Tuesday, December 20, 2005

Jesse Livermore - Part I

Jesse Livermore is a genuine legend of Wall Street. He experienced cycles of Jesse Livermore is a legend of Wall Streetmonumental success and catastrophic failure on a scale unimaginable to most of us. He had the iron discipline to follow his trading plan to spectacular rewards when everybody else said he was wrong. He let his emotions for the approval of others run him ahead of his instincts into perdition's dark abyss. At other times he did everything right and still lost it all when what he could not control in his life went terribly wrong.

Jesse Livermore ran away from home and a future as a rural farm hand at the age of fifteen. He started his financial career, more from necessity than plan, by posting stock quotes at the Paine Webber brokerage in Boston. While working as a board boy he noticed repeating patterns in the ebb and flow of the stock prices he chalked onto the board. He watched how the people in the room reacted to those ebbs and flows, took notes, and learned. Impressed by his discoveries a friend encouraged Livermore to make his first stock trade. Livermore invested $5. The trade was profitable and convinced of his success he quit his board boy job and started trading for himself.

Before his sixteenth birthday he had amassed a little fortune of over $1,000 (more than most people made in a year in the 1890's). Livermore spent his adolescence growing his skill and his nerve in the Boston and New York bucket shops. These bucket shops were storefront and back room casinos where people wagered on ticker tape prices. No stocks were bought or sold. The house kept all the money and paid off winners accordingly. Most people lost their money to the bucket shops. Livermore regularly beat the bucket shops and as his reputation grew he was eventually banned from them. He moved from the bucket shops to the Big Board. What worked at the bucket shops didn't play on Wall Street. Within six months of the start of his legitmate trading career Livermore was wiped out. Did he quit? No. He learned from his mistakes. He adapted to his new environment and continued a success.

During his lifetime Livermore gained and lost several million dollar fortunes, sometimes wiping out his entire trading account in a single day. He once lost $50,000 in a day making the right calls against what turned out to be a slow and misleading ticker tape. He lost $3 million on a cotton trade after abandoning his winning position on "expert" advice. Despite a string of catastrophes that would crush the spirit and self-confidence of so many, the young Livermore was able to find something in himself that would not accept failure as anything other than a lesson. "The game taught me the game. And it didn’t spare the rod while teaching."

Livermore's net worth was more than $100 million after the 1929 market crash, an enormous sum even in today's inflated dollars. Personal tragedies began to overwhelm Livermore at his zenith. The unflinching spirit that stood against the wealth and power of Wall Street's barons was subdued by the caress of a destructive relationship. His fortune dissipated, Jesse Livermore committed suicide in a New York hotel room in 1940.

Jesse Livermore - Part II will focus on Livermore's systematic and disciplined approach to market timing.

Wednesday, November 30, 2005

Fibonacci Pinball

The picture shows a type of pinball machine that you can build yourself. You will need 10 finishing nails, 5 small cups, a wooden board and a pinball (marble). Nail the nails part way into the board in the triangular pattern shown, with one nail in the top row, two in the second, three in the third and so on, and with enough space for the pinball to fit between the nails.

To operate the machine, tilt the board at a slight angle and release the pinball so that it hits the top nail dead center. If the machine is not tilted the pinball will be deflected either left or right with equal probability by the first nail. It will then continue falling and hit one of the nails in the second row and be deflected either left or right around that nail with equal probability.

The result is that the pinball follows a random path, deflecting off one pin in each of the four rows of pins, and ending up in one of the cups at the bottom. The various possible paths are shown by the gray lines and one particular path is shown by the red line.

How many random paths are there through your pinball machine, and what are they?

The answer is 16. The brief explanation is:

The first row has one pin. The number of possible paths through the first row = 2.

The second row has two pins. Since what happens in the second row is completely independent of what happened in the first row, the number of possible paths the pinball could travel from the top through the second row = 4 (2 x 2).

The third row has three pins. Since what happens in the third row is completely independent of what happened in the second row, the number of possible paths completed from the top through the third row = 8 (2 x 2 x 2).

The fourth row has four pins so the number of possible paths from the top through the fourth row = 16 (2 x 2 x 2 x 2).

If you drop 16 pinballs into the top of your machine and repeat that event one million times, what is the average number of pinballs per event that will fall into each cup at the bottom? The answer, from left to right, shown in our pinball machine image below is 1-4-6-4-1. The image to the right is known as Pascal's Triangle. Pascal's Triangle is very useful for analysing the pinball machine. Pascal's Triangle also pops up in a variety of other seemingly unrelated areas. First we mention that the triangle continues on forever and we have only shown the first five rows. Can you see the pattern and guess what the next row of numbers is?

If we superimpose Pascal's Triangle on top of the pinball machine then we see the connection between the two: Each number of Pascal's Triangle represents the number of distinct paths that a pinball can take to arrive at that point in the pinball machine. Without knowing any more at this point it is still fair to say that Pascal's Triangle is a logically ordered description of the outcome of a series of completely random events.

Although Pascal did not discover the sequence of numbers that bears his name, the origin is believed to be hundreds of years earlier in China, he did popularize the sequence in the 17th century from his research, of all things, on improving his betting odds at the gaming tables. If Blaise Pascal were around today he would probably be running some hundred billion dollar derivative heddge fund that kept the Fed Chairman up at nights.

Pascal's Triangle is an oddity. The construction of the triangle is simple. The numbers on each new row are derived by adding the numbers immediately above and to the right and left. We use letters to make words, words to make sentences, and sentences to tell stories that inform us. Numbers are really no different. Clusters of numbers are scale. Sequences of numbers are a process. For us numbers are abstract symbols but to the Pythagoreans numbers had an actual form and a shape. The dots on the right side of the page are the number 34 - a triangle and a square. Sometimes it is useful to think of numbers, including stock and commodity prices, as shapes and forms. Shapes occupy space. They have scale. And they reside in time.

Here's an image of Pascal's Triangle filled out to ten rows.

It looks interesting. But so what? That would be the normal and expected reaction from a generation with hundreds of years of learning that numbers are only abstract symbols used as a convenience to measure something else that is tangible and real. But wait. Didn't we say that Pascal's Triangle is a logically ordered description of the outcome of a series of completely random events? Could there not also be a hidden order within the description itself?

It gets curiouser and curiouser but finally we arrive. Maybe even back to the beginning. When you add the diagonal rows of Pascal's Triangle. Left to right and right to left. You derive the sequence of Fibonacci ratios.

The deeper you get into the heart of Pascal's Triangle the closer you get to the Divine Proportion. What does it all mean? Who knows for sure. Perhaps it is enough to leave with the thought that the detritus of large numbers of simple binary decisions, like the left or right of the pinball, or the buy or sell in the pits, leave footprints in space and time that may be impossible to recognize while happening but become clear enough down the road if you know where to look.

The pinball machine discussion and illustrations are from the math department at the British Columbia Institute of Technology.

Monday, July 25, 2005

Fibonacci Retracements (Part II)

Almost everybody is familiar with measuring retracements. A ticker advances 100 points and then declines by 62 points before taking off again in another rally leg.

In this case the retracement is 62%. Along with 38% and 50% (which is not a Fibonacci number) these are the most common retracement levels. For many people this all they know about Fibonacci Retracements, and perhaps Fibonacci Numbers in general, and even for them this is a good piece of information to have. If your work tells you that this pullback is most likely a temporary decline before the beginning of the next upleg, when it appears likely that the top is in at 100 you can mark your charts and watch for a reaction at the different Fibonacci levels. We call this a Reaction or Decay Retracement. During this Retracement phase Price is moving againt the major trend, and if you are correct about the direction of the major trend, price should decay somwhere between 14.6% and 78.6% before resuming its move in the direction of the major trend. Easy enough.

But Fibonacci Retracements are not limited to the garden variety Decay type. Fibonacci Numbers appear so frequently in nature because they demonstrate the pattern of change and growth. And so too can this pattern of change and growth be applied to the financial markets. In the first example we limited ourselves to describing the likely
extent of the pullback from the high at 100. In Figure 2, once the low point of decay is known, we can apply the Fibonacci growth ratios to the 62 point decline and project an advance from the retracement low price at 38 to about 100 (100%) or 117 (127%) or to 138 (162%).

For Fibonacci Retracements you always base your forecast from the measure of one swing or one leg of the swing if it's a complex pattern. For the Decay Retracement the swing was from 0 - 100. The Fibonacci Retracement was 62%. For the Growth Retracement the swing was from 100 - 38. We applied the 100%, 127% and 162% growth ratios to that 62 point swing to project future price targets.

That's two applications of Fibonacci Retracement ratios for financial forecasting. These applications occur frequently enough across all price levels and time frames to have genuine forecasting value.

Fibonacci Retracements have one more application. We use them to create what we call the "Death Zone." In Figure 2 we used the Growth Ratios to project likely targets for what we believed was the beginning of the next upleg in the direction of the major trend. Needless to say things don't always work out as planned. From experience with the major stock indexes we never take a breath or start imagining what wonderful forecasters we are until the new upleg has safely cleared the Death Zone. The Death Zone narrowly drawn is the 62% - 79% retracement zone measured from the low point of the decay phase. In this case it would be the 76 - 87 price area (see Figure 3). We call it the Death Zone because this is where many promising new swings die an early death. A broader application of the Death Zone has it from 50% - 79%.

The corollary application of the Death Zone Retracement is that any Decay Retracement that exceeds the 79% retracement level immediately becomes suspect as the start of a major change in trend and not a pullback as first believed. Under most pattern recognition methods, including Elliott Wave, retracements up to 100% of the prior swing are acceptable without causing a change in outlook. That's OK too. But we never, never take a suspected Decay Retracement that exceeds the 79% level as a normal event that can be ignored with impunity. Maybe this would be the time to lighten up on usual positions size when making the reversal trade off the suspected Decay Retracement low. All these examples cover retracements of a bull move. The exact same principles apply for bearish swings

Thursday, July 14, 2005

Fibonnaci Numbers (Part I)

What do the Great Pyramid, your credit cards, your teeth, Beethoven's 5th Symphony, moth wings, daVinci's Madonna and Child, the Parthenon, the geometrical arrangement of the solar system, and the exact way that seeds propagate on a flower (to name a few) have in common? The Golden Section, the Divine Proportion. Perhaps the most important single number in the universe - 1.618

Leonardo Pisano, a 13th century mathematician, has many significant achievements but will probably always be remembered for his rabbit counting exercise which popularized the sequence of numbers known as the Fibonacci numbers. Leonardo Pisano was the son of Guglielmo Bonacci. The shortening of the Latin "filius Bonacci" (son of Bonacci) is how Leonardo Pisano came to be known as Leonardo Fibonacci, or more simply Fibonacci

The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34... The next number in the sequence is the sum of the prior two. As the sequence gets larger the relationship between adjoining numbers gets closer to the Divine Proportion: ±0·61803 39887... and ±1·61803 39887...

So, even though this sequence of numbers will forever be known as the Fibonacci Numbers, it's not the numbers themselves that are important...it's the relationship between them that matters.

You could spend a lifetime exploring the intricacies and interconnectedness of the Divine Proportion. Here's two excellent sites to get you started. Fibonacci Numbers and the Golden Section and   The Golden Proportion

It's easy enough to go off in a tangent with this topic. For our purposes it's enough to say that we believe that the Divine Proportion is terribly important for stock market work because the human brain is hard-wired to respond to it. The stock market, indeed, every publicly traded liquid market, is a never ending succession of action-reaction, rally-decline. We can use the Divine Proportion to discover how those growth phases have related to each other in the past and how they may relate to each other in the future.

The three categories of relationships are; Retracement, Expansion and Parallel Projection. We'll get into them in the next installment.

Thursday, June 23, 2005

The Square Root Theory

References to the Square Root Theory as a predictor of stock prices pops up every now and then in financial writings. Norman Fosback used the theory in a 1976 publication called Stock Market Logic to make the case that the normal trading range of low price stocks provides greater profit opportunities than the normal trading range of high price stocks. In 1983, a book entitled The Templeton Touch, by William Proctor, disclosed that one of Templeton's 22 principles for stock market investing was that stock price fluctuations are proportional to the square root of the price.

In the 1950s William Dunnigan developed two stock trading systems called the Thrust Method and the One Way Formula. Both methods had several advantageous entry techniques but each had an absence of exit techniques. Dunnigan was above all a portfolio manager and not happy with the risk-reward aspects of his own trading methods, Dunnigan supported and publicized the Square Root Theory. He went so far as to call this theory the "golden key" and claimed recognition from some economics and statistical trade journals of the era.

The theory holds that stock prices move over the long and short term in a square root relationship to prior highs and lows. For example, IBM made a monthly closing low of 4.52 in June, 1962 and monthly closing high of 125.69 in July, 1999. This is within a few percentage points of the square of the sum of the square root of the low price + 9 or (2.12+9)^2. GM made a low of 15 in November, 1974 and a high of 95 in May, 1999. Again, a few percentage points from the square of the sum of the square root of the low + 6 or (3.87+6)^2. There are hundreds of these examples across the stock, financial and commodity markets. Even a few minutes with a pile of stock charts and a calculator will build confidence that major highs and lows are related to each other by additions and subtractions to their square roots.

Let’s go through a recent example and see how it works. The chart is Eurodollars continuous futures.

Eurodollars made a high of 1.37 on December 30, 2004. First step is to convert the actual price into a useable number so that we will not be dealing with tiny decimals. In this case multiply the actual Eurodollar price by 1,000. That makes the December high 1370. The square root of 1370= 37.01. Subtract 1 from the square root 1370 (37.01) = 36.01. Square 36.01 to get 1297. The low on February 9, 2005 was 1.28. Not bad. Now that you know the drill let’s look at the remaining swings on the Eurodollar chart.

Feb 9 low = 1.28 = 1280 = Square Root 35.77
35.77 + 1 = 36.77
36.77 ^2 = 1352. Bingo!

March 14 high = 1.35 = 1350 = Square Root 36.74
36.74 – 2 = 34.74
34.74 ^2 = 1207 = June 13, 2005 low!

Before Dunnigan and Templeton, probably starting in the early 1900s, W.D. Gann was using square roots to forecast stock and commodities prices. His method was more complex and appears to have been based on some ideas he picked up on during his trips to India or Egypt. Gann used an ennegram, a diagram of numbers constructed in such a way to show square and square root relationships. This ennegram is what’s come to be known as the Square of Nine from the Greek root “enneas” which is the word for “nine.”

Although Gann never revealed exactly how he used the ennegram we can gather from his words that it was probably very important to him: "We use the square of odd and even numbers to get not only the proof of market movements, but the cause." W. D. Gann, "The Basis of My Forecasting Method" (the Geometrical Angles course), p. 1

Thursday, June 09, 2005

Something You Didn't Know About Moving Averages

A moving average is about as plain vanilla an indicator as you can get. You can make it more complicated if you want to with weighted, geometric, harmonic, exponential, front-loaded, and double or triple smoothing variations, but the basic function of the moving average remains the same – to smooth fluctuations in time series data like stock or commodity prices.

J.M. Hurst, an aerospace engineer of 1970 vintage, saw something about stock market data that nobody else before him was able to see in quite the same way: that a stock price history was not a record of a continuously changing price, but a profile of a discrete sequence of individual numbers related to each other only by a common wedge of time. That little thought experiment made a simple moving average analogous to a digital filter that could slice stock price history into bins of frequency, amplitude and phase and, when desired, numerically recombine them into the everyday stock chart.

Such that, something like this:

Can be combined into this, which could be an extract from any of a gazillion stock or commodity charts you’ve seen over the years.

Hurst seemed to feel that if you took enough slices from different time frames of a stock’s history that you would have a high probability of determining, in advance, which of the classic chart patterns would fail or succeed at any particular time.

This isn’t a recap of Hurst’s book, The Profit Magic of Stock Transaction Timing . So much has been left out that we do the man a disservice. Hurst was first an engineer and he provided the mathematical details to support what he called his “price motion model.” If we accept Hurst’s thought experiment for what it is, that a history of stock (or commodities) prices can be sliced into discrete components of frequency, amplitude and phase, then the statement that moving averages “can be designed to clarify and allow inference of spectral status of stock prices at any given time” doesn’t necessarily have to be attributed to a cosmic alien.

Hurst’s contribution to our understanding of moving averages isn’t just that they smooth time series data. His contribution is that a properly designed moving average:

• exactly reduces the magnitude of cyclical fluctuations equal to that time span to zero;
• diminishes, but does not eliminate, the magnitude of cyclical fluctuations of periodicities less than the moving average; and
• all fluctuations of durations greater than the periodicity of that moving average stay visible with the smoothing effect diminishing as periodicity increases.

Hurst went on to say that one of the most important elements of a properly designed moving average is that it be plotted alongside a price point that is one-half the span of the moving average removed from the current or last price. That means that Hurt’s moving averages always lag the associated stock data by one-half the period of the moving average. Here’s what that looks like:

The net effect of understanding that (a) stock and commodities prices are discrete elements of a time series, and (b) that properly designed moving averages are analogous to digital filters is that the moving averages can be used to make price and time predictions of stock and commodity prices. In shameless promotion we explain how to do that in a few ways that Hurst did not show in our book J.M Hurst Cycle Trading without the Rocket Math, but even if you don’t buy our book you just have to buy J.M. Hurst’s book. It’s one of the real classics of technical analysis.

Friday, June 03, 2005

Continuation Bars

Bar charts also provide easily recognized continuation signals. If you suspect that a change in trend has occurred but for one reason or another was unwilling to commit at the turn, a continuation signal can usually get you involved relatively close to the pivot point. Continuation bars are either Outside Bars or Inside Bars.