Principles of Trading System Design
If not the gods, put the
odds on your side.
Introduction
This
chapter presents some basic principles of system design. 'You should try
to understand these issues and adapt them to your preferences.
First, assess your trading
beliefs—these beliefs are fundamental to your success and should be at the core
of your trading system. You may have several strong beliefs, and they can all
be used to formulate one or more trading systems. After you have a list of your
core beliefs, you can build a trading system around them. Remember, it will not
be easy to stick with a system that does not reflect your beliefs.
The six major rules of system
design are covered in this chapter in considerable detail. The specific issues
to be examined are why your system should have a positive expectation and why
you should have a small number of robust rules. The focus in the later sections
of this chapter is on moneymanagement aspects such as trading multiple
contracts, using risk control, and trading a portfolio of markets. The real
difficulties lie in implementing a system, and hence, the chapter ends by
explaining why a system should be mechanical.
12
Principles of Trading System Design
By the end
of this chapter, you should be able to write down your trading beliefs, as well
as explain and apply the six basic principles of system design.
What
Are Your Trading Beliefs?
You can
trade only what you believe; therefore, your beliefs about price action must be
at the core of your trading system. This will allow the trading system to
reflect your personality, and you are more likely to succeed with such a system
over the long run. If you hold many beliefs about price action, you can develop
many systems, each reflecting one particular belief. As we will see later,
trading multiple systems is one form of diversification that can reduce
fluctuations in account equity.
The
simplest way to understand your trading beliefs is to list them. Table 2.1
presents a brief checklist to help you get started.
You can
expand the items in Table 2.1 to include many other items. For example, you can
include beliefs about breakout systems, movingaverage methods, or volatility
systems. Your trading beliefs are also influenced by what you do. For example,
you may be a market marker, with a very short term trading horizon. Or, you may
be a proprietary trader for a big bank, trading currencies. You may wish to
keep an eye on economic data as one ingredient in your decision process. As a
former floor trader, you may like to read the commitment of traders report.
Perhaps you were once a buyer of coffee beans for a major manufacturer, and you
like to look at crop yield data as you trade coffee. The range of possible
beliefs is as varied as individual traders.
You must
ensure that your beliefs are consistent. For example, if you like fast action,
you probably will not use weekly data, nor hold positions as long as
necessary. Nor are you likely to use fundamental data in your analysis. Hence,
a need for fast action is more consistent with day trading, and using cycles,
patterns, and oscillators with intraday data. Similarly, if you like a
trendfollowing approach, you are more likely to use daily and weekly data,
hold positions for more than five days, trade a variable number of contracts,
and trade a diversified portfolio. If you hold multiple beliefs, ensure that
they are a consistent set and develop models that fit those beliefs. A set of
consistent beliefs that can be used to build trading systems is listed below as
an example.
1. I like to trade with the trend (5 to 50 days).
2. I like to trade with a system.
What Are Your Trading Beliefs? 13
3. I like to hold positions
as long as necessary (1 to 100 days).
4. I like to trade a variable
number of shares or contracts.
5. I like to use stop orders
to control my risk.
Pare down your list to just
your top five beliefs. You can review and update this list periodically. When
you design trading systems, check that they reflect your five most strongly
held beliefs. The next section presents other rules your system must also
follow.
Table
2.1 A
checklist of your trading beliefs
Beliefs That Can Influence Your Trading Decisions

Yes,l Agree

No,l Disagree

1 like to trade using fundamentals only.

a

a

1 like to trade with technical analysis only.

a

a

1 like to trade with the trend (you define time frame).

a

a

1 like to trade against the trend (you define time frame).

a

a

1 like to buy dips (you define time frame).

D

a

1 like to sell rallies (you define time frame).

a

a

1 like to hold positions as long as necessary (1 to 100 days).

a

a

I like to hold positions for a short time (1 to 5 days).

a

a

I like to trade intraday only, closing out all positions.

a

a

I like to trade a fixed number of shares or contracts.

a

a

I like to trade a variable number of shares or contracts.

a

a

I like to trade a small number of markets or stocks (1 to 5).

a

a

1 like to trade a diversified portfolio (more than10 stocks or

a

a

markets).



1 like to trade using cycles because 1 can anticipate changes.

a

a

1 like to trade price patterns because 1 can react immediately.

a

a

1 like to trade with price oscillators.

a

a

1 like to read the opinions of others on the markets 1 trade.

a

a

1 like to use only my own analysis of price action.

a

a

1 like to use daily data in my analysis.

a

a

1 like to use intraday data in my analysis.

a

a

1 like to use weekly data in my analysis.

a

a

1 like to trade with a system.

a

D

1 like to use discretion, matching wits with the market.

a

a

1 like lots of fast action in my trading.

a

a

1 like to use stop orders to control my risk.

a

a

1 like to trade with variablelength movingaverage systems.

a

a

14
Principles of Trading System Design
Six
Cardinal Rules
Once you
identify your strongly held trading beliefs, you can switch to the task of
building a trading system around those beliefs. The six rules listed below are
important considerations in trading system design. You should consider this list a starting point for your own trading
system design. You may add other rules based on your experiences and preferences.
1. The trading system must have a positive
expectation, so that it is 'likely to be profitable.'
2. The trading system must use a small number of
rules, perhaps ten rules or less.
3. The trading system must have robust parameter
values, usable ^ over many different time periods and markets.
4. The trading system must permit trading multiple
contracts, if possible.
5. The trading system must use risk control, money
management, and portfolio design.
6. The trading system must be fully mechanical.
There is a
seventh, unwritten rule: you must believe in the trading principles governing
the trading system. Even as the system reflects your trading beliefs, it must
satisfy other rules to be workable. For example, if you want to daytrade, then
your shortterm, daytrading system must also follow the six rules.
You can
easily modify this list. For example, rule 3 suggests that the system must be
valid on many markets. You may modify this rule to say the system must work on
related markets. For example, you may have a system that trades the currency
markets. This system should 'work' on all currency markets, such as the
Japanese yen, deutsche mark, British pound, and Swiss franc. However, you will
not mandate that the system must also work on the grain markets, such as wheat
and soybeans. In general, such marketspecific systems are more vulnerable to
design failures. Hence, you should be careful when you relax the scope of any
of the six cardinal rules.
Rule 1: Positive
Expectation 15
Another way
to modify the rules is to look at rule 6, which says that the system must be
fully mechanical. For example, you may wish to put in a volatilitybased rule
that allows you to override the signals. Be as specific as possible in defining
the conditions that will permit you to deviate from the system. You can likely
test these exceptional situations on past market data, and then directly
include the exception rules in your mechanical system design.
In summary,
these rules should help you develop sound trading systems. You can add more
rules, or modify the existing ones, to build a consistent framework for system
design. The following sections discuss these rules in greater detail.
Rule
1: Positive Expectation
A trading
system that has a positive expectation is likely to be profitable in the
future. The expectation here refers to the dollar profit of the average trade,
including all available winning and losing trades. The data may be derived from
actual trading or system testing. Some analysts call this your mathematical
edge, or simply your 'edge' in the markets.
The terms
'average trade' and 'expectation' represent the same object,
so they are freely interchanged in the following discussion. Expectation can
be written in many different ways. The following formulations are identical:
Expectation($) = Average Trade($), Expectation($) =
Net profit($)/(Tbtal number of trades),
Expectation($) = [(Pwin) x (Average win($))]  (1 
Pwin) x (Average loss($))].
The
expectation, measured in dollars, is the profit of the average trade. The net
profit, measured in dollars, is the gross profit minus the gross loss over the
entire test period. Pwin is the fraction of winning trades, or the probability
of winning. The probability of losing trades is given by (1Pwin). The average
win is the average dollar profit of all winning trades. Similarly, the average
loss is the average dollar loss of all losing trades.
16
Principles of Trading System Design
The
expectation must be positive because, on balance, we want the trading system to
be profitable. If the expectation is negative, this is a losing system, and
money management or risk control cannot overcome its inherent limitations.
Assume that
you are using system test results to estimate your average trade. Note that
your estimate of the expectation is limited by the available data. If you test
your system on another data set, you will get a different estimate of the
average trade. If you test your system on different subsets of the same data
set, you will find that each subset gives a different result for the average
trade. Thus, the expectation of a trading system is not a 'hard and fixed'
constant. Rather, the expectation changes over time, markets, and data sets.
Hence, you should use as long a time period as possible to calculate your
expectation.
Since the
expectation is not constant, you should stipulate a minimum acceptable value
for the average trade. For example, the minimum value should cover your trading
costs and provide a 'risk premium' to make it attractive. Hence, a
value such as $250 for the expectation could be used as a threshold for
accepting a system. In general, the larger the value of the average trade, the
easier it is to tolerate its fluctuations.
Note that
the expectation does not provide any measure of the variability of returns. The
standard deviation of the profits of all trades is a good measure of system
variability, system volatility, or system risk. Thus, the expectation does not
fully quantify the amount of risk (read volatility) that must be absorbed to
benefit from its profitability.
The expectation is also related to
your risk of ruin. You can use statistical
theory to calculate the probability that your starting capital will diminish to
some small value. These calculations require assumptions about the probability
of winning, the payoff ratio, and the bet size. The payoff ratio can be defined
as the ratio of the average winning trades to the average losing trades. As
your payoff ratio increases, and your Pwin increases, your risk of ruin
decreases. The risk of ruin is also governed by bet size, that is, percentage
of capital risked on every trade. The smaller your bet size, the lower the risk
of ruin. Detailed calculations of risk of ruin are presented in chapter 7.
In summary,
it is essential that your system have a positive expectation, that is, a
profitable average trade. The value of the average trade is not fixed, but
changes over time. Hence, you can specify a threshold value, such as $250,
before you will accept a trading system. The expectation is also important
because it affects your risk of ruin. Avoid trading systems that have a
negative expectation when tested over a long time.
Rule 2: A Small Number
of Rules 17
The
expectation of your system is determined by its trading rules. The next section
examines how the number of trading rules affects your system design.
Rule
2: A Small Number of Rules
This book
deals with deterministic trading systems using a small number of rules or
variables. These trading systems are similar to systems people have developed
for tasks such as controlling a chemical process. Their experience suggests
that robust, reliable control systems have as few variables as possible.
Consider two wellknown
trendfollowing systems. The common dual movingaverage system has just two
rules. One says to buy the upside crossover, and the other says to sell the
downside crossover. Similarly, the popular 20bar breakout system has at least
four rules, two each for entries and exits. You can show with testing software
that these systems are profitable over many markets across multiyear time
frames.
You can contrast this approach with
an expert systembased trading system that may have hundreds of rules. For
example, one commercially available system apparently has more than 400 rules.
However, it turns out that only one rule is the actual trigger for the trades.
The deterministic systems differ from neuralnetbased systems that may have
an unknown number of rules.
The statistical theory of design of
experiments says that even complex processes are controllable using five to
seven 'main' variables. It is rare for a process to depend on more
than ten main variables, and it is quite difficult to reliably control a
process that depends on 20 or more variables. It is also rare to find processes
that depend on the interactions of four or more variables. Thus, the effect of
higherorder interactions is usually insignificant. The goal is to keep the
overall number of rules and variables as small as possible.
There are many hazards in designing
trading systems with a large number of rules. First, the relative importance of
rules decreases as the number of rules increases. Second, the degrees of
freedom decrease as the number of rules or variables increases. This means
larger amounts of test data are needed to get valid results as the number of
rules or variables increases.
A third problem is the danger of
curvefitting the data in the test sample. For example, given a data set, a
simple linear regression with just
Principles of Trading
System Design
two
variables may fit the data adequately. As the number of variables in the
regression increases to, say, seven, the line fits the data more closely.
Therefore, we can pick up nuances in the data when we curvefit our trading
system, only to pick up patterns that may never repeat in the future. The
total degrees of freedom decrease by two for the simple linear regression, but
will decrease by seven for the polynomial regression.
These ideas
can be illustrated by using regression fits of daily closing data for the
December 1995 Standard and Poors 500 (S&P500) futures contract. The data
set covers 95 days from August 1, 1995, through December 13, 1995. Two
regression lines are fitted to the same data: Figure 2.1 presents a simple
linear regression; Figure 2.2 fits higherorder polynomial terms, going out to
the fifth power. As higherorder terms are added, the regression line becomes a
curve, and we pick up more nuances in the data.
For
simplicity, the daily closes are numbered 1 through 95 and denoted by D. All
numbers represented by C (such as Ci) are constants. Est Close is the closing
price estimated from the regression.
SPZ5 Dally Close with OLS Line
40 60 80 Days since 08/01/95
Figure
2.1
SScP500 closing data with simple linear regression straight line.
Rule 2: A Small Number
of Rules 19
SPZ5 dally close with 5th order
regression
40 60 Days since 08/01/95
Figure 2.2 SScP500 closing data
with regression using terms raised to the fifth power.
Est Close = Co + (Ci x D)
Est Close = Co + (Ci x D) + (C^ x D^{2}) + (Cj x D^{3})
+ (C4 x D^{4}) + C; x D^{5})
Table 2.2
illustrates several interesting features about curvefitting a data set. First,
observe that the value of the constant Co is approximately the same for each
equation. This implies that the simplest model, the constant Co, captures a
substantial amount of information in the data set.
Then, notice that the absolute
value of the constants decreases as the order of the term increases. In other
words, in absolute value, Co is greater than Ci, which is greater than C2 and on down the line. Therefore, the
relative contribution of the higherorder polynomial terms becomes smaller and
smaller. However, as you add the higherorder polynomial terms, the line takes
on greater curvature and fits the data more closely, as seen in Figures 2.1 and
2.2.
20
Principles of Trading System Design
Table
2.2 Comparison of linear regression coefficients
Co Ci C2 C3 C4 Cs
Equation 560.0865 0.537870
2.1
Equation 570.2379 1.94509
0.131279 0.00154 0.00003 0.0000006
2.2
This
exercise illustrates many important ideas. First, any model you build for the
data should be as simple as possible. In this case, the simple linear
regression, with a slope and intercept, captured essentially all the
information in the data. Second, adding complexity by adding higherorder terms
(read rules) does improve the fit with the data. Thus, we pick up nuances in
the data as we build more complex models. The probability that these nuances
will repeat exactly is very small. Third, the purpose of our models is to
describe how prices have changed over the test period. We used our data to
directly calculate the linear regression coefficients. Thus, our model is
hostage to the data set. There is no reason why these coefficients should
accurately describe any future data. This means that overfitted trading
systems are unlikely to perform as well in the future.
Another
example, a variant of the movingaverage crossover system, illustrates why it
makes sense to limit the number of rules. In the usual case, the dual moving
average system has just two rules. For example, for the long entry the 3day
average should cross over the 65day average and vice versa.
Now,
consider a variant that uses more than two averages. For example, buy on the
close if both the 3day and the 4day moving averages are above the 65day
average. Since there are two 'short' averages, this gives us four
rules, two each for long and short trades. Using more and more
'short' averages rapidly increases the number of rules. For example,
if the 3, 4, 5, 6, and 7day moving averages should all be above the 65day
average for the long entry, ten rules would apply.
Consider 10
years of Swiss franc continuous contract data, from January 1, 1985, through
December 31, 1994, without any initial stop, but allowing $100 for slippage and
commissions. The number of rules is varied from 2 to 128 to explore the effects
of increasing the number of rules. As the number of rules increases, the number
of trades decreases, as shown in Figure 2.3. This illustrates the fact that as
you increase the number of rules, you need more data to perform reliable tests.
Rule 2: A Small Number
of Rules 21
More rules need more data
2
4 8 12
16 24 32
48 64 96
128 Number of rules
Figure 2.3 Adding rules reduced
the number of trades generated over 10 years of Swiss franc data. Note that the
horizontal scale is not linear.
Figure 2.4
shows that the profit initially increased as we added more rules. This means
that the extra rules first act as filters and eliminate bad trades. As we add
even more rules, however, they choke off profits and moreover increase equity
curve roughness. Thus, you should be careful to not add dozens of rules.
As stated, this example did not
include an initial stop. Hence, as we increase the number of rules, the maximum
intraday drawdown should increase because both entries and exits are delayed.
You can verify this by using Figure 2.5, page 23.
Calculations for the U.S. bond
market from January 1, 1975, through June 30, 1995, illustrate that the general
pattern still holds. Figure 2.6, page 24, shows that as the number of rules
increases, the profits decrease. The exact patterns will depend on the test
data. Data from other markets confirm that increasing rules decreases profits.
Thus, adding rules does not produce
endless benefits. Not only do you need more data, but the rising complexity may
lead to worsening system performance. A complex system with many rules merely
captures
22
Principles of Trading System Design
Increasing rules first filter, then choke
profits
25000
2 4 8
12 16 24
32 48 64 96 128
Number of rules
Figure 2.4 Adding rules increased profits moderately on 10years of
Swiss franc continuous contracts from January 1, 1985, through December 31,
1994. Note that the horizontal scale is not linear.
nuances
within the test data, but these patterns may never repeat. Hence, relatively
simple systems are likely to perform better in the future.
Rule
3: Robust Trading Rules
Robust
trading rules can handle a variety of market conditions. The performance of
such systems is not sensitive to small changes in parameter values. Usually,
these rules are profitable over multiperiod testing, as well as over many
different markets. Robust rules avoid curvefitting, and are likely to work in
the future.
An example of a system with delayed
long entries illustrates the use of nonrobust parameters. The entry rule is as
follows: if the crossover between 3 and 12day simple moving averages (SMAs)
occurred x days ago, and the low is
greater than the parabolic, then buy tomorrow at the
Rule 3: Robust Trading
Rules 23
MIDD follows same pattern as profits
Number
of rules
Figure 2.5 Adding more rules
delayed entries and exits, increasing maximum intraday drawdown. Note that the
horizontal scale is not linear.
today's
high + 1 point on a buy stop. A $1,500 initial stop was used and $100 was
charged for slippage and commissions.
The results
above are for an IMM (International Monetary Market) Japanese yen futures
continuous contract, from August 2, 1976 through June 30, 1995. The dollar
profits are sensitive to the number of days of delay, and can vary widely due
to small changes in parameter values. It also does not seem reasonable to wait
12 days after a crossover for such shortterm moving averages. Hence, the
flattening out of the curve after a 9day delay is of little practical relevance.
The delay parameter is not robust because a small change in the value of this
parameter can make system performance vary widely with markets and time frames.
Next
consider the effect of nonrobust, curvefitted rules, illustrated by the August
1995 N.Y. light crude oil futures contract (Figure 2.8, page 26). The market
was in a narrow trading range during February and March, and then broke out
above the $18.00 per barrel price level. The market moved up quickly, reaching
the $20 level by May. A volatile consolidation period ensued through June,
before prices broke down toward the $17 per barrel level by July.
24
Principles of Trading System Design
More rules, less profit in US Bonds
Number
of rules
Figure 2.6 Increasing the number
of rules decreased profits in the U.S. bond market from January 1,
1975 through June 30, 1995. Note that the horizontal scale is not linear.
The
following trading rules were derived simply by visual inspection of the price
chart in an attempt to develop a curvefitted system that picked up specific
patterns in this contract.
Rule 1: Buy
tomorrow at highest 50day high + 5 points on a buy stop (breakout rule).
Rule 2: Sell tomorrow at low 2 x (h1)  5 points on
a sell stop (downside rangeexpansion rule).
Rule 3: If this is the twentyfirst day in the trade,
then exit short trades on the close (timebased exit rule).
Rule 4: If
Rule 3 is triggered, then buy two contracts on the close (countertrend entry
rule).
Rule 5: If short, then sell tomorrow at the highest
high of last 3 days +1 point limit (sell rallies rule).
Rule 3: Robust Trading
Rules 25
Effect of delayed entry on profits: 3/12
SMAXO
Delay (»
of days) after crossover
Figure 2.7 The effect on profits of changing the number of days of
delay in accepting a crossover signal of a 3day SMA by 12day SMA system is
highly dependent on the delay.
The first
rule is a typical breakout system entry rule, albeit for a breakout over prior
50bar trading range. The second rule is a volatilityinspired sell rule. The
idea was to sell at a point five ticks below twice the previous day's trading
range subtracted from the previous low. This will typically be triggered after
a narrowrange day, if the daily range expands on die downside due to selling
near an intermediate high. The third rule is a timedependent exit rule,
optimized by visual inspection over the August contract. The idea behind
timebased exits is that one expects a reaction opposite the intermediate trend
after x days of trending prices.
Rule 4 merely reinforces rule 3 by not only exiting the short position but
putting on a twocontract long position at the close. Rule 5 is a conscious
attempt to sell rallies during downtrends. In this case, limit orders were used
to sell, to avoid slippage. These rules assumed diat as many as nine contracts
could be traded at one time, using a $1,000 initial moneymanagement stop.
The results of the testing are
summarized in Table 2.3, page 27. The first clue that this may be a curvefitted
system is the number of
26
Principles of Trading System Design
^
M 1 9

.'''ll^{1})

h,

te
A^{1}

^



•20.00 •I 9.50 19.00

All ^2 3 ® TaJnf'l^{1}}!?
^A,^ ^{;1}


( '

tl^t

.
1'

5
46
1/1,

•,•

18.50 18.00






I^{11},!

Iflllll

17.50 17.00







l2 ^{1}

16.50









Figure
2.8 The August 1995 crude oil contract with
curvefitted system
profitable
trades. As many as 87 percent of all trades (20 out of 23) were profitable. A
second clue was in the 14 consecutive profitable trades. A third clue was in a
suspiciously large profit factor (= gross profit/gross loss) of 13.49. These
results are what you might see in curvefitted systems tested over a
relatively short time period. The computergenerated buy and sell signals are
shown in Figure 2.8.
This
curvefitted system was tested by using a continuous contract of crude oil
futures data from January 3, 1989, through June 30, 1995. Not surprisingly,
this system would have lost $107,870 on paper, as shown in Table 2.4. Note how
only 32 percent of the trades would have been profitable. There would have been
as many as 48 consecutive losing trades, requiring quite an act of faith to
continue trading this system. Also, the profit factor was a less impressive
0.61, a sharp drop from the 13.49 value in Table 2.3. These calculations show
that curvefitted systems may not work over long periods of time.
Interestingly,
this system has its merits. When tested over 12 other markets to check if these
rules were robust enough to use across many
Rule 3: Robust Trading
Rules 27
Table 2.3 Results of
testing August 1995 crude oil curvefitted system N.Y. Light Crude Oil
08/95Daily 12/01 /94  07/20/95
Total net profit ($) 12,990.00
Gross profit ($) 14,030.00
Total number of trades 23
Number of winning trades 20
Largest winning trade ($) 1,370.00
Average winning trade ($) 701.50
Maximum
consecutive 14
winners
Average number of bars 20
in winners
Maximum intraday 1,670.00
drawdown ($)
Profit factor 13.49
Open position profit/loss ($) 520.00 Gross loss ($) 1,040.00
Percent profitable 87
Number of losing trades 3
Largest losing trade ($) 860.00
Average losing trade ($) 346.67
Average trade ($) 564.78
Maximum consecutive losers 2
Average number of bars in 1 losers
Maximum number of contracts held
markets
(Table 2.5), the results were better than expected; on some markets the system
tested very well. This result was surprising because (1) this particular
combination of rules had never been tested on these markets and were derived by
inspection of just one chart; and (2) the
Table 2.4
Results of testing crude oil curvefitted system over a long time period
Performance

Summary: All Trades 01/03/89  06/30/95

Total net profit ($)

107,870



Total number of trades

538

Percent profitable

32

Number of winning trades

173

Number of losing trades

365

Largest winning trade ($)

7,160

Largest losing trade ($)

3,670

Average winning trade ($)

983

Average losing trade ($)

761



Average trade ($)

200

Maximum consecutive

9

Maximum consecutive

48

winners


losers


Average number of bars in

12

Average number of bars in

6

winners


losers


Maximum intraday

120,950



drawdown ($)




Profit factor

0.61

Maximum number of

9



contracts held


28
Principles of Trading System Design
Table
2.5 A check for robustness: crude oil curvefitted
system over 12
markets (test period:
1 /3/896/30/95, using continuous contracts, $100 slippage, and commission
charge)
Market

Paper Profit (S)

Average Trade ($)

Coffee

132,908

445

S&P500

145,545

547

Cotton

84,925

284

U.S. bond

84,319

324

Japanese yen

67,975

176

Swiss franc

1 7,975

51

10year Tnote

1 3,538

48

Gold, Comex

1 3,270

33

Copper, highgrade

22,167

49

Soybeans

^1,656

117

Heating oil

45,868

80

Sugar #11

56,394

136

long
entries and short entries are asymmetric. A symmetrical trading system uses
identical rules for entries and exits, except that the signs of the required
changes are reversed. For example, a moving average system would require an
upside crossover or a downside crossunder for signals.
A closer
look at the rules shows that they do follow some sound principles. For example,
during an uptrend, each successive 50bar breakout adds a contract until nine
contracts are acquired. Thus, market exposure is increased during strong
uptrends. The sell rule tends to lock in profits close to intermediate highs.
As we sell rallies in downtrends, we are increasing exposure in the direction
of the intermediate term trend. Also, a relatively tight $1,000 initial money
management stop was used. Thus, even though these rules were derived by
inspection, they followed sound principles of following the trend, adding to
withthetrend positions, letting profits run, and cutting losses quickly.
In summary,
it is easy to develop a curvefitted system over a short test sample. If these
rules are not robust, they will not be profitable over many different market
conditions. Hence, they will not be profitable over long time periods and many
markets. Such rules are unlikely to be consistently profitable in the future.
Hence, you should try to develop robust trading systems.
Rule 4: Trading Multiple Contracts 29 Rule 4: Trading Multiple
Contracts
Multiple
contracts allow you to make larger profits when you are right. However, the drawdowns
are larger if you are wrong. You are
betting that with good risk control, the overall profits will be greater than
the drawdowns. An essential requirement is that your account equity must be
sufficiently large to permit trading multiple contracts. Your risk control
guidelines must permit multiple contracts to benefit from this approach. If
your account permits you to trade just one contract at a time, then this
approach must be deferred until your equity has increased.
Multiple
contracts also allow you to add a nonlinear element to your system design. This
means the results of trading, say, five contracts using this nonlinear logic
are better than trading five contracts using the usual linear logic. The linear
logic trades one contract per signal. The nonlinear logic uses a pricebased
criterion such as volatility. The volatility rule buys more contracts when
volatility is low. Markets often have low volatility after they have
consolidated for many weeks. If a strong trend develops as the market emerges
from the consolidation, then the nonlinear effect is to boost profits
significantly.
A simple
example illustrates these ideas. Assume that your account is so large that
trading up to 15 contracts in the 10year Tnote market is well within your risk
control guidelines. For example, with a 1 percent risk per position and a
$1,000 initial money management stop, you would need $1,500,000 in equity to
trade 15 Tnote contracts. This assumes that the 15lot margin is also within
your moneymanagement guidelines.
Consider a simple moving average
crossover system using 5day and 50day simple moving averages. The trade day
is one day after the crossover day. You will buy or sell on the next day's open
if you get a 5/50 crossover tonight after the close. Use a $1,000 initial stop
on each contract and allow $100 for slippage and commissions.
Let us compare system performance
with one contract versus variable contracts, rising to a maximum of 15
contracts. The test period is from January 3, 1989, through June 30, 1995,
using a continuous contract. Table 2.6 compares four variations of the 5/50
crossover system. The column labeled 'fixed 1 contract' shows the
results over the test period for always trading one contract per trade. The
next column, 'fixed 15 contracts' shows the calculated results for
always trading 15 contracts per trade. The column, 'variable #1'
trades a maximum of
30
Principles of Trading System Design
Table
2.6 Performance comparison using variable number of
contracts
Number
of winning
trades
Average trade ($) Standard deviation
of trades ($) Average trade/
standard deviation Standard deviation:
losing
trades ($)




Variable #1

Variable #2


Fixed

Fixed

Maximum

Maximum

Item

1 Contract

15 Contracts

15 Contracts

15 Contracts

Net profit ($)

24,018.75

360,281

339,774

294,869

Maximum intra

6,918.75

103,781

66,650

62,763

day drawdown (MIDD) ($)





Net profit /MIDD

3.47

3.47

5.10

4.70

Largest losing trade ($)

1,100

16,500

1,350

13,200

Total number of trades

48

48

594

48

Number of winning

15

15

215

15

500.39 2,448
0.09 340
15
contracts with the contracts added at the open on successive days. The
'variable #2' trades a maximum of 15 contracts with all the contracts
bought on the same day. The volatility in dollars here is four times the
average 20day true range. The volatility divided into $15,000 gives the number
of contracts. Thus, variable #2 uses a volatilitybased criterion for
calculating the number of contracts, always trading 15 or less.
Let us
compare the net profit produced by the four strategies. It should come as no
surprise that the absolute amount of profit increases as we trade more
contracts. However, as the next row of Table 2.6 shows, the maximum intraday
drawdown also increases as we trade more contracts. The ratio of net profits to
maximum intraday drawdown shows whether we gain anything by trading multiple
contracts. This ratio is 3.47 for fixed contract trading strategy. The ratio
increases to 4.7 or 5.1 for the variable contracts strategies. This is a 39 to
47 percent improvement, a strong reason to consider multiple contracts. Hence,
profits can increase without proportionately increasing drawdowns.
Observe
from Table 2.6 that the largest losing trade for variable #1 is considerably
less than simply trading a fixed number of 15 contracts.
Rule 4: Trading
Multiple Contracts 31
Similarly,
the largest losing trade in variable #2 is less than always trading 15
contracts. This too confirms the benefits of going to the multiplecontract
strategy.
The total
number of trades remains the same for the fixed1, fixed15 and variable #2
strategies, since all the contracts are bought on the same day. The number of
trades increases for variable #1 since not all the contracts are bought on the
same day.
The average
trade for each strategy is relatively high, suggesting that this simple model
seems to catch significant trends. The average trade is higher when all the
contracts are bought at the same time. This is merely an artifact of system
design. As pointed out before, the average trade does not provide a measure of
variability in system results.
The
standard deviation per trade is naturally smaller when we trade one contract at
a time rather than all at once. The standard deviation in trade returns
increases as the number of contracts increases. As Table 2.6 shows, there is a
higher volatility in trade returns ($36,721) for fixed 15contract trading than
either of the variable contract strategies. This means volatility can be
reduced by trading a variable number of multiple contracts, rather than a fixed
number of multiple contracts. This is another desirable design goal.
Dividing
the average trade profit by the standard deviation in trade profitability
yields a composite picture of model performance. The higher this number, the
more desirable the system. For the fixed 1contract strategy, this reward to
risk ratio is only 0.09, and it increases to 0.24 for the variable #2 strategy.
Remember, however, that the volatility in trading profits increases
significantly with multiple contracts.
The last
line of Table 2.6, the downside volatility, explains that the increased
volatility occurs due to rising profits of winning trades. Note that the fixed
15contract downside volatility is the highest, followed by the variable #2 and
variable #1 strategies. There is not a large difference in downside volatility
between the fixed 1contract strategy and variable #1 strategy, which buys one
contract at a time but on multiple days. Note also that the standard deviation
of all trades (including winning trades) is much greater than the downside
volatility. Thus, rather than all volatility being undesirable, note that
adding multiple contracts increases upside volatility more than downside
volatility. Increasing upside volatility is easier to cope with than sharply
rising downside volatility.
In summary,
if your account equity and mental makeup permit, consider the benefits of a
multiple contract strategy.
32 Principles of Trading System Design
Rule
5: Risk Control, Money Management, and Portfolio Design
All traders
have accounts of finite size as well as written or unwritten guidelines for
expected performance over the immediate future. These performance guidelines
have a great influence over the existence and longevity of an account. For
example, consider a trading system that produces a 30 percent loss over five
months. The same trading system then goes on to perform extremely well. One
person may close the account after the 30 percent drawdown. Another may go on
to reap excellent returns. Your money management rules could cause you to
close out an account too soon, or keep it open too long. Thus, money management
guidelines are crucial to trading success.
Given
performance expectations and finite size of the trading account, it is
essential to maintain good risk control, sensible money management, and good
portfolio design. Risk control is the process of managing open trades with
predefined exit orders. Money management rules determine how many contracts to
trade in a given market and the amount of money to risk on particular
positions. Portfoliolevel issues must be considered to obtain a smoother
equity curve.
Table 2.7 illustrates the effects
of not using an initial money management stop versus adding an initial money
management stop of $2,000. The trading system, a 'canned' system
using four consecutive up or down closes to initiate a trade, comes with the
Omega Research's System Writer Plus™.
As expected, the largest losing
trade can be horrifying, and most realworld accounts would probably close
before swallowing such huge losses. Of course, recent headlines of
billiondollar plus losses in sophisticated trading firms illustrate that
trading without adequate risk control is not uncommon.
Adding a
money management stop constrains the worst initial loss to predictable levels.
Even with slippage, the largest loss is usually lower than trading without any
stop at all. Thus, your profitability is likely to improve with improved risk
control. Observe that average net profits improved from a loss of $5,085 with
no stop to a loss of $424 using risk control. The maximum drawdown also
improved with the added risk control. The lesson from this comparison is clear.
There is much to gain if you use proper risk control.
You can
reduce swings in equity and improve account longevity if you combine risk
control with sound money management ideas. Your money management guidelines
will specify how much of your equity to
Rule 5: Risk Control,
Money Management, and Portfolio Design
33
Table 2.7
Effect of adding an initial money management stop, May 1989June 1995 (dollars)
Market


No Stop



$2000 Stop


Net Profit

Largest Loss

Maximum Drawdown

Net Profit

Largest Loss

Maximum Drawdown

Coffee

4,206

50,868

24,149

33,776

2,594

13,970

Copper

5,082

3,542

14,810

5,455

2,302

20,430

Cotton

4,370

4,620

14,585

7,580

3,025

13,800

Crude oil

14,350

12,350

20,760

8,690

2,870

15,100

Gold, Comex

7,180

2,250

6,560

3,750

2,340

6,650

Heating oil

16,758

4,174

16,350

378

3,989

16,334

Japanese

36,800

6,550

65,673

23,675

3,388

50,300

yen







Sugar

9,770

3,594

14,428

7,799

2,194

12,456

Swiss franc

8,225

7,613

16,438

15,688

2,663

15,263

10year Tnote

15,913

4,413

29,444

8,788

2,100

21,881

U.S. bond

16,506

6,194

28,969

10,625

2,100

22,856

Worst

36,800

50,868

65,673

23,675

3,989

50,300

Best

16,758

2,250

6,560

33,776

2,100

6,650

Average

5,085

9,652

22,924

424

2,688

19,004

risk on any
trade. These guidelines convert the initial stop into a specific percentage of
your equity. One common rule of thumb is to risk or 'bet' just 2
percent of your account equity per trade.
The
2percent rule converts into a $1,000 initial stop for a $50,000 account. This
$1,000 initial stop is often called a 'hard dollar stop,' applied to
the entire position. A position could have one or more contracts. Thus, if you
had two contracts, you would protect the position with a stop loss order placed
$500 away from the entry price. Chapter 7 discusses the bet size issue in
detail.
Overtrading
an account is a common problem cited by analysts for many account closures. For
example, if you consistently bet more than 2 percent per trade, you are
overtrading an account. If you do not use any initial money management stop,
then the risk could be much greater than 2 percent of equity. In the worst
case, you risk your entire account equity. Some extra risk, say up to 5 percent
of equity, may be justified if the market presents an extraordinary market
opportunity (see chapter 4). However, consistently exceeding the 2 percent
limit can cause large and unforeseen swings in account equity.
Principles of Trading
System Design
As another
rule of thumb, you are overtrading an account if the monthly equity swings are
often greater than 20 percent. Again, there may be an occasional exception due
to extraordinary market conditions.
You mast also consider the benefits and
problems of diversification, that is, trading many different markets in a
single account. The main advantage of trading many markets is that it
increases the odds of participating in major moves. The main problem is that
many of the markets respond to the same or similar fundamental forces, so their
price moves are highly correlated in time. Therefore, trading many correlated
markets is similar to trading multiple contracts in one market.
For
example, the Swiss franc (SF) and deutsche mark (DM) often move together, and
trading both these markets is equivalent to trading multiple contracts in
either the franc or the mark. Let us look specifically at SF and DM continuous
contracts from May 26, 1989, through June 30, 1995, with a dual moving average
system using a $1,500 stop and $100 for slippage and commissions. The two
moving averages were 7 and 65 days. As Figure 2.9 shows, the equity curves have
a correlation of 83 percent. For example, you would have made $60,619 trading
one
Comparison of equity curves: DM and SF
Date
Figure 2.9 Swiss franc and deutsche mark equity curves are highly
correlated at 83 percent.
Rule 5: Risk Control,
Money Management, and Portfolio Design
35
contract
each of SF and DM, but your profits would have been $63,850 trading two
contracts of DM and $57,388 trading two contracts of SF.
Note one
important difference between the two cases. Since the two markets may have
negative correlation from time to time, the drawdown for both SF and DM
together may be in between trading two contracts of just DM or SF. For
example, the drawdown for SF and DM in this case was $10,186 versus $22,375
for two DM contracts and $9,950 for two SF contracts. Hence, the benefits of
trading correlated markets are relatively small. Thus, it may be better to
trade uncorrelated or weakly correlated markets in the same portfolio.
The
benefits of adding usually unrelated markets to a portfolio can be illustrated
by an example of trading the Swiss franc (SF), cotton (CT) and 10year Treasury
note (TY) in a single account, using the same dual moving average system as
above. The paper profits from trading three SF contracts add up to $86,801
versus $85,683 for SF plus TY and CT. The equity curve for the two combinations
is shown in Figure 2.10. The smoothness of the two curves can be compared by
using linear regression analysis to calculate the standard error (SE) of the
daily equity
Equity Curve: 3SF vs SF+TY+CT
Days (5/896/95)
Figure 2.10 Adding 10year Tnote
(TY) and cotton to the portfolio trading just Swiss francs provides a smoother
equity curve versus trading three SF contracts.
36
Principles of Trading System Design
Simulated 'Jagged' equity curve
4 5 6
7 8 9 Time (months)
Figure 2.11 This contrived jagged equity curve has a
standard error of 2.25. The perfectly smooth equity curve has an SE of zero.
The standard deviation of monthly returns is 33 percent.
curve. The
SE for trading three SF contracts in $6238, and the SE for SF and TY plus CT is
just $4,902, a reduction of 21 percent. Thus, adding TY and CT to a portfolio
of SF produced a smoother equity curve with essentially the same nominal
profits.
The
relevance of the standard error is illustrated in Figure 2.11, which shows a
contrived equity curve. The SE for that curve was 2.25, since it was quite
'jagged.' A perfectly smooth equity would have an SE reading of zero.
Diversification
can be more than just adding markets. You
can also trade multiple trading systems and multiple time frames within a
single account. You should try to use
uncorrelated or weakly correlated systems. In summary, risk control, money
management, and portfolio design are important issues in designing trading
systems.
Rule
6: Fully Mechanical System
The simplest
answer to why a system must be mechanical is that you cannot test a
discretionary system over historical data. It is impossible to
Summary 37
forecast
what market conditions you will face in future and how you will react to those
conditions. Therefore, in this book, we will restrict ourselves to fully
mechanical systems.
If you can
define how you make discretionary decisions, then these rules could be
formalized and tested. The process of formalization could itself provide many
interesting ideas for further testing. Hence you are encouraged to move toward
mechanical systems.
You are more likely to make consistent
trading decisions if you use mechanical systems. The manner in which a
mechanical system will process price data is predictable, and hence assures
that you will make consistent trading decisions. However, there is no assurance
that these logically consistent decisions will also be consistently profitable.
Nor is there any assurance that these trading decisions will be implemented
without modification by the trader.
Summary
This
chapter developed a checklist for narrowing your trading beliefs. You should
narrow your beliefs down to five or less to build effective trading systems
around them.
This
chapter also reviewed six major rules of the system design. A trading system
with a positive expectation is likely to be profitable in the future. The
number of rules in a system should be limited because increasing complexity
often hurts performance. Relatively simple systems are likely to fare better in
the future. The rules should be robust, so they will be profitable over long
periods and over many markets. You should trade multiple contracts if possible
because they allow you to make more profits when you are right. Risk control,
money management, and portfolio design give you a smoother equity curve and
are the keys to profitability. Lastly, a system should be mechanical to
provide consistent, objective decision making. You should follow the six major
rules to build superior systems that are consistent with your trading beliefs.