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:
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:
|Max DD (%)||
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:
|Max DD (%)||
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.