Co‐evolved genetic programs for stock market trading

• Author: Jason F. Nicholls,Andries P. Engelbrecht
• Date: 01 July 2019
• DOI: http://doi.org/10.1002/isaf.1458
• Published date: 01 July 2019

RESEARCH ARTICLE

Co‐evolved genetic programs for stock market trading

Jason F. Nicholls

1

|Andries P. Engelbrecht

2

1

Department of Computer Science, University

of Pretoria, Pretoria, South Africa

2

Department of Industrial Engineering and

Computer Science Division, Stellenbosch

University, Stellenbosch, South Africa

Correspondence

Jason F. Nicholls, Department of Computer

Science, University of Pretoria, Pretoria, South

Africa.

Email: jason.nicholls@tuks.co.za

Summary

The profitability of trading rules evolved by three different optimised genetic pro-

grams, namely a single population genetic program (GP), a co‐operative co‐evolved

GP, and a competitive co‐evolved GP is compared. Profitability is determined by trad-

ing thirteen listed shares on the Johannesburg Stock Exchange (JSE) over a period of

April 2003 to June 2008. An empirical study presented here shows that GPs can gen-

erate profitable trading rules across a variety of industries and market conditions. The

results show that the co‐operative co‐evolved GP generates trading rules perform

significantly worse than a single population GP and a competitively co‐evolved GP.

The results also show that a competitive co‐evolved GP and the single population

GP produce similar trading rules. The profits returned by the evolved trading rules

are compared to the profit returned by the buy‐and‐hold trading strategy. The

evolved trading rules significantly outperform the buy‐and‐hold strategy when the

market trends downwards. No significant difference is identified among the buy‐

and‐hold strategy, the competitive co‐evolved GP, and single population GP when

the market trends upwards.

KEYWORDS

co‐evolution, co‐operative co‐evolution, competitive co‐evolution, genetic programming,

Johannesburg Stock Exchange, stock market trading, technical analysis

1|INTRODUCTION

A genetic program (GP) is a domain‐independent meta‐heuristic algo-

rithm that genetically breeds a population of computer programs to

solve a problem (Koza & Poli, 2005). Meta‐heuristic algorithms search

the solution space by avoiding parts of the search space that produce

poor solutions. The result is an approximate solution to the optimisa-

tion problem under consideration (Bäck, 1996; Bäck & Schwefel,

1996; Engelbrecht, 2007; Fogel, 2006a).

Originally developed by Koza (Koza, 1992) in the late 1980s to

evolve computer programs, a GP can evolve trading rules using basic

mathematical operations. Allen and Karjalainen (Allen & Karjalainen,

1995; 1999) used a GP to evolve trading rules for the S&P 500 index

using daily prices from 1928 to 1995. Their approach used a single

population of individuals to evolve a trading rule over a fixed number

of generations. The single population GP of Allen and Karjalainen was

reimplemented by Neely et al. (Neely et al., 1997), Telbany

(El‐Telbany, 2004), Mahfoud and Mani (Mahfoud & Mani, 1996; Mani

et al., 1995), Li and Tsang (Tsang, 2009; Tsang et al., 1998), and

Potvina et al. (Potvina et al., 2004) with varying degrees of success.

In nature, populations rarely evolve in isolation. Instead, popula-

tions evolve in co‐operation with other populations or in competition

with other populations (Rosin & Belew, 1997). This paper proposes a

co‐operative and competitive co‐evolutionary approach to GP for

evolving trading rules. The performance of trading rules evolved

through co‐operative and competitive co‐evolution is compared to

trading rules derived by the single population GP of by Allen and

Karjalainen (Allen & Karjalainen, 1995, 1999). It is shown that co‐

operative co‐evolved GP generated trading rules perform significantly

worse than trading rules generated by a single population GP and a

competitively co‐evolved GP. The results also show that a competitive

co‐evolved GP and the single population GP produce similar trading

rules. The profits returned by the evolved trading rules are compared

to the profit returned by the buy‐and‐hold trading strategy. The

Received: 2 May 2019 Revised: 26 August 2019 Accepted: 26 August 2019

DOI: 10.1002/isaf.1458

Intell Sys Acc Fin Mgmt. 2019;26:117–136. © 2019 John Wiley & Sons, Ltd.wileyonlinelibrary.com/journal/isaf 117

results show that the evolved trading rules significantly outperform

the buy‐and‐hold strategy when the market, including fees trends

downwards. No significant difference is found among the buy‐and‐

hold strategy, the competitive co‐evolved GP, and single population

GP when the market (including fees) trends upwards.

Section 2 provides a short background on the use of technical anal-

ysis in stock market trading and the application of evolutionary algo-

rithms (EAs) in stock market trading. Section 3 discusses Allen and

Karjalainen's implementation of a GP for stock market forecasting

and how it was adapted for this study. Section 4 describes both co‐

evolved strategies in detail. Section 5 presents the empirical process

and stock market data used for the purpose of this study. Section 6

presents the results of the study. This paper is concluded by Section

7 which presents a summary of the findings and proposals for

future work.

2|BACKGROUND

Stock market analysis is generally ex‐ante, focusing on the impacts of

long‐term cash flows, earnings and revenue. This type of ex‐ante anal-

ysis is known as fundamental analysis Peterson (2007). Fundamental

analysis focuses on analysing company fundamentals such as revenue,

assets, production rates, demand, and interest rates. Fundamental

analysis often relates back to the share price to determine the future

price. Analysis of the share price is known as technical analysis (Peter-

son, 2007). A belief that the share price reflects all known fundamen-

tal information is referred to as the efficient market hypothesis (EMH)

(Fama, 1965).

Charles Dow (Cowles, 1933; Edwards et al., 2007; King, 1934)

argued that the market is not completely efficient, but that fundamen-

tal information rather takes time to propagate through the market. The

propagation of fundamental information is therefore reflected in the

movement of the share price. Dow believed that if the share price is

on the rise, the probability of a continued rise is greater than a fall

and vice versa, resulting in a perceived direction overtime known as

a trend (Cowles, 1933; James, 1968; King, 1934). Dow proposed the

first scientific stock movement theory known as Dow theory (Bishop,

1961; Edwards et al., 2007). Dow theory states that a market is either

in an upward trend, downward trend, or continuing in the same direc-

tion (Bishop, 1961; Edwards et al., 2007; Rhea, 1993).

Technical analysis techniques use the historic share price to find

which of the three Dow trends the market is in and if the trend may

change. Knowledge of the trend, and if the trend is changing, gives

guidance as to when a trader should buy or sell a share. A simple mov-

ing average (SMA) is a technical analysis function used to determine

the current market trend. Summing the share price for nconsecutive

days before a specific day tand dividing the result by nreturns the

average price of the share over time for the day t.

A comparison of different moving averages can reinforce the trend

certainty. For example, if the 10‐day SMA follows the same direction

as the 50‐day SMA, then it can be assumed that the trend is set. If

the two moving averages do not follow the same direction, it could

signify a trend reversal. Brock et al. (Brock et al., 1992) examined

the returns generated by various SMAs against the Dow Jones Index

from 1897 to 1986. Brock et al. showed that when costs are excluded,

SMAs can generate profitable buy and sell rules. Many variations of

the SMA function exist. Two variations are:

•the weighted moving average (WMA), defined as:

WMAðnÞ¼ωPtþðω−1ÞPt−1þ…þPt−nþ1

ωþðω−1Þþ …þ1(1)

where P

t

is the opening, closing, high, or low share price on day t,ω

is a weight. In this example, ωis equal to n.

•the exponential moving average (EMA), defined as:

EMAðnÞ¼αnPtþαn−1Pt−1þ…þαPt−nþ1

αnþαn−1þ…þα(2)

where α¼1−2

nþ1and αis the weight.

A common technique used to determine the trend using two dif-

ferent moving averages is to subtract the longer (i.e. slower) moving

average from the shorter (i.e. faster) one. A positive result indicates

an upward trend, a negative result indicates a downward trend, and

a zero result indicates a moment of uncertainty. In the 1960s, Appel

(Achelis, 2013; Bäck et al., 1997; Tilkin, 2001) subtracted a 26‐day

EMA from a 12‐day EMA, and called this the moving average conver-

gence divergence (MACD) (Achelis, 2013; Tilkin, 2001).

The SMA, EMA, WMA, and MACD are just four of the many tech-

nical analysis functions that exist (Edwards et al., 2007). Each function

requires a set of parameters that may be unique to a specific stock or

market. Technical analysis functions are combined to form a trading

rule. An example of a trading rule is to buy shares when the 20‐day

SMA is greater than its 50‐day WMA; otherwise sell the shares held.

Selecting which technical analysis functions to use, and determin-

ing the correct parameters to form a trading rule is an optimisation

problem. Bauer (Bauer, 1994) was one of the earliest researchers to

use a class of meta‐heuristics known as genetic algorithms (GAs) (Hol-

land, 1992) to optimise the combination of technical analysis functions

and parameters to maximise return on a set of stock trades.

A GA is based on simulated evolution (Bäck et al., 1997; Fogel,

2006b). Simulated evolution breeds a population of candidate solu-

tions called individuals to solve a specific problem (Koza & Poli,

2005). Specifically, GAs iteratively transform a population of individ-

uals into new generations of individuals by applying the analogue of

naturally occurring genetic operations. Each individual has a set of

phenotypes encoded as genes within a chromosome.

Friedman and Fraser (Bäck et al., 1997; Fogel, 2006b; Friedman,

1956) are recognised as the first to experiment with GAs. However,

it was Holland (Bäck et al., 1997; Holland, 1992, 2000, 1995) that

formalised the first version of a GA. Holland's emulation of evolution

used a fixed length binary string representation of a chromosome.

Rather than optimising which technical analysis functions to use

with which parameters for a given stock, a technical analysis function

118 NICHOLLS AND ENGELBRECHT