note struck is free to vibrate through the end of the piece.

Harmonic waves are mathematically quantifiable as integer multiple components of base waves, equally divisible wave segments that seem driven at higher energies than standard wave oscillations. As integer multiples, harmonic waves can be anticipated along Abacus Road®. Harmonic waves graphed in one time frame (hourly, daily) may coincide with a price surge in a shorter time frame.

Any investment that has traded for more than a short while will develop repetitive vibrations, repetitive wave structures. While some waves may be generated seasonally from year to year, the wave that is generated on a yearly basis does not preclude the creation of wave patterns generated in shorter time periods: month to month, week to week, day to day, moment to moment. But how can any one mathematical rule, any numerical law, encompass so much commotion, all this jitter? Like muons bouncing around in a metaphysical soup, the whole system must dance with chaotic abandon. Yet given the commonality of accounting periods, the seasons, the way in which man moves, there must exist some answer. If the investment activity from one year can be quantified mathematically, why not multiple years, multiple days, multiple moments in time? There must be some means to create a complex algorithm, a mathematical progression, regression, amalgamation, or other conglomeration to explain the chaotic way in which the waves interact, the way investors behave in the determination of price.

For the rule to be valid, there must be some means to capture the wave effects of amplitude, attenuation, recurrence, harmonics; there must exist some coincidental nature, some common denominator. The waveforms are similar. The time periods in which they exist are similar, even constant, month to month, year to year. Surely there must be a means to quantify the waves, to quantify their actions based on observation. Perhaps one could place the waves in tile format over a logarithmic time scale to see if there might be some constantly recurring theme in their motions that would explain the interrelationship between supply and demand in the determination of price. Perhaps we could assemble the waves that occur from year to year, period to period, in cascading fashion to see if their juxtaposition might generate some overlap in their oscillations at near and distant points that would reflect the true movement of price. Perhaps we could overlap the waves in seriatim to discover some recurring continuity, paint a pretty picture, like shingles on a roof. Of course, to be valid, the serial nature must mimic the results of the real world.

Few things in nature are random. Organisms rely on one another for survival. They rely on one another as food, as shelter, to cull excessive or diseased populations. Populations initiate, grow, expand, overpopulate, exceed the available range, and then decline, fall prey to the four horsemen. Stronger for the experience, the few that remain begin anew.

From heartbeats to wing beats, everything in the living world pulsates. Even the rings of a tree that respond to the change of seasons pulsate. The warmth that is spring excites the cambium layer to put down an abundance of thin-walled cellulose building blocks for easier transmission of nutrients to and from the canopy; the scarceness that is fall causes the layer to withdraw, to produce dense reinforcing layers in the wood to harden the organism against adversity. From heartbeats to wing beats, regardless of their differences in propagation — add, subtract, multiply, divide — everything endowed with life in the universe, and some things that are not like winds, tides, pulsars, protons, neutrons, electrons, muons, and neutrinos; everything vibrates, everything pulsates, everything generates waves. Matter itself has been defined as no more than a conglomeration of energy waves. Energy at rest, energy in motion, all actions of the waves are natural; they simply must be quantifiable.

For the rule to be valid, the law itself must be both provable and be reproducible. The rule must be easily assimilable for use in legal argument as well as regulatory defense. The law must be readily verifiable; yet, because it is a regulatory tool, the law, the formula, must be sufficiently complex, adequately sophisticated at conception to preclude its discovery by the general investing public. After all, those who direct financial markets wouldn’t want the common investor to understand the ways and workings of the world now, would they? To be proper then, the law, the formula, should be inaccessible to all but a few savvy professionals.

ABACUS ROAD® MEETS THE CRITERIA

To facilitate an understanding of the mathematical construct that is Abacus Road® and to prove its importance to world commerce, one needs to familiarize himself with a few basic principles regarding crowd psychology, wave theory, institutional program trading, and modern, computerized, electronic charting methods.

Before the advent of the modern computer, simple statistical averages of price were developed in an attempt to establish a universal rule to anticipate how price might trend over time. This led to the development of fixed and exponential (front loaded) moving averages of price over daily, weekly, monthly, and yearly time frames. The most universally accepted became the 50-, 100-, and 200-day moving averages. These averages are common to any discussion of investment price today. Astute investors compare short-term moving averages of price against long-term moving averages to judge whether investor interest in a stock or commodity is on the rise or in decline, but something more is needed. Moving averages are static; there is no throughput to simple moving averages. They generate no direct rule of anticipation.

In 1977, Gerald Appel created the Moving Average Convergence/Divergence (MACD) indicator. The MACD is in essence the difference that results when subtracting a simple twenty-six-period moving average of price from a simple twelve-period moving average of price. The MACD quickly became a standard indicator for measuring investor activity; however, like a simple moving average of price, the MACD by itself doesn’t express the true habits of the buying public, especially during the frantic buying periods one encounters around extreme highs and intense lows in price. Nor does the MACD express any degree of anticipation as to where price might be headed. How could investment sleuths outsmart the market and forecast future trends, such as stock sector rotation or commodity rotation using the MACD alone? The MACD is an example of a static, where-we-are-at-the-moment type of indicator. It does not catalogue seasonal or historical investment events. Still, this indicator waveform does impart a high degree of reliability of momentary investment supply relative to demand in weekly or longer time frames.

Perhaps it is the rate at which price moves that is the key. Price rate of change is an age-old statistical indicator. However, it also is too static. When graphed, price rate of change provides little in the way of information, more at data. The indicator can be viewed in seriatim to provide a wavelike pattern; however, the recurring sine waves generated neither flow with nor represent investor sentiment. There is no humanity, no warmth expressed in the resultant graph, just a simple, statistical portrayal of how fast price moves up and down through time. Price rate of change is unimportant. No need to delve further; no need to provide a graphic example. C’est mort.

Governments, investment houses, market makers, and other professionals need a statistical tool to help them forecast future investment trends based on investor response to current and historical investment performance. They need the ability to reliably anticipate the way in which price will move in the future. The way does exist to log investor response. Investor response can be reduced to mathematical formula, a common, simple average of price fluctuation and its significant derivative.

Psychologist Dr. Alexander Elder, in his excellent book Trading for a Living, explains that the rush experienced at the investment desk is natural and has its roots firmly planted in crowd psychology.1 To expand, the rush at the investment desk is mirrored by the rush at the grocery when one customer heads for the counter followed by everyone else, each bent on beating the crowd to the door. (Life isn’t so random after all.) The crush for investments is mirrored also by populations that expand under an improved nutrient supply; they multiply and outstrip their food source only to experience massive die-offs from overpopulation. The populations accumulate and experience exponential growth just before collapse. A few survive the ordeal, and the process begins anew.

These are natural phenomena that pulse and throb in the same fashion, like the flash of a strobe and the recharging of its battery, the slip at the fault and the tsunami that covers the globe. All such form a part of the universe; all create waves as they go.


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Whether they understood wave theory or not, investor magnates at the turn of the twentieth century understood buyer psychology and became practitioners of the sequential nature of price waveforms long before the advent of modern computers. There can be little question that early twentieth-century entrepreneurs like J.P. Morgan and Bernard Baruch understood human sentiment and followed periodic averages of price similar to the twelve/twenty-six-period MACD. They must have understood that the crux, the essence of investing success lay not in the static statistical analysis of price (where price resides from moment to moment) but in the way in which price moves, a resonant, fluid approach.

As computers became smaller and less costly, brokerage houses, trust companies, mutual funds, and hedge funds were able to afford machines that could closely monitor the investment portfolios of a public that seemed ever bent on increasing its ownership share in world capital markets. Today, standard indicators are applied en masse by shrewd financiers and rogue speculators alike. From moving average, to MACD, to price rate of change, there are more than fifty standard indicators commonly in use today that, when augmented by fundamental analysis of earnings, inventories, tax implications, competitive practices, anon, help investment managers perform their jobs with great dexterity. With advancing computer capability, the few smart managers that understand the way in which price moves (Peter Lynch, Warren Buffet, George Soros) have profited handsomely. The fundamentalists who peruse earnings reports and monitor market sectors alone have excelled, but they have not realized their true potentials. Even the average manger and private investor have gotten by, but it is the lemmings that die in droves at the cliffs. The lemmings follow the crowds, they are late to all the parties, they know little of computers, and they know little if anything about earnings reports and inventories. By way of example, a senior preferred customer service representative at one of the most highly recognized electronic trading services (that shall remain nameless) unabashedly confided in the author, “Only 10 percent of our investors make money!” This at the gold preferred customer level. Outrageous! The lemmings have no idea whatsoever that investor psychology and wave theories even exist. It is the lemmings that die in droves, especially at the cliffs.

Most brokerage houses, financial institutions, and serious investors rely heavily on computerized electronic graphs and charts to monitor their investments. In a world where global news events are reported instantaneously and the trend in international financial markets is toward twenty-four-hour trading, current electronic financial software provides real-time oversight of investment portfolios, a necessity where investment prices remain in a constant state of flux.

Today, with high-speed Internet hookups, even home computers can accumulate fast-changing investment prices on a real-time, moment-to-moment basis much more efficiently than in the past. Newer, sophisticated software programs accumulate and store the data on high capacity hard drives, manipulate the data, then recalculate and redeploy price information on a real-time basis over any time frame desired. Standard minute-by minute, hourly, and daily time frames are the norm; however, more sophisticated programs can display odd time frames like 130 minutes, thirteen days, or twenty-six weeks, simultaneously. They can screen multiple charts of one or more investments over these time frames and instantly plot moving trend indicators directly over the charts to facilitate forecasting future price movement. Thanks to improved monitoring capability, investors can obtain a true picture of how their investments are faring over short and long-term frames. They can compare their investments against others on the same exchange or within the same market sector. They can compare their investments against alternative, unrelated positions to be certain of maximizing investment returns. The software not only provides individual graphs and charts of price and price movement, but also the graphs and charts can be overprinted simultaneously with numerous volume and trend indicators that give portfolio managers a means to anticipate price movement based on past price performance and current supply-demand trends.

Investor buying patterns logged around the first of the twentieth century ultimately lead to the formula depicted by Abacus Road®. When it was created, the Road was difficult for the average investor to discover. The formula was sufficiently complex. It was difficult to decipher its outwardly chaotic nature. Currently, only a few are aware of the concept. But the element of secrecy regarding Abacus Road® erodes through time.

Notwithstanding promises by mutual funds and trust companies to crush day traders, the advent of the modern desktop computer places the capability to assess one’s investments literally at the doorstep of any investor. Today, even the lemmings have an ability to compete. Continuous, real-time construction of the Road is possible using current investment software. Monitoring the effects, the brilliance of the formula is available to anyone willing to invest in a PC, an Internet hookup, and advanced investment software. With the Road, there is hope.

From the initial propagation of a single sine wave generated by the first trade to a massive     [Words Witheld]     . Abacus Road® is born. With knowledge of the Road, it is possible for shrewd investors to model and easily predict man’s movements into and out of markets with a great deal of reliability.