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Two-Phase vs. Three-Phase Systems

October 12th, 2010 · 3 Comments · Strategies

One of the (many) decisions during the design of trading system is whether the system will be two-phased or three-phased.

A two-phase system, also called reversal system, simply has two modes:

  • Long
  • Short

It is always in the market, most likely in the direction of the trend. This is fairly simple: it closes the previous position by opening a new one in the opposite direction. Think of the golden cross-style systems: buy when the short MA crosses up with the long MA and sell when it crosses down.

A three-phase system adds a third mode: neutral, where it is not in the market. This usually means that closing a position does not coincide with opening a new one and exits are triggered by a different signal (stop-loss, trailing stop or target profit).
Think of the Turtle system for example, which had an initial stop-loss and an exit signal period different from the entry one (20 or 55-day breakout for entry and 10 or 20-day breakout for exit).

Of course, the additional possibility of scaling in and out of a positions blurs the lines between long/neutral and short/neutral in the three-phase system.

Two v Three: a Comparison

Both types of systems are widely used and some Wizards do include this information in their prospectus (Dunn uses a two-phase system, JWH a mixture of the two, etc.). Although some managers – like BlueTrend – use a “continuous process” of adjusting positions, with no discrete entries or exits. The line between long/neutral/short is really blurred in that case.

It is not straight-forward to compare two-phase systems vs. three-phase systems as they usually have different entry/exit signals, which can affect the comparisons. To test, I decided to tinker with a couple of systems from the State of Trend Following report:

  • Donchian System
  • Triple Moving Average

These two systems are both three-phase.

The Donchian system is a simple breakout system with an entry period (eg 50-day) different from the exit period (typically half that of the entry one, eg 25-day), with an additional entry stop (defined in ATR-multiple for example).

The first modification to the Donchian system was to modify it to a “two-and-a-half” phase system by removing the exit signal but leaving the stop-loss: in effect if a trade is not stopped out, it will be reversed when a new opposite entry signal is triggered.

The second modification was to remove the stop altogether – making it a real two-phase system.

Below is a comparison between the “typical” Donchian system (exit breakout period = half of entry breakout period) and the modified systems described above. I ran these systems over a range of timeframes (different entry breakout periods from 20 days to 200 days) and different position sizing. About 25 combinations of systems were run – the results are the averages of each system performance stats:

Average Stats 3-Phase 2.5-Phase 2-Phase
CAGR (%)
Max DD (%)
MAR 0.78 0.72 0.77
Sharpe ratio 0.77 0.86 0.80
Longest DD 23.65 26.49 26.95

The differences between the results are relatively small and probably not statistically significant. Also note that there might be slight leverage differences as both CAGR and MaxDD increase together over the three different cases.

The Triple Moving Average uses three exponential moving averages (long, medium and short). A long (short) entry is triggered when the short MA is above (below) the medium MA, which must be above (below) the long MA. The system I picked also had a condition for the close to be above (below) the short MA. The position is closed when the short MA crosses back with the medium MA. It also has an ATR-based stop-loss.

I modified it by simply transforming it to a two-phase system (by removing any exit signals): an entry simply exits the previous position in the opposite direction. The average stats across a combination of parameters can be found below:

Average Stats 3-Phase 2-Phase
CAGR (%)
Max DD (%)
MAR 0.88 0.76
Sharpe ratio 0.69 0.84
Longest DD 17.81 24.96

There are no real obvious conclusions to draw from these examples, just ideas of how to design and modify systems for testing. I suspect every system might react differently to these sort of changes.

Position sizing and Number of Trades

An interesting observation though, is that a smaller position size is required in the two-phase system to match the performance numbers of the equivalent three-phase system (there is also a dependence on stop levels for the three-phase systems). This could be interesting with regards to the use of margin.

The difference in position size as a percent of equity was non-negligible (factor 2 for the Triple MA system and factor 5 for the Donchian system)

There are also (quite logically) less trades in the two-phase approach – about 30% less for the Donchian system and 50% less for the Triple Moving Average. The simulations above were all executed with slippage set to 0. When adding slippage into the mix, a system trading less frequently should be less penalized by slippage costs.
Credits: The definition of “two-phase” and “three-phase” systems can be found on this Trading Blox forum thread and on this page from the John W Henry website.

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3 Comments so far ↓

  • Pumpernickel

    Russell Sands, one of the original Turtles and a somewhat controversial figure, suggests a type of analysis that may assist you in this endeavor. He recommends a sort of Donchian Breakout Oscillator given by X = (C – LLn) / (HHn – LLn). It tells you where todays closing price C is, within the Donchian Breakout channel whose highest high over the past n days is HHn and whose lowest low over the past n days is LLn. When X = 1.00 you are at the top of the channel and when X = 0.00 you are at the bottom of the channel.

    Sands suggests that you ask and answer the question, when I’m in a trade and the oscillator equals some value “Z”, what is my expectation? For all trades that had an oscillator value equal to Z at some point during the trade, what was the average P-and-L result, between hitting osc=Z and trade exit? He suggests that you do this for Z = 0.0 to 1.0 in steps of 0.05; once for Long trades and again for Short trades.

    Now you can make a pair of plots, one for Longs and the other for Shorts, showing expected-result-from-here versus oscillator value. The shape of these plots may tell you whether to exit the trade “prematurely” (before you get an exit signal), if expectation goes negative. If the shape of the plots show significant benefits from premature exit, the system under test “wants” to be Three Phase.

    It’s also possible that the shape of the oscillator vs expectation-from-here plots will suggest it is unwise (less profitable) to exit prematurely, in which case the system under test “wants” to be Two Phase.

    (the “Donchian Breakout Oscillator” above is isomorphic to “Williams Percent R” and also to “Unsmoothed Fast Stochastic”, with the occasional change of sign here and there. They all tell your relative position between the top and bottom of a Donchian HHn-LLn channel).

  • Jez Liberty

    Thanks Pumpernickel – an interesting comment (as usual) and definitely worth testing. Maybe the subject of a next post – thanks!

  • Pumpernickel

    Your results will, naturally, depend upon the goal you seek. In mathematical optimization terms, the solution (the “optimum”) depends upon the objective function you choose.

    In particular, institutional customers often set different goals for the investment managers they employ, than private traders set for themselves. Institutions typically employ several managers (for diversification) and use prime brokers who offer cross-margining across asset classes and managers, to allow “efficient” application of precious margin capital. These institutions typically rate their managers NOT in terms of Return On Account (and its various risk adjusted manifestations like CAGR%, MAR ratio, Sharpe ratio, etc), but rather in terms of Return On Margin (risk adjusted). When they apply their margin capital across several managers, these institutions seek managers who will give the highest return per unit margin allocated. And so Three Phase managers (who take no position when expected return is low, thereby using up zero margin) are more highly prized than Two Phase managers (who always have a position, gobbling up margin, all the time).

    Private traders, by contrast, tend to optimize Return On Account, and mostly disregard margin. They will gladly choose system B rather than system A, if B has 1% higher Sharpe ratio with 50% higher margin-to-equity ratio. For these kinds of traders with this type of objective, Two Phase systems are not automatically disadvantaged.

    So: the answer you get will depend on the question you ask. No surprise there.

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