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QUANTITATIVE FINANCE VOLUME 1 (2001) 397–413 RESEARCH PAPER

INSTITUTE OF PHYSICS PUBLISHING quant.iop.org

A real-time adaptive trading system

using genetic programming

M A H Dempster andCMJones

Centre for Financial Research

, Judge Institute of Management, University of

Cambridge, Trumpington Street, Cambridge, CB2 1AG, UK

E-mail: mahd@jims.cam.ac.uk and cmj24@cam.ac.uk

Received 15 October 2000

Abstract

Technical analysis indicators are widely used by traders in ﬁnancial and

commodity markets to predict future price levels and enhance trading

proﬁtability. We have previously shown a number of popular indicator-based

trading rules to be loss-making when applied individually in a systematic

manner. However, technical traders typically use combinations of a broad

range of technical indicators. Moreover, successful traders tend to adapt to

market conditions by ‘dropping’ trading rules as soon as they become

loss-making or when more proﬁtable rules are found. In this paper we try to

emulate such traders by developing a trading system consisting of rules based

on combinations of different indicators at different frequencies and lags. An

initial portfolio of such rules is selected by a genetic algorithm applied to a

number of indicators calculated on a set of US Dollar/British Pound spot

foreign exchange tick data from 1994 to 1997 aggregated to various intraday

frequencies. The genetic algorithm is subsequently used at regular intervals

on out-of-sample data to provide new rules and a feedback system is utilized

to rebalance the rule portfolio, thus creating two levels of adaptivity. Despite

the individual indicators being generally loss-making over the data period,

the best rule found by the developed system is found to be modestly, but

signiﬁcantly, proﬁtable in the presence of realistic transaction costs.

1. Introduction

Some ﬁnancial and commodity market traders study market

price history with a view to predicting future price changes in

order to enhance trading proﬁtability. This study is known

as technical analysis. In their surveys, Taylor and Allen

(1990, 1992) found that over 90% of surveyed London foreign

exchange (FX) dealers and traders use technical analysis of

some sort. Furthermore, a 1995 survey of FX dealers in Hong

Kong by Lui and Mole (1998) found technical analysis to be

signiﬁcantly more popular than fundamental analysis at shorter

time horizons. Many traders aim to practice technical analysis

Now Director, Portfolio Management, Gensec International Asset

Management and Visiting Teaching and Research Associate, Centre for

Financial Research, Judge Institute of Management, University of Cambridge.

Web address: www-cfr.jims.cam.ac.uk

as systematically as possible without automation while others

use technical analysis as the basis for constructing systems

that automatically recommend trade positions. In this paper

we construct such a system in an attempt to analyse the actions

of the wide body of traders who practice technical analysis.

An introduction to the practice of technical analysis is given

by Neely (1997) from an academic viewpoint and a classic

practitioner text is Colby and Meyers (1988).

Despite the wide coverage of trading systems in the

existing practitioner literature, the majority of academic work

in the area of systematic trading concerns itself with individual

trading rules. When trading systems are discussed in either

the practitioner (for example, Pardo (1992), Schwager (1996))

or academic (for example, Gencay et al (1998)) literature,

little attention is paid to system construction as opposed to

rule construction. An exception is Pictet et al (1992) who

M A H Dempster and C M Jones QUANTITATIVE F INANCE

presented a system-based approach, but here the emphasis

is on a broad-based system that encompasses data-capture

and storage through to bookkeeping, as opposed to a trading

system per se. Furthermore, there has been little attention

paid to systematic adaptation within trading systems (with the

exception of Moody et al (1997)) despite the degree to which

systematic traders constantly change their rules. In this paper

we focus on system construction and consider adaptation.

Also, for realism, we use intraday data in this work. The

consideration of such data is particularly useful when analysing

returns of technical trading rules; many traders apply rules at

intraday frequencies

and of those traders who only analyse

daily data for entry signals, many will use intraday data for

trade exit, especially when stops

are placed in the market.

Thus, the use of intraday data adds realism when analysing

trading rules.

Other work in this area includes Levitt (in Refenes (1995))

who has proposed using the method of genetic-based global

learning in a FX trading system. Here, genetic algorithms are

used to attempt to ﬁnd the best combination indicators (out

of the moving average crossover and a more complex moving

average-based indictor—the ADX) for prediction and trading.

Results are shown to be proﬁtable but are reported in too little

detail for objective scrutiny.

Dunis et al (in Dunis and Zhou (1998)) have developed

a FX trading system that uses genetic algorithms to optimize

parameters (in the style of Colin in Deboeck (1994)) for a

simple technical trading indicator—the RSI. This work has

considerable merit since intraday data are used. However, the

study considers a period of only 129 days and so results are

far from conclusive. It is noted that the ultimate aim of such a

project would be to create a system based on an ensemble of

indicators—a task we attempt below.

In this paper, we introduce a framework for systematic

trading system construction and adaptation, based on genetic

algorithms (GAs)—in fact, genetic programmes (GPs).

Previously, Neely et al (1997) and Allen and Karjalainen

(1999) have used genetic programming to discover proﬁtable

trading rules, this work is further discussed in section 4. Here,

our aims are twofold: to develop a system that trades proﬁtably

and to emulate the behaviour of a technical trader who adapts

to the market. Previously, academics have asked the question

‘can technical trading rules consistently make a proﬁt?’ being

driven by the implications for market efﬁciency. Here we

ask the questions: ‘can a technical trader consistently make a

proﬁt?’ and ‘should a technical trader or trading system adapt

to market conditions or is it better to use a static system?’ The

work that follows provides at least some provisional answers,

which are further investigated in Dempster and Jones (2000)

and Dempster et al (2000).

The paper is laid out as follows. Sections 2 and 3

respectively introduce brieﬂy the concepts of GAs and GPs

As a whole, the operations of intraday FX traders account for 75% of FX

market volume (Bank of International Settlements 1998).

A stop is a predetermined price level at which the trader will exit the trade.

A stop that is placed in such a way that a trade is exited after the price moves

down a set amount from the maximum price attained during the trade (and

similarly mutatis mutandis for short trades) is known as a trailing stop (see

Schwager (1996) and James and Thomas (1998)).

and describe the GBP/USD data used. The trading system

developed is described in section 4, while the details of the

genetic programme utilized are given in section 5. Section

6 contains our trading results for both static and dynamic

trading strategies. Conclusions are drawn and current research

described in section 7 and an appendix contains precise

speciﬁcations of the six technical indicators used in this study.

2. Genetic algorithms and genetic

programming

Genetic algorithms, initially developed by Holland (1992,

revised reprint of his 1975 PhD thesis, see also Holland (1976,

1980, 1986)), are iterative systems that aim to ﬁnd near-optimal

solutions to multi-extremal problems by imitating the process

of evolution. GAs are search algorithms that differ from more

standard search algorithms in that the search is conducted using

a population of structures rather than a direction or single

structure. GAs consider many structures as potential candidate

solutions and work with a high level of global sampling of the

search space which increases the probability of convergence

to a global optimum. Although convergence to the global

optimum is not guaranteed, GAs are quite robust in producing

near-optimal solutions to a wide range of problems including

problems with high levels of uncertainty and problems which

are not easily reduced to a precise mathematical formulation.

The search is carried out in a ‘survival of the ﬁttest’ fashion

by evolving a set of potential solutions until the most superior

ones come to dominate. GAs are highly efﬁcient in searching

large spaces for attractive solutions to complex problems and

so would seem well suited to trading rule selection using a

large search space of rules tested over a considerable number

of time series data.

The starting point in using GAs to solve a problem is

to represent the problem in a way that a GA can work with.

This often amounts to representing the solution space as a

ﬁnite number of strings of binary digits. Binary strings are

an effective form of representation since complex statements

of Boolean logic as well as numerical values of parameters can

be represented in this form, e.g. the statement

IF (Function 1 evaluated at Frequency 1) = TRUE

AND (Function 2 evaluated at Frequency 2) = TRUE

THEN Buy US T-Bond Futures

can be easily expressed as a binary string. The resulting

search space is ﬁnite when parameters take only discrete values

to yield a binary representation as a string of ﬁxed length.

Secondly, there needs to be a means of evaluating the ﬁtness

of the constituents of the solution space, i.e. the suitability

of each potential solution, for how well they perform. For

example, in the case of selecting trading rules the ﬁtness could

be viewed as the proﬁtability of the rule tested over a time

series of historical price data. Finally, an initial population

of suitable solutions needs to be generated. The population

is the subset of the solution space on which the GA operates

at any one time step and in each trial it operates ﬁrst on the

initial population. The initial population is usually generated

by randomly sampling a number of potential solutions from

398

QUANTITATIVE F INANCE A real-time adaptive trading system using genetic programming

the search space. There are no strict rules for determining the

population size, although populations of 100–200 are common

in GA research. Users often experiment with population size,

however, since larger populations ensure greater diversity at

the cost of requiring greater computational resources. Once

the problem has been developed as described above, GAs

can be used to search for attractive solutions. Each stage of

the algorithm is discussed in detail in section 4 and further

information on genetic algorithms can be found, for example,

in Haupt and Haupt (1998).

As we have implied above, a genetic algorithm only

considers solutions with the same, ﬁxed string length. An

extension by Koza (1992), called genetic programming, allows

string length to vary within the solution space. With GPs,

strings (and hence solutions) can be seen as non-recombining

decision trees with the non-terminal nodes as functions

(including Boolean operators) and the root as the function

output. We use GPs rather than GAs in our system, in order

to harness their ﬂexibility but restrict the form of the binary

strings—equivalently decision trees—to prevent over-ﬁtting

(see section 5).

3. The data

This analysis was carried out on spot FX tick

data for the

British Pound/US Dollar exchange rate (BPUS, or ‘spot cable’

as it is sometimes called) ranging from 6.89 to 12.97 inclusive.

These data were supplied by CQG Data Factory and

FutureSource, two well-known data providers. The CQG

data—ranging from 6.89 to 3.96 inclusive—were gathered

from a number of FX brokers, whereas the FutureSource data,

stored from a live satellite feed via the Omega TradeStation

utility, are the amalgamated product of major bank FX quotes

and make up the remaining part of the data set. The fact that

the data set consists of actual quotes from two different source

providers is not ideal, but such problems are typical with the

analysis of high-frequency data based on non-exchange traded

instruments, since the majority of live tick data providers do

not retain historical data

The convention for quoting BPUS is to quote a ﬁve-digit

ﬁgure that represents the value of one British Pound in US

Dollars (most other currencies are quoted in a style opposite

to this) with an implicit decimal point after the ﬁrst digit; e.g.

a BPUS rate quoted 15104 means £1 = $1.5104.

The CQG data consist of bid and ask prices—the price that

the quoter would buy and sell British pounds for, respectively,

if approached in the market. The difference between the bid

and the ask (bid–ask) is called the spread. The convention

when dealing with such data is to convert them to midpoint

data:

(bid + ask) or, by deﬁnition, (bid +

spread) or (ask −

spread). In the event that bid and ask quotes are uncoupled

(which sometimes occurs), the bid or ask is converted to the

Here a new data point, or tick, is recorded with every change in price. As a

result there are often several ticks per minute.

It should be noted that the data consist of real quotes as opposed to the

‘representative quotes’ sometimes supplied by real-time data providers such

as Reuters and collected by Olsen and Associates.

midpoint by respectively adding or subtracting one half of the

spread calculated from the last bid/ask pair.

The above data tend to be well checked for errors by the

vendor. All the same, the data have been screened for structural

breakdown and irregular quotation by sweeping them with

simple software that checks for conformity to the conventional,

ﬁxed-width, comma-separated ASCII format, for well-ordered

temporal structure and for irregularly high or low ticks (which

are more than 500 pips

from the last quote). This last

screening has been backed up by graphical inspection of the

data.

The data have then been aggregated to various

frequencies in the standard open-high–low-close (OHLC)

format. Consider the set of time-stamped tick data {(q

)|0 <

i  K; i, K ∈ Z

} where K is the number of ticks in the set,

is the price level of the ith midpoint quote and t

is the time

at which the ith tick occurred (converted to be measured in

minutes elapsed since the start time—22:00 hours—and date

and so, on each day, t

= 0). The ticks are ordered temporally

but more than one tick may occur within the same minute and

so we have a weak inequality t

 t

i+1

. When such multiple

ticks occur they are listed in order of occurrence.

This data set is converted to sets of data aggregated to

various frequencies τ , denoted as τ minute frequencies; e.g. if

τ = 1, then frequency is minutely and is denoted 1 minute (but

1440 minute is called daily).

The aggregation to OHLC τ minute frequencies results in

the following data set:

{(o

)|0 <j  L; j, L ∈ Z

where o, h, l, c denote, respectively, open, high, low and close

quotes for bar b which for bar number j>0 is determined by

= (b

j−1

+ nτ )

n := inf{s|∃i ∈ [1,K]s.t.t

∈ [b

j−1

+ sτ ), s ∈ Z

}

:= 0

and

= q

where io := inf{m|t

∈ [b

− τ, b

)}

= q

where ic := sup{m|t

∈ [b

− τ, b

)}

= max {q

io+1

,...,q

}

= min {q

io+1

,...,q

By convention, b

is converted from minutes elapsed to time

and date format when quoted. These somewhat esoteric

deﬁnitions are required since the data are sometimes sparse

out of peak trading times.

4. Trading system

As previously discussed, the aims of constructing a software

entity that systematically trades ﬁnancial markets are two-

fold. Primarily, we have tried to develop a system that closely

A pip is the minimum allowable change in price—in this case $0.0001—-

also referred to as a basis point (bp) of a notional dollar.

399

M A H Dempster and C M Jones QUANTITATIVE F INANCE

Figure 1. System user interface.

resembles a technical trader who rationally

chooses his or her

trading strategies from an arsenal of popular technical trading

rules.

Another aim of this work is to analyse the impact of

changes in market conditions. Typically, after prolonged

trading loss most systematic traders will change their trading

rules (otherwise, they would lose the sponsorship of their

backers or institution). By developing a trading system that

has the potential to adapt to shifts in market conditions, we

hope to evaluate the performance of such strategies relative to

the more usually analysed static ‘select and hold’ strategy for

trading rule utilization.

System architecture

The system consists of a genetic-programming-based rule

selection engine which chooses trading strategies that are

combinations of popular technical analysis indicators and

rules. Choice is on the basis of selection criteria in terms of

trading proﬁt and downside risk over a user-deﬁned period of

time. The system has the capacity to use the chosen strategies

to subsequently perform out-of-sample testing on unseen data

or to live-trade in real-time using a live data feed. The trading

recommendations of the selected strategies are overlaid by

That is, systematically, based on prespeciﬁed evaluation criteria.

a cash management ﬁlter that exits trades when trading loss

exceeds a user-deﬁned threshold.

Outcomes (proﬁts, drawdowns, trades, etc) are reported

by means of a ‘trader’s log’ which summarizes individual

rule performance over the chosen selection and out-of-sample

periods. Below, we discuss each of these components in detail.

Figure 1 displays the user interface and a diagram of the system

architecture is given in ﬁgure 2.

Trading strategies

As is consistent with proprietary FX trading in a ﬁnancial

institution, we assume a ﬁxed-credit line in dollars with

notional principal one million to buy (long) pounds and the

equivalent amount in pounds to short dollars. Thus the system

buys or sells either currency in trades of a ﬁxed size of $1 m

equivalent. Trading proﬁt or loss over a speciﬁed period (one

quarter) is the cumulated value (in dollars) of net gains or losses

on these trades when they are exited after allowing for (round

trip) transaction costs (slippage).

As with previous work (see Dempster and Jones (1999a,

b, 2000)), we use the following model for slippage. Slippage

is a concept that is often alluded to but rarely speciﬁed. In this

work, we take slippage to be the penalty incurred when a trade

is placed as a result of the difference between actual price at

transaction execution time and previously quoted mid-price.

400

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