DISSERTATION. THANH THUY HOANG. 1201119.docx

Table of ContentsCHAPTER 1 3

INTRODUCTION 3

CHAPTER 2 6

LITERATURE REVIEW 6

2.1. The efficient market hypothesis 6

2.2. Literature of the wild bootstrapping variance ratio test 7

2.3. Literature of technical trading rules testing 9

CHAPTER 3 11

FOREIGN EXCHANGE MARKET, TECHNICAL TRADING RULES AND THE METHODOLOGIES OF TESTING 11

3.1. Foreign exchange market mechanism and features 11

3.2. Technical trading rules 12

3.3. Methodologies of testing 15

3.3.1. Variance Ratio test with Bootstrap methodology 15

3.3.2. Technical trading rules testing 17

CHAPTER 4 22

DATA 22

CHAPTER 5 25

EMPIRICAL RESULTS 25

5.1. Wild bootstrapping Variance ratio test 25

5.2. Traditional statistics of trading rules 27

CHAPTER 6 39

IMPLICATION AND EXPLANATION 39

CHAPTER 7 43

CONCLUSION 43

ACKNOWLEDGEMENTS 44

REFERENCES 45

APENDIX 1 49

1

Dissertation of MSc International

Money and Banking 2011-2012

TESTING EFFICIENCY OF FIVE MAJOR CURRENCY MARKETS BY A WILD BOOTSTRAPPING VARIANCE

RATIO TEST AND TECHNICAL TRADING RULES THANH THUY HOANG

Abstract:

This dissertation investigates the efficiency of five major currency markets which are

USD/JPY, USD/CHF, USD/AUD, USD/EUR, and GBP/USD. In this study, the market

efficiency hypothesis is examined by a wild bootstrapping variance ratio test and the

technical trading rules. According to the wild bootstrapping variance ratio test,

USD/AUD and USD/EUR follow the random walk process while the others do not. In

general, the results from testing the moving average rules and trading range

breakout rules support for the variance ratio test results, except for Australian Dollar

case. In more details, there are some evidences of the predictive power of technical

trading rules in the exchange rates which are confirmed that they do not follow

random walk by the variance ratio test.

2

TESTING EFFICIENCY OF FIVE MAJOR CURRENCY MARKETS BY A WILD BOOTSTRAPPING VARIANCE RATIO TEST AND TECHNICAL TRADING RULES

Keywords: Market efficiency hypothesis, Exchange rates, Variance ratio test,

Bootstrap, Technical trading rules, Dummy variables.

CHAPTER 1

INTRODUCTION

The foreign exchange (FX) market has a long history of development; especially it

has developed dramatically since the era of high technology revolution. With high-

speed Internet connection and supercomputers, a very large proportion of trade now

can be done electronically, automatically and the FX market becomes the most liquid

financial market in the world. Consequently, it attracts an enormous amount of

speculators who want to get a profit from the market. As the number of market

participants in FX market continues to increase, a debate about FX market efficiency

has been raised. Is it possible to enjoy excess returns on FX market just based on

historical trading data and automatic trading rules? Or is the market simply

unpredictable and no speculators can beat the market? There are two principal

schools of thought about this issue. The first school supposes that the FX market

follows the efficient market hypothesis (EMH), so exchange rates follows random

walk and it is impossible to earn abnormal returns on this market. By contrast,

advocates of the second school do not believe in EMH and there are some technical

trading rules can be utilized to make excess profit. In order to test this hypothesis,

random walk test and technical trading rules can be considered as the popular and MSc International Money and Banking

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favourite proxies. Indeed, these proxies were used to examine EMH by Lee et.al

(2001), Tabak and Lima (2009).

About the first proxy, if an exchange rate follows a random walk process, that FX

market can be considered as following the weak form of market efficiency and that

exchange rate cannot be predicted. There are many tools to test the random walk

hypothesis, however the variance ratio test is judged as the most powerful one

because of its advantages. This methodology is well known and used widely. For

example, Charles and Darne (2009) tested the random walk behaviour of exchange

rate of Euro against US dollar by a variance ratio test. However, in this dissertation,

the variance ratio test will be improved by combining with the bootstrap methodology

to test the random walk hypothesis.

Another way to test the predictability of the foreign exchange market is examining

the profitability of technical trading rules. According to Brock et.al (1992), technical

analysis has been used from 19th century and become well-known now. Although it

was originally developed in the stock market, technical analysis then has been

employed broadly in other markets such as gold, commodity or foreign exchange. It

is obvious that if trading rules can generate excess returns, it implies that exchange

rates can be forecasted and the market is inefficient. This dissertation explores two

simplest and the most popular technical rules in the foreign exchange market, which

are moving average strategy and trading break range. There were several papers

which investigated about the application of these rules in foreign exchange trading

and whether they make a profit or not. Some of them (Lee et.al (2001), Neely and

Weller (2003)) said that the technical trading rules are useless, however; others

MSc International Money and Banking4


(Neely et.al (1997), LeBaron (1999), Saacke (2002)) pointed out some evidences of

excess returns to technical trading rules in foreign exchange market.

It is apparent that variance ratio test, bootstrapping and the profitability of trading are

not new topics to finance literature. The initial contribution of this dissertation is,

however, using these techniques to investigate the profitability of trading rules in the

context of market efficiency hypothesis with updated data of the selected currency

pairs. Firstly, this dissertation applies bootstrap techniques into variance ratio test to

research the randomness of exchange rates. Secondly, my study uses t- test in

order to examine the significance of abnormal returns from trading rules. Moreover,

utilizing update data of five currency pairs (USD/JPY, USD/CHF, USD/AUD,

USD/EUR, GBP/USD) would help to revise the profitability of trading rules in a big

picture of the FX market and compare the application of trading rules in a pool of the

researched currency pairs. Some concepts in this dissertation are influenced by

Brock et.al (1992) and Lee et.al (2001) but my studied objects are different. Another

striking contribution of this study is providing some suggestions which based on

practical experiences, for why some currency pairs follow random walk and others

do not.

This study reveals that the results from wild bootstrapping variance ratio test are

generally consistent with the test of trading rules profitability. The variance ratio tests

suggest that USD/CHF, GBP/USD, USD/JPY do not follow the random walk process.

Indeed, there are some evidences of excess returns from trading these exchange

rates by examined trading rules. By contrast, in accordance with the variance ratio



tests, USD/AUD and USD/EUR follow random walk, which means that there is

impossible to earn abnormal returns from these currency pairs. Another remarkable

result is that, according to t- test statistics, there is little evidence of trading rules

profitability with USD/AUD data.

The structure of this dissertation is organised as follows: Literature of the wild

bootstrapping variance ratio test and technical analysis will be discussed in Chapter

2. Chapter 3 describes the foreign exchange market, technical trading rules and

testing methodology. The data will be explained clearly in the Chapter 4. Chapter 5

assesses the significance of results from the wild bootstrapping variance ratio test

and traditional statistics. Chapter 6 expresses the implication and explanation of

results. Finally, the conclusion is drawn in Chapter 7.

CHAPTER 2

LITERATURE REVIEW

2.1. The efficient market hypothesis

The efficient market hypothesis (EMH) states that a market is efficient when all

available information in the market is fully reflected into prices (exchange rates).

According to Fama (1970), there are three forms of market efficiency which are the

strong, the semi-strong and the weak form hypothesis (the return predictability

hypothesis by Fama (1991)). Among these forms, the weak- form EMH which



indicates a random walk is the most commonly examined topic in the empirical

literature.

If an exchange rate follows a random walk process, it means the market is the weak

form of the EMH. In this case, the exchange rate cannot be forecasted, so it is

impossible for speculators to earn abnormal returns. By contrast, if the null

hypothesis of random walk is rejected, the exchange rate is predictable and excess

returns could be generated using specific investment strategies.

2.2. Literature of the wild bootstrapping variance ratio test

Based on the above concept, there are enormous numbers of papers which

investigated the randomness of exchange rates. Lee et.al (2001) stated that the

variance ratio test is considered to be more powerful than other methods, such as

unit root tests and Box–Pierce Q test for serial correlations. In more details, Lee et.al

(2001) argued that the hypothesis of unit root only refers to the “zero-mean

stationary process” of the error, so an exchange rate which has a unit root can still

be forecasted, ultimately leading to the wrong conclusion of randomness. In fact, the

conventional form of variance ratio test was introduced first by Lo and MacKinlay

(1988). Applying this methodology, Liu and He (1991) found that five examined

currency pairs (CAD, JPY, GBP, FF and DM relatives to USD) reject the random

walk hypothesis at 5% significance level. With the set of Asian data, Ajayi and

Karemera (1996) indicated that the Malaysian ringgit, the Taiwanese dollar and the

Thai baht do not follow the EMH, whereas the rest five pairs (Hong Kong dollar,

Indonesia rupiah, Singaporean dollar, Korean won, Philippine peso) follow the

random walk process. The multiple variance ratio test then was developed by Chow



and Denning (1993). However, “These VR tests are asymptotic tests, which can

show small sample deficiencies”, stated by Kim (2006, p.1). Therefore, Kim (2006)

suggested the wild bootstrapping methodology to increase small sample properties

of these tests.

It is necessary to review the literature of this bootstrap method. Bootstrapping is

considered as “a procedure to measure the accuracy of an estimator” by Ruiz and

Pascual (2002, p4). The outstanding benefit of bootstrapping is that it does not

require any special assumption of the distribution of researched data. Another

advantage of this methodology is that it is very simple to use independently of the

complexity of statistics interest. Therefore, bootstrap is applied broadly to null

models such as GARCH models, Value at risk (VaR), Variance ratio test, to name

just a few. For example, Brock (1992) applied bootstrap methodology to generate

distribution of statistics under four null models which are a random walk with a drift,

AR(1), GARCH-M, EGARCH in order to test the trading rules profitability in the US

stock market. Bootstrap technique was also utilized by LeBaron (1999) in examining

the profitability of trading rules as central bank intervention.

Combining the bootstrap methodology with the Variance ratio test helps to check the

random walk hypothesis without the necessity of normality and homoscedasticity.

Therefore, there are many empirical studies which used both these methodologies.

Indeed, by applying Lo and MacKinlay (1988) test and resampling technique of

bootstrap, Chang (2004) concluded that the Japanese Yen reject the random walk

hypothesis while the Canadian dollar, the French Franc, the German mark and the

British pound are inclusive. In a different way, Lee et.al (2001) used multiple

variance ratio tests of Cecchetti and Lam (1994) with bootstrap technique to test MSc International Money and Banking

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EMH in nine currency pairs. From their conclusion, only the Korean won does not

reject the null hypothesis while the rest does. By mixing Lo and MacKlay VR (1988),

Cecchetti and Lam VR (1994) and bootstrapping, Lima and Tabak (2007) found

evidences of the randomness in 10 selected currency pairs.

It can be said that there are several ways to combine the variance ration test and the

bootstrapping technique. Kim (2006) proposed one of that, which is a wild

bootstrapping variance ratio test. According to Kim (2006, p.39), “It is a resampling

method that approximates the sampling distribution of a statistic, and is applicable to

data with unknown forms of conditional and unconditional heteroskedasticity”. This

combination of these methodologies becomes famous and is introduced to the

econometrics software as Eviews 7. This dissertation applied this method of Kim

(2006) and found there are evidences of random walk in USD/AUD and USD/EUR

data. The finding about the Australian Dollar is consistent with the recent results from

Lee et.al (2001) and Azad (2009). Accordingly, the randomness of USD/EUR

confirms the conclusion of Chen (2008).

2.3. Literature of technical trading rules testing

As stated above, testing profitability of technical trading rules can be considered as

another way to test the efficient market hypothesis. According to Murphy (1986) and

Pring (1991), technical analysis is based on three following principles. Firstly, prices

and volume in the market incorporate related information, so it is not necessary to

analyse fundamentals. Secondly, there are trends in the price movements. Thirdly,

“history tends to repeats itself”. Technical analysis method can be categorized into

two main schools: charts and indicators. The effectiveness of using technical



indicators in trading foreign currencies is still a controversial topic and it is mentioned

in numerous previous papers. Regarding to stock markets, Brock et.al (1992)

researched the moving average rules and trading range break out rules which are

the simplest and most popular by utilizing the Dow Jones index. In this paper, Brock

et.al (1992) tested in two cases which are trading rules with 1% band and without

band. The test results reported that there are several evidences of excess returns by

using these rules. However, when Hudson et.al (1996) repeated similar tests with the

UK stock market, the results found that although trading rules can predict the

movement of stock prices, it is impossible to earn abnormal returns in the presence

of costly trading. Hudson et.al (1996) also studied the relationship between technical

trading rules and the weak form of market efficiency.

For foreign exchange market, Lee and Mathur (1996) applied bootstrap methodology

in and out of sample tests to study the profitability of moving average trading rules

with six European spot cross rates data. They found that the moving average trading

rules only makes positive profits in case of JY/DM and JY/SF, whereas, in case of

other exchange rates, the profitability of these rules is not significant. From a

different perspective, LeBaron (1999) investigated trading rules profitability in the

context of central bank intervention in the United States. In particular, LeBaron

(1999) applied bootstrap methodology into testing whether moving average rules can

produce abnormal returns. The test results indicated that the simple moving average

rules can forecast movements in USD/JPY and USD/DM pairs noticeably.

Nevertheless, LeBraron (1999) findings also concluded that the forecast ability of the

trading rule declines significantly if the Fed’s intervention period was excluded.



Among previous studies, there are several papers which combine two above proxies

in order to test the random walk hypothesis. Lee et.al (2001) applied joint variance

ratio test and technical trading rules (moving average and channel) to test whether

nine Asian exchange rates follow the random walk process or not. Eight over nine

currency pairs rejected the null hypothesis at 5% significant level, which implies little

evidence of randomness of these exchange rates. The test results concluded that

these rules do not bring significant excess returns.

By replicating the methodologies, the study of Tabak and Lima (2009) employed

Brazilian exchange rate data to test the weak form efficiency. The variance ratio

tests of this work are used in combination with block bootstrap methodology to

prevent size distortions. Their first finding is that there are evidences of random walk

in the short run, but the null hypothesis is rejected in the long run. The second

conclusion is that the trading rules – Moving average rules and Trading range

breakout rules- are not significant in generating abnormal returns.

CHAPTER 3

FOREIGN EXCHANGE MARKET, TECHNICAL TRADING RULES

AND THE METHODOLOGIES OF TESTING

3.1. Foreign exchange market mechanism and features

Foreign exchange market is considered as the largest and the most liquid market on

the world with more than $4 trillion average daily trading volume (Bank for MSc International Money and Banking

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International Settlement, 2010). In this market, goods are not exchanged for money;

goods are indeed currencies - the monetary units. Indeed, the FX market is not a

physical place; it is mainly an electronic linking system among big banks, large

financial companies, brokers, dealers and so on. It can be said that this is the most

liquid market in comparison with others markets.

In the scope of this dissertation, there are two main concepts in this market which

should be considered. Firstly, the exchange rate is described as the price of foreign

currency denominated in domestic currency. Exchange rates can be expressed by

quoting the amount of domestic currency against U.S.Dollar (the most common way)

or vice-versa, for example GBP/USD. Secondly, bid and offer rate are often quoted

by two numbers which are bid (buys mark) and offer (sells mark) for example:

GBP/USD= 1.5675/85. Spread is the difference between two prices and it is often

very small. In order to calculate returns easily, this dissertation will ignore the spread

and use the middle rate instead of bid and offer rate.

Due to the wide availability of leverage using (up to 1:100), foreign exchange market

offers high potential profit, people always try to analysis in order to find any chance

of making money. There are two schools of analysing this market which are

fundamental analysis and technical analysis. The fundamental analysis refers to

economic growth, inflation, interest rate, monetary and fiscal policies, balance of

payment and so on. By contrast, the technical analysis refers to trading volume,

chart, price movement and theories.



3.2. Technical trading rules

Technical analysis originated with the simple form from the late of 1800s with the

work of Charles Dow. According to Edwards et.al (2007)- Bassetti 9 th ed, technical

analysis can be considered as “the study of the action of the market itself”. Indeed, it

utilizes the historical data of the exchange rates and summarizes in graphic forms in

order to deduce the movement of exchange rates in the past then forecast the

exchange rates in the future. As the main concept of technical analysis is that the

history repeats itself, technical analysis tend to studies the market background and

habits, consequently it includes a great variety of rules which represent for various

forms and trends of the exchange rate movement.

Two simplest rules can be listed as the moving average- oscillator and the trading

range break-out. The moving average strategy is a simple but popular and useful

tool, and another advantage of the moving averages is that it makes the volatile

series smoother. Along with the development of computers, there are various forms

of the moving averages which can categorized as Simple Moving Averages (SMA),

Weighted or Exponential Moving Averages (EMA), and Linear Moving Averages

(LMA). This study, however, just concentrates the simple-but-useful SMA, in which

buy and sell signals are generated when two moving averages of the exchange rates

cross each other. In more details, buy signals are created since the short- period

moving averages cross the long- period moving averages from below. By contrast,

sell signals are generated when the short - period moving averages cross the long-

period moving averages from above. The length of the period of moving averages

could be various, however the most popular length are 50 and 200 days. In order to

improve the sensitivity of moving averages, this dissertation will examine additionally MSc International Money and Banking

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10 and 20 days moving averages. The way of building up these moving averages is

the same with every moving average. For instance, 10 days moving average (MA-

10) is equal to the sum of the exchange rate of 10 days divided by 10. Repeating the

same procedure will create MA-50, MA-100 and MA-200. The moving average

strategy can lead to different decisions if band is introduced or not. In other words,

introducing band to moving average rules can bring various signals. Thus, this

dissertation will investigate both the moving average with band and without band

(1% band).

With the simple moving average strategy, this study will analyse thoroughly two

specific types which are the variable length moving average (VMA) and the fix length

moving average. Firstly, the variable length moving average is the rule in which buy

signals are generated when the short moving average penetrates the long moving

average on the upside; while sell signals are created as the short moving average

falls below the moving average line. Without band or a band of zero, the traders can

either buy or sell. By contrast, with a band, if the short moving average line is inside

the band, no signal is generated and trading signals would only are generated when

the short moving average is out of the band.

Secondly, the fix length moving average indicates that buy (sell) signals will be

generated when the short moving average line goes above (below) the long moving

average, then that position will be hold for x days. In next x days, any signals

generated will be ignored. Return of x days holding will be recorded to examine. This

study will investigate the fix length moving average with ten days returns. It should

be noted that there are several forms of moving average rules and this dissertation

just researches two simple types among them. MSc International Money and Banking

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The final rule which is tested in this dissertation is the trading range break out

(resistance and support levels). In technical analysis, resistance and support level

are the concepts related to the local maximum and minimum respectively. Because

traders believe that others will sell when the exchange rate reaches the peak, and

sell when the exchange rate goes to the bottom, it will create the resistance (support)

levels where the exchange rate will fall (increase) again. However, in case the

exchange rate does not fall, continues to increase and break the resistance level, it

is the buy signal. By contrast, if the exchange rate fall below the support level, sell

signal is generated. With trading range break rule, this study will also introduce band

to investigate the effect of band on the trading rules. Trading range strategy

researches 50, 150 and 200 days maximum (minimum).

3.3. Methodologies of testing

3.3.1. Variance Ratio test with Bootstrap methodology

For testing random walk hypothesis, this study utilized the variance ratio (VR) test

which was developed Lo and MacKinlay (1988) and then became popular tool in

random walk testing. This test helps to examine the predictability of exchange rates

by comparing variances of differences of the data gauged over various intervals. The

main concept of this test is that the variance of the random walk increments must be

linear function of the time intervals. In more details, if the exchange rate follows a

random walk, the variance of theq th- period difference equals q times the variance of

the first difference one. Let denote VR (q) is the variance ration at lag q. This

variance ratio is calculated by following function.



VR(q)= σq2

qσ12

Where σ q2 is an unbiased estimator of the variance of the q thdifference of the

exchange rate and σ 12 is unbiased estimator of the variance of the 1st difference of

that exchange rate. As main concept of VR stated above, if an exchange rate follow

a random walk, its VR value should be equal to 1 for any q. In the context of testing

EMH for evaluating the probability of trading rules, this dissertation investigates 5

test periods which are 10, 20, 50, 150 and 200 days. If the variance ratio is less than

one, it suggests negative serial correlations and vice versa.

For testing the hypothesis of random walk, there are two versions of VR can be

applied which are standard normal test- statistics under homoscedasticity and

variance ratio test under hetroscedasticity Lo and MacKinlay (1988). Nevertheless,

due to the advantages of bootstrap method, this study will utilize this technique to

provide the p- value of VR test.

In particular, this dissertation uses a wild bootstrapping method of Kim (2006) to

increase the small sample properties of VR tests. Wild bootstrapping uses the below

functions of Wright (2000), Lo and MacKinlay (1988) and Chow and Denning (1993)

to compute the individual and joint variance ratio test statistics.

Where



Where

There are three main steps of the wild bootstrapping tests. The wild bootstrap

version of MV(X,ki) can be cited as a good example of this process. The first step is

forming a bootstrap sample (Xt*) of T observations. The second step is measuring

the variance ratio test statistics from the bootstrap sample which is originated in the

1st step. Then the 1st step and 2nd step are repeated n times to create a bootstrap

distribution of the test statistics{MV (X¿ , k j ; j) }j=1m . The bootstrap p- values are

measured from the fraction of bootstrap sample greater than the sample value of

MV(X, k i). The detail process is presented clearly by Kim (2006).

In order to use the wild bootstrapping variance ratio test, this dissertation uses the

Eviews 7 software. Numbers of replications in wild bootstrapping technique are

1000.

3.3.2. Technical trading rules testing

Traditional statistics will be used to examine the profitability of the above trading

rules. General concept of this method is using t- test in order to test the significance

of the excess returns from trading rules. This concept is borrowed from Brock (1992).



In more details, this study calculates the return of exchange rate without any signal

and the return of trading in accordance with the trading rules, and then makes the

comparison. The procedure to test is explained clearly as follows.

Firstly, with the moving average strategy, this dissertation computes the moving

average line as below function.

MA (n)=∑t=1

n

S t /n

Where

MA(n) is the moving average in n days

St is the exchange rate in date t

It should be noted that the data which is used to test is not exchange rate, is return

of trading rules. Therefore, it is necessary to indicate buy (sell) signals then calculate

return with respect to those signals. In order to indicate buy (sell) signals with

variable moving average (VMA), this study utilized dummy variables- D with values

as following:

Case: Band of zero

Dt= +1 if St > MA(n) or MA(n1) > MA(n2)

-1 if St < MA(n) or MA(n1) < MA(n2)

Dt-1 if St= MA(n) or MA(n1)=MA(n2)

Case: Band of 1%



Dt= +1 if St >1.01 x MA(n) or MA(n1) > 1.01x MA(n2)

-1 if St < 0.99 x MA(n) or MA(n1) <0.99 x MA(n2)

0 if 0.99 x MA (n) <=St<= 1.01 x MA(n)

or 0.99 x MA (n2) <=MA (n1) <= 1.01 x MA(n2)

Where

Dt is dummy variable of VMA at date t

MA(n1) is the short moving average in n1 days and MA(n2) is the long moving

average in n2 days with n1<n2.

According to the simple moving average rule indicated above, dummy variable (D)

equals to +1 is buy signal, D t equals to -1 is sell signal and 0 is no signal. Returns

from the trading in accordance with above signal are gauged as below

Rt= Dt x (ln (St+1)- ln (St) – 1/260 (it – it*))

Where

Rt: Return of date t

Dt: Dummy variable of VMA at date t

St+1: Exchange rate at date t

St: Exchange rate at date t

it: annual interest rate of domestic currency at date t

it*: annual interest rate of foreign currency at date t

In this study, it is assumed that there are 260 trading days per year (5 days per

weeks and 52 weeks per year), so it would be more precise if calculate interest rate

of holding currency per day is equal to annual interest rate divided by 260 (not 365).



This function was used to test technical analysis on USD/DEM pair by Saacke

(2002).

The way of defining dummy variable with the fix length moving average (FMA) is little

bit different because this rule indicates that after the buy (sell) signal is generated,

other signals within 10 days are ignored. Dummy variable and 10days returns of

FMA are explained as below:

Dt’= Dt if average of Dt’ within 10 days is equal to 0

0 if average of Dt’ within 10 days is not equal to 0

R_10t= Dt’ x (ln (St+10)- ln (St) – 10/260 (it – it*))

Where:

Dt’ is the dummy variable of FMA at date t

Dt is the dummy variable of VMA at date t

St+10 is the exchange rate at date t+10

St is the exchange rate at date t

it: annual interest rate of domestic currency at date t

it*: annual interest rate of foreign currency at date t

Secondly, with trading range break out (TRB), buy (sell) signals and returns are

defined as follow:

Dt”= +1 if St > Max ( St, St+1, …, St+1)

-1 if St < Min (St, St+1, …, St+1)

0 if Min (St, St+1, …, St+1) < St < Max (St, St+1, …, St+1)



Rt= Dt” x (ln (St+1)- ln (St) – 1/260 (it – it*))

Let denote Dt” is the dummy variable of TRB at date t.

Thirdly, t- statistics for buy (sell) signal are gauged as the function which Brock et.al

(1992) used

t- value Buy (Sell) = (μr−μ)

√ ( σ2

N+ σ

2

N r)

Where

μr, N r is respectively the mean return and the number of buy or sell signals

μ❑,N❑is respectively the unconditional mean return and the number of observations.

σ 2 is the estimated variance for entire sample.

t- value Buy- Sell=(μb−μs)

√ ( σ2

N b+ σ

2

N s)

Where

μb , μs are the mean return of buy signals and sell signals.

N b , N s are the number of buy signals and sell signals.

The t- value of Buy (Sell) is utilized to test whether or not the mean return from Buy

(sell) signals is higher than the mean return of unconditional trading (daily return of

exchange rate). In other words, t- test will examine whether buy (sell) signals create MSc International Money and Banking

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excess returns. Accordingly, t- value of Buy- Sell is applied to test whether or not

mean return of buy signals is equal to mean return of sell signals. T- test helps to

define the significance of the excess return from the trading rules. Given the

confidence intervals, the number of sample and the t-value, this dissertation will

compare t-value with the critical value in a standard table of significance to conclude

whether the t-value is significant or not. If it is significant, it means that the mean

return from trading rules is different from the unconditional mean return. The same

definition of t-test is applied for the case of Buy- Sell.

CHAPTER 4

DATA

In order to test the profitability of trading rules in the foreign exchange market, this

dissertation examines the Euro (EUR), the Japanese Yen (JYP), The British Pound

(GBP), the Swiss Franc (CHF) and the Australian Dollar (AUD). These currency

pairs can be considered as the main pairs which enjoy the largest volume of trading

in the foreign exchange market. Analysing five currency pairs provides the whole

truer picture of trading rule application on making a profit on the FX market. The

exchange rates of above currencies with the Dollar are the middle exchange rate at

5pm London time. Interest rates of the currencies are the daily offer rate of the

annual interest rates in the interbank at 5pm London time. All data are obtained from

the Datastream resource and the detail code and link of data will be indicated clearly

in the reference.



The data of the Euro is examined from the first trading day of the Euro at 04/01/1999

to 29/06/2012, or approximately 3519 daily observations. However, the data of the

rest currencies are collected from 01/05/1990 to 29/06/2012, which means that there

are 5754 daily observations with each currency data. The purpose of choosing the

same period for 4 currency pairs (USD/AUD, USD/CHF, GBP/USD, USD/JPY) is for

making comparison and having a big picture of trading rules effects on various

exchange rates. Nevertheless, the Euro has just been generated from 1999, so the

examined period of this currency is different.

It also should be noted that the exchange rate and the interest rate are just the raw

data. In order to test the profitability of the trading rules, it is necessary to convert the

data to return data which would be the input data for testing. An unconditional daily

return Rt and an unconditional 10 days holding return R_10 t is measured respectively

as following

Rt= ln (St+1)- ln (St) – 1/260 (it – it*)

R_10t = ln (St+1)- ln (St) – 10/260 (it – it*)

Table I

Summary statistics for daily and 10- day return



R_CHF R_JPY R_AUD R_GBP R_EUR R_CHF10 R_JPY10 R_AUD10 R_GBP10 R_EUR10Mean -0.000129 -0.000225 0.000029 -0.000070 0.000013 -0.001244 -0.002233 0.000338 -0.000729 0.000144Standard Error 0.000094 0.000090 0.000101 0.000079 0.000112 0.000297 0.000278 0.000302 0.000257 0.000352Standard Deviation 0.007143 0.006878 0.007706 0.005977 0.006659 0.022541 0.021098 0.022955 0.019536 0.020879Sample Variance 0.000051 0.000047 0.000059 0.000036 0.000044 0.000508 0.000445 0.000527 0.000382 0.000436Kurtosis 5.918834 4.995331 13.095772 3.993830 1.180004 1.228618 3.389330 7.719509 5.124643 1.171909Skewness 0.130819 -0.559872 0.713520 -0.120053 0.017649 -0.044038 -0.668176 1.050059 -1.057783 0.064111Minimum -0.054193 -0.066328 -0.065381 -0.039921 -0.029145 -0.130065 -0.161041 -0.124394 -0.161516 -0.091526Maximum 0.084764 0.033856 0.086377 0.044185 0.036774 0.118118 0.089966 0.237274 0.074939 0.125795Count 5783 5783 5783 5783 3518 5774 5774 5774 5774 3509Confidence Level(95.0%) 0.000184 0.000177 0.000199 0.000154 0.00022 0.000582 0.000544 0.000592 0.000504 0.000691

Table I presents the statistics of unconditional daily return and unconditional 10-

days return of five exchange rates. From the results on Table I, it is obvious that all

of the return data have evidence of skewness. In addition, the daily and 10 days

return of all currency pairs have highly leptokurtic distribution which causes thick tails

on both sides. These results proved that daily and 10 day return data do not follow

the normal distribution1 rule. Among data, the daily return of AUD has the highest

leptokurtic distribution. Making comparison between these currency pairs could find

that the unconditional one-day mean return of EUR is the highest (0.000029) among

the one of the 5 pairs while JPY’s counterpart is the lowest (-0.000225).

Analysing standard deviation, it can be seen that the standard deviation of AUD is

the highest. According to the definition of standard deviation, the high standard

deviation illustrates the points of data are distributed far away from the mean and

vice versa. Therefore, it can be said that the values of AUD are the most scattered

whereas the values of GBP are the least of all data.

1 Normal distribution is one of the assumptions of t- test. However, an enormous number of empirical studies such as Srivastava (1958) demonstrated that “with the increase in the sample size, the effect of non- normality on the power of the t- test diminishes”. Therefore, with large samples (more than 3500 samples of USD/EUR and more than 5700 samples of other currency pairs), t- test can arguably be considered as an effective comparative test without normality assumption. Brock (1992) also did not check the normality of data when he utilized t- test to examine the profitability of trading rules.MSc International Money and Banking

24


CHAPTER 5

EMPIRICAL RESULTS

5.1. Wild bootstrapping Variance ratio test

The null hypothesis of the variance ratio test which is used in this study is exchange

rate is random walk. Table II describes the variance ratio test results with two sets of

test results which are joint test results for all periods and individual tests for different

lags. P- value (Probability) is shown in Table II is the probability that the variance

ratio is less (greater) than the sample variance ratio if the sample one is less

(greater) than the median of the bootstrap distribution in 1000 replications. Analysing

p- value of joint tests illustrates that the null hypothesis can be rejected at 1% level

with CHF, GBP and JPY data. It implies that these exchange rates do not follow the

random walk. In the contrary, there are evidences of the random walk in USD/AUD

and USD/EUR data. In more details, the joint tests of these data cannot reject the

null hypothesis. The Wald test results are also consistent with these results.

The results from individual tests absolutely support for the joint test. All individual

tests of CHF, GBP and JPY with 10, 20, 50, 150, 200 periods reject the null

hypothesis of a random walk while the rest does not. Indeed, the probability with q

equals to 200 of AUD and EUR are significantly high (92.5% and 96.5%

respectively). By contrast, almost probability with examined periods of CHF, GBP

and JPY is equal to zero. Moreover, taking the variance ratio value of individual tests

into account, it points out that these values of both AUD and EUR data are close to

1, especially EUR data. For instance, variance ratio values of EUR for q equals 10,



20, 50, 150, 200 are 0.99, 1.04, 1.04, 1.05, 0.99 respectively. As stated in the

methodology part, these figures support for the random walk hypothesis.

Table II

Variance ratio test

Panel A Panel B

Panel C Panel D



Panel E

5.2. Traditional statistics of trading rules

The first test of this part is examining the profitability of the various- length moving

average (VMA) rules. The standard test results for five currency pairs with VMA are

presented in table II. The first noticeable point is that USD/AUD and USD/EUR are

two currency pairs which have positive average returns from both buy and sell



signals – column 4th and 5th. It implies that the Variable- length moving average rules

bring excess returns with these pairs without respect to buy or sell signals. By

contrast, the rest pairs (USD/CHF, USD/JPY, GBP/USD) have negative average

returns from buy signals and positive returns from sell signals. Returns from buying

these currencies in accordance with variable-length moving rules are also consistent

with the unconditional one-day mean returns of these pairs. Moreover, the average

returns from buy-sell are all negative except for EUR data. The second noteworthy

point to note is that more than 50% sell signals of GBP and JPY in all tests brought

positive returns while these features of AUD, CHF, EUR sometimes are lower than

50%. According to these results, it can be concluded that in the long term- the whole

investigated period, selling GBP or JPY in accordance with these rules certainly

made a profit whereas the others do not. The third striking point is that the return of

trading JPY is always the most significant. In more details, the buy return of JPY is

the lowest in comparison with the others while the sell return of this currency is the

highest one.

The second and third column on the table II show the number of buy and sell signals,

which are generated by the variable- length moving average rules. It is obvious that

almost VMA rules create more sell signals than buy signals for AUD, CHF, JPY

(except for (1,10,0) rule with JPY data), whereas these rules produce less sell

signals than buy one for USD/EUR and GBP/USD. It implies that AUD, CHF and

JPY seem to be on a downward trend while EUR and GBP tend to be on an upward

trend.

About t- test for buy signals, all tests with 5 currency pairs do not reject the null

hypothesis that the returns are equal to the unconditional one-day returns at the 5% MSc International Money and Banking

28


significance level using the two tails tests. For the sells, the results of AUD, EUR are

still negative while the results of GBP and CHF are little positive with some trading

rules and these features of JPY are much stronger. T- value of selling GBP in

accordance with only (1,10,0.01) and (1,20,0.01) rules are higher than 1.972 (the

percentage point of the t distribution at 5%). The t-test of equality of CHF sells

returns and unconditional one day returns are stronger than GBP with 4/14 tests

rejects the null hypothesis at 5% level. Selling JPY is the most significant because

11 over 14 t-value are much higher than 2.

The 11th and 12th column illustrate returns from buy signals minus returns from sell

signals and their t-test results. It is easy to see that the buy- sell returns of all

currencies except for EUR are both negative. The t-test of equality of buys returns

and sells returns are not significant with EUR, AUD, CHF data, are partially

significant with GBP and strongly significant with JPY data. There are only three over

fourteen tests indicate that the difference between buys and sells returns is equal to

zero cannot be rejected at 5% significance level.

Introducing a band of 1% has various impacts on the returns of trading rules. In more

details, for CHF, the band introduction increases the average returns with both buy

and sell signals. By contrast, with the rest data, applying a band of 1% brings

ambiguous results. For instance, AUD average returns from buy signals with 1%

band is lower than the one without a band (0.000051 compared to 0.000025)

whereas the similar figure of sell signals after introducing 1% band is higher than the

band of zero feature (-0.000011 in comparison with 0.495626). Taking standard

deviation into consideration shows that all standard deviation of AUD, GBP, JPY

returns from rules with 1% band are higher than the feature with a band of zero. This MSc International Money and Banking

29


result denotes that the values of return with the band will are much more discrete

than the one without a band. However, the addition of 1% band into (1,20) and

(1,200) rule with EUR data and (1,20) rule with CHF data decrease the standard

deviation of returns from buy signals. The trading rules using 10 days MA and 20

days MA of EUR (Panel C) can be cited as good examples for the influence of the

band introduction. While the buying and selling return of these rules without a band

are 0.000126 and 0.00096 respectively, the feature with 1% band are 0.000379 and

0.000110. For the standard deviation, this feature of buy signals is 0.006509 with a

band of 1% and 0.007236 with a band of zero. The feature of sell signals is 0.006796

and 0.008132 respectively.

Table III

Standard test results for the Variable- length Moving Average rule

Panel A

AUD N(BUY) N(SELL) BUY SELL BUY>0 SELL>0Std.dev

BUYStd.dev

SELLt-value (BUY)

t-value (SELL)

BUY-SELLt-value

(BUY_SELL)(1,10,0) 2694 3089 0.000107 0.000039 0.499629 0.495306 0.008761 0.006648 0.431638 0.055085 0.000068 0.335373(1,20,0) 2674 3109 0.000060 -0.000002 0.496260 0.492441 0.008668 0.006768 0.174155 -0.182158 0.000063 0.308014(1,50,0) 2649 3134 0.000036 -0.000023 0.500189 0.495852 0.008809 0.006631 0.040294 -0.304532 0.000059 0.291754(1,200,0) 2600 3183 0.000056 -0.000007 0.509231 0.500471 0.008880 0.006575 0.147593 -0.212473 0.000063 0.309228(1,10,0.01) 944 1044 -0.000283 0.000060 0.470339 0.487548 0.010955 0.007621 -1.152779 0.118970 -0.000343 -0.990069(1,20,0.01) 1415 1630 -0.000086 -0.000070 0.480565 0.492025 0.009922 0.007226 -0.502766 -0.458488 -0.000016 -0.056528(1,50,0.01) 1752 2180 0.000091 -0.000014 0.500000 0.501835 0.009624 0.006919 0.295802 -0.224834 0.000106 0.427523(1,200,0.01) 2151 2753 -0.000013 0.000062 0.507671 0.507810 0.009412 0.006680 -0.215073 0.182273 -0.000074 -0.335411(10,20,0) 2719 3064 -0.000020 -0.000072 0.493196 0.489556 0.008199 0.007238 -0.272780 -0.589964 0.000053 0.259602(20,50,0) 2657 3126 0.000066 0.000002 0.508468 0.502879 0.008620 0.006831 0.205337 -0.156118 0.000064 0.313725(50,200,0) 2599 3184 0.000049 -0.000013 0.511351 0.505025 0.008778 0.006704 0.111272 -0.245107 0.000062 0.304012(10,20,0.01) 616 690 0.000072 0.000002 0.498377 0.511594 0.021396 0.008416 0.131248 -0.088853 0.000070 0.164912(20,50,0.01) 1324 1641 -0.000067 0.000082 0.500000 0.517977 0.010419 0.007444 -0.408222 0.243660 -0.000148 -0.521154(50,200,0.01) 2252 2684 0.000010 0.000055 0.512433 0.507824 0.009049 0.006876 -0.102152 0.144507 -0.000046 -0.206896Average 0.000006 0.000007 -0.000001

Panel B



CHF N(BUY) N(SELL) BUY SELL BUY>0 SELL>0Std.dev

BUYStd.dev

SELLt-value (BUY)

t-value (SELL)

BUY-SELLt-value

(BUY_SELL)(1,10,0) 2824 2959 -0.000164 0.000096 0.491501 0.499493 0.006909 0.007358 -0.210747 1.397602 -0.000260 -1.384703(1,20,0) 2862 2921 -0.000112 0.000146 0.492662 0.500514 0.007012 0.007268 0.107332 1.700938 -0.000258 -1.374746(1,50,0) 2784 2999 -0.000013 0.000237 0.499641 0.506836 0.006791 0.007452 0.703383 2.278372 -0.000250 -1.331550(1,200,0) 2574 3209 -0.000102 0.000152 0.506993 0.512309 0.006782 0.007419 0.164326 1.786728 -0.000253 -1.339256(1,10,0.01) 1047 1108 0.000222 0.000170 0.501433 0.500000 0.007110 0.007908 1.462430 1.278583 0.000051 0.166763(1,20,0.01) 1585 1697 0.000046 0.000228 0.509148 0.510902 0.006822 0.007446 0.863891 1.811156 -0.000182 -0.730269(1,50,0.01) 1999 2255 -0.000035 0.000248 0.504252 0.512639 0.006822 0.007687 0.506876 2.127482 -0.000283 -1.291277(1,200,0.01) 2182 2932 -0.000062 0.000154 0.510999 0.496589 0.006865 0.007533 0.373337 1.748202 -0.000216 -1.070075(10,20,0) 2803 2980 -0.000081 0.000174 0.504460 0.511409 0.007008 0.007266 0.291093 1.885080 -0.000256 -1.360914(20,50,0) 2773 3010 0.000004 0.000252 0.507032 0.513621 0.006969 0.007297 0.806640 2.374678 -0.000248 -1.319802(50,200,0) 2496 3287 -0.000120 0.000136 0.508413 0.512930 0.006935 0.007296 0.053264 1.701884 -0.000256 -1.352193(10,20,0.01) 697 825 0.000032 0.000375 0.493544 0.520000 0.008002 0.008016 0.563721 1.898161 -0.000343 -0.933761(20,50,0.01) 1557 1823 -0.000113 0.000125 0.502890 0.511245 0.007321 0.007805 0.079198 1.323945 -0.000238 -0.964995(50,200,0.01) 2021 2760 -0.000087 0.000051 0.511133 0.508333 0.007086 0.007501 0.231117 1.091076 -0.000138 -0.658208Average -0.000042 0.000182 -0.000224

Panel C

EUR N(BUY) N(SELL) BUY SELL BUY>0 SELL>0Std.dev

BUYStd.dev

SELLt-value (BUY)

t-value (SELL)

BUY-SELLt-value

(BUY_SELL)

(1,10,0) 1795 1723 0.000040 0.000015 0.493593 0.481138 0.006362 0.006954 0.141058 0.009849 0.000025 0.112728(1,20,0) 1764 1754 0.000016 -0.000011 0.486395 0.474344 0.006502 0.006812 0.012918 -0.122952 0.000026 0.117757(1,50,0) 1771 1747 0.000201 0.000177 0.510446 0.498569 0.006474 0.006834 0.969223 0.842305 0.000024 0.106345(1,200,0) 1953 1565 0.000155 0.000163 0.517665 0.508626 0.006140 0.007249 0.753227 0.742229 -0.000009 -0.038243(1,10,0.01) 602 605 0.000277 -0.000329 0.488372 0.457851 0.006572 0.007336 0.896895 -1.168737 0.000606 1.580726(1,20,0.01) 971 906 0.000159 0.000137 0.496395 0.475717 0.006469 0.007305 0.602404 0.497524 0.000022 0.071483(1,50,0.01) 1264 1229 0.000216 0.000168 0.513449 0.489015 0.006497 0.007163 0.930553 0.703284 0.000048 0.180043(1,200,0.01) 1753 1388 0.000170 0.000180 0.516258 0.505043 0.006023 0.007382 0.804181 0.792223 -0.000011 -0.044554(10,20,0) 1797 1721 0.000126 0.000096 0.509182 0.500291 0.006509 0.006796 0.585132 0.424754 0.000030 0.132579(20,50,0) 1786 1732 0.000100 0.000051 0.516237 0.508661 0.006318 0.006985 0.449356 0.195547 0.000049 0.216936(50,200,0) 1978 1540 0.000132 0.000085 0.506572 0.508442 0.006061 0.007348 0.634425 0.354823 0.000047 0.205628(10,20,0.01) 403 392 0.000379 0.000110 0.488834 0.479592 0.007236 0.008132 1.044051 0.274240 0.000268 0.568139(20,50,0.01) 974 951 0.000081 0.000150 0.525667 0.511041 0.006591 0.007535 0.282051 0.560480 -0.000068 -0.225333(50,200,0.01) 1762 1243 0.000138 0.000128 0.516459 0.514079 0.006004 0.007615 0.641009 0.520328 0.000010 0.041554Average 0.000156 0.000080 0.000076

Panel D

GBP N(BUY) N(SELL) BUY SELL BUY>0 SELL>0Std.dev

BUYStd.dev

SELLt-value (BUY)

t-value (SELL)

BUY-SELLt-value

(BUY_SELL)

(1,10,0) 3051 2732 -0.000069 0.000071 0.485742 0.500732 0.005586 0.006384 0.007492 1.011731 -0.000139 -0.885349(1,20,0) 3088 2695 -0.000073 0.000066 0.488990 0.504267 0.005498 0.006482 -0.025403 0.971209 -0.000139 -0.880778(1,50,0) 3058 2725 -0.000035 0.000108 0.490844 0.506422 0.005412 0.006552 0.257640 1.281001 -0.000143 -0.911198(1,200,0) 3110 2673 -0.000037 0.000107 0.497749 0.514403 0.005417 0.006567 0.243072 1.265103 -0.000145 -0.916922(1,10,0.01) 799 814 -0.000306 0.000532 0.476846 0.530713 0.005967 0.007736 -1.048464 2.690150 -0.000838 -2.816829(1,20,0.01) 1335 1214 -0.000086 0.000410 0.486142 0.514827 0.005792 0.007413 -0.090443 2.540949 -0.000496 -2.091945(1,50,0.01) 1910 1687 -0.000054 0.000117 0.487435 0.506817 0.005621 0.007210 0.096160 1.127240 -0.000171 -0.857616(1,200,0.01) 2534 2081 -0.000051 0.000052 0.494870 0.503123 0.005563 0.006954 0.131174 0.798486 -0.000103 -0.584335(10,20,0) 3082 2701 -0.000024 0.000122 0.491888 0.507590 0.005678 0.006299 0.341548 1.372701 -0.000146 -0.924777(20,50,0) 3017 2766 -0.000071 0.000068 0.491216 0.506869 0.005552 0.006408 -0.011354 0.995855 -0.000139 -0.884243(50,200,0) 3250 2533 -0.000091 0.000043 0.494462 0.510857 0.005538 0.006496 -0.159648 0.789441 -0.000133 -0.841737(10,20,0.01) 443 538 0.000181 0.000122 0.528217 0.513011 0.006497 0.008718 0.850613 0.711580 0.000059 0.153679(20,50,0.01) 1311 1189 -0.000198 0.000010 0.497330 0.506308 0.006121 0.007706 -0.703369 0.419371 -0.000208 -0.870697(50,200,0.01) 2323 1759 -0.000129 0.000127 0.496771 0.521319 0.005733 0.007088 -0.402312 1.210238 -0.000256 -1.355289Average -0.000075 0.000140 -0.000214



Panel E

JPY N(BUY) N(SELL) BUY SELL BUY>0 SELL>0Std.dev

BUYStd.dev

SELLt-value (BUY)

t-value (SELL)

BUY-SELLt-value

(BUY_SELL)

(1,10,0) 2959 2824 -0.000263 0.000184 0.472795 0.504603 0.006290 0.007444 -0.247816 2.588531 -0.000447 -2.471828(1,20,0) 2848 2935 -0.000172 0.000275 0.484551 0.516865 0.006332 0.007369 0.331650 3.206063 -0.000448 -2.473824(1,50,0) 2784 2999 -0.000161 0.000283 0.481322 0.513838 0.006276 0.007392 0.398578 3.280943 -0.000445 -2.455932(1,200,0) 2406 3377 -0.000319 0.000158 0.482959 0.515546 0.006215 0.007313 -0.563837 2.564914 -0.000476 -2.594886(1,10,0.01) 865 1012 -0.000234 0.000166 0.461272 0.512846 0.006733 0.008302 -0.037040 1.665393 -0.000400 -1.254654(1,20,0.01) 1417 1554 -0.000177 0.000271 0.472124 0.509653 0.006544 0.008049 0.234402 2.520591 -0.000448 -1.771575(1,50,0.01) 1841 2165 -0.000187 0.000318 0.481803 0.521478 0.006388 0.007854 0.205533 3.129048 -0.000504 -2.313284(1,200,0.01) 1973 2920 -0.000305 0.000112 0.480993 0.515411 0.006255 0.007388 -0.448029 2.154859 -0.000417 -2.079444(10,20,0) 2834 2949 -0.000084 0.000359 0.493296 0.525263 0.006621 0.007113 0.889606 3.751908 -0.000444 -2.451961(20,50,0) 2776 3007 -0.000148 0.000295 0.486311 0.518457 0.006385 0.007303 0.479980 3.359283 -0.000443 -2.448379(50,200,0) 2516 3267 -0.000297 0.000169 0.487281 0.518825 0.006804 0.006934 -0.439617 2.613872 -0.000466 -2.552634(10,20,0.01) 529 760 -0.000160 0.000273 0.497164 0.501316 0.007402 0.008569 0.207821 1.873132 -0.000432 -1.109669(20,50,0.01) 1346 1616 -0.000317 0.000303 0.476226 0.514851 0.007191 0.008279 -0.441662 2.724771 -0.000619 -2.439845(50,200,0.01) 1962 2683 -0.000378 0.000070 0.484200 0.516213 0.006878 0.007077 -0.851746 1.834439 -0.000448 -2.191660Average -0.000229 0.000231 -0.000460

The second moving average test of this part is the fix- length moving average (FMA)

rule which examines the 10 days holding returns after two moving averages crosses

each other. Replicating the similar procedure with FMA rule gave the following result

which is illustrated in Table IV. First of all, it is obvious that the sell signals of AUD,

CHF and JPY data are almost more than buy signals while EUR’s and GBP’s

counterpart are contrary. This characteristic of FMA results is also in harmony with

the VMA results. To an extent, the feature could imply that three currencies AUD,

CHF and JPY tend to be in an overall down trend.

In contrast with VMA rules, introducing a band to FMA rules make equivocal results

for all examined currency pairs even with EUR data. In other words, trading rules

with 1% band sometimes can increase the returns or decrease them. Data of AUD

can be cited as an excellent example for this stimulus. Average returns from buy

signals of this currency without a band is much higher than the one with a band

(0.00077014 in comparison with 0.00000980), while introducing 1% band raises the

average returns from sell signals dramatically from 0.00005310 to 0.00014047. The



addition of one per cent band also has an enormous impact on the standard

deviation.

All tests with 5 currency data do not reject the null hypothesis that returns from FMA

buy signals are equal to unconditional 10 day returns at 5% level using two tails. In

all cases, t- tests of buy signals are insignificant. The t- tests with sell signals have

various results. Fourteen over fourteen tests with AUD and EUR data denote that the

null hypothesis of equality between sell signals returns and unconditional 10 day

returns cannot be rejected at 95% the confident interval. By contrast, all tests with

JPY data imply that the differences between these returns are extremely significant

and the null hypothesis can be rejected at 5% level. For GBP data, there is only test

of (1,10, 0.01) rule is significant while the others are both insignificant. Nine over 14

tests with CHF data can reject the null hypothesis at the five per cent significance

level. For all data, the null hypothesis about the equality of buy signal returns and

sell signal returns do not be rejected at 5%. Among the examined data, only AUD

has higher returns from buy signals in comparison with returns from sell signals. In

the contrary, the average buy- sell value of the rest data is all negative.



Table IV

Standard test results for the Fix- length Moving Average rule

Panel A


BUYStd.dev

SELLt-value (BUY)

t-value (SELL)

BUY-SELLt-value

(BUY_SELL)

(1,10,0) 273 305 0.00071 1.14E-05 0.501832 0.547541 0.022428 0.022009 0.26115 -0.24252 0.000698 0.3651559(1,20,0) 265 313 0.000251 -0.0004 0.483019 0.530351 0.022536 0.021932 -0.06034 -0.55062 0.000647 0.3373942(1,50,0) 274 304 0.001459 0.000689 0.492701 0.539474 0.024949 0.019359 0.789515 0.259558 0.00077 0.4026508(1,200,0) 262 316 0.001104 0.000313 0.48855 0.53481 0.024408 0.020187 0.527807 -0.01923 0.000791 0.4123111(1,10,0.01) 192 203 -0.00191 -0.00074 0.489583 0.536946 0.025069 0.024703 -1.3345 -0.6595 -0.00117 -0.5046444(1,20,0.01) 219 237 -0.0004 -0.00068 0.52968 0.518987 0.024501 0.023114 -0.46493 -0.6675 0.000281 0.1304982(1,50,0.01) 228 268 -0.00088 -0.00077 0.45614 0.518657 0.029242 0.020116 -0.78774 -0.77569 -0.00011 -0.052381(1,200,0.01) 243 300 0.001314 0.000552 0.510288 0.546667 0.023256 0.020721 0.64907 0.157203 0.000762 0.3846368(10,20,0) 269 309 0.000512 -0.00017 0.475836 0.524272 0.024269 0.020248 0.12136 -0.37928 0.000682 0.3563588(20,50,0) 264 314 0.000811 7.59E-05 0.458333 0.509554 0.024387 0.020193 0.32711 -0.19741 0.000735 0.383544(50,200,0) 261 317 0.000544 -0.00015 0.490421 0.536278 0.023589 0.021007 0.141288 -0.37087 0.000696 0.3629355(10,20,0.01) 93 105 0.002596 0.001912 0.505376 0.571429 0.028361 0.021396 0.940934 0.695962 0.000684 0.2094114(20,50,0.01) 153 184 -0.001 0.000499 0.464052 0.532609 0.026904 0.022026 -0.70942 0.093514 -0.00149 -0.5951078(50,200,0.01) 234 275 0.000341 0.000214 0.478632 0.541818 0.027067 0.021029 0.001759 -0.08784 0.000127 0.0622805Average 0.00039 9.68E-05 0.000293

Panel B


BUYStd.dev

SELLt-value (BUY)

t-value (SELL)

BUY-SELLt-value

(BUY_SELL)

(1,10,0) 275 303 -0.00034 0.002099 0.490909 0.557756 0.021133 0.024137 0.648923 2.516555 -0.00244 -1.2999002(1,20,0) 289 289 -0.00075 0.001777 0.467128 0.536332 0.020922 0.024477 0.364396 2.223168 -0.00253 -1.3468412(1,50,0) 275 303 -0.00049 0.001961 0.476364 0.544554 0.019962 0.025035 0.539304 2.412364 -0.00245 -1.3074072(1,200,0) 260 318 -0.001 0.001479 0.469231 0.537736 0.021105 0.024051 0.172245 2.097534 -0.00248 -1.3144129(1,10,0.01) 205 218 0.000219 0.001312 0.492683 0.541284 0.023126 0.023242 0.913034 1.643595 -0.00109 -0.4986063(1,20,0.01) 227 248 -0.00058 0.000721 0.45815 0.508065 0.022762 0.025332 0.433534 1.344253 -0.0013 -0.6296718(1,50,0.01) 249 272 0.000133 0.002574 0.506024 0.536765 0.021155 0.022962 0.944199 2.73002 -0.00244 -1.2344848(1,200,0.01) 243 308 -0.00042 0.001734 0.493827 0.545455 0.021278 0.02372 0.560328 2.259455 -0.00215 -1.1123279(10,20,0) 276 302 -5.4E-05 0.002367 0.478261 0.546358 0.02173 0.023636 0.85659 2.714007 -0.00242 -1.2900549(20,50,0) 274 304 -0.00042 0.00202 0.474453 0.542763 0.020551 0.024583 0.589296 2.460736 -0.00244 -1.3008793(50,200,0) 249 329 -0.00138 0.00117 0.461847 0.531915 0.022146 0.023239 -0.09651 1.889763 -0.00256 -1.3495601(10,20,0.01) 102 101 0.000463 0.004175 0.5 0.594059 0.022846 0.024107 0.757999 2.395278 -0.00371 -1.1733025(20,50,0.01) 176 205 -0.00096 0.00139 0.448864 0.536585 0.021951 0.024034 0.166736 1.644228 -0.00235 -1.0130312(50,200,0.01) 206 285 -0.00108 0.000477 0.470874 0.498246 0.022458 0.024281 0.104706 1.258422 -0.00155 -0.7538072Average -0.00048 0.001804 -0.00228



Panel C


BUYStd.dev

SELLt-value (BUY)

t-value (SELL)

BUY-SELLt-value

(BUY_SELL)

(1,10,0) 181 170 0.000585 0.000339 0.480663 0.452941 0.020522 0.019961 0.277309 0.118887 0.000246 0.1104884(1,20,0) 176 175 0.002106 0.001842 0.539773 0.514286 0.020036 0.020285 1.216659 1.05005 0.000264 0.118492(1,50,0) 177 174 0.001567 0.001316 0.536723 0.511494 0.019708 0.0207 0.884623 0.722844 0.000251 0.1124795(1,200,0) 195 156 0.001425 0.001471 0.553846 0.538462 0.01794 0.022726 0.833603 0.776698 -4.6E-05 -0.0206771(1,10,0.01) 123 125 0.000207 0.001132 0.520325 0.504 0.021493 0.020613 0.032707 0.519728 -0.00093 -0.3488562(1,20,0.01) 151 126 8.1E-05 0.001995 0.503311 0.5 0.02194 0.019426 -0.03633 0.977948 -0.00191 -0.7599186(1,50,0.01) 157 153 0.001581 0.000402 0.541401 0.529412 0.019902 0.02208 0.843953 0.149628 0.001179 0.4972414(1,200,0.01) 185 150 0.001433 0.001593 0.524324 0.553333 0.018679 0.025713 0.818644 0.832211 -0.00016 -0.0694689(10,20,0) 180 170 0.001604 0.001386 0.538889 0.517647 0.021195 0.020416 0.915119 0.757511 0.000218 0.0976861(20,50,0) 176 173 0.001422 0.000977 0.528409 0.50289 0.019997 0.021613 0.792518 0.512184 0.000445 0.1992225(50,200,0) 192 154 0.001337 0.000911 0.53125 0.506494 0.018752 0.023174 0.771074 0.446409 0.000426 0.1885464(10,20,0.01) 60 54 0.001627 0.002151 0.483333 0.555556 0.020464 0.019888 0.545595 0.700883 -0.00052 -0.1336701(20,50,0.01) 111 108 0.000796 0.002654 0.558559 0.555556 0.019355 0.023513 0.323741 1.230419 -0.00186 -0.6584409(50,200,0.01) 179 126 0.001268 0.001301 0.581006 0.539683 0.018719 0.023108 0.702298 0.610976 -3.3E-05 -0.0136235Average 0.001217 0.001391 -0.00017

Panel D


BUYStd.dev

SELLt-value (BUY)

t-value (SELL)

BUY-SELLt-value

(BUY_SELL)

(1,10,0) 317 261 -0.0003 0.001203 0.526814 0.467433 0.018773 0.019878 0.378408 1.56258 -0.00151 -0.9218944(1,20,0) 326 252 -0.0009 0.00046 0.509202 0.444444 0.018378 0.020396 -0.15543 0.945466 -0.00136 -0.8308697(1,50,0) 307 271 -0.00042 0.001041 0.504886 0.442804 0.017755 0.020879 0.27347 1.457607 -0.00146 -0.8947723(1,200,0) 313 265 -0.00077 0.000633 0.520767 0.460377 0.017447 0.021252 -0.0394 1.109514 -0.00141 -0.8623861(1,10,0.01) 178 171 0.000819 0.004088 0.522472 0.532164 0.018091 0.022052 1.041084 3.177684 -0.00327 -1.562858(1,20,0.01) 209 198 -0.00082 0.000895 0.502392 0.459596 0.020878 0.020315 -0.0669 1.150005 -0.00172 -0.8855992(1,50,0.01) 248 222 4.82E-05 0.001384 0.512097 0.468468 0.017693 0.021476 0.613179 1.580888 -0.00134 -0.7398531(1,200,0.01) 284 241 -0.00106 0.000655 0.5 0.485477 0.018864 0.019816 -0.28313 1.077484 -0.00172 -1.0053409(10,20,0) 305 273 -0.00135 -4.1E-06 0.501639 0.43956 0.018452 0.020151 -0.53906 0.598744 -0.00134 -0.8252303(20,50,0) 300 278 -0.0004 0.001042 0.533333 0.47482 0.018699 0.019893 0.283941 1.476324 -0.00144 -0.8869343(50,200,0) 326 252 -0.00114 0.000146 0.521472 0.460317 0.017874 0.020958 -0.37377 0.695615 -0.00129 -0.787357(10,20,0.01) 64 79 -0.00321 0.001477 0.484375 0.468354 0.023672 0.024866 -1.01032 0.996835 -0.00469 -1.4265107(20,50,0.01) 151 138 -0.00151 0.000296 0.496689 0.463768 0.020442 0.023716 -0.48413 0.608611 -0.0018 -0.7840416(50,200,0.01) 243 183 -0.00118 0.001018 0.506173 0.502732 0.019829 0.022205 -0.35319 1.191033 -0.0022 -1.1499934Average -0.00087 0.001024 -0.0019

Panel E


BUYStd.dev

SELLt-value (BUY)

t-value (SELL)

BUY-SELLt-value

(BUY_SELL)

(1,10,0) 291 287 -0.0019 0.002612 0.487973 0.557491 0.020942 0.021587 0.262971 3.797172 -0.00451 -0.5208174(1,20,0) 285 293 -0.00112 0.003357 0.477193 0.546075 0.020296 0.022115 0.870666 4.424727 -0.00448 -0.5218192(1,50,0) 278 300 -0.00187 0.002609 0.464029 0.533333 0.021122 0.021395 0.280338 3.875499 -0.00448 -0.5280763(1,200,0) 240 338 -0.00246 0.002107 0.475 0.54142 0.01973 0.022292 -0.16266 3.676123 -0.00457 -0.5695838(1,10,0.01) 182 205 -0.00137 0.002636 0.489011 0.526829 0.022095 0.021875 0.540384 3.246981 -0.00401 -0.3907064(1,20,0.01) 208 240 -0.00078 0.002531 0.504808 0.529167 0.021429 0.02199 0.978057 3.427754 -0.00331 -0.3485851(1,50,0.01) 241 263 -0.00191 0.002718 0.481328 0.547529 0.021004 0.022406 0.233054 3.722301 -0.00463 -0.5109044(1,200,0.01) 219 322 -0.00258 0.001263 0.497717 0.543478 0.020484 0.022223 -0.23575 2.894176 -0.00384 -0.4670589(10,20,0) 289 289 -0.00148 0.003025 0.470588 0.539792 0.022148 0.020319 0.591013 4.134781 -0.00451 -0.5219841(20,50,0) 279 299 -0.00202 0.002468 0.462366 0.531773 0.020642 0.021832 0.162315 3.757044 -0.00449 -0.5287336(50,200,0) 252 326 -0.00337 0.001392 0.456349 0.527607 0.020989 0.02144 -0.8356 3.018346 -0.00476 -0.5837406(10,20,0.01) 84 114 -0.00052 0.00225 0.5 0.45614 0.020672 0.023434 0.738224 2.246739 -0.00277 -0.20087(20,50,0.01) 156 183 -0.00263 0.003193 0.455128 0.497268 0.022704 0.023776 -0.22987 3.425345 -0.00582 -0.5354227(50,200,0.01) 204 276 -0.00402 0.000616 0.470588 0.5 0.022193 0.020539 -1.18618 2.191586 -0.00463 -0.5223622Average -0.002 0.002341 -0.00434



Table V

Standard test results for the Trading range breakout rule

Panel A


BUYStd.dev

SELLt-value (BUY)

t-value (SELL)

BUY-SELLt-value

(BUY_SELL)(1,50,0) 368 512 -0.000582 -0.000167 0.470109 0.484375 0.009711 0.005818 -1.475768 -0.551888 -0.000415 -0.788582(1,150,0) 195 330 -0.000807 0.000237 0.461538 0.518182 0.009962 0.005509 -1.490197 0.476457 -0.001044 -1.499766(1,200,0) 182 290 -0.000819 0.000061 0.467033 0.510345 0.009891 0.005416 -1.462390 0.068694 -0.000880 -1.207892(1,50,0.01) 67 40 -0.001749 -0.000507 0.447761 0.500000 0.014909 0.006072 -1.878209 -0.438289 -0.001243 -0.806984(1,150,0.01) 38 24 -0.003239 0.000777 0.447368 0.583333 0.015235 0.006300 -2.606073 0.474611 -0.004016 -1.999075(1,200,0.01) 33 18 -0.003782 0.000382 0.484848 0.555556 0.015339 0.004847 -2.833161 0.193955 -0.004164 -1.844204

-0.001830 0.000131 -0.001960

Panel B


BUYStd.dev

SELLt-value (BUY)

t-value (SELL)

BUY-SELLt-value

(BUY_SELL)

(1,50,0) 443 499 0.000052 0.000094 0.510158 0.505010 0.006139 0.007533 0.514985 0.671303 -0.000042 -0.090899(1,150,0) 220 327 0.000427 0.000443 0.531818 0.535168 0.006342 0.007869 1.133388 1.410753 -0.000017 -0.026804(1,200,0) 173 287 0.000257 0.000492 0.543353 0.543554 0.006472 0.008093 0.700921 1.438525 -0.000235 -0.341950(1,50,0.01) 47 71 0.001030 -0.000199 0.574468 0.577465 0.007844 0.011683 1.108185 -0.081862 0.001229 0.915075(1,150,0.01) 27 44 0.001781 0.001099 0.629630 0.636364 0.007846 0.012034 1.386395 1.136533 0.000682 0.390418(1,200,0.01) 20 39 0.000385 0.001140 0.600000 0.641026 0.006851 0.012725 0.321645 1.105947 -0.000755 -0.384116Average 0.000655 0.000512 0.000144

Panel C


BUYStd.dev

SELLt-value (BUY)

t-value (SELL)

BUY-SELLt-value

(BUY_SELL)

(1,50,0) 319 253 0.000422 -0.000128 0.523511 0.486166 0.005426 0.007342 1.049968 -0.326631 0.000550 0.981810(1,150,0) 214 147 0.000568 -0.000362 0.537383 0.496599 0.004683 0.007963 1.183626 -0.668603 0.000930 1.303358(1,200,0) 191 128 0.000470 -0.000415 0.523560 0.492188 0.004618 0.007870 0.922791 -0.714688 0.000885 1.163183(1,50,0.01) 20 45 0.000116 0.000265 0.500000 0.533333 0.007723 0.008133 0.068543 0.251777 -0.000149 -0.083358(1,150,0.01) 7 31 0.001562 -0.000329 0.714286 0.483871 0.004947 0.009146 0.614753 -0.284796 0.001891 0.678575(1,200,0.01) 7 28 0.001562 -0.000111 0.714286 0.500000 0.004947 0.009062 0.614753 -0.097982 0.001673 0.594392Average 0.000783 -0.000180 0.000963

Panel D


BUYStd.dev

SELLt-value (BUY)

t-value (SELL)

BUY-SELLt-value

(BUY_SELL)

(1,50,0) 499 357 0.000231 0.000988 0.515030 0.504202 0.004974 0.008064 1.076360 3.244992 -0.000758 -1.828424(1,150,0) 279 188 0.000374 0.001368 0.544803 0.526596 0.005145 0.008981 1.210129 3.245970 -0.000994 -1.763273(1,200,0) 233 158 0.000320 0.001210 0.545064 0.525316 0.005245 0.009298 0.975414 2.656016 -0.000891 -1.445712(1,50,0.01) 28 43 0.001182 0.004243 0.428571 0.627907 0.005854 0.011774 1.105422 4.713685 -0.003061 -2.108766(1,150,0.01) 14 30 0.000434 0.002035 0.285714 0.566667 0.003981 0.010895 0.314877 1.923683 -0.001601 -0.827599(1,200,0.01) 10 26 0.000303 0.002202 0.200000 0.576923 0.003654 0.011427 0.196870 1.933713 -0.001899 -0.853992Average 0.000474 0.002008 -0.001534



Panel E


BUYStd.dev

SELLt-value (BUY)

t-value (SELL)

BUY-SELLt-value

(BUY_SELL)

(1,50,0) 381 441 -0.000006 0.000368 0.454068 0.498866 0.005737 0.007958 0.599610 1.745292 -0.000375 -0.779260(1,150,0) 206 262 -0.000085 0.000386 0.456311 0.496183 0.005890 0.008942 0.287059 1.405054 -0.000470 -0.734496(1,200,0) 170 213 -0.000280 0.000092 0.452941 0.488263 0.006082 0.008644 -0.102809 0.659776 -0.000372 -0.525373(1,50,0.01) 33 75 -0.000054 0.000694 0.424242 0.533333 0.007093 0.011937 0.141976 1.149004 -0.000748 -0.520591(1,150,0.01) 18 54 0.000491 0.002372 0.500000 0.592593 0.008201 0.012585 0.440754 2.760653 -0.001880 -1.004458(1,200,0.01) 15 43 -0.000326 0.000827 0.466667 0.581395 0.007805 0.010889 -0.057028 0.998598 -0.001153 -0.558886Average -0.000043 0.000790

With the trading range breakout, this dissertation tests three specific rules which the

exchange rates break out the resistance/support level within 50, 150, 200 days

respectively. In comparison with the VMA rule, it is easy to see that the number of

signals declines dramatically. T- test is utilized in order to test whether the returns

from trading rules is equal to the unconditional daily returns. The striking point is that

all t-value of CHF and EUR are not significant, so they cannot reject the null

hypothesis at 5% level. In the other way of expression, the difference between CHF,

EUR returns from TRB and their unconditional returns is not significant. By contrast,

there is some evidence of excess returns in the rest data. For JPY sell signals, there

is only one (1, 150, 0.01) test which can reject the null hypothesis with 95%

confidence interval. With AUD data, it seems that the excess returns can be earned

with using (1,150, 0.01) and (1,200, 0.01) rules because the equality of conditional

and unconditional returns from buying are rejected at 5% level. Applying TRB on

selling GBP illustrates that excess returns can be generated. Four over six tests with

buy signals are absolutely significant and the rest are marginally significant. Taking

the GBP t- test of BUY-SELL into consideration, there is only test with (1,50,0.01)

rules which can reject the null hypothesis of equality at five per cent using a two- tail

test.



Analysing the efficiency of TRB signals shows that all TRB signals create almost

positive returns only with CHF data. More than 50% of buy and sell signals from all

examined rules provide positive returns. In contrast with CHF, TRB buy and sell

signals of the others sometimes have more negative returns than the positive one.

These features are presented as fractions of signals which have positive returns

(Column 6 and 7 in Table V).

Introducing a band into TRB rules works similarly to VMA rules. The addition of 1%

band has different impacts on the selected currency returns. While it increases the

average profitability of TRB rules with CHF, GBP and JPY data, it has abstruse

effects on the TRB with the rest data. Sell signals of AUD using a 1% band have

higher average returns than the zero band one, but buy signals do adversely. In the

case of EUR, the addition of a 1% band has contrast impacts which are an increase

of mean returns with buy signals and a decrease with sell signals. Another worthy

point is that introducing a band of 1% reduces the number of signals considerably.

For example, the number of GBP buy signals from (1,200) rule declines more than

60 times from 127 signals without a band to 2 signals with a band. Moreover, in

almost tests except for (1, 200) the sell signal of AUD and (1, 150) and (1,200) the

buy signal, the introduction of 1% band raises the standard deviation of returns

which means that it makes the returns more scattered.



CHAPTER 6

IMPLICATION AND EXPLANATION

The results of wild bootstrapping variance ratio tests show that only USD/AUD and

USD/EUR pairs follow the random walk hypothesis, hence there are evidences of

weak form efficient in these markets. As a result, there is probably no way to create

excess returns from any speculate strategies these currencies.

The randomness of USD/ AUD exchange rates is due to the fact that this pair is

generally viewed as the proxy of growth by many currency market participants;

hence its movement is extremely sensitive to economic growth. Due to that reason,

speculative action of this currency pairs almost depends on news about global

growth. As the efficient market hypothesis stated, exchange rates should reflect all

relevant information. This hypothesis seems to be suitable for the Australian dollar.

When a currency is traded by news, it is impossible to predict its movements, so it

likely follows the random walk process.

Explanation of randomness of USD/EUR currency pair is different. Dollar and Euros

are the currencies which have the largest volume of trading in foreign exchange

markets (Euromoney, 2011). Therefore, this currency pair is traded most frequently,

so the number of speculators in this market is also extremely high. Unlike flow

traders, speculators only trade on news. If a market has an enormous amount of

speculators who trade by news, that market is probably more efficient than the

others.



By contrast to EUR and AUD, all VR tests of GBP, JPY and CHF report that these

exchange rates reject the null hypothesis at 1% significance level. The results of JPY

and GBP from this dissertation support and confirm the findings of previous literature

such as Liu and He (1991) and Wright (2000).

In order to explain why these pairs’ VR tests do not support for EMH, the

characteristics of these currencies can be considered. JPY and CHF are often

viewed as “safety heaven” currencies by traders and hedge funds. Indeed, JPY’s

demand often rises when there are risks of growth because its interest rate

extremely low. In fact, JPY is regularly used in “carry trade” which means borrowing

low-yield currencies and sell them to facilitate investment into high-yield currencies.

When there is bad news of economics growth, normally high-yield currencies will

tend to lose value, hence market participants will have to close their carry trade

position by purchasing JPY to pay back their debts. Due to that reason, trading this

currency may not follow the null hypothesis of weak form efficient. From a slightly

different perspective, CHF is often viewed as safety heaven when there are politics

risks. In a similar way of JPY expression, it is possible that CHF does not follow the

random walk hypothesis.

Making comparison between returns of three examined trading rules states that the

profitability of trading rules is various with different exchange rates. First of all, the

average returns from buy and sell signals of FMA are higher than the others in case

of AUD, CHF, and EUR data. For instance, TRB average return is -0.000850,

whereas VMA and FMA average return is 0.000006, 0.000243 respectively. By

contrast, with JPY and GBP, it seems to be that TRB rules are the most effective

rules among researched rules because average returns from TRB rules higher than MSc International Money and Banking

40


average returns from VMA and FMA. For example, with GBP data, average return

from TRB rules is 0.001241, in comparison with 0.000033 of VMA and 0.000076 of

FMA. It means that the average profit of TRB is 38 times higher than VMA and 16

times higher than FMA. Therefore, although numbers of VMA signals is absolutely

more than TRB (stated in Chapter 5), the effectiveness of these rules are adverse. It

can conclude that Fix-length variable average rules should be used to trade AUD,

CHF, EUR while GBP and JPY should be traded by applying signals from Trading

range break out rules.

In summary, all t-tests of equality between average returns from conditional buy

signals (from VMA, FMA rules) and unconditional returns are insignificant. It means

that the null hypothesis cannot be rejected and there is no evidence of abnormal

returns. About sells signals of VMA rules and FMA rules, the results show that it is

possible to earn excess returns in with specific rules. In more details, 11/14 tested

VMA trading rules prove that they can generate abnormal returns by selling

USD/JPY pair. On the other hand, it is possible to create excess profit by applying

FMA trading rules into selling signals, as 14/14 tests of FMA trading rules confirmed..

Besides, there are some evidences of VMA profitability in GBP and CHF data when

this dissertation studies returns of sell signals.

All of Trading range breakout rules do not create excess profit for USD/CHF and

USD/EUR pair. Only (1,150,0.01) rule proved that it can bring abnormal returns for

USD/JPY by selling this pair. The other striking point is that buying AUD in

accordance with (1,150,0.01) and (1,200,0.01) rules make unusual profit. According

to the t- test results, 4 over 6 examined TRB rules are supposed to earn excess

return by buy GBP/USD.MSc International Money and Banking

41


It is worth noting that the evidence of trading rules profitability with AUD data is not

consistent with the variance ratio test. According to the wild bootstrapping VR tests,

USD/ AUD exchange rate follows random walk and supports the weak form of

market efficiency. Hence, it is impossible to earn abnormal return from trading this

currency. However, t- test of trading rules indicates that (1,150,0.01) and

(1,200,0.001) TRB rules can be used to make excess profit with AUD. The

inconsistency can be explained by transaction costs, which is ignored in this study.

In order to research thoroughly this issue, it is necessary to take trading cost into

account. Therefore, it is possible that after including transaction costs, the above

rules cannot generate abnormal returns for USD/AUD.

In the contrary with AUD, t- test results of the rest foreign exchange rates pair

confirm the results of variance ration test. USD/EUR can be cited as a good

example. As the variance ratio test stated, this exchange rate follows the random

walk process and there is no chance to earn abnormal returns through speculation.

Indeed, all t-tests of this exchange rate do not reject the null hypothesis of equality

between trading rules returns and unconditional returns. In other words, trading rules

profitability is not significant. In final, both variance ratio tests and t- test demonstrate

that USD/EUR follow the EMH. Because the randomness of GBP/USD, USD/JPY

and USD/CHF are concluded to be insignificant, the evidence of trading rule

profitability with these pairs is plausible.

Even though GBP/USD, USD/JPY and USD/CHF do not support for the random walk

hypothesis, there are still some specific trading rules which are not significant in

generating excess returns for these currency pairs. There are two principal reasons

which can be used to explain. Firstly, these specific trading rules are useless MSc International Money and Banking

42


themselves. Secondly, applying these simple rules is probably not efficient and

powerful enough to gain excess returns. It supposes that these rules should be

combined with patterns analysis or other indicators such as volume, relative strength

index (RSI), Stochastic Oscillators, Fibonacci waves, channels and lines namely.

CHAPTER 7

CONCLUSION

This dissertation investigated the weak form efficient of five currency pairs which are

USD/CHF, USD/JPY, USD/EUR, GBP/USD (from 01/05/1990 to 29/06/2012) and

USD/EUR (from 04/01/1999 to 29/06/2012) by two ways. The first method used is

the variance ratio test in combination with wild bootstrapping. The second one is

employing t-test to examine the profitability of Variable length moving average rules

(VMA), Fix- length moving average rules (FMA) and Trading range break out rules

(TRB). These rules are examined with a band of zero and band of 1%.

Overall, the results of variance ratio test are consistent with some previous studies.

In more details, they find that AUD and EUR support for the weak form of market

efficient while the rest does not. This dissertation provides enormous evidences of

generating excess returns by trading JPY in accordance with trading rules. Besides,

in this dissertation, there are some proofs of trading rules profitability with USD/CHF

and GBP/USD. In general, the results of variance ratio test are consistent with

results from t- test of trading rules profitability, except for AUD case. Furthermore,



some practical experiences of the foreign exchange market are also applied to

explain the drawn results from testing.

However, this dissertation still has little limitation which can be improved by other

further researches. The first drawback is that this study does not include transaction

costs since calculating returns of trading. As analysed in the implication chapter, this

issue perhaps is a reason for the difference between the results of two testing

methodologies. The second limited point refers to examining the moving average

rules and the trading range breakout rules by t- test .Although t- test is a good tool to

test the trading rules profitability, it cannot run a comprehensive test across all

technical trading rules. Based on the stated limitation, there are two main

suggestions for enhancing this research. Firstly, transaction costs should be taken

into account in order to measure precise returns from trading currency pairs.

Secondly, the results of this dissertation can be extended by applying bootstrap

technologies for calculating distribution of the null models such as: AR(1), GARCH-

M, EGARCH, a random walk with a drift as the process of Brock et.al (1992).

ACKNOWLEDGEMENTS

I am extremely grateful for time, help, instruction and comments of Prof Zhenya Liu

– Department of Economics at the University of Birmingham- during the time which I

do this dissertation. Moreover, I also want to thank Dr James Reade – Department of

Economics at the University of Birmingham- for his useful guides about econometrics

softwares.



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APENDIX 1

PERCENTAGE POINTS OF THE T DISTRIBUTION

Tail Probabilities

One Tail 0.10 0.05 0.025 0.01 0.005 0.001 0.0005

Two Tails 0.20 0.10 0.05 0.02 0.01 0.002 0.001

-------+---------------------------------------------------------+-----

D 1 | 3.078 6.314 12.71 31.82 63.66 318.3 637 | 1

E 2 | 1.886 2.920 4.303 6.965 9.925 22.330 31.6 | 2

G 3 | 1.638 2.353 3.182 4.541 5.841 10.210 12.92 | 3

R 4 | 1.533 2.132 2.776 3.747 4.604 7.173 8.610 | 4

E 5 | 1.476 2.015 2.571 3.365 4.032 5.893 6.869 | 5

E 6 | 1.440 1.943 2.447 3.143 3.707 5.208 5.959 | 6

S 7 | 1.415 1.895 2.365 2.998 3.499 4.785 5.408 | 7

8 | 1.397 1.860 2.306 2.896 3.355 4.501 5.041 | 8

O 9 | 1.383 1.833 2.262 2.821 3.250 4.297 4.781 | 9

F 10 | 1.372 1.812 2.228 2.764 3.169 4.144 4.587 | 10

11 | 1.363 1.796 2.201 2.718 3.106 4.025 4.437 | 11

F 12 | 1.356 1.782 2.179 2.681 3.055 3.930 4.318 | 12

R 13 | 1.350 1.771 2.160 2.650 3.012 3.852 4.221 | 13MSc International Money and Banking

49


E 14 | 1.345 1.761 2.145 2.624 2.977 3.787 4.140 | 14

E 15 | 1.341 1.753 2.131 2.602 2.947 3.733 4.073 | 15

D 16 | 1.337 1.746 2.120 2.583 2.921 3.686 4.015 | 16

O 17 | 1.333 1.740 2.110 2.567 2.898 3.646 3.965 | 17

M 18 | 1.330 1.734 2.101 2.552 2.878 3.610 3.922 | 18

19 | 1.328 1.729 2.093 2.539 2.861 3.579 3.883 | 19

20 | 1.325 1.725 2.086 2.528 2.845 3.552 3.850 | 20

21 | 1.323 1.721 2.080 2.518 2.831 3.527 3.819 | 21

22 | 1.321 1.717 2.074 2.508 2.819 3.505 3.792 | 22

23 | 1.319 1.714 2.069 2.500 2.807 3.485 3.768 | 23

24 | 1.318 1.711 2.064 2.492 2.797 3.467 3.745 | 24

25 | 1.316 1.708 2.060 2.485 2.787 3.450 3.725 | 25

26 | 1.315 1.706 2.056 2.479 2.779 3.435 3.707 | 26

27 | 1.314 1.703 2.052 2.473 2.771 3.421 3.690 | 27

28 | 1.313 1.701 2.048 2.467 2.763 3.408 3.674 | 28

29 | 1.311 1.699 2.045 2.462 2.756 3.396 3.659 | 29

30 | 1.310 1.697 2.042 2.457 2.750 3.385 3.646 | 30

32 | 1.309 1.694 2.037 2.449 2.738 3.365 3.622 | 32

34 | 1.307 1.691 2.032 2.441 2.728 3.348 3.601 | 34

36 | 1.306 1.688 2.028 2.434 2.719 3.333 3.582 | 36



38 | 1.304 1.686 2.024 2.429 2.712 3.319 3.566 | 38

40 | 1.303 1.684 2.021 2.423 2.704 3.307 3.551 | 40

42 | 1.302 1.682 2.018 2.418 2.698 3.296 3.538 | 42

44 | 1.301 1.680 2.015 2.414 2.692 3.286 3.526 | 44

46 | 1.300 1.679 2.013 2.410 2.687 3.277 3.515 | 46

48 | 1.299 1.677 2.011 2.407 2.682 3.269 3.505 | 48

50 | 1.299 1.676 2.009 2.403 2.678 3.261 3.496 | 50

55 | 1.297 1.673 2.004 2.396 2.668 3.245 3.476 | 55

60 | 1.296 1.671 2.000 2.390 2.660 3.232 3.460 | 60

65 | 1.295 1.669 1.997 2.385 2.654 3.220 3.447 | 65

70 | 1.294 1.667 1.994 2.381 2.648 3.211 3.435 | 70

80 | 1.292 1.664 1.990 2.374 2.639 3.195 3.416 | 80

100 | 1.290 1.660 1.984 2.364 2.626 3.174 3.390 | 100

150 | 1.287 1.655 1.976 2.351 2.609 3.145 3.357 | 150

200 | 1.286 1.653 1.972 2.345 2.601 3.131 3.340 | 200

-------+---------------------------------------------------------+-----

Two Tails 0.20 0.10 0.05 0.02 0.01 0.002 0.001

One Tail 0.10 0.05 0.025 0.01 0.005 0.001 0.0005

Tail Probabilities


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