Analyze your equity curve

October 24, 2012 03:00 AM

In general terms, mechanical trading systems are derived from statistical observations that forecast a market’s upcoming likelihood to trend or trade sideways. Considering the cyclical nature of markets and the fluctuating volatility of market prices, systems’ returns naturally ebb and flow over time as market conditions shift.

Usually at high volatility levels, trending systems perform well and sideways systems tend to fail. Likewise, during periods of low volatility, trading-range systems perform whereas trending systems lag. Therefore, regardless of the nature of the system, the equity curve will experience drawdown periods. 

Traders, of course, are always in search of techniques to reduce drawdowns and even turn losing periods into winning ones. There are several ways to measure volatility in an attempt to forecast this, but one of the most practical simply is monitoring the performance of the system itself. Analyzing the equity curve is a straightforward way to predict how a particular system will perform. Here, we will show how equity curve analysis can improve mechanical trading system results by not only identifying changes from congestion periods to trending ones, but also allowing the trader to capitalize on this shift. 

Trading the equity curve

One simple way to gauge the cyclical effect of markets on trading systems is to apply percentage-based drawdown stops to the system’s performance. Percentage-based equity stops do not refer to a percentage drop in the underlying market, they refer to a percentage drop in the system’s equity, from the highest measured point of the equity curve to the present. (Both kinds of stops can be used simultaneously.)

Because the equity level is dynamic, it must be monitored either manually or by a programmed algorithm. This approach is a money management method that can be applied to any system, flattening the equity line.

Another useful technique involves performing trend analysis of the equity curve itself. Moving averages can be applied to the equity curve of a trading system to determine when and how to take trades from that trading system.

The calculation begins with a basic technical trading strategy. Such a system is one that currently does not employ any money management techniques. Such systems may be nothing more than a single indicator. This basic system will provide the equity curve that will be analyzed. The moving average will be calculated based on the equity curve of the basic system. The equity curve will be defined as “good” when it is above its moving average and “poor” when it is below it.

With this information, we can take several approaches to trade our system:

  • Allow signals when the equity is above the moving average, and block trades when below.
  • Allow larger trades when the equity is above the moving average, and smaller trades when below.
  • Administer positions by filtering with different moving averages.
  • Allow signals when the equity is above the moving average, but trade opposite to the system’s signals when the equity curve is below.

Scaling in, scaling out

We’ll demonstrate one approach on a trend-based system that will filter trades based on moving average analysis of the equity curve. After applying the basic system to one-hour euro charts for a period of six years, we get a sample of 1,950 trades. The equity curve goes through peaks and valleys as market volatility cycles affect the performance of the basic system. The basic system, without equity curve analysis, provides only $300 of profits for this period. Our results are based on a $10,000 account. 

We’ll compare these results using an approach that administers positions based on a moving average filter of the equity curve. Normal trading takes place on crossovers above the moving average; no trading takes place on crossovers below the moving average. Our filter of the basic system is done by applying several moving averages to the raw equity curve. In the first chart in “Raw vs. filtered” (below), the basic system equity curve is shown in red, and a 21-period moving average of the equity curve is in blue.

The three filtered equity curves in “Raw vs. filtered” are generated by a system filtered using three different moving average lengths, as indicated: a five-period moving average, a 13-period moving average and a 34-period moving average. Clearly, the results of each are markedly different, but this was expected. The three different averages provide for different levels above the equity line for taking entries and exits.

Interestingly, we also can combine the results of the moving averages. In “Working together” (below), we show the results for a system that includes all three averages. This system divides its lot sizes into thirds, trading 33% of a lot based on each filter.

As we can see, not only does moving average filtering produce a rising equity curve with more profit and a lower drawdown, but it also does so with fewer trades. Profits increased from $300 to an average of $20,000 across all systems, using the same lot sizes and the same trading system signals on the same underlying instrument over the same period of time and without any additional money management rule.

Do the switch

As noted earlier, there are other ways to use equity curve analysis to improve trading systems. For example, instead of starting and stopping trading on crossovers of the equity curve, you can switch the system logic and trade the opposite on moving average crossovers. 

Consider the trading results in “Switch hitter” (below). In this case, we applied a 10-period moving average to the equity curve for our basic euro system. The results are clearly impressive. They are based on fading the system — that is, going short when the system says to go long and vice versa — when the equity curve is below the moving average.

Normal trading takes place on signals that happen when the equity curve is above its moving average. Opposite trading takes place on signals that happen when the equity curve is below its moving average. As shown, this test produced a hypothetical equity curve with more profit and a lower drawdown. Profits increased from $300 to $35,000, using the same lot sizes and the same trading system signals on the same underlying instrument over the same period of time and without any additional money management rule.

Changing market conditions can be a window of opportunity rather than a source of trading system drawdowns. Sometimes the answers are beyond the trading system logic itself. Applying a different approach to trading, such as equity curve-based money management, can not only help minimize drawdowns, but it also can help maximize profits.

Octavio Riaño is a project manager at 

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