Mendelbrot had the problem pegged long ago, chaos and randomness…there has been no real explanations because a degree of randomness exists in the market and it is difficult to account for irrational behavior, or market noise.
I am a fairly opinionated fellow and felt like I would like to express my ideas of financial events but felt “The Fractal Trader” should be devoted to matters pertaining to trading and theory. So, Voila! You can now here me rant and rave, if you choose to, at The Fractal Traders Commentary.
Hope you enjoy it and laugh some and get mad some. I will be adding articles periodically.
OK, I see that Scott Sumner has written an open letter to me. But I’m puzzled. He writes:
I think you have acknowledged that there is some level of quantitative easing that would boost demand. If I am not mistaken you are concerned that if such a policy boosted inflation expectations sharply, the Fed would have to quickly sell off these assets, suffering massive capital losses.
Um, you are mistaken. I’ve never said such a thing. Did you mean to address this letter to someone else?
My view, which I thought was pretty clear, is that the liquidity trap is real: no matter how much the Fed increases the monetary base, it has no effect, because it just substitutes one zero-interest asset for another. If the Fed could credibly commit to inflation at rates higher than the 2-ish percent target it’s already believed to have, that would be effective. But right now I don’t see that as a realistic option, hence the emphasis on fiscal policy and bank recapitalization.
Source of some of this article is Wikipedia.
A fractal is generally “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,”[1] a property called self-similarity. The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning “broken” or “fractured.”
A fractal often has the following features:
* It has a fine structure at arbitrarily small scales.
* It is too irregular to be easily described in traditional Euclidean geometric language.
* It is self-similar (at least approximately or stochastically).
* It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).
* It has a simple and recursive definition.
Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, and snow flakes. However, not all self-similar objects are fractals—for example, the real line (a straight Euclidean line) is formally self-similar but fails to have other fractal characteristics.
Benoit Mandelbrot, in one of his pioneering articles on the problems with linear based market predictions states:
“The risk-reducing formulas behind portfolio theory rely on a number of demanding and ultimately unfounded premises. First, they suggest that price changes are statistically independent of one another: for example, that today’s price has no influence on the changes between the current price and tomorrow’s. As a result, predictions of future market movements become impossible. The second presumption is that all price changes are distributed in a pattern that conforms to the standard bell curve. The width of the bell shape (as measured by its sigma, or standard deviation) depicts how far price changes diverge from the mean; events at the extremes are considered extremely rare. Typhoons are, in effect, defined out of existence.
Modern portfolio theory poses a danger to those who believe in it too strongly and is a powerful challenge for the theoretician. Though sometimes acknowledging faults in the present body of thinking, its adherents suggest that no other premises can be handled through mathematical modeling. This contention leads to the question of whether a rigorous quantitative description of at least some features of major financial upheavals can be developed. The bearish answer is that large market swings are anomalies, individual “acts of God” that present no conceivable regularity. Revisionists correct the questionable premises of modern portfolio theory through small fixes that lack any guiding principle and do not improve matters sufficiently. My own work – carried out over many years – takes a very different and decidedly bullish position”
Okay, okay, you are shaking your head what in the world does this have to do with actual investing? Yea, yea…there are lots of these little duplicating irregular shapes, but how does this help me?
I borrow again from Benoit Mandelbrots earlier article:
“In a detail of a graphic in which the features are higher than they are wide – as are the individual up-and-down price ticks of a stock – the transformation from the whole to a part must reduce the horizontal axis more than the vertical one. For a price chart, this transformation must shrink the time-scale (the horizontal axis) more than the price scale (the vertical axis). The geometric relation of the whole to its parts is said to be one of self-affinity.
The existence of unchanging properties is not given much weight by most statisticians. But they are beloved of physicists and mathematicians like myself, who call them invariances and are happiest with models that present an attractive invariance property. A good idea of what I mean is provided by drawing a simple chart that inserts price changes from time 0 to a later time 1 in successive steps. The intervals themselves are chosen arbitrarily; they may represent a second, an hour, a day or a year.
The process begins with a price, represented by a straight trend line (illustration 1). Next, a broken line called a generator is used to create the pattern that corresponds to the up-and-down oscillations of a price quoted in financial markets. The generator consists of three pieces that are inserted (interpolated) along the straight trend line. (A generator with fewer than three pieces would not simulate a price that can move up and down.) After delineating the initial generator, its three pieces are interpolated by three shorter ones. Repeating these steps reproduces the shape of the generator, or price curve, but at compressed scales. Both the horizontal axis (timescale) and the vertical axis (price scale) are squeezed to fit the horizontal and vertical boundaries of each piece of the generator.
Interpolations Forever
Only the first stages are shown in the illustration, although the same process continues. In theory, it has no end, but in practice, it makes no sense to interpolate down to time intervals shorter than those between trading transactions, which may occur in less than a minute. Clearly, each piece ends up with a shape roughly like the whole. That is, scale invariance is present simply because it was built in. The novelty (and surprise) is that these self-affine fractal curves exhibit a wealth of structure — a foundation of both fractal geometry and the theory of chaos.
A few selected generators yield so-called unifractal curves that exhibit the relatively tranquil picture of the market encompassed by modern portfolio theory. But tranquillity prevails only under extraordinarily special conditions that are satisfied only by these special generators. The assumptions behind this oversimplified model are one of the central mistakes of modern portfolio theory. It is much like a theory of sea waves that forbids their swells to exceed six feet.
The beauty of fractal geometry is that it makes possible a model general enough to reproduce the patterns that characterize portfolio theory’s placid markets as well as the tumultuous trading conditions of recent months. The just described method of creating a fractal price model can be altered to show how the activity of markets speeds up and slows down — the essence of volatility. This variability is the reason that the prefix “multi-” was added to the word “fractal.”
To create a multifractal from a unifractal, the key step is to lengthen or shorten the horizontal time axis so that the pieces of the generator are either stretched or squeezed. At the same time, the vertical price axis may remain untouched. In illustration 2, the first piece of the unifractal generator is progressively shortened, which also provides room to lengthen the second piece. After making these adjustments, the generators become multifractal (M1 to M4). Market activity speeds up in the interval of time represented by the first piece of the generator and slows in the interval that corresponds to the second piece (illustration 3).
Such an alteration to the generator can produce a full simulation of price fluctuations over a given period, using the process of interpolation described earlier. Each time the first piece of the generator is further shortened — and the process of successive interpolation is undertaken — it produces a chart that increasingly resembles the characteristics of volatile markets (illustration 4).
What should a corporate treasurer, currency trader or other market strategist conclude from all this? The discrepancies between the pictures painted by modern portfolio theory and the actual movement of prices are obvious. Prices do not vary continuously, and they oscillate wildly at all timescales. Volatility — far from a static entity to be ignored or easily compensated for — is at the very heart of what goes on in financial markets. In the past, money managers embraced the continuity and constrained price movements of modern portfolio theory because of the absence of strong alternatives. But a money manager need no longer accept the current financial models at face value.
Instead multifractals can be put to work to “stress-test” a portfolio. In this technique the rules underlying multifractals attempt to create the same patterns of variability as do the unknown rules that govern actual markets. Multifractals describe accurately the relation between the shape of the generator and the patterns of up-and-down swings of prices to be found on charts of real market data.
On a practical level, this finding suggests that a fractal generator can be developed based on historical market data. The actual model used does not simply inspect what the market did yesterday or last week. It is in fact a more realistic depiction of market fluctuations, called fractional Brownian motion in multifractal trading time. The charts created from the generators produced by this model can simulate alternative scenarios based on previous market activity.
These techniques do not come closer to forecasting a price drop or rise on a specific day on the basis of past records. But they provide estimates of the probability of what the market might do and allow one to prepare for inevitable sea changes. The new modeling techniques are designed to cast a light of order into the seemingly impenetrable thicket of the financial markets. They also recognize the mariner’s warning that, as recent events demonstrate, deserves to be heeded: On even the calmest sea, a gale may be just over the horizon.
Many people believe that the markets are random. In fact, one of the most prominent investing books out there is “A Random Walk Down Wall Street” (1973) by Burton G. Malkiel, who argues that throwing darts at a dartboard is likely to yield results similar to those achieved by a fund manager (and Malkiel does have many valid points).
However, many others argue that although prices may appear to be random, they do in fact follow a pattern in the form of trends. One of the most basic ways in which traders can determine such trends is through the use of fractals. Fractals essentially break down larger trends into extremely simple and predictable reversal patterns. This article will explain what fractals are and how you might apply them to your trading to enhance your profits.
What Are Fractals?
When many people think of fractals in the mathematical sense, they think of chaos theory and abstract mathematics. While these concepts do apply to the market (it being a nonlinear, dynamic system), most traders refer to fractals in a more literal sense. That is, as recurring patterns that can predict reversals among larger, more chaotic price movements.
These basic fractals are composed of five or more bars. The rules for identifying fractals are as follows:
* A bearish turning point occurs when there is a pattern with the highest high in the middle and two lower highs on each side.
* A bullish turning point occurs when there is a pattern with the lowest low in the middle and two higher lows on each side.
The fractals shown in Figure 1 are two examples of perfect patterns. Note that many other less perfect patterns can occur, but the basic pattern should remain intact for the fractal to be valid.
Applying Fractals to Trading
Like many trading indicators, fractals are best used in conjunction with other indicators or forms of analysis. Perhaps the most common confirmation indicator used with fractals is the “Alligator indicator”, a tool that is created by using moving averages that factor in the use of fractal geometry. The standard rule states that all buy rules are only valid if below the “alligator’s teeth” (the center average), and all sell rules are only valid if above the alligator’s teeth.
I am a scalper, so I am not terribly interested in long term trends, Elliot Wave theory or any market trading technique that requires me to think ahead much more than one half day. That is to say that I am trying to carve out 2 pts. or more out of intraday directional movement. I truly believe that the market is random, so when I use the word “trend” I am not using in the sense that a technical trader would. The truth is, I use the “trend” for lack of a better word to describe intraday directional movement.
Since the market moves in many random ways, my trading method only seeks to take advantage of a tendency for people “hop on the bandwagon”. People will generally watch the market and jump into a trade when they see it heading one way or the other, and they generally stay in the trade too long. People tend develop strong emotional ties to a trade they make. They get into the mindset that the market “ought” to do something based upon some information they have gleaned, or some event that has occurred or is occurring. From the onset, let me say that the market does not “have” to do anything and freeing yourself from this mindset will greatly improve your trading. The markets are not rational, and you will drive yourself crazy trying to rationalize the movement you see unfolding on your chart.
Since I believe that the market moves randomly via fractals, or fractal movement, I do not believe that identifiable patterns form. This always gets my technically oriented friends in a ruffle, and I am often cursed for this belief. An overwhelming amount of evidence has been collected by academics to prove that the market is random that it is difficult for me to fathom that some people trade with chart patterns. By chart patterns I am talking about the species of technical formations typified by “head and shoulders patterns, pennants, double tops, double bottoms, etc” In short, I do not use any chart patterns in my trading.
On the other end of the spectrum, I do not have any use for fundamental trading either. For scalping, it should be self evident that we do not use fundamental principles. If they actually worked, most fundamentals take at an intermediate period of time to develop. My trades are anywhere from 1 minute to 30 minutes….I have been in very few trades longer than thirty minutes. But I’ll go a step further on this topic and offend all the disciples of Ben Graham and Modern Portfolio Theory….I think it’s about as valid to use as chart formations. Note to self: Is the screaming and yelling I am hearing from the back of the room? Are they throwing things at me yet?
My thesis for rejecting Modern Portfolio Theory is really simple: just because a company is well run, has products of high quality, and a healthy cash flow does not mean that the stock price will go up…just look at Cisco for the five years before it’s big move last year. Here was a company that was doing everything right but the stock price stayed pegged at around $20 for years, and there are countless examples of this being true. So I don’t use P/E ratios, beta coefficients, alpha coefficients and all the other investment terms that go hand in hand with this style of investing.
No, what I like are little spurts of unpredictable momentum. Other than fractal theory, there is no viable explanation for the gentle (and sometimes violent) rocking pattern that is part of every chart. Of course, the problem has always been ascertaining when these little bursts of momentum take place. How can you time your entry and exit points to take advantage of rocking (or swaying) that is on every chart? How do you know which sway is going to be 5 pts and which one will be a sideways move?
I have taken the liberty of drawing a dark line so you can see the swaying action in the market, and you will notice that some market moves are very short and some are very long. How do we get into the market for the long moves, and stay out of the short moves?
So…..now that I have offended every modern day investment theory out there…lets talk some about what I DO…INSTEAD OF DWELLING ON WHAT I DON’T DO.
There are many things I keep in mind when I trade, but I have 4 rules that I never deviate from. Some of these rules were hammered into my head by my mentor nearly 20 years ago, others were learned the hard way- through experience.
1. Never trade without stops in place. I can’t imagine a trader trading without a stop order in place, and am amazed when I talk with other traders at how many trade without placing stops. I suppose you might try to justify trading without stops by saying that you are sitting right there at the computer and will be able to trade out of any position before you can get in trouble. This is not true….without stops you have no way to account for the lightening fast moves that can come about from catastrophic news…The ES contract moved 71 pts in one 1 minute bar after one of the last rate cut announcements. Granted, you can have a move gap through one of your stops, but this is so rare as to have only happened to me once. Even on the 71 point move I was able to exit with a stop executed. Without stops you are taking excessive risk. Also, the stop is also a mental stop. As I have said, traders can become emotionally attached to their positions and the stop serves to remind them that they are getting out of the market whether they like it or not.
2. Never let a winning trade become a losing trade...this is one of the most difficult things to learn. When do you pull the trigger to exit? Of course, there are many oscillators that can give you a pretty good idea when the trade is over….but I have watched trader after trader get 3 points up and become convinced that market is going through the roof. It seldom does, and what generally happens is the trader rides the trade right back down to breakeven or a losing position. We will talk at length about how to avoid this….but exit strategy is seldom easy. And for those of you wondering, I can’t stand trailing stops.
3. Avoid trading against the trend…but if you must, cut the number of contracts you normally trade in half. I chant “the trend is my friend” twenty times before going to bed every night. And I still make bad trades, almost always against the trend. How do you know what the intermediate and short term trends are? I make it easy, I chart an 89 period Simple Moving Average and when the price is above the moving average I concentrate on long trades, and conversely, when it is below the 89 period average I concentrate on short trades…this silly little rule will save you money.
4. Be on the right side of the trade…have you ever done this? You have considered a trade carefully after watching it set up exactly the way you dream of. Everything is perfect, except the trade skitters sharply the wrong way when you execute. Most traders will watch the price crash into their stops and chalk it up to experience. You don’t have to be stopped out on every losing trade. If the darn thing looks like a dog out of the gate, and your oscillators even confirm this, get out….I’ll say it again, you don’t have to ride every trade into your stops. It takes a tremendous amount of ego reduction to do this….you have to admit to yourself that you were dead wrong from the onset and take a smaller loss than hitting your stops. It not as easy as it sounds.
I generally trade from 6:30 a.m. until about noon, and today I am stopping at 11:00 a.m. I had emergency hernia surgery three days ago and feel like I am losing my mental edge on the market. I usually trade the ES contract pre-open, and then switch to the NQ contract once the markets are open and settle down some. The NAR released data this morning that suggested that some relief might be in sight for the housing problems that have been a component in the markets recent volatility.
As a trader I am not particularly concerned about data in the report, only what kind of impact the news will have on the markets or, more importantly, how the other traders will react to the news in the report. It is not unusual for the market to receive news and react instantly then take a moment to digest the information and turn the other way. This phenomena is especially true on the reports released before the opening, usually at 7:30 a.m. Of course, it’s important to keep abreast of when these reports and announcements will be released and tread very lightly as they become public. Since it is not unusual for the markets to gap up or down as the information becomes available, stops are of little value. I prefer to not to be in the market when the news is about to be released…..but I will have OCO orders bracketing a position to take advantage of the exaggerated movement in the market, if there are any.
I run my stops in the 12 tick range and set multiple profit targets so I can take advantage of any exaggerated movement that may occur unexpectedly. Like most traders, I want my trades to run, if possible….of course, I am usually looking for the fractal-type configurations to formulate my exit strategies. I also calculate pivot points, but use a logarithmic methodology to avoid the straight line mentality you will hear me rail about. I will calculate the Fibonacci retracement levels in a run, but use them with guarded reliance, as they are irrelevant on many days. On the other hand, especially days that are low volume and traded very technically, the market may follow the Fibonacci levels to the tee. Of course, I am always drawing support and resistance levels as they become obvious…..add some Bollinger bands, CCI and mathematically altered MACD oscillators and I am set. I do not use trend lines, or any other linear type calculation.
Today was a relatively easy day to trade as the market moved for extended periods of time in one direction, which is a traders dream. I captured 11 points @ 10 contracts.
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