Carry Trading & Uncovered Interest Rate Parity - An overview and empirical study of its applications

M.Westman

F.Tafazoli 2011

Carry Trading & Uncovered Interest Rate Parity - An overview and empirical study of its applications

Bachelor thesis Linköping University VT 2011

Authors: Mathias Westman & Farid Tafazoli

Abstract.

The thesis examine if the uncovered interest rate parity holds over a 10 year period between Japan and Australia/Norway/USA. The data is collected between February 2001 - December 2010 and is used to, through regression and correlation analysis, explain if the theory holds or not. In the thesis it is also included a simulated portfolio that shows how a carry trading strategy could have been exercised and proof is shown that you can indeed profit as an investor on this kind of trades with low risk. The thesis shows in the end that the theory of uncovered interest rate parity does not hold in the long term and that some opportunities for profits with low risk do exist.

Uppsatsen undersöker om det icke kurssäkrade ränteparitetsvilkoret har hållit på en 10-års period mellan Japan och Australien/Norge/USA. Månadsdata från februari 2001 till december 2010 används för att genom regressionsanalys samt undersökning av korrelationer se om sambandet håller eller inte. I studien finns också en simulerad portfölj som visar hur en carry trading portfölj kan ha sett ut under den undersökta tidsperioden och hur man kan profitera på denna typ av handel med låg risk. Studien visar i slutet att teorin om det kursosäkrade ränteparitetsvilkoret inte håller i det långa loppet och att vissa möjligheter till vinst existerar.

Keywords: Uncovered Interest Rate Parity, Australian Dollar, Norwegian Kronor, US Dollar, Japanese Yen, Carry Trading.

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Table of Contents

Cover page ...... 1 Foreword ...... 4 1. Background ...... 5 1.1 Introduction ...... 5 1.2 Problem area ...... 5 1.3 Formulation of the problem ...... 6 1.4 Limitations ...... 6 2. Methodology ...... 7 2.1 Scientific approach ...... 7 2.2 Research approach ...... 8 2.3 Collection of data ...... 8 2.4 Research methods ...... 9 2.5 Research directions ...... 10 2.6 Analyzing the research ...... 10 2.7 Method critiques ...... 11 2.8 Choice of countries, time-periods and interest rates ...... 11 2.9 Source critique ...... 12 3. Theory ...... 13 3.1 Uncovered interest rate parity ...... 13 3.2 Linear regression ...... 15 3.3 Problems with the regression methods ...... 15 3.4 Forex & Interest rate risks ...... 16 3.5 Currency spot rate...... 16 3.6 Treasury bills & Zero-Coupon Bonds ...... 16 3.7 Arbitrage ...... 17 3.8 Carry trading ...... 18 3.9 Earlier studies ...... 19 4. Empirical ...... 20 4.1 Regressions ...... 20 4.2 Simulated portfolio ...... 25

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5. Analysis ...... 28 5.1 Analysis of the regressions ...... 28 5.2 Carry trading portfolio ...... 30 6. Discussion ...... 36 7. Closing words ...... 37 8. References ...... 38 8.1 Literature ...... 38 8.2 Electronic references ...... 39 9. Appendix ...... 40 9.1 Data ...... 40

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Foreword

The ultimate dream for every investor has always been the perfect arbitrage opportunity. Something that would provide you with high returns with low or no risk at all, preferably over longer periods of time. For some investors, especially hedge funds and institutional investors, carry trading is just that opportunity. In this thesis we aim to shed some light on this relatively unknown, at least for the common investor, kind of currency exchange and interest rate trading and show how it is possible for anyone to profit from this.

Mathias Westman & Farid Tafazoli - Linköping, Sweden 2011

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1. Background

In this chapter we present why carry trading is an interesting phenomenon to investigate further. We also present the purpose and problem area for the thesis.

1.1 Introduction

For a long time, investors around the world have used a trading strategy that very simplified means that you borrow money in a country with low interest rate and invest this amount in one where the interest rate is higher. The countries’ different interest rates should, as the Uncovered Interest rate Parity (from here on UIP) states it, affect the value of the countries’ currencies. This should remove all chances of arbitrage opportunities as currencies appreciate and depreciate. As we are about to show, the UIP theory has not held up and as a result, U.S. hedge funds and other investors worldwide have been able to make profits at a low risk. We choose to write this thesis on this subject since both the authors have great interest in both the currency and interest rate markets and this subject covers both of them. It is also a good way to get acquainted with central theories in two of the most important markets in today’s financial world.

1.2 Problem area

When doing investments with carry trading models there is an interest rate differential risk and there is also an exchange rate risk. Both of these parameters are included in the Uncovered Interest rate Parity model. Many carry trading investors have through out the last two decades chosen Japan as the country to borrow money in because of the low held interest rate due to their long term economic problems. The Japanese central bank has held the interest rate as low as zero or close to zero per cent during this time. Countries such as Australia and New Zeeland have on the other hand been countries that investors have been looking to invest in due to their high interest rate during a long period of time. This difference in interest rate should have been fully reflected in the UIP model, hence the higher interest rate in Australia should have strengthen the Australian dollar to offset the possibility do arbitrage earnings. But this has not been the case and carry trading investors have been able to achieve great profits investing in a non-efficient market.

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1.3 Formulation of the problem

When UIP has been shown, in some cases not to hold, and when there also have been opportunities of arbitrage in fixed income trading / forex trading there is a great interest according to us to investigate how this is possible and under what circumstances carry trading can be exercised successfully. It is also interesting to see why the arbitrage opportunity does not close up as it should according to UIP.

In this thesis we will firstly test if the uncovered interest rate parity holds between some selected

currencies during the last ten years and secondly we will analyze if investors can profit from possible deviations from the UIP.

1.4 Limitations

In this thesis we are going to examine interest rates and currency exchange rates of the following countries: Japan, Norway, Australia, and United States. We will not take transaction costs and taxes in consider due to the difficulty to estimate these variables. We will use the UIP as the only model to explain currency exchange rate movements. In this thesis we will not use other models or theories to explain these movements in currency rates.

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2. Methodology

2.1 Scientific approach

The scientific approach deals with the discussion between science and research1. There are two different approaches to use when doing the research. These two approaches have many similarities and many differences when it comes to methods of collecting data and the methods of processing the collected data. One of these scientific approaches does not rule out the other one2.

2.1.1 Hermeneutics

Within hermeneutics, the big picture, the entirety, is premiered and it is based on a holistic point of view. This means that it is more important to see and understand the big picture than concentrating on smaller parameters of the entirety. Using this approach the researcher is not aiming for generalization of the problem to the same extent as he would be using positivism. In hermeneutics it is considered that the world is constantly changing and what is described today may be described differently tomorrow3.

2.1.2 Positivism

Positivism is an approach within science philosophy that says that the researcher has an objective point of view and is neutral throughout the research. Furthermore the researcher is interested in generating different hypotheses which can be tested and analyzed4. Within positivism human has only two sources of knowledge, by observation using our senses and by what we can logically come up to. A positivist uses a critical point of view and he examines critically all observations to pick out only the true or probable ones5.

In this thesis we are going to collect the relevant data, test different hypotheses and investigate if the outcome can be generalized thus we will be using a positivistic approach.

1 Forskningsmetodikens grunder, Patel & Davidsson, 2003 2 Vetenskapsteori och forskningsmetodik, Wallén, 1996 3 Ibid 4 Business research methods, Bryman & Bell, 2007 5 Vetenskapsteori för nybörjare, Thurén, 2007

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2.2 Research approach

When choosing a scientific approach it is important to gather relevant theories and empirical data and relate these two parameters to each other6.

2.2.1 Inductivism

When using an inductive approach the investigator collects the relevant data. This data is then used to create a new theory. A research with an inductive approach is not based on earlier released theories. It is based on the empirical data that the researcher has collected7.

2.2.2 Deductivism

If the researcher is using a deductive approach the data is collected and then used to verify or falsify an already known theory by using one or several hypotheses8. The theory decides which data that is collected. When using this approach it is important that the researcher is objective so that the results are not biased by his thoughts and views9.

In this thesis we are going to use a deductive approach. We will apply our empirical data on already known, well used economic theories.

2.3 Collection of data

There are different ways to collect the data needed for the research. It depends on what the researcher wants to achieve with the research and which method that generates best results. One can gather data by interviews, observations, surveys or studying earlier researches10.

2.3.1 Primary data

Primary data is information that has not been collected or published earlier. It is data that has been collected from a certain source by the researcher and that has not been manipulated in any kind. Primary data is collected from first hand sources such as interviews, experiments or observations11.

6 Forskningsmetodikens grunder, Patel & Davidsson, 2003 7 Ibid 8 Ibid 9 Business research methods, Bryman & Bell, 2007 10 Forskningsmetodikens grunder, Patel & Davidsson, 2003 11 Ibid

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2.3.2 Secondary data

Secondary data is data that has earlier been collected or published by another party12. When using secondary data it is of great importance that the researcher examines if that data is useable in his work. It may have been collected for another purpose or it may be outdated13.

In this thesis we are going to use secondary data from historical currency spot rates, historical interest rates, articles and literature.

2.4 Research methods

When the collection of the data is finished, the researcher continues by processing the information to be able to answer the questions asked in the research. The information can be processed by for example statistical methods to interpretation of texts. There are basically two different methods to process the collected material14.

2.4.1 Qualitative data

Qualitative data is a description of a certain type of information that is supposed to give a deeper understanding of a phenomenon. The data can be collected from interviews and from observations15.

2.4.2 Quantitative data

Quantitative data is used to explain the cause of a certain phenomenon. It is data that can be quantified and verified and is used to describe a type of information that can be expressed numerically. The quantitative research is based on parameters such as quantity and frequency. These parameters are then processed and analyzed by for example statistical methods16.

In this thesis we are going to use quantitative data such as historical currency exchange rates and interest rates.

12 Forskningsmetodikens grunder, Patel & Davidsson, 2003 13 Business research methods, Bryman & Bell, 2007 14 Forskningsmetodikens grunder, Patel & Davidsson, 2003 15 Business research methods, Bryman & Bell, 2007 16 Ibid

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2.5 Research directions17

A research has a certain goal and certain conditions. It can be categorized in the following categories:

Explorative - The explorative research is used when the previous knowledge is limited. It can concern a new problem area or if there are limited previous theories.

Descriptive - The descriptive research is used to collect data for answering well described questions. It is called descriptive since it describes a certain situation, person or phenomenon.

Explaining - Explaining research is used to explain a cause/result-relation. Why this relation is the way it is.

Predictive - The predictive research is used to research the future development of a certain subject.

2.6 Analyzing the research

When it comes to analyzing a research there are several central terms that are used. We will define reliability and validity more in detail.

2.6.1 Reliability

The term reliability measures to what extent the research results are achieved depending on random occurrences or not. A research is considered reliable if the result of this research is identical to another research done with identical parameters used. If a phenomenon is researched several times and the results are fluctuating heavily, the research may be considered unreliable18.

2.6.2 Validity

Validity is an estimate of how well the study explains the phenomenon of which is observed and how well it reflects the truth. It is also an estimate of the research result, how well the researcher has collected relevant data and if it was used correctly to answer the questions the researcher wanted to answer in the beginning of the research.

Because of the use of historical data that is available to anyone we think that this thesis has a high grade of reliability. If anyone would use the same data and do the same statistical tests they would yield the

17 Research methods for business students, Saunders, 2007 18 Business research methods, Bryman & Bell, 2007

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same results. But, if a different time period was used and/or different currency pairs, the results could differ substantially. Other frequencies of the data used or different dates of which the data have been collected on could also yield other results than the ones we have acquired19.

2.7 Method critiques

The problems with our choice of method as we see it is that empirical and statistical studies rely in a great extent on the data. The fact that we use secondary data, and that the data have been collected in a time of great disturbance in the financial markets may affect the study negatively since the results may not show the reality as it is.

2.7.1 Justification

We have chosen this subject due to our great interest in the financial markets and because of the extra attention carry trading and UIP received in connection with the recent financial crisis. Due to a low level of light shed on this we believe that it deserves some extra attention. Other studies that have been done have also been, in many cases, quite heavy on the mathematical side. They also are a couple of years old and a lot have changed in both the currency and interest rate markets since then.

2.8 Choice of countries, time-periods and interest rates

2.8.1 Countries

We choose to include Japan, Australia, Norway and United States in this study. Japan is used as the country where the investor lends its capital. The choice fell on Japan because of its relatively long history of very low interest rates and dominant force in the world economy.

The other three countries are where we have chosen the investors to place their borrowed funds. We took USA because of its top position in the financial world and because of the many investors and hedge funds that resides there. Australia and Norway were chosen for their history of high interest rates. The currency exchange rates are mean values over each month for the whole time period to get consistent data.

19 Business research methods, Bryman & Bell, 2007

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2.8.2 Time periods

The time period we have chosen to test in this thesis is 2001-02-28 to 2010-12-31. This gives a reasonable amount of data to study and in this time frame there have been financial crises and a lot of changes in the markets. We believe that this gives a good picture of the currency exchange and interest rate markets and enough data to exercise a reliable study.

2.8.3 Interest rates

One month deposit notes or their equivalents in the different countries have been used as the interest rates in this thesis. The average interest rate over each one month period is used and we regard these as risk free because of their AAA rating and stable governments and/or central banks.

Because of the use of short term rates and notes we have not taken any duration or coupons into account. The short term rates also shows the day to day rates in a better way than longer term rates where expectations of future interest rate hikes/reductions are included in the yield.

2.9 Source critique

The sources that we have used in this thesis is for almost all parts well acclaimed authors ranging from employees of central banks to well know authors of student literature and educational books. All sources should be viewed from a critical point of view and even if the authors of our reference literature are well acclaimed we have cross-referenced these for extra objectivity.

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3. Theory

In this chapter we will examine the theories on which this thesis rests and explain what these mean. We also explain different relevant phenomena and instruments and review other studies that have been made on this subject.

3.1 Uncovered interest rate parity

The theory of uncovered interest rate parity was originally formed through the “law of one price” and “the purchasing power parity” which were both developed in the early 20th-century. It states that the difference between the interest rates of two currencies will be equal to the expected depreciation of a currency. That means that if one countries’ interest rate raise by two percent, the other country’s currency must be worth two percent less in relation to the country which raised their interest rate. This is to remove the possibility of arbitrage opportunities that otherwise would occur. Basically it links the interest rate and spot exchange rate between two countries.

The formula for the uncovered interest rate parity is as follows20:

=The exchange rate between the two countries examined and its expected value at a time in the future.

= The exchange rate at the time . = The interest rate r at the time .

= The interest rate in the other country examined.

This formula tells us that the expected depreciation of the domestic currency should be equivalent to the positive change in interest rate between the domestic and the foreign currency.

More easily described you can say that the change in spot rate equals the spread between the

interest rates .

20The economics of exchange rates, L.Sarno, M.P.Taylo, 2002.

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In this thesis we will use logarithmic values of the UIP formula for its resemblance to the linear regression model. The logarithmic version of the formula is written,

Below is a timeline of what happens and how the UIP theory removes the arbitrary elements that can occur in the market.

•Country X raises its interest rate in relation to country Y

•As the demand for investing in country X rises with the more attractive interest rate, investors exchange their Y money for X money

•When investors exchange their Y money for X money, the cross-currency rate changes giving investors less Y money for every X money.

•The higher exchange rate lowers the value of the Y money, effectively removing the incentive to invest in the higher yielding currency as the arbitrage disappears.

This simple example shows that according to UIP, a risk neutral investor can invest his Japanese Yen to the Japanese interest rate and receive this return on his investment. He can also exchange the initial investment to Australian Dollar and receive the higher foreign interest rate on his investment. When the preferred investment period is over he simply exchanges the original investment plus the return back to Japanese Yen. If the UIP holds the investor should in the end receive the exact same return on both investment options.

If this parity does not hold, the investor could exchange the initial investment to Australian dollars. He can then invest these Australian dollars at the higher Australian interest rate and exchange it back to Japanese Yen whenever the investment period is over. This way the investor has received a higher return on his investment with a low risk.

One important factor is that the demonstration above and the formula do not take in to account any transaction cost or any credit risk. It also assumes that there are no limits on capital flows between the two countries.

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3.2 Linear regression

In statistics, straight line regression, or linear regression is used as an easy way of showing how a series of data correlate with each other. That means, how well one set of data can explain how another set of data behaves or what their values are. Basically you try to draw a straight line and see how well / badly your data set fits and correlate with that line. The standard formula for a linear regression is21:

is the dependent variable, the one that is affected and the is the independent variable, the variable that affects. is the point of interception with the Y-axis and the coefficient is the slope of the line which is being calculated to be the best fit of the observation points. When this is done you can then calculate how much the data differs from the line and how well it “fits”. This is called standard deviation. You also include a random variable, also called a stochastic variable. This is included to describe small differences and randomness in the data. In this case is the sign for the random variable.

In this thesis we will use linear regression to check how the different currencies react to changes in the spread between the countries interest rates.

3.3 Problems with the regression methods

One of the major problems with linear regression is that if you have data points in your data set that deviate a lot from the other observations the results could get distorted or you could end up with bad or low correlations even though almost all of the other data is highly correlated. This is extra significant if you have a small data set.

The data set itself, as mentioned above is also an important factor. If the data for the study is too small it does not give a correct view of the real world or the phenomenon that you want to explain with your statistical model. The bigger the data set, the higher the reliability of the test. You could also get problems with auto-correlation and low p-values.

Auto-correlation is when your data points affect each other and therefore changes the values after. This could lead to strange regression results as auto-correlation gives wrong input values.

A high p-value means that the fitted model is not statistically proven. You always try your hypothesis on a 95% or 99% confidence level. In this thesis we use the 95% confidence level.

21Regression och tiddsserie analys, G.Andersson et.al, 2007

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3.4 Forex & Interest rate risks22

As mentioned earlier there is an exchange rate risk as well as an interest rate differential risk involved in borrowing money in one country, changing the amount to another currency and investing it in another country. Currency exchange rates are highly volatile and if the investor would take a position and the currency would move in the opposite direction the investor would obviously risk losing the profits made in the interest rate market and even more if the position is not closed. This forex exchange risk is in some cases hedgeable by using for example forwards, but we are not going to focus on that in this thesis. The interest rate risk is less volatile and more predictable than the currency exchange rates. But in extreme market conditions, such as during the latest financial crisis, there is always a risk of fast climbing or declining interest rate in a specific country due to the conditions of this countries’ financial health. In extreme financial conditions the currency and the interest rate often deviate even more from the UIP theory.

3.5 Currency spot rate

The spot rate between two currencies is the rate that the buyer and the seller want to exchange the currencies at for immediate exchange and delivery. If the spot rate between the currencies Japanese Yen and the Norwegian Krona is 0.06 (JPY/NOK = 0.06) then the buyer and the seller exchange their currencies at the rate of 1 JPY = 0.06 NOK. This is also known as the avista price, from the Latin word for “for showing”.

3.6 Treasury bills & Zero-Coupon Bonds23

Treasury bills (American name) are the kind of bonds that governments emit to fund their spending and short term lending needs. The Swedish equivalent is “Statsskuldsväxlar”. Since governments (in most cases) always can repay the money they owe or can borrow new funds their bonds are rated AAA and Aaa. AAA and Aaa are the highest ratings for a securities and in many cases government bonds with short term is referred to as the “risk free” alternative due to its high rating and extremely low risk of default. In recent months these standards have come under pressure since some countries such as Greece, Spain and even USA have had warning about their ratings or outright downgrading.

22Bond market analysis, Fibozzi, Frank J, 2010 23Ibid

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In almost all cases, the Treasury bills with short terms, less than one year, does not pay any coupons. This kind of bond is called a zero-coupon bond. The zero-coupon bond is emitted below its face value. What that means is that if the nominal price of the bond is 100 and the nominal value is 100.000 USD the price on emit is lower than 100, for example 97. When the bill matures after 3 months the value is equal to the face value of 100 and the full amount, nominal and interest is paid out. The formula for the bond value is24:

= Time to maturity = Face value of bond = Interest rate or yield

And the formula for the discount of the face value is25:

= Discount value = Face value of bond = Purchase price = Days to maturity

In this thesis we use Treasury bills or equivalents in other countries with a one month term as the risk free rate that an investor can receive by investing in the country. Any credit risk that might exist is not taken into account since we refer to it as the risk free alternative.

3.7 Arbitrage

As we use the term arbitrage in this thesis it justifies an explanation. Arbitrage, in its purest form is the possibility of a risk-free profit at zero cost. In this thesis we will use a more liberal approach to the subject. In many situations arbitrage is also used to explain a way to make money on something that is away from its true value or differences between one or more markets. In the case of carry trading, that we are about to explain more about, the arbitrage element is the part of the trade where one make money because of the UIP theory not working as it should. In other cases it can be an arbitrage when you buy the same security, for example a currency in one market for one price and sell the same asset just seconds later on another markets, making a profit totally risk free.

24Bond market analysis, Fibozzi, Frank J, 2010 25Ibid

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3.8 Carry trading

Carry trading is the name of the trading technique where you take advantage of the market deficiencies that UIP says does not exist. This is not a true arbitrage as explained above since the currency exchange rates can appreciate/depreciate in the opposite direction than you intend. But as we are about to show, there are ways to make money on this market deficiency and therefore we, in some contexts, call it arbitrage.

The most common carry trader borrows his money in Japan that has had one of the lowest interest rates in the whole world. He then invests this money in a country that has a higher interest rate, like Australia that has a history of high interest rates. In this thesis we construct a carry trading portfolio with these countries and two additional countries for better reference.

A simple example of a carry trade could look something like this:

An investor borrows 100.000 Yen at 0.5 % interest rate and exchanges this in the currency market to 1140 Australian dollars (0.0114 exchange rate). He can then take these Australian dollars and buy high investment grade bonds with an interest rate of 5 %. If the relationship between the two countries’ interest rates stay the same and the currencies do not appreciate/depreciate the investor makes a profit of 450 Yen with little risk (100.000 ¥ * (0.05-0.005) = 450¥).

*Assuming that the exchange rate does not depreciate as much as UIP suggests.

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3.9 Earlier studies

Before this thesis, a wide variety of other studies have been done on the subject and related topics. Most notably there have been three major recognized studies that we also have looked closer into,

● Harvey, John (2004)

Harvey looks in to the subject from a different view in relation to many others by mostly focusing on the capital flows between countries and exterminating if this is a case for the UIP not to hold. He also looks at the risk premium and, as opposing to many others, views this as a small part in why UIP does not hold and regard other factors as more important including the just mentioned capital flows and restriction on these.

 Durcakova, Mandel and Tomsik (2005)

This study examines the UIP in a way close to ours. They test UIP between the Czech Krona and USD/EUR and get clear results that UIP in fact doesn't hold. The β-value results are in the area -1.6 to - 3.9 and the α-value results is between 0.5 and 0.7. They conclude by claiming that a lot of the interest rate differential is in fact countered by transaction costs and interventions of central banks to control the different currencies.

● Alexius, Annika (1998)

Alexius study from 1998 tries UIP on longer terms and with treasury bonds rather than bills. This is done because almost all other studies have been done on shorter term rates. The study is very comprehensive and tests 14 different countries against the US dollar and for a period of 40 years. The problem with the study is that longer bonds have coupon payments that need to be reinvested and that the rates fluctuate in a different way over these periods. In the end Alexius concludes that in this her study, opposite to many other, UIP does in fact hold and all the β-values in her regressions are positive. Her findings show that the longer the interest rates, the higher the β-values get and around 30 weeks it gets close to 1. On the other hand her study also proves that with short term interest rates UIP does not hold as almost all other studies show.

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4. Empirical

In this section the results of the study will be reviewed and examined. Both the portfolio and regression results are included and will be explained. The full data is included in the appendix.

The data have been collected through mainly two different sources, Reuters and DataStream. We have used one month data on both the interest rate and currency exchange rates. Both the exchange rates and interest rates are calculated as mean values over the month and the interest rates have been recalculated to one month interest rates from the per annum rates. This was done by taking the per annum rate dividing it by 12.

We have 118 data points which relates to 10 years of one month data. With the calculated monthly rates and exchange rates we have also calculated the interest rate spreads between the different countries and also the month to month change of both the interest rate spread and the currency exchange rate. Since UIP includes logarithmic values, we have also logged the interest rate data for a correct fit of the model. We have included the printouts of the regressions in the boxes.

4.1 Regressions

We ran the regressions as straight regressions without any extra modules. We did include a plot of the fitted model for reference. The regressions where made in two different stages. First we ran the whole data set including all 10 years’ worth of data for a full image of the alpha and beta coefficients of the different currencies. Since the data itself shouldn’t auto-correlate we did not include any model to account for that either. The model itself is really close to both the logarithmic UIP formula and the formula for the linear regression. The regression model is as follows with the same variables as before.

In this case the - value represents a risk premium or the intercept of the regression line. If UIP should hold the risk premium should be 0. stands for the beta value, the coefficient of which interest rate spread is multiplied with or the slope of the regression line. is the random variable that always is included. For the UIP to hold the –value should be equal to 1. In essence, the equation should look as follows for the UIP to hold.

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FX rate change = the currency exchange rate change IR spread change = Interest rate spread change

This basically gives that the FX rate change should be equal to the IR spread change, just as UIP says. As mentioned earlier we have used one month average currency exchange rates and one month average interest rates as input data.

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4.1.1 AUD/JPY Regression

Coefficients Least Squares Standard T Parameter Estimate Error Statistic P-Value Plot of Fitted Model AUDJPY FX change = -0,0000388962 - 0,581682*AUDJPY log spread change Intercept -0,0000388962 0,0000529999 -0,733891 0,4645 (X 0,0001) Slope -0,581682 0,23635 -2,46111 0,0153 35

25 Analysis of Variance

Source Sum of Squares Df Mean Square F-Ratio P-Value 15 Model 0,00000200723 1 0,00000200723 6,06 0,0153 Residual 0,000038441 116 3,31388E-7 5

Total (Corr.) 0,0000404482 117 AUDJPYchange FX -5

Correlation Coefficient = -0,222766 -15 R-squared = 4,96248% -16 -12 -8 -4 0 4 8 AUDJPY log spread change (X 0,0001) Standard Error of Est. = 0,000575663 Mean absolute error = 0,000404808 Durbin-Watson statistic = 1,91819 (P=0,3294)

The equation of the fitted model i:

FX change = -0,0000388962 - 0,581682*IR Change

Since the P-value is less than 0,05, there is a statistically significant relationship between the variables at the 95,0% confidence level. The R-Squared statistic indicates that the model as fitted explains 4,96248% of the variability FX rate. Since the P-value in the Durbin-Watson test is greater than 0,05, there is no indication of serial autocorrelation in the residuals at the 95,0% confidence level.

In the regression with the Australian dollar against the Japanese yen we got an value of -0.00003. Even if the number is small the this could reflect a risk rebate in this case instead of a premium.

As we said earlier the –value should be 1 for the UIP to hold. In this case we got -0.581. Note that this is significantly different from zero and from what the UIP addresses. This indicates that a change in the interest rate spread only reflects to a 58% change in the exchange rate between the two countries. It also points to that the change in exchange rate ran in the opposite way as UIP designates since it was a negative number. Of course this disapproves the theory since it only reflects about half of the change in the exchange rate and moves in an opposite direction.

The -values in this case was 0.4645 for the -value and 0.0153 for the –value as described above. This is good since the results are significant on a 95% level for the –values. Unfortunately -value for the risk premium was too high for a 95% confidence level and the value that tells how well the model describes the results was low at just 4.96%. The plot of the model also shows the really bad fit of the values and the low results.

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4.1.2 NOK/JPY Regression

Coefficients

Least Squares Standard T Plot of Fitted Model Parameter Estimate Error Statistic P-Value NOKJPY FX change = -0,0000921328 - 1,69904*NOKJPY log spread change (X 0,001) Intercept -0,0000921328 0,000228224 -0,403695 0,6872 13 Slope -1,69904 0,634859 -2,67624 0,0085 9 Analysis of Variance 5 Source Sum of Squares Df Mean Square F-Ratio P-Value

Model 0,0000436902 1 0,0000436902 7,16 0,0085 1 Residual 0,000707607 116 0,00000610006 NOKJPY FX change NOKJPY FX Total (Corr.) 0,000751297 117 -3

-7 Correlation Coefficient = -0,24115 -23 -13 -3 7 17 27 (X 0,0001) R-squared = 5,81531% NOKJPY log spread change Standard Error of Est. = 0,00246983 Mean absolute error = 0,00173775 Durbin-Watson statistic = 1,87959 (P=0,2577)

The equation of the fitted model is:

FX change = -0,0000921328 - 1,69904*IR Change

Since the P-value is less than 0,05, there is a statistically significant relationship between the variables at the 95,0% confidence level. The R-Squared statistic indicates that the model as fitted explains 5,81531% of the variability in the FX rate. Since the P- value in the Durbin-Watson test is greater than 0,05, there is no indication of serial autocorrelation in the residuals at the 95,0% confidence level.

On the Norwegian krona against the Japanese yen we got an even smaller -value of -0.000009. This is once again in the favor of the UIP since the theory assumes a zero value. The –value should be 1 for the UIP to hold as mentioned earlier. For this currency pair we got a negative number, -1.699. This indicates that a change in the interest rate spread reflects to a -169% change in the exchange rate between the two countries. This means that the exchange rate moves more than UIP designates by almost 270%. Of course this also disapproves the theory.

The -values was 0.6872 for the -value and 0.0085 for the –value. Once again the beta value is significant on a 95% level. The -value for the risk premium was too high for a 95% confidence level just as the last time and the value was a bit higher but still low at 5.81%. This is also reflected in the plot of the results.

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4.1.3 USD/JPY Regression

Coefficients Least Squares Standard T Parameter Estimate Error Statistic P-Value Plot of Fitted Model USDJPY FX change = 0,0000275995 - 0,1129*USDJPY log spread change Intercept 0,0000275995 0,000024583 1,1227 0,2639 (X 0,0001) Slope -0,1129 0,0858109 -1,31568 0,1909 8

5 Analysis of Variance Source Sum of Squares Df Mean Square F-Ratio P-Value 2 Model 1,21918E-7 1 1,21918E-7 1,73 0,1909 -1 Residual 0,00000817008 116 7,04317E-8 Total (Corr.) 0,00000829199 117 -4 USDJPYchange FX -7 Correlation Coefficient = -0,121256 R-squared = 1,47031% -10 Standard Error of Est. = 0,00026539 -17 -7 3 13 23 (X 0,0001) Mean absolute error = 0,000204371 USDJPY log spread change Durbin-Watson statistic = 2,10689 (P=0,7181)

The equation of the fitted model is:

FX change = 0,0000275995 - 0,1129*IR change

Since the P-value is greater or equal to 0,05, there is not a statistically significant relationship between the variables at the 95,0% or confidence level. The R-Squared statistic indicates that the model as fitted explains 1,47031% of the variability in FX rate. Since the P-value in the Durbin-Watson test is greater than 0,05, there is no indication of serial autocorrelation in the residuals at the 95,0% confidence level.

The -value we got for the U.S dollar vs. Japanese yen regression was 0.000002. As both the other regressions this is so close to zero. Again, this works in the favor of the UIP theory. The –value once again showed a negative number like in the AUD/JPY regression at -0.1129. In relation to the Norwegian regression this shows a small change of just 11% in the exchange rate when the interest spread changes. Once again this disapproves the UIP theory.

The -values of the and –value was too high at 0.2639 and 0.1909 and therefore can not be statistically proven on a 95% confidence level. The value was the lowest of all the three regressions at just 1.47% giving a low explanation grade for the model. The plot shows how bad the model fits since the line should be linear and tilting upwards, not downwards as in these cases.

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4.2 Simulated portfolio

To better show how an investor can profit from the carry trade and the shortcomings of the UIP model we have created a simulated portfolio. Included are the three currencies we used in our regressions, Australian dollars, Norwegian kronor and American dollars. At the beginning of the trade, February 2001, we borrowed 1.000.000 worth of YEN in Japan. This money was then invested in three equally large portions of 333.333 Yen in the currencies mentioned earlier. We ended the trade in October 2010 resulting in some significant profits for the aggregated portfolio.

The portfolio was also split up in to two parts, one from 2001 ending just before the financial crisis and one after the crisis rolling on to 2010. This was done to show how big the impact of the crisis was to this kind of trades and to exclude a time when the market wasn't functioning correctly. We believe that the post-crisis time in a poor way reflects the true functions of the market and hence the importance of showing this separately.

The graphs below shows the development of the individual trades on each currency and also the aggregated portfolio with all three currencies. The index start at 100 in February 2001 and shows the time where the 1.000.000 YEN where invested.

Carry trade returns 01'-10' 250 01'-10' Yearly Total 200 return return 150 Portfolio 4,49% 55,10% 100 AUD 7,62% 108,37% NOK 4,36% 53,27% 50 USD -1,40% -13,11% Feb-01 Feb-02 Feb-03 Feb-04 Feb-05 Feb-06 Feb-07 Feb-08 Feb-09 Feb-10 Aug-01 Aug-02 Aug-03 Aug-04 Aug-05 Aug-06 Aug-07 Aug-08 Aug-09 Aug-10

NOK AUD USD Portfolio

As one easily see on the graph and in the table above a 1 YEN investment in NOK more than doubled the money (105%) during the pre-crisis time of the trade (8 years). As a result of the crisis, the profits took a sharp turn downwards but still gave a nice profit of 53% during the 10 year period. The yearly return for the NOK investment was 4.36% and for the pre-crisis years the yearly return was 10.83%. In the post- crisis period the NOK got hit the hardest and made a total loss of 24.90% reflecting a yearly loss of 9.10%.

The results of 1 YEN invested in USD were not as good as an investment in NOK, but still yielded some return during the pre-crisis years. The profit was around 10% during this time. In the aftermath of the crisis the profits dropped just as in the other trades and ended on around -10% in 2010. This represents

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a yearly return of 2.18% before the crisis and a yearly loss of -1.4% on the whole trade. In the post-crisis period the USD got hit among the hardest and the trade lost 23.46% during the last three years. In relation to the other currencies the USD did not recover any of the losses after the crisis as the other currencies did.

In the graph below is the pre-crisis return for all the currencies and for the aggregated portfolio. As the graph and table show, the returns for the countries with the highest nominal interest rates where phenomenal and still decent for the USD trade.

Carry trade returns 01'-07' 250 200 01'-07' Yearly Total 150 return return Portfolio 9,12% 84,25% 100 AUD 11,47% 113,85% 50 NOK 10,83% 105,42%

Feb-01 Feb-02 Feb-03 Feb-04 Feb-05 Feb-06 Feb-07 USD 2,18% 16,26% Aug-01 Aug-02 Aug-03 Aug-04 Aug-05 Aug-06 Aug-07

NOK AUD USD Portfolio

Much like the NOK, the AUD had really high yield on their interest rates both before and after the financial crisis. As we see on the graphs and tables this gave similar and even higher results as the NOK trade. With a total return of 108% for the whole 10-year period and a 113% return for the pre-crisis years the AUD was by far the best investment of the three currencies. The yearly return for the whole period was 7.62% and for the first period an impressive 11.47%. The post-crisis return of the AUD was also the best with a small profit of 0.39%. This was great returns in relation to the other currencies and the AUD also recovered fastest in the post-crisis period.

The aggregated portfolio returned yields way beyond our expectations during the 10-year period. The profit of 55.10% is extremely good in relation to the risk level of the trade. The yearly return of 9.12% is more than the average yearly return on the S&P 500 (3.55%) for the same period.

Even if the risks are significant with both the interest rate risk and the currency risk (which we have seen is correlated) the portfolio evens out some of the risk with the diversification in the different currencies.

To reduce the risk even further, more countries could have been used as the source of the borrowed money. This would have diversified the interest rate risk and not only the currency risk as in our case. One prominent feature of this kind of trades is the low margin requirement for forex trading which gives

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the investor pulling the trade together easy access to a lot of leverage. This means that the invested money could yield a lot more on own equity. Below are the post-crisis returns of the different currencies and the aggregated portfolio, in table and graph form.

Carry trade returns 07'-10' 120 110 100 07'-10' Yearly Total 90 80 return return 70 Portfolio -5,64% -15,99% 60 AUD 0,13% 0,39% 50 NOK -9,10% -24,90% USD -8,58% -23,46%

NOK AUD USD Portfolio

The post-crisis return of the portfolio was as expected very bad. The total loss ended at 15.99% which translate to a yearly loss of 5.64%.

One interesting thing is how well the graphs correlate over time. All the different currencies basically shows the same results only leveraged differently giving the NOK a higher return and the USD a lower. The leverage of course comes from higher interest rate differential between Japan and Norway relative to Japan and USA.

All the underlying data is included in the appendix.

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5. Analysis

5.1 Analysis of the regressions

In the analysis part of this thesis we review the results that were displayed in the empiric’s chapter and go in to greater depths to explain what they mean and why we received these results.

5.1.1 Australia/Japan

The results from this test showed non-existent or close to non-existent risk premium which is also what the UIP states. When it comes to the –value we find that it works in an opposite manner than what the UIP theory states. The –value for this test was -0,58 which basically tells us that for every 1 percent increase in interest rate spread, the exchange rate depreciates 0,58 percent. We will discuss this mechanism later on in this chapter.

5.1.2 Norway/Japan

The statistical test of this currency pair shows as well that the risk premium is non-existent. The regressions also show that the –value is strongly contradicting to the theories behind UIP. A one percent increase in the interest rate spread has generated a 1.6 percent depreciation of the exchange rate during our test period. This is however in line with earlier studies as we will find out later in this chapter.

5.1.3 USA/Japan

In the case of USA and Japan these two countries had the smallest interest differential and also the cross currency pair with the best liquidity. This should render better valuation of the currency and also better premises for UIP. This proved not to be the case as the USD regressions got a beta value far from the theory. The main reason for this is probably, as mentioned earlier, the USD´s financial place as a “safe currency”. In times of crisis or turmoil investors tend to flee to the USD. At the same time the USD always drops when investors turn to riskier investments. This gives the dollar more volatility and also tends to over appreciate/depreciate the currency. This works in a negative way for the UIP.

There is not much to add that has not already been mentioned in this thesis about the alpha value. You could see this as a small risk premium but the values on this, and all other regressions, are very small. Therefore there is no value in trading just the risk premium.

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5.1.4 Overall results

The results from the regressions made on the chosen input data show that the Uncovered Interest rate Parity does not hold over this period of time. This subject has been under research many times before and the dominant part of the researches that we have been studying show this very same result. What might seem odd reviewing our results is that there is a negative beta value. This means that if the interest rate spread increases the exchange rate actually depreciates rather than appreciating which is totally contradicting to what the UIP states. This is the case for all three of our studied currency pairs. However, the results are in accordance with earlier researches done on this subject.

The negative beta value is a standard finding in earlier studies using short interest rates states Annika Alexius 1998. Furthermore she states that this is the cause of short interest rates having the characteristics of being used as the principal monetary policy instrument in most countries with flexible exchange rates. The movements of short interest rates and exchange rates in response to shocks generate the observed negative relationship between short interest rates and exchange rate change. This relationship is researched by McCallum in 1994 and his statement is that the negative relationship is due to the fact that the short interest rate is used as a monetary policy instrument to stabilize the nominal exchange rate.

McCallum’s model was used by Meredith and Chinn in 1998 in their research of the UIP. They simulated a model where inflation and output were functions of the real exchange rate and where it was assumed that monetary policy responds to movements in inflation and output and not to the exchange rate. In their model they had also a long interest rate that was not assumed to be used as a monetary policy instrument. The simulation of the model showed an average beta value of -0.50 for the short interest rate. For the long interest rate they received an average beta value of 0.82. Their thought about the negative relationship between short interest rates and the exchange rate is that it is due to a temporary increase of the risk premium. This temporary increase depreciates the exchange rate while inflation and output increases because they are functions of the exchange rate. The central bank raises the short interest rate to move inflation and output to equilibrium levels which leaves us with an increased interest rate and a depreciated exchange rate.

In the next period the risk premium shock disappears and the exchange rate effectively appreciates while the output, inflation and the short interest rate decreases. The interest rate change is lagged in relation to the exchange rate changes leaving us with the possibility of negative beta values using short interest rates as input data. The included long term government bonds investment in the model worked more or less according to the UIP.

The purpose of our thesis is to examine whether the Uncovered Interest rate Parity holds or not during the chosen period. The purpose is not to investigate why the UIP does not hold or why a negative relationship occurs but it is very interesting and informative to study what other researchers that have studied this subject came up to and vital for us to take part of these studies to be able to fully understand why we received these results in our regression test.

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5.2 Carry trading portfolio

5.2.1 Aggregated portfolio

As we and others before us have shown the UIP does not hold over longer terms. There are large problems with the model, especially in the last year with great uncertainty on both the currency market and the interest market. The results also show that a risk premium does exist but it is so small that we can rule that out as an explaining factor for the flaws of the model.

These erroneous market pricings have given investors the possibility to easily use a carry trading strategy to generate great returns over a long period of time.

The portfolio showed impressive results as we mentioned earlier and the yearly return of 4.49% is close to the expected return of a standard equity index. As also said earlier, the portfolio actually gave better return as the S&P 500 during our test period.

The interest rate for Japan during the period was extremely low mostly due to the economic crisis they experienced during the 90’s. The rates were actually negative during a period between 2003 and 2005.This in conjunction with the large domestic savings rendered large quantities of money leaving Japan for other countries with better returns. This is a kind of carry trading even though the average person in Japan didn't know it.

As one can see on the graph below the rate have not gone over 1% in the last 10 years. This is unique for Japan and why Japan always has been regarded as the base for carry-traders.

1,2 1 0,8 0,6 0,4 0,2 0 -0,2 Feb-01 Feb-02 Feb-03 Feb-04 Feb-05 Feb-06 Feb-07 Feb-08 Feb-09 Feb-10 Aug-01 Aug-02 Aug-03 Aug-04 Aug-05 Aug-06 Aug-07 Aug-08 Aug-09 Aug-10

Japan 1 Month Interest rate

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The black sheep in the portfolio was the USD. The AUD and NOK had phenomenal profits but the USD actually showed losses after the full period. This was much due to the severity of the financial crisis where USA got the worst hit. The inflow of money during this period, the USD is regarded as a safe haven during times of crisis, made the USD depreciate less than the other two countries. Australia and Norway didn't have the same inflow of cash, rather the opposite as they are regarded as “high risk” currencies.

This affected our portfolio very negatively since the interest incomes became minimal. Furthermore and more importantly all three currencies in the long basket depreciated to the Japanese Yen.

It is hard to evaluate the exact risks involved in these kinds of portfolios but as the regressions and the returns suggest there is a high probability that you are able to profit from it. The standard deviations / volatility for the currency pairs we have used are not the most volatile but still in the top quartile. This is of course for some part due to the carry trading that is being done between these countries but also the recent financial crisis that has driven up the mean volatility for currency rates over the whole spectrum.

This portfolio clearly shows two sides of the carry trade. On one side we have the trade that works nearly perfectly when the markets are calm and on the other hand the trade that generates large losses. This isn’t so hard to imagine since markets tend to overreact / act irrational in times of crisis. As a result forex exchange rates and interest rates can be very wrongly priced at time and therefore work in the favor of the UIP theory or in some cases, the carry trader.

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5.2.2 AUD

The Australian dollar trade was the trade with the by far best return of the three currencies we examined. Australian interest rates have always been high, mostly since they export a lot of natural resources which gives them a large export sector. This gives a constantly high interest rate which works great togheter with the extremely low Japanese interest rate.

8 7 6 5 4 3 2 1 0 Feb-01 Feb-02 Feb-03 Feb-04 Feb-05 Feb-06 Feb-07 Feb-08 Feb-09 Feb-10 Aug-01 Aug-02 Aug-03 Aug-04 Aug-05 Aug-06 Aug-07 Aug-08 Aug-09 Aug-10

Australian 1 Month Interest rate

During the crisis, the AUD got hit hard. As investors over the world wanted to reduce their risk and unwind positions prices of natural resources, the AUD fell sharply. This in conjunction with a lot of people selling of carry positions created a short squeeze in the JPY. This made the situation of the AUD/JPY exchange rate even worse. As one can see on the graph above the Australia central bank lowered their interest rate from around 6% down to 2.5%. Even thou it’s significantly higher than in Japan the risk adjusted return weren’t good enough. Since the basically all money from carry trades come from borrowed money or margin accounts a lot of traders had to unwind their positions even if they didn't want to, since banks and lenders had a lot of problems during the crisis and the liquidity/lending basically disappeared.

The AUD has the highest volatility of the three currencies we used in this thesis. This should yield the best result for the trading. Since the exchange rates move rapidly and a lot there is always larger possibilities for the market to reflect the wrong price instead of the most efficient one. It also poses the highest risks as the quick changes in the exchange rate can easily and quickly diminish any profits gained from the interest rate spread and earlier exchange rate movements. This is always something you have to account for when trading currency pairs and carry trading.

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5.2.3 NOK

As we talked about earlier the returns from the NOK trade was great and highly contributed to the success of the portfolio. The yearly return of 4,36% and total return for the 10 year period of 53,27% is phenomenal but the NOK was also the currency that got hit the hardest when the financial crisis unraveled. The Norwegian economy is highly dependent on the oil price level and when the financial crisis began the demand and price for oil crashed and the Norwegian interest rates also fell sharply. The interest rate spread decreased and generated less interest profit in the trade. The NOK depreciated heavily relatively to the Japanese Yen and generated a substantial loss in our portfolio.

During this period the oil price fell as much as 70% in a very short period of time and without doing any kind of analyze we believe that this has affected the Norwegian economy in a way that the Norwegian interest rates has only risen marginally. Furthermore the NOK has depreciated more rather than appreciating on a rising interest rate spread which we believe shows that the market has an uncertain view on the future Norwegian economy.

10 9 8 7 6 5 4 3 2 1 0 Feb-01 Feb-02 Feb-03 Feb-04 Feb-05 Feb-06 Feb-07 Feb-08 Feb-09 Feb-10 Aug-01 Aug-02 Aug-03 Aug-04 Aug-05 Aug-06 Aug-07 Aug-08 Aug-09 Aug-10

Norway 1 Month Interest rate

The similarities with the AUD are many. As we said above Norway is highly dependent on oil and that is just like Australia’s dependency on mining. The volatility of the NOK is also high, especially relative the USD. This is clearly visible in the graph and data. NOK has always been highly correlated with oil price changes and that can partly explain why the NOK changed a lot when the interest rate differential stayed the same. This also gives good opportunities for carry trading which also shows in the returns of the trade.

The interest rate hasn’t been as stable as in Australia but has still been high over the whole period in relation to the Japanese interest rates. This has given good returns on the interest rate spread even if

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the spread narrowed significantly between 2004-2005 and 2009-2010. The mean interest rate was still high and clear parallels can once again be drawn to the Australian dollar.

5.2.4 USD

The yield on the USD carry trade wasn’t all to our liking. The pre-crisis yearly profits of 2.18% and total profits of 16.26% are mediocre over the 8 year period that it reflects the return for the post-crisis period where even worse. With a yearly loss of -8.58% and a total loss of -23.46% it’s easily the worst trade of the three and the worst component in the portfolio.

The financial engine that USA always has been experienced a plunge in the interest rate level to almost zero percent during the last financial crisis. This clearly affected the interest incomes in our carry trading model, even though the currency didn’t appreciate as much as the UIP would suggest.

6

5

4

3

2

1

0 Feb-01 Feb-02 Feb-03 Feb-04 Feb-05 Feb-06 Feb-07 Feb-08 Feb-09 Feb-10 Aug-01 Aug-02 Aug-03 Aug-04 Aug-05 Aug-06 Aug-07 Aug-08 Aug-09 Aug-10

USA's 1 Month Interest rate

The USD depreciated to the JPY by approximately 25% while the interest rate spread fell from 3,8% pa to around 0,2 % pa. The depreciation of the USD is effectively more or less all our losses in the portfolio regarding the USD investment during this period. We believe that the historically stable USD worked as a safe haven for the investors during this chaotic time thus helping the USD from depreciating less than the UIP would state. As we see on the graph above the interest rate also fell sharply after the 9/11 incident in 2001 to boost the economy. This together with the financial crisis was just too much for our carry trade to handle.

One other significant thing is that in the last years, during and after the financial crisis interest rates and exchange rates have been kept artificially low due to the quantative easing conducted by the Federal Reserve Bank. This leads to market forces being put out of place by external forces and thereby also reducing the effectiveness of the carry trade.

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In conclusion you could say that the USD was a bad choice as a currency due to its natural place as a safe haven and dominant role in the world. We did believe that this currency pair would yield the worst returns since it is the most actively traded of the three. This proved to be true but not because of these reasons as the regressions earlier also showed.

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6. Discussion

The purpose of this thesis was to test if the Uncovered Interest rate Parity does hold over a longer period of time. Our statistical research showed that it does not hold over our test period which is in accordance with earlier similar studies. In our research we found that there are problems with the model during the whole tested period but especially during the last couple of years when the financial markets encountered great instability and insecurity.

The results that we received with R-square values around 1-5% clearly show the problems with the model. The results also show that a risk premium does exist but it is so small, and close to zero, that we can rule that out as an explaining factor. Most importantly the beta values differ significantly from what the UIP theory suggests which again was in accordance with earlier research. It was interesting though to find that they could differ in such manner and we proceeded by studying earlier research done on this subject. This was not the purpose of our thesis. However we found that important for us to be able to understand the mechanisms behind our own results.

We believe that our study has a purpose since we included new data containing the financial crisis. This has not been done as far as we know. All earlier studies that we could find were pre-crisis studies. The p- values we got also suggest that the results are statistically significant which gives some ground to our results. In other cases where the UIP have been tested, this has not been the case.

The simulated trading portfolio in this thesis is something new. A lot of the earlier studies have been quite heavy on the theoretical side and we wanted to show with an easy to understand example how you can make money taking advantage of the faulty pricings in the model. We believe that we have shown this in a pedagogic and easy to understand manner and as a bonus the results where great too. Furthermore, it gave us, the writers, an insight in how many arbitrary funds and investors think and act in both financial crises and calmer financial times. In the recent crisis this kind of trades attracted a lot of heat and discussions since it connects markets in a global tightly connection. This thesis has also helped us to better understand both sides of this debate.

The carry trading is big business in the financial markets but largely unknown for the public. We hope that this has shed some light on this kind of trading and that we have enlightened the readers to do more research within this area or maybe even to try a carry trade themselves or buy a structured product resting on a carry trading index.

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7. Closing words

In this thesis we just scratched the surface of carry trading and uncovered interest parity. As we mentioned above we wanted to give an overview of what carry trading is and how the UIP theory fails. There are many different angles which we have not been exploring in this study and we believe that there are a lot of interesting topics to do further research on. Some ideas have crossed our minds while writing this thesis. Future studies could check the possibilities for cross-currency arbitrage and how it is possible to lock in different profits with the wide variety of derivatives available in the market today.

Something that is also over looked is that the carry trading strategy affects a lot of the exchange rate movements since the trade raises the demand for the currencies included in the trades. Since this is the case, how come the markets do not move to equilibrium forcing arbitrary elements to disappear? The trades should adjust the exchange rates to the favor of the UIP. As we mentioned earlier carry trading was a heavily debated topic during the recent crisis and we believe that this is something that could be the basis of another thesis.

Since there are some financial instruments connected to this kind of trades, there would also be interesting to see if there are possibilities for pair trading /arbitrage between the basket and the security.

As we mentioned earlier, there are many angles that have not been looked upon and still a lot to explore in the UIP and the carry trading field.

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8. References

8.1 Literature

Business research methods, second edition By A. Bryman, E Bell, Oxford University press 2007, ISBN 978-0-19-928498-6

Forskningsmetodikens grunder, third edition By R. Patel, B. Davidsson, Studentlitteratur 2003, ISBN 9789144022888

Vetenskapsteori och forskningsmetodik By G. Wallén, Studentlitteratur 1996, ISBN 9144366523

Vetenskapsteori för nybörjare, second edition By T. Thurén, Liber 2007, ISBN 9789147086511

Research methods for business students, fourth edition By M. Saunders, Financial Times/Prentice Hall 2007, ISBN 0273701487

The economics of exchange rates By L.Sarno, M.P.Taylor 2002 Cambridge university press. ISBN 0-521-48584-3

Options, Futures and other Derivatives, seventh edition By J.C.Hull, S.Basu. Pearson Hall 2010, ISBN 978-81-317-2358-6.

Bond market analysis, seventh edition By Fibozzi, Frank J, Pearson Hall 2010, ISBN 0-13-6099974-2

Statistisk dataanalys (Statistical data analysis), By S.Körner, L.Wahlgren, Studentlitteratur 2006, ISBN978-91-44-01573-6.

Regression och tidsserieanalys (Regression and time series analysis), third edition By G.Andersson, U.Jorner & A.Ågren. Studentlitteratur 2007, ISBN 978-91-44-02987-0.

Modern investment theory, fifth edition By R.A.Haugen, Pearson Hall, 2001, ISBN 0-13-019170-1.

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8.2 Electronic references

UIP for short investments in long-term bonds, By Alexius, Annika, Swedish Riksbank, 1998. Fetched: 2011-05-11 http://www.riksbank.se/templates/Page.aspx?id=25437

Dynamic model of uncovered interest rate parity - (theory and empirical verification in the transitive economies), By Durcakova, Mandel and Tomsik, University of Economics, Prague, 2005. Fetched: 2011-05-20 http://ideas.repec.org/a/prg/jnlpol/v2005y2005i3id506p291-304.html

Deviations from Uncovered Interest Rate Parity: A Post Keynesian Explanation By Harvey, John, Texas Christian University, 2004. Fetched: 2011-05-17 http://ideas.repec.org/p/tcu/wpaper/200301.html

A Reconsideration of the Uncovered Interest Parity Relationship By McCallum, Bennet, Journal of Monetary Economics vol.33, 1994. Fetched: 2011-05-04 http://www.nber.org/papers/w4113

Long-Horizon Uncovered Interest Rate Parity By Chinn, Menzie and Meredith, Guy, National Bureau of Economic Research, 1998. Fetched: 2011-04-23 http://www.nber.org/papers/w6797

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9. Appendix

9.1 Data

JPY AUD NOK USD FX Date MID 1M Deposit FX MID 1M Deposit FX MID 1M Deposit FX MID 1M Deposit 2001-02-28 1 0,4 0,016390756 5,505 0,077041602 7,15 0,008591065 5,26 2001-03-31 1 0,1 0,016431153 5,185 0,073421439 7,23 0,008071025 5,07 2001-04-30 1 0,07 0,015792798 4,815 0,073099415 7,48 0,008093889 4,37 2001-05-31 1 0,045 0,016281342 4,865 0,076863951 7,09 0,008316008 4,06 2001-06-30 1 0,06 0,015873016 4,925 0,074682599 7,255 0,008025682 3,84 2001-07-31 1 0,07 0,015913431 4,935 0,073046019 7,09 0,007993605 3,75 2001-08-31 1 0,045 0,015730691 4,805 0,073746313 6,97 0,008385744 3,54 2001-09-30 1 0,09 0,017188037 4,345 0,073964497 7,045 0,008375209 2,59 2001-10-31 1 0,07 0,01621797 4,345 0,072202166 6,985 0,008190008 2,22 2001-11-30 1 0,07 0,015547264 4,26 0,0723589 6,985 0,008064516 2,07 2001-12-31 1 0,05 0,014976786 4,16 0,0683527 6,49 0,007578628 1,83 2002-01-31 1 0,015 0,014858841 4,175 0,068306011 6,475 0,007524454 1,81 2002-02-28 1 0,015 0,014417532 4,155 0,066269052 6,535 0,007443245 1,81 2002-03-31 1 0,07 0,014090461 4,43 0,066312997 6,58 0,00750469 1,84 2002-04-30 1 0,015 0,014444605 4,365 0,065359477 6,58 0,007791196 1,8 2002-05-31 1 0,025 0,014338973 4,675 0,064267352 6,55 0,008100446 1,79 2002-06-30 1 0,015 0,014799467 4,91 0,062539087 6,9 0,008368201 1,8 2002-07-31 1 0,015 0,015288182 4,835 0,063051702 7,045 0,008326395 1,78 2002-08-31 1 0,015 0,015360983 4,795 0,063572791 6,98 0,008478169 1,8 2002-09-30 1 -0,015 0,015003751 4,805 0,06090134 7,065 0,008156607 1,75 2002-10-31 1 0,015 0,014679977 4,735 0,060716454 6,99 0,008116883 1,67 2002-11-30 1 -0,025 0,01453911 4,75 0,059844405 7,06 0,008169935 1,41 2002-12-31 1 0,06 0,014819206 4,7 0,058207218 6,42 0,008340284 1,33 2003-01-31 1 -0,015 0,014310246 4,71 0,057803468 5,93 0,008399832 1,3 2003-02-28 1 -0,015 0,014037058 4,695 0,06116208 5,55 0,008492569 1,29 2003-03-31 1 -0,015 0,01384083 4,675 0,060679612 5,505 0,008319468 1,27 2003-04-30 1 -0,015 0,013403029 4,695 0,058548009 5,075 0,00835771 1,25 2003-05-31 1 -0,02 0,012934937 4,69 0,056022409 4,98 0,008453085 1,28 2003-06-30 1 -0,02 0,012528188 4,565 0,060569352 4,045 0,008347245 1,06 2003-07-31 1 -0,02 0,012748598 4,695 0,059808612 3,535 0,008319468 1,06 2003-08-31 1 0,045 0,013329779 4,735 0,064977258 2,94 0,008536065 1,08 2003-09-30 1 0,0255 0,013281976 4,815 0,062932662 2,68 0,008988764 1,05 2003-10-31 1 -0,02 0,013073604 4,83 0,064892927 2,675 0,009191176 1,07 2003-11-30 1 0,0125 0,012656626 5,19 0,062539087 2,72 0,009136592 1,11

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2003-12-31 1 -0,045 0,012554928 5,33 0,062893082 2,3195 0,009334453 1,06 2004-01-31 1 -0,02 0,012370114 5,44 0,066666667 2,07 0,009426848 1,04 2004-02-29 1 -0,045 0,011820331 5,36 0,064267352 1,85 0,009122423 1,04 2004-03-31 1 -0,0225 0,012540757 5,325 0,065231572 1,825 0,009461633 1,04 2004-04-30 1 -0,05 0,012589702 5,41 0,062073246 1,83 0,009062075 1,04 2004-05-31 1 -0,05 0,012724265 5,355 0,061087355 1,89 0,009084302 1,05 2004-06-30 1 -0,05 0,013358269 5,345 0,063694268 1,8265 0,00922254 1,315 2004-07-31 1 -0,05 0,012804097 5,405 0,062617408 1,883 0,008919015 1,455 2004-08-31 1 -0,055 0,012992075 5,235 0,063211125 1,843 0,009100837 1,625 2004-09-30 1 -0,035 0,012562814 5,255 0,06097561 1,835 0,009004953 1,8 2004-10-31 1 -0,015 0,012635835 5,315 0,060240964 1,87 0,009417969 1,97 2004-11-30 1 -0,025 0,012456403 5,24 0,059276823 1,8745 0,009691801 2,26 2004-12-31 1 -0,09 0,012394646 5,25 0,058309038 1,835 0,009596008 2,355 2005-01-31 1 -0,015 0,012471938 5,28 0,061124694 1,675 0,009651578 2,55 2005-02-28 1 -0,015 0,012112403 5,405 0,059453032 1,765 0,009547451 2,69 2005-03-31 1 -0,06 0,012065637 5,67 0,058962264 1,91 0,009311854 2,81 2005-04-30 1 -0,06 0,012121212 5,53 0,059136606 1,86 0,009402915 3,06 2005-05-31 1 0,005 0,01218472 5,535 0,059206631 1,91 0,009249838 3,11 2005-06-30 1 -0,04 0,011842729 5,49 0,059136606 2,035 0,009039957 3,305 2005-07-31 1 0,005 0,01170686 5,46 0,05800464 2,03 0,00889126 3,51 2005-08-31 1 -0,015 0,012022121 5,49 0,058038305 1,995 0,008976661 3,64 2005-09-30 1 0,015 0,011625203 5,51 0,057636888 2,13 0,008834703 3,84 2005-10-31 1 0,015 0,011538018 5,515 0,055991041 2,285 0,008639309 4,05 2005-11-30 1 0,015 0,011310938 5,505 0,056338028 2,345 0,008355615 4,27 2005-12-31 1 -0,015 0,01156738 5,525 0,057405281 2,355 0,008469552 4,4 2006-01-31 1 0,005 0,011339154 5,525 0,057208238 2,315 0,008492569 4,56 2006-02-28 1 0,025 0,01167406 5,47 0,058377116 2,36 0,008600671 4,62 2006-03-31 1 0,045 0,01189768 5,48 0,055803571 2,72 0,008512812 4,79 2006-04-30 1 0,05 0,011570057 5,58 0,054288817 2,66 0,008741259 5 2006-05-31 1 0,115 0,011709602 5,73 0,05425936 2,87 0,008907892 5,07 2006-06-30 1 0,185 0,011730205 5,79 0,054288817 2,82 0,008677543 5,32 2006-07-31 1 0,335 0,011368804 5,97 0,053850296 2,86 0,008707009 5,37 2006-08-31 1 0,305 0,011184431 6 0,053908356 3,05 0,008524422 5,3 2006-09-30 1 0,355 0,011357183 6,02 0,054794521 3,22 0,008481764 5,28 2006-10-31 1 0,335 0,011047282 6,15 0,055834729 3,38 0,008496177 5,28 2006-11-30 1 0,395 0,010944511 6,225 0,053561864 3,47 0,008585165 5,29 2006-12-31 1 0,42 0,010620221 6,21 0,052742616 3,66 0,008395601 5,3 2007-01-31 1 0,36 0,01063943 6,23 0,051599587 3,865 0,008214902 5,31 2007-02-28 1 0,66 0,010729614 6,23 0,051652893 4,025 0,008443094 5,3 2007-03-31 1 0,63 0,010486577 6,31 0,051599587 4,225 0,008470987 5,25 2007-04-30 1 0,62 0,010106114 6,19 0,04995005 4,16 0,008347245 5,26 2007-05-31 1 0,6 0,009992006 6,2 0,049850449 4,41 0,008217602 5,26 2007-06-30 1 0,61 0,009573959 6,24 0,047938639 4,6 0,008112932 5,31

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2007-07-31 1 0,605 0,00979336 6,37 0,048971596 4,66 0,0084076 5,295 2007-08-31 1 0,8 0,010551862 6,61 0,050125313 4,85 0,008615491 5,54 2007-09-30 1 0,76 0,009837678 6,5 0,047147572 5,15 0,008663259 5,18 2007-10-31 1 0,63 0,009449117 6,615 0,046576619 5,195 0,008712319 4,66 2007-11-30 1 0,975 0,010250103 6,925 0,049925112 5,75 0,009078529 5,2 2007-12-31 1 0,675 0,009982032 6,6 0,047869794 5,625 0,008760403 4,49 2008-01-31 1 0,63 0,010592098 7,09 0,051046452 5,475 0,009398496 3,05 2008-02-29 1 0,825 0,010108157 7,35 0,049480455 5,65 0,009543806 2,985 2008-03-31 1 0,68 0,010900371 7,6 0,050916497 5,78 0,009981036 2,705 2008-04-30 1 0,65 0,010303967 7,46 0,049407115 6,245 0,009602458 2,83 2008-05-31 1 0,69 0,00989903 7,31 0,048076923 5,88 0,009456265 2,55 2008-06-30 1 0,64 0,009767533 7,36 0,047573739 5,95 0,00939673 2,49 2008-07-31 1 0,57 0,009796238 7,34 0,047641734 5,855 0,009248983 2,51 2008-08-31 1 0,55 0,010580891 7,03 0,049212598 5,98 0,009144111 2,45 2008-09-30 1 0,75 0,012067093 7,315 0,056022409 8,63 0,009655306 4,5 2008-10-31 1 0,8 0,015232292 6,38 0,067934783 5,79 0,010162602 2,5 2008-11-30 1 0,95 0,015926103 4,62 0,072780204 6,11 0,01046682 1,8 2008-12-31 1 0,45 0,015971889 4,53 0,077700078 3,78 0,010985389 0,5 2009-01-31 1 0,33 0,017250302 3,8 0,077220077 2,81 0,011166946 0,43 2009-02-28 1 0,675 0,015830299 3,2 0,071174377 2,64 0,010223903 0,585 2009-03-31 1 0,33 0,014923146 3,375 0,069204152 2,695 0,010180189 0,63 2009-04-30 1 0,28 0,014023279 3,225 0,067069081 2,22 0,01022704 0,49 2009-05-31 1 0,23 0,013178703 3,05 0,066445183 1,865 0,010364842 0,415 2009-06-30 1 0,23 0,012845215 3,295 0,066577896 1,44 0,010415582 0,42 2009-07-31 1 0,23 0,012663037 2,9 0,065061809 1,345 0,010474495 0,29 2009-08-31 1 0,135 0,012779553 3 0,065019506 1,325 0,010782834 0,39 2009-09-30 1 0,185 0,01266464 3,35 0,064641241 1,4 0,011085246 0,29 2009-10-31 1 0,185 0,011947431 3,485 0,061766523 1,515 0,010936133 0,31 2009-11-30 1 0,195 0,012586532 3,66 0,065231572 1,655 0,01151941 0,23 2009-12-31 1 0,18 0,012153622 3,86 0,063091483 1,82 0,010857763 0,22 2010-01-31 1 0,215 0,012504689 3,94 0,065703022 1,88 0,011139579 0,285 2010-02-28 1 0,175 0,012581782 3,9 0,066269052 1,92 0,01118193 0,21 2010-03-31 1 0,175 0,011726079 4,05 0,064267352 1,865 0,010748065 0,27 2010-04-30 1 0,175 0,011431184 4,35 0,062893082 2,015 0,010630382 0,29 2010-05-31 1 0,175 0,012933264 4,7 0,071022727 2,155 0,010951703 0,31 2010-06-30 1 0,175 0,013319126 4,625 0,073637703 2,39 0,011301989 0,415 2010-07-31 1 0,26 0,012815584 4,75 0,070372977 2,365 0,011534025 0,33 2010-08-31 1 0,205 0,013250298 4,76 0,074515648 2,315 0,011825922 0,305 2010-09-30 1 0,07 0,012277471 4,65 0,069832402 2,26 0,011930327 0,335 2010-10-31 1 0,09 0,012653423 4,55 0,072833212 2,22 0,012362468 0,335 2010-11-30 1 0,16 0,012280486 5,12 0,072992701 2,23 0,011866619 0,26 2010-12-31 1 0,2 0,012029352 4,8 0,072411296 2,325 0,012271444 0,425

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