

The Breakout
Bulletin
The following article was originally published in the February 2005 issue of
The Breakout Bulletin.
Equity
Curve Trading Techniques
Anyone who's been reading this
newsletter for a while knows I like money management methods. There's a reason
professional traders often cite money management as the most important element
of trading. Once you've found your "edge" in the markets  a profitable system
or method  money management is the next logical step to improve your
trading. You've probably heard of Larry Williams' remarkable trading results in
the 1987 World Cup Trading Championship, in which he turned $10,000 into 1.1
million in 12 months. Referring to the position sizing method he used
during this period, he wrote "What this formula did for my trading results was
phenomenal." [reference 1]
In my view, position sizing is
the foundation of good money management for futures trading. But we don't have
to stop there. We can build on that foundation with other money management
methods, such as techniques for trading the equity curve. Equity curve
trading methods are based on the idea that how well our system or method
has been doing lately can tell us something about how we should be trading it.
As a simple
example, we might decide to stop trading a system if its equity curve starts to
turn down, indicating the start of a losing streak.
Let's begin by introducing an
example and see what happens when we apply different equity curve trading
techniques. Consider the equity curve shown below in Fig. 1. This is from a
day trading system called English Channel developed by Joe Krutsinger
and applied to the mini Russell 2000 futures. Many of you are probably
familiar with Joe Krutsinger's work through his books and articles
on trading system development. In reference to English Channel
he writes "This strategy is based on the same math that is the basis of the
famous Richard Donchian system and the Turtle system. I have put a 'little
English' or twist that keeps it in the market less than 5% of the time."
The red line is the equity curve plotted from the 1contract system
profit/losses, and the blue line is a 30trade moving average of the equity
curve.
Fig. 1. Equity curve
for English Channel day trading system on the mini Russell 2000 with
one contract per trade.
Although this system is
pretty impressive as is, let's see if we can improve it by applying an equity
curve trading technique. Two of the most common methods
for trading the equity curve use crossovers of the moving average of the equity
curve with the equity curve itself. In one variant, you stop trading when the
system's equity curve crosses below it's moving average and resume trading when
the equity curve crosses back above the moving average. Alternatively, you
could stop trading when the equity curve crosses above its moving average and
resume trading when it crosses back below the moving average. Keep in mind that
when we refer to the equity curve and its moving average, we're referring to the
continuously traded equity curve plotted from all system trades. If we skip
a trade in a realtime because of the equity curve crossover, this skipped trade
is still included in the equity curve for purposes of calculating the moving
average and the equity curve crossovers.
Whether we might want to skip
trades on crossovers below the moving average of the equity curve or above it
depends on the characteristics of the trading system. Generally speaking, you would stop trading on crossovers below
the moving average if the system tends to produce streaks of wins and
losses, so that when it starts to lose, it's best to stop trading until it
starts winning again. On the other hand, if the system tends to
"revert to the mean"  after several wins, it starts to lose, and viceversa 
then it's generally better to stop trading on crossovers above the moving
average and resume trading on crossovers back below the moving
average. A dependency analysis, as I discussed in the September 2002 issue
of this newsletter, can be used to determine
if a trading system has either of these tendencies with statistical
significance.
Take another look at the equity curve for the English Channel
system in Fig. 1. It appears that when the system gets either above or
below the moving average, it tends to stay there for a number of trades. This
suggests that we might want to try skipping trades on crossovers
below the moving average and resume trading on crossovers back
above the moving average. Fig. 2 shows how this
works.
Fig. 2. Equity curve
for English Channel system on the mini Russell 2000, skipping trades on
crossovers of the equity curve below its moving
average.
Notice that
the plot for the number of contracts below the equity curve contains empty
(white) spaces. This is where the trades have been skipped due to the
equity curve crossover rule. Compared to the results shown in Fig. 1, there are
29% fewer trades (365 with the crossover rule vs. 513 before), a higher profit
factor (1.62 vs. 1.46), a higher average trade ($122 vs. $93), and a
substantially lower drawdown (17% vs. 30%) with nearly the same net profit.
Although
skipping trades based on crossovers of a system's equity curve with its
moving average is the most common method of trading the equity curve, it's not
necessary to skip trades entirely. Above, I stated that I considered
position sizing to be the foundation of good money management for futures
trading. We can easily devise a method that combines equity curve
crossovers with position sizing. Let's say, for
example, that we want to use fixed fractional position sizing with the English
Channel system. Fixed fractional position sizing is a refinement of the Kelly
formula that Larry Williams cited in his victory in the World Cup Trading
Championship [reference 1]. The key parameter in fixed fractional position
sizing is the fixed fraction ("f"), which represents the fraction of account
equity risked on each trade. Let's say we normally risk 3% (f = 0.03) of
account equity on each trade. If our account equity is $50,000, for example, we
would be risking 3% of $50k or $1500 on the next trade. If the risk of the next
trade is $500 per contract, for example, we would take three contract for the
next trade.
Consider the
following equity curve crossover method. Instead of skipping trades on
crossovers of the equity curve with its moving average, we adjust the fixed
fraction by a certain amount on crossovers of the equity curve. For example, if
the equity curve crosses above the moving average, we might increase f from 0.03
to 0.05. When the equity curve crosses back below its moving average, we could
decrease it to 0.01 (or just reset f to 0.03). The effect in this case would be
to increase the number of contracts more quickly than with our baseline fixed
fraction of 3% when the system is winning and reduce the number of
contracts more quickly when the system is losing. Alternatively, we could
increase the fixed fraction on crossovers below the moving average and decrease
it (or just return it to baseline) on crossovers back above the moving average.
As above, the method that's likely to work best depends on whether the trading
system tends to have prolonged streaks of wins and losses or tends to be
meanreverting.
For the
English Channel system, we'll first apply fixed fractional position sizing with
a fixed fraction of 2%. This means the number of contracts is chosen so that 2%
of account equity is risked on each trade. Making this change alone results in a
doubling of the net profit with no increase in worstcase percentage drawdown,
as shown in Fig. 3.
Fig. 3. Equity curve
for English Channel system on the mini Russell 2000 with fixed fractional
position sizing (f = 0.02).
Now we'll add
the following equity curve crossover rule: Increase the fixed fraction 20% when
equity crosses above the moving average, and decrease the fixed fraction 20%
when equity crosses below the moving average. The result is shown in Fig. 4. The
rate of return has increased from 625% to 1036% with no increase in worstcase
drawdown. The profit factor has also gone up slightly from 1.44 to
1.5.
Fig. 4. Equity curve
for English Channel system on the mini Russell 2000 with fixed fractional
position sizing and an equity curve crossover rule.
I've found
that in many cases this more subtle method of varying the position sizing rather
than skipping trades altogether is a better method of trading the equity curve.
I suspect the reason for this is that no equity curve crossover method is
perfect. If you skip trades, for example, you'll be skipping losing trades in
some cases but skipping winners at other times. By changing the position sizing
(relative to baseline) on equity curve crossovers, we're hedging our bets
somewhat. We still take each trade  even if at a reduced level  so even if
the crossover rule gets it wrong, we're still participating in a winning trade.
There are other possible ways
to trade the equity curve. In fact, Joe Krutsinger developed a method based on
the slope of the 30day moving average of a system's equity curve
[reference 2]. I've focused on methods involving moving average crossovers
because most traders are familiar with moving averages and such methods tend to
be broadly applicable. By design, equity curve trading techniques rely on the
historical sequence of trades. This implies that you should use a fairly
long sequence of trades when evaluating such methods. Otherwise, you might
be relying on a statistical fluke in the trade sequence. Not all trading systems
or methods will be amenable to equity curve trading techniques, but if you have
a system that is, the results may be well worth the effort.
Notes:
2. To request
more information about Joe Krutsinger's English Channel day trading
system for the mini Russell 2000, please contact [link not available].
That's all for now. Good luck with your
trading.
Reference

Williams, Larry. LongTerm
Secrets to ShortTerm Trading. John Wiley & Sons, Inc., NY. 1999. p
175.

Krutsinger, Joe. "Trading the
Equity Curve," Active Trader. September 2000. pp. 336.
Mike Bryant
Breakout Futures


