## Avoiding drawdown breakdowns

#2

### Cumulative chart

Another method of tracking if and when a strategy goes off course is through a cumulative equity chart. For a given strategy, once the average trade and standard deviation of the strategy are known, upper and lower limits for how the strategy “should” perform can be constructed. For example, limits can be established for the upper and lower 5% curves, and can be built as follows:

- Lower Bound = average * number trades − square root (number of trades) * std deviation * 1.645
- Upper Bound = average + square root (std deviation) * 1.645

Such a set of curves is shown in “Cumulative equity” (below). For a strategy performing normally, 90% of the time the cumulative equity curve will be between these two curves. When the cumulative equity curve goes outside of the bounds, it might be time to take action with the strategy.

### Methods in action

Obviously, for each of the quitting methods, the results will depend a great deal on the parameters used to define the process. For this article, the following rules were established:

- Maximum Drawdown Method: Quit trading when maximum drawdown is twice the out-of-sample backtest maximum drawdown
- Control Chart Method: Quit trading when any one of the four out-of-control rules is violated
- Cumulative History Method: Quit trading when lower or upper bound is breached

“Two systems” (above) shows how these methods compare for actual trading systems. They include the equity curves for a Nasdaq (NQ) and crude oil (CL) trading system. The NQ system was chosen because after an initial rise, its performance deteriorated and never recovered. Clearly, we would want to stop this system before too many trades were taken. The CL system was chosen because it suffered a major drawdown before eventually recovering. In this case, when would each of these methods have stopped the system? “Method comparison” (below) shows the results.

As shown in the table, all three methods eventually stop trading the strategy, which is the intent. The maximum drawdown method, however, trades for a longer period and results in a bigger net loss than the other two methods. Although many times this will be the case, there are strategies where the maximum drawdown method will yield a better result than the control chart methods. Because of this, it might be useful to monitor a strategy with all three methods, and stop trading when any one of them produces a “stop” signal. That would be the most conservative approach.

### Potential problems

As with any mathematical technique, unavoidable assumptions might have a negative impact on the analysis. For example, typical trading system results have distributions with long tails—that is, large gains that may be more than three standard deviations away from the average. Plus, losses are usually capped by a stop loss, so the distribution on the negative side is not smooth, either.

In addition, it may be typical for a trading system to have many small consecutive losses, followed by a big winning trade. While this might be perfectly acceptable to the trader, the control chart approach may flag such systems as being “out of control,” when in fact the strategy is not out of control. Therefore, care must be taken to eliminate false warnings.

The lesson here is that these techniques may have to be modified for a particular trading system, and a trained statistician may take exception to the application of these charts. But, remember the goal is just to have an acceptable method to quit a trading system.

If the method is biased to the conservative side—turning off poorly performing strategies before things get too bad—that is probably a good thing in the long run. Certainly, it is better than the alternative—letting bad strategies drain your account.

Many traders, when faced with a failing trading strategy, get trapped by inaction, just as a deer freezes in front of car headlights. Of course, that is the worst thing one can do, because many times a poorly performing strategy will continue to perform poorly. A good trader needs to know when a system is broken and when to take decisive action.

We reviewed the pros and cons of three potential methods to quit trading a strategy: Multiple of maximum drawdown, control chart and cumulative equity. While no method is perfect, and may not be appropriate in all cases, the key point is it still takes a good trader to determine how and when to stop a trading strategy before you start trading it. Regardless of the method, as long as capital is preserved, the result will be better than letting the trading account dwindle to zero dollars.