To understand how and why the iSigma trading system works, we'll first present a framework of how any approach to trading might work. When a trader completes a series of N trades, his final equity will be his initial equity multiplied by (1 + P), where P is the percent profit after the series of trades. For example, if the profit after 4 trades is 50%, and the trader starts with an initial equity of $1000, the ending equity will be $1000 * (1 + 0.5) or $1500. Since we know the number of trades, we can also determine the outcome of the average trade. We find this by using the formula [(1 + P) ^ (1 / T)] - 1, where P is the total profit after the series of trades and T is the number of trades in the series. In the case above, the outcome of the average trade is a profit of 1 - [(1 + 0.5) ^ (1 / 4)] ~= 0.1066, or about 10.7%.

In real trading, the outcome of each trade is unique to that particular trade. In the case above, the average outcome may have been 10.7%, but this doesn't mean that the actual trades weren't more widely distributed. The four trades may have resulted in -7.4%, -2.6%, +14.5%, +45.2%, respectively, or one of any other combination of numbers which, after adding 1 to each, multiply to produce 1.5.

A somewhat more organized way to present all of this information is to treat wins and losses separately. In the case of the example above, the average loss is ([(1 + -0.074)(1 + -0.026)] ^ (1 / 2)) - 1 ~= -0.05 or about -5%. The average win can be calculated the same way to yield approximately 28.9%. From these two figures it becomes rather easy to compute total profit as well as the average outcome per trade. the formula for total profit is [(1 + L) ^ l] * [(1 + W) ^ w], where L and W represent the average loss and win, respectively and l and w represent the total number of losses and wins respectively. Calculating the average outcome per trade is done using [(1 + L) ^ (l / (l + w))] * [(1 + W) ^ (w / l + w))].

When a trader uses stop loss orders as the sole means of exiting positions, this creates a scenario where two things happen. Because all losses are limited to the initial stop, the average loss will tend to a mean which is bounded to the range between the initial amount risked and 0. Also, because no trades are closed before reaching the stop, the average winning trade won't tend to any mean at all. Rather, the average win will continue to increase as more and more trades are added to the data. Consequently, the outcome of the average trade will continue to increase unbounded as more trades are added into the data.

This inexorable creep of the average win toward infinity is the basis of why all trend following systems work as well as they do. This includes the turtle approach, the abberation system, the trendchannel system, and any other system that uses a stop to exit. It's not that breakouts or moving average crossovers or volatility bands correspond to any sort of special "market inefficiency" or support and resistance levels. Profit in these types of systems comes from the fact that once a trade is on, so long as the exit only takes place with a stop loss order, the average win becomes unbounded. The question to a system designer is then, "Which system will cause the average win to approach infinity the fastest?"

It's nearly an intractable problem to try to directly answer the question above. Instead, we look at the problem from a different perspective. What causes systems that exit using stops to have the average win approach infinity slowly? Once all of the seriously troubled approaches are eliminated (trading with too close a stop, lack of sound money management, etc.) the most common reason for the average win to limp along is that most trading systems are rather sensitive to parameter selection. Typically, traders will want to use whatever parameters worked extremely well in the past, hoping that these "optimized" parameters will work as well in the future. Our solution has been, among other things, to design the system from the ground up so that parameter selection is rather unimportant. Accross any combination of the four parameters of our system, performance is nearly the same. We call this property robustness.

In addition to our design around avoiding the parameter selection rut, our entry and exit rules are designed to ensure that our average win is several times our average loss, while our number of winning trades versus losing trades remains comparable (or better) with other trading systems. We recognize the limits of backtesting, but it's worth noting that over historical data, our system has about 40% winning trades, just as do most moving average, volatility band and breakout systems, but our average win / average loss ratio is signifigantly higher, often more than double what other systems produce.

We've tried to present a lot of information here in a very small space so if it seems we've not explained anything clearly enough, we apologize. We want to make sure that you understand how and why the system works. If you have any questions or points that you would like clarified, please follow one of the contact links on this site to get a personal response.