Exploiting Trade Dependency

I recently discovered a pattern to the trades for MiniMax II that can be exploited to increase the profitability of the system. In addition to being of interest to MiniMax traders, this presents a good opportunity to discuss trade dependency.

It's often useful to think of financial markets in statistical terms. For example, the trades produced by a trading system can be represented by a statistical distribution, which shows the frequency of occurrence of trades of different sizes. For example, you might find that 5% of trades are between $200 and $300, 7% are between $301 and $400, etc. Another statistical concept that is sometimes useful in trading is trade dependency. With trading systems, dependency refers to the relationship between consecutive trades. If a loss is more likely to follow a win than a loss, for example, there is negative dependency. This means that wins tend to follow losses and losses tend to follow wins. Positive dependency means that wins tend to follow wins and losses tend to follow losses.

In most cases, there is no statistically significant dependency among trades. In this respect, most trading systems are analogous to flipping a coin. The odds of a coin landing heads up is 50-50, regardless of how many times in a row you get tails. Each coin flip is independent of every other one. Intuitively, it may feel like the odds of getting heads is higher if you've landed 10 tails in a row, but the coin doesn't know that you've landed 10 tails in a row. With each flip of the coin, you still have a 50-50 chance of getting heads. Most trading systems produce a similar lack of dependency. Whether the next trade is a win or a loss doesn't depend on the previous trade. If your system historically has 53% winners, the odds of the next trade being a winner are 53%, regardless of whether you had 10 losses in a row or 10 winners in a row.

However, there are exceptions. I created an indicator I call Trade Dependency (available for free download). This indicator uses a statistical test called a runs test to determine if there is any statistically significant dependency among the last N trades produced by a trading system. While there may be no significant dependency for a long history of trades, there can be periods of dependency that crop up from time to time. The Trade Dependency indicator can find these anomalies. When I recently plotted it on MiniMax II, I found significant negative dependency on the E-mini Nasdaq using N=30 (i.e., over the last 30 trades); see Figs. 1 and 2, below.

Fig. 1. The trade dependency indicator is plotted at the bottom of the price chart for the E-mini Nasdaq during late 2001. The white horizontal line is the zero (neutral) line indicating no dependency. Where the line is colored red the dependency is not significant. Where the line is colored green there is significant negative dependency.

Fig. 2. Trade dependency is plotted for the E-mini Nasdaq during recent months. Notice that the line is mostly green, indicating persistent negative dependency that is statistically significant.

Recall that negative dependency means that winners tend to follows losses, and vice versa. Provided the dependency persists long enough, it can be exploited. I tested various methods to vary the position size based on the prior trade. The most effective method I discovered was to decrease the fixed fraction slightly after a win and increase it after a loss provided the Trade Dependency indicator was showing significant negative dependency. In particular, if there is no significant dependency (red line), I keep the fixed fraction at 4%. This means I risk 4% of my account equity on the next trade. However, if there is significant negative dependency (green line) and the last trade was a win, I only risk 3% on the next trade. If there is significant negative dependency and the last trade was a loss, I risk 6% on the next trade.

Applying these rules to the available history of MiniMax II applied to the E-mini Nasdaq (9/99 to present) results in a final equity of $3.3M on a starting account balance of $50K with a worst-case drawdown of 18.6%. If the fixed fraction is kept at 4% regardless of trade dependency, the final equity is $1.3M with a worst-case drawdown of 20%. So by exploiting trade dependency, we obtain a greater return with a smaller drawdown. I tried different size adjustments to the fixed fraction, but these numbers (3% after a win; 6% after a loss) worked best. Notice that I'm not suggesting you do anything as dramatic as skipping the next trade after a win or doubling up after a loss. That kind of crude adjustment doesn't seem to work well historically. The more subtle approach that I've outlined is preferable. The idea is to make small adjustments to your position size based on trade dependency and only when the dependency has been statistically significant over the last 30 trades.

I should also point out that there are periods of significant dependency with MiniMax II on the E-mini S&P, but the dependency doesn't seem to last long enough to profitably exploit.

Answers to Your Questions

Q:  I tried using the EasyLanguage output bar in TS 6 to read the trade orders for MiniMax, but it seems to combine the output statements for all systems that are running. This is confusing. Is there a way to avoid this?

A:  The Output bar of TS 6 replaces the print log in older versions of TradeStation. It's a common location where the output from EasyLanguage "print" statements is written. Whenever the EasyLanguage processor encounters a print statement, that output goes to the output bar. For this reason, the order of statements in the output bar depends on the order in which your systems are run in all the open chart windows. This, in turn, is controlled by TradeStation, so you basically never know the order that statements will appear in the output bar.