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The Cost of Technical Trading Rules in the Forex Market:

A Utility-based Evaluation

Hans Dewachter and Marco Lyrio

ERIM R EPORT S ERIES R ESEARCH IN M ANAGEMENT

ERIM Report Series reference number

ERS-2003-052-F&A

Publication status / version

May 2003

Number of pages

Email address corresponding author

hdewachter@fbk.eur.nl

Address

Erasmus Research Institute of Management (ERIM)

Rotterdam School of Management / Faculteit Bedrijfskunde

Rotterdam School of Economics / Faculteit Economische

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B IBLIOGRAPHIC DATA AND CLASSIFICATIONS

Abstract

We compute the opportunity cost for rational risk averse agents of using technical trading rules in

the foreign exchange rate market. Our purpose is to investigate whether these rules can be

interpreted as near-rational investment strategies for rational investors. We analyze four di.erent

exchange rates and find that the opportunity cost of using chartist rules tends to be prohibitively

high. We also present a method to decompose this opportunity cost into parts related to investor’s

irrationality and misallocation of wealth. The results show that irrationality of chartist beliefs is an

important component of the total opportunity cost of using technical trading rules.

5001-6182

Library of Congress

Classification

(LCC)

Business

5601-5689

4001-4280.7

Accountancy, Bookkeeping

Finance Management, Business Finance, Corporation Finance

HG 4638

Technical analysis securities

Journal of Economic

Literature

(JEL)

Business Administration and Business Economics

M 41

G 3

Accounting

Corporate Finance and Governance

F 31

G 15

Foreign Exchange

International Financial Markets

European Business Schools

Library Group

(EBSLG)

85 A

Business General

225 A

220 A

Accounting General

Financial Management

220 T

Quantitative methods for financial methods

Gemeenschappelijke Onderwerpsontsluiting (GOO)

85.00

Bedrijfskunde, Organisatiekunde: algemeen

85.25

85.30

Accounting

Financieel management, financiering

Keywords GOO

85.33 Beleggingen

Bedrijfskunde / Bedrijfseconomie

Accountancy, financieel management, bedrijfsfinanciering, besliskunde

Effectenhandel, Beleggingen, wisselkoersen, Rationaliteit

Free keywords

technical trading rule, exchange rate

Classification GOO

The Cost of Technical Trading Rules in the Forex Market:

A Utility-based Evaluation

and Marco Lyrio a

a CES, Catholic University of Leuven

b RIFM and ERIM, Erasmus University Rotterdam

Hans Dewachter a,b∗

May 2003

Abstract

We compute the opportunity cost for rational risk averse agents of using technical trading

rules in the foreign exchange rate market. Our purpose is to investigate whether these rules

can be interpreted as near-rational investment strategies for rational investors. We analyze

four diﬀerent exchange rates and ﬁ nd that the opportunity cost of using chartist rules tends

to be prohibitively high. We also present a method to decompose this opportunity cost

into parts related to investor’s irrationality and misallocation of wealth. The results show

that irrationality of chartist beliefs is an important component of the total opportunity

cost of using technical trading rules.

Keywords: technical trading rule, exchange rate.

J.E.L.: F31, G15.

Corresponding author. Address: Center for Economic Studies, Catholic University of Leuven, Naamses-

traat 69, 3000 Leuven, Belgium. Tel: (+)32(0)16-326859, e-mail: hans.dewachter@econ.kuleuven.ac.be. We are

grateful for ﬁ nancial support from the FWO-Vlaanderen (Project No.:G.0332.01). The latest version of this pa-

per can be downloaded from http://www.econ.kuleuven.ac.be/ew/academic/intecon/Dewachter/default.htm.

The authors are responsible for remaining errors.

∗

1In odu ion

Despite the numerous studies reporting the pervasive use of technical trading rules and their

pro ﬁ tability, 1 there is still a considerable amount of scepticism in the academic literature

regarding their true value. Critics of chartist rules often point to the seemingly suboptimal

nature of the portfolio composition implied by these rules (e.g. Skouras, 2001). After all,

investment strategies based on technical trading rules (i) restrict the information set to a

narrow group of pre-de ﬁ ned information variables, (ii) assume a positive relation of the signal

with future expected excess returns 2 , and (iii) imply a bang-bang type of investment strategy,

i.e. a strategy where all wealth is invested either short or long. Each of these assumptions

goes against the standard rational investor paradigm. The ﬁ rst two assumptions possibly go

against the rationality of expectations formation, while the third is in general at odds with

the assumption of risk aversion.

In this paper, we assess the value of technical trading rules for rational risk averse investors.

The main motivation being that even if technical trading rules turn out to be suboptimal

rules, the observed practice of using these rules could still be near rational for a large class

of risk averse agents. More speci ﬁ cally, if the cost (as measured, for instance, by certainty

equivalents) for risk averse agents of using technical trading rules is low, one may argue that

following these (irrational) rules of thumb may come close to the optimal trading strategy

and could, therefore, be rationalized in terms of information cost type of arguments.

The opportunity cost associated with the use of technical trading rules for risk averse

agents can be decomposed in two components: the ﬁ rst component relates to the potential

error in the assumed relation between the chartist signal and the expected future return (ex-

pectational error); the second component originates from the suboptimality of the investment

strategy (allocation error). We present a simple method to compute each of these components.

The method involves the introduction of a hypothetical risk neutral agent. Risk neutral liq-

uidity constrained agents have in common with technical traders that investment strategies

will be typically bang-bang solutions, i.e. either invest all wealth in the long or in the short

side. In fact, as argued by Skouras (2001), as long as the chartist signal is one-to-one with

the expected future excess return, chartist trading strategies are equivalent to those of a ra-

tional risk neutral liquidity constrained agent. In this case, chartist rules are, therefore, also

rational. Diﬀerences in the trading positions of a risk neutral and a technical trader isolate,

therefore, the costs associated with expectational errors in the relation between the technical

trading signal and the expected return. The second cost component -associated with the

misallocation of wealth- can be recovered by contrasting the portfolio positions of risk averse

and risk neutral agents. Since both agents have identical expectations, the diﬀerence in their

trading positions can be linked to the costs of risk averse agents investing according to bang-

bang investment strategies. Combining these cost components results in a total opportunity

1 See, among others, Gençay (1999); LeBaron (1992, 1999, 2000); Neely et al (1997); and Taylor (1980).

2 We assume here a standardized rule where a positive (negative) technical trading signal corresponds to a

long (short) investment position.

cost for a rational risk averse agent of using technical trading rules. We use this technique

to identify possible classes of risk averse agents for which these opportunity costs are limited.

In this case, one could perhaps rationalize the use of trading rules in terms of near-rational

behavior.

Computing the costs of chartist trading rules implies both the identi ﬁ cation of technical

trading signals and the design of a statistical model to relate the conditional moments of the

excess returns to the technical trading signal. In this paper, we restrict the analysis to the

class of moving average signals, or rules. We select this class as it constitutes the most widely

used class of technical trading rules in the foreign exchange market. These rules have also

been shown to be robust in their pro ﬁ t generating capacities. We also opt for a relatively

simple model relating return moments to the trading signal. While more advanced techniques

such as the nonparametric regression technique of Brandt (1999), or nonlinear models such as

neural nets (Gençay, 1999) or Markov switching models (e.g. Dewachter, 2001) could be used,

we try to strike a balance between generality and computational costs. We, therefore, use a

regression approach to estimate possible time-varying parameters of a Taylor expansion of the

relation between return moments and trading signals. This approach is suﬃciently ﬂ exible

to allow for nonlinearities in the signal-return moment relation while at the same time it is

computationally tractable so as to allow for continuous updating of the parameters.

The remainder of the paper is organized in three main sections. In section 2, we discuss

the proposed decomposition of the costs associated with the use of technical trading rules.

The empirical results are presented in section 3. In this section, we ﬁ rst analyze the statistical

models relating trading signals to return moments. We do ﬁ nd evidence of a nonlinear relation

both for the expected return and for the conditional variance. Using these models to construct

the optimal portfolio rule for classes of risk averse agents, we subsequently analyze the value

of technical trading signals and the costs associated with following technical trading rule

strategies. We summarize the main ﬁ ndings of the paper in the concluding section.

2 The opportunity cost of technical trading rules

Technical trading rules are typically rules of thumb that relate a certain information variable,

the technical trading signal, to a trading position. Denoting the time t technical trading signal

by z t , the technical trading rule speci ﬁ es a mapping from the signal z t to an advised trading

position ω CH (z t ) . A typical feature is the discontinuity in the mapping ω CH (z t ).Weassume

that the trading signal has been standardized such that the trading rule, i.e. the mapping

from the signal to the trading position, can be described by:





b if z t > 0

ω CH (z t )=

0 if z t =0

(1)

−b if z t < 0

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