This week’s idea is based on the concept of Fractals, popularized by Bill Williams in his books Trading Chaos and New Trading Dimensions. This is the second fractal system I have featured here on Systematic Algo Trader. The first one, SAT2021-07 Fractals 1, was successful, but it used different exit criteria. I call this one Just Fractals, because I use the fractal signal for entries and reversals. Plus, my wife came up with that name for one of her fractal systems and I like it. It amuses me.
If you are a mathematician, the word fractal in this respect probably makes your hair bristle, so let me get this out of the way. Fractals, as described by Bill Williams, are not mathematical fractals. He had to call these something, so he picked fractals. Market data is considered fractal: we are measuring the same thing, but with different levels of granularity and detail. A more accurate term for what we are doing here is pivot, but the fractal term has embedded itself in the minds and hearts of market technicians high and low, so ‘fractal’ it is.
[This explanation of fractals is a repeat of SAT2021-07, so you can skip to Step 1 if you want. I won’t be offended.]
A fractal high occurs when the highest high of five bars is on the third, or middle, bar. A fractal low occurs when the lowest low of five bars is on the third bar.
A high fractal looks like this:
- First bar High < Third bar High
- Second bar High < Third bar High
- Fourth bar High < Third bar High
- Fifth bar High < Third bar High
This is a high fractal:
A fractal low would be the opposite:
- First bar Low > Third bar Low
- Second bar Low > Third bar Low
- Fourth bar Low > Third bar Low
- Fifth bar Low > Third bar Low
Fractals can be very confusing and deceiving. If you use them on a chart, do not fall for the illusion that they can predict the future. The fractal will appear only after that fifth bar has closed and the conditions for the fractal have been met.
Fractal trading signals can be used several ways. This idea uses the fractal high as a resistance level and fractal low as a support level. When we break through resistance or support, we go long or short, respectively. Below is an example of how this is used for support and resistance (Chart: daily Euro FX futures):
This is pure counter-trend trading. Scary, but can be rewarding. There are no exits, only reversals. I will use a 1 ATR stop loss.
Phase 1: Plan & Design
1. Trading Idea
The idea is simple:
- Buy at market when if the Close is greater than the latest Fractal High
- Sell short at market if the Close is less than the latest Fractal Low
- Reverse our position if we receive a buy or sell short signal
- Profit Target: None
- Stop Loss: 1 ATR (20 period)
2. System Definition
- Futures: 1 contract
No inputs for this system, which means no optimization later.
|FractalHigh||Double||0||If High[2 bars ago] > High and|
High[2 bars ago] > High[1 bar ago] and
High[2 bars ago] > High[3 bars ago] and
High[2 bars ago] > High[4 bars ago] then
FractalHigh = High[2 bars ago]
|FractalLow||Double||0||If Low[2 bars ago] < Low and |
Low[2 bars ago] < Low[1 bar ago] and
Low[2 bars ago] < Low[3 bars ago] and
Low[2 bars ago] < Low[4 bars ago] then
FractalLow = Low[2 bars ago]
|ATR||Double||0||ATR = Average True Range over 20 periods|
- If Close > FractalHigh, then buy next bar at market
- If Close < FractalLow, then sell short next bar at market
- Stop Loss = ATR * Full Contract Size
3. Performance Objectives
The system will meet the following objectives:
|System Type (trend, mean-reversion, day, swing, etc.)||Counter-trend|
|Risk of Ruin||0%|
|Profit Factor||>= 1.3|
|Win Percent||>= 35%|
|Max Drawdown %||< 35%|
|Profit/Drawdown Ratio||>= 2.0|
This idea is S.M.A.R.T.: Specific, Measurable, Achievable, Realistic, Time-bound
4. Market Selection
|Energies||Gasoline, Crude Light, Natural Gas, Heating Oil||RB, CL, NG, HO|
|Agriculture||Soft Red Wheat, Oats, Lean Hogs||W, O, LH|
|Metals||Silver, Gold, Copper||SI, GC, HG|
Chart Type, Timeframe, Session, Time Zone:
|Chart Type||Regular Candlestick||Charting is only useful for validating entry and exit signals|
|Timeframe / Interval(s)||Daily, 360 minutes|
Phase 2: Build
5. Manual Test
I have done so much work using fractals, I am confident that this is a good idea. In this case, I have manually tested this idea hundreds of times and am confident in continuing to the Build step.
Nothing spectacular here.
7. Unit Test
The unit test was fine. Simple systems are the best, in this respect. Below is a screenshot of the system on a gasoline futures (RBOB) chart. The blue dots indicate fractal lows; the red dots indicate fractal highs.
Note: Unit Test verifies that the system is executing the trading rules correctly. It is, essentially, quality control.
Phase 3: Test
No optimization here. I could have optimized fractal strength, which is the number of bars we evaluate, but since this is called Just Fractals, I’ll be a purist and go with the classic 5-bar fractal.
9. Walk-Forward Analysis
I tested over nearly a 10 year period, from January 2011 to November 2020. All instruments failed spectacularly. This does not require a ton of analysis mainly because the best profit factor we saw 1.09, Crude Light futures (CL). Heating Oil, predictably, was very close to CL. I will explain some reasons why this failed in the Notes and Commentary section.
10. Monte Carlo Simulation
We did not make it this far.
We did not make it this far.
Phase 4: Deploy
We did not make it this far.
Trading System Result: FAIL
Notes and Commentary
Fractals, as implemented here, identify some spectacular breakouts through support or resistance, but they also give plenty of false signals. Just by themselves, fractals are too simple and too obvious to trade alone. I am actually struggling here to think of improvements, but that may just be fatigue speaking.
Ideas for Future Systems
- Do not stop and reverse and use Average True Range (ATR) exits only
- Use a trend filter,, such as a simple moving average or Kaufman’s adaptive moving average KAMA)
- Use the Alligator (three moving averages), as suggested by Bill Williams, as a confirmation
That is about it. This system idea seems kind of lame in retrospect, though I find fractals, both the trading and mathematical kinds, fascinating. I have written dozens of fractal systems, most failures (as most ideas are), a couple of winners, and a couple in incubation. I will continue to explore this idea to see if I can make it work.
- Trading Chaos, 2nd edition, Bill Williams
- New Trading Dimensions, Bill Williams
- Wikipedia – Fractal , the mathematical kind just for fun
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