uncovering the interest parity

Bachelor Thesis Economics

Uncovering the Interest Parity Does the UIP hold between STIBOR and other Interbank

Offered Rates?

Hanna Marklund & Johan Thureson May, 2014

Supervisor: Mikael Bask

UPPSALA UNIVERSITY DEPARTMENT OF ECONOMICS

Abstract In this paper we examine whether the UIP holds between STIBOR and six

other Interbank Offered Rates (IBORs). We use OLS regressions to see if the

change in spot exchange rate can be explained by 1-month, 3-months and 6-

months IBOR differential. The estimates show an inverse relationship than

that predicted by the UIP theory. We find stronger statistically significant

estimates when testing STIBOR against IBORs in large economies than when

tested against IBORs in small economies. We also find that when testing

STIBOR against IBORs in small economies the estimates tend to be more in

line with the theory than when tested against IBORs in large economies.

Keywords: UIP, STIBOR, IBOR, OLS, Newey-West, Risk premium

Table of Contents

1 Introduction 1

2 Theoretical framework 3

3 Data 7 4 Method 10

5 Results 13 5.1 Stationarity 13 5.2 Regression on 1-month IBORs 13 5.3 Regression on 3-month IBORs 15 5.4 Regression on 6-month IBORs 16

6 Conclusion 18

7 References 21

8 Appendix 22 List of Tables 5.1 Test for Unit Roots 13 5.2 1-month Regressions 14 5.3 3-month Regressions 16 5.4 6-month Regressions 17 8.1 Average 𝜷-estimates 22

1

1 Introduction The efficient market hypothesis says that in an efficient speculative market all

prices should be based on the information known by the market participants,

which means that no excess return should be possible by speculating. If

expectations are rational then the expected gain from holding foreign versus

domestic currency should be offset by the opportunity cost of holding the

foreign currency. The opportunity cost of holding the foreign currency instead

of the domestic is the interest rate differential (Taylor 1995). This implies that

the interest rate differential can be used to estimate the future change in

exchange rate (Froot & Thaler 1990). If the interest rate on domestic assets is

higher than on foreign, the domestic currency is expected to depreciate

against the foreign. The relationship between the interest rate differential, the

spot exchange rate and the expected change in spot exchange rate is called the

uncovered interest parity (UIP). This is not to be confused with the covered

interest parity (CIP), which describes the relationship between the interest

rate differential, the spot exchange rate and the forward exchange rate.

Although the theory behind the UIP seems reasonable most studies

find no such relationship between the interest rate differential and the change

in spot exchange rate. In a survey of 75 published estimates by Froot &

Thaler (1990) few of the estimates show a relationship like that of the theory.

The results show estimates that not only differ from what the theory predicts,

but are close to the exact opposite of it. This phenomenon is named the

forward premium puzzle since no economic model is widely accepted to

provide an explanation of the empirical findings (Yu 2013).

Some authors try to explain the forward premium puzzle with the

existence of a risk premium with a larger variance than that of the expected

change in exchange rate and the interest rate differential (Fama 1984). As

pointed out by Froot & Thaler (1990) the risk premium cannot directly be

observed hence it is hard to disprove theories that include a risk premium. It

is therefore important to test the interest parity (both covered and uncovered)

with different research methods, which might shed new light on the forward

premium puzzle. Froot & Thaler (1990) argue that the expectational errors

2

caused by market inefficiency should be seriously investigated. The interest

parity (both covered and uncovered) is most often tested on interest rates with

maturities shorter than 12 months. The main reason for this is that the

exchange rates are required to be floating to be able to depreciate. Since the

dollar did not float until the 1970s earlier studies could not find sufficient

observations (most studies are tested with the dollar). Recent studies, which

use interest rates with longer maturities, find results that are more in line with

the UIP theory than earlier studies (Chinn & Meredith 2004).

Our paper tests the uncovered interest parity (UIP) between the

Stockholm Interbank Offered Rate (STIBOR) and the Interbank Offered

Rates (IBORs) in six other countries. The chosen countries are: the United

Kingdom, the United States, Japan, Iceland, Norway and “the eurozone”1.

The IBORs are used as proxies for each country’s risk-free rate. The chosen

maturities are: 1-, 3-, and 6-month. We regress the logarithmic interest rate

differential on the realized change in spot exchange rate expressed as foreign

currency in units of domestic. The data used is collected from Thomson

Reuters DataStream and ranges from 1993-2014. We perform two t-tests, one

to see if we can reject the UIP theory and another to see if the change in the

spot exchange rate can be explained at all by the interest rate differential. Our

estimates are in line with earlier studies when testing with short-horizon

maturities. We find the existence of a risk premium plausible since our data

covers the financial crisis in 2008 and the financial instability that followed.

The statistical significance is stronger for the estimates represented by the

larger economies than those represented by the small. The estimates for the

smaller economies are more in line with the UIP theory and we suggest that

the UIP between assets in two small economies should be further

investigated.

Our paper is structured as follows. Section two describes the theory

behind the UIP. In section three we describe our data. The fourth section

presents our method. In section five we present the results from our

regressions and t-tests. Section five concludes.

1 The Eurozone will in this paper be referred to as a country for convenience. We are aware of the fact that it consists of a number of different countries sharing the same currency.

3

2 Theoretical framework The uncovered interest parity (UIP) and the covered interest parity (CIP) are

two non-arbitrage conditions, which say that the future exchange rate

differential between two countries can be explained by the interest rate

differential. The UIP and the CIP are very similar but differ in one aspect. As

mentioned earlier the UIP refers to the relationship between the interest rate

differential, the spot exchange rate and the expected future spot exchange rate

while the CIP refers to the relationship between the interest rate differential,

the spot exchange rate and the forward exchange rate. If the expected future

spot exchange rate equals the forward exchange rate then the UIP equals the

CIP (Gottfries 2013, pp.438-441). If these relationships do not hold arbitrage

opportunities exist.

Let’s assume that the 3-month interest rate in Sweden is 10 % and the

corresponding interest rate in the US is 5 %. The interest rate differential in

our example is 5 percentage points and for the CIP to hold the forward

contract of changing SEK into USD must be bought with a 5 percentage point

discount. If not, one way of making arbitrage is to borrow in USD at a 5 %

interest rate, change the USD into SEK, invest the SEK at a 10 % interest rate

and buy a forward contract. If the forward contract is bought with a 3

percentage point discount, then a 2 percentage point arbitrage profit is made

(Froot & Thaler 1990).

If the UIP does not hold similar arbitrage can be made, which the

market would not allow. We assume that the interest rate differential is the

same as in the previous example. If the SEK is expected to depreciate 3

percentage points, investors would again borrow in USD and lend in SEK.

This would cause the Swedish interest rate to fall and the American to rise

until the interest rate differential is 3 percentage points. If the investors’

expectations are rational then the expectation of the future exchange rate

based on the interest rate differential is said to be unbiased (Froot & Thaler

1990). To test this unbiasedness we will regress the change in exchange rate

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on several interest rate differentials. To derive the equation used for our

regressions we start with the expression for CIP.

The CIP describes the relationship between two countries’ interest rate

differential, the spot exchange rate and the forward exchange rate. The CIP is

given by:

𝐹!,!!! 𝑆! = 𝐼!,!/𝐼!,!∗ (1)

where 𝑆! is the spot exchange rate at time t (foreign currency in units of

domestic currency), 𝐹!,!!! is the forward rate contract of S formed in time t

expiring in k periods. 𝐼!,! is one plus the k-period interest rate of the domestic

asset while 𝐼!,!∗ is one plus the k-period interest rate for the corresponding

foreign asset (Chinn & Meredith 2004). Taking the logarithm (denoted with

lowercase letters) of expression (1) gives us:

𝑓!,!!! − 𝑠! = 𝑖!,! − 𝑖!,!∗ (2)

If the left hand side and the right hand side are not equal equation (2) implies

there is risk-free arbitrage to be made. This arbitrage can be made regardless

of the investors risk preference. If investors find foreign assets riskier than

domestic, risk avers investors want to be compensated for this risk. The

forward rate contract of S then differs from the expected spot exchange rate

by a risk premium:

𝑓!,!!! = 𝑠!,!!!! + 𝑟𝑝!,!!! (3)

where 𝑠!,!!!! is the expected spot exchange rate at time t+k formed at time t

and 𝑟𝑝!,!!! is the k-period risk premium formed at time t. By substituting

equation (3) into equation (2) and rearranging the terms we get the expected

change in exchange rate from time t to t+k as a function of the interest rate

differential and the risk premium:

∆𝑠!,!!!! = 𝑖!,! − 𝑖!,!∗ − 𝑟𝑝!,!!! (4)

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The left hand side of the equation shows the difference in the expected spot

exchange rate between time t and t+k. If investors are risk neutral (no risk

premium) equation (4) essentially describes the UIP. However, since the

markets expectations are not directly observable equation (4) is non-testable.

The market includes a vast number of investors each and every one with their

own expectation. Because of this problem the UIP is often tested with the

assumption of rational market expectations (Chinn & Meredith 2004). The

future spot exchange rate is therefore said to consist of the rational

expectation plus a white noise error term, which is uncorrelated with anything

known at time t:

𝑠!!! = 𝑠!,!!!!" + 𝜉!,!!! (5)

where 𝑠!!! is the spot exchange rate at time t+k, 𝑠!,!!!!" is the rational

expectation of 𝑠!!! formed at time t and 𝜉!,!!! is the white noise error term.

Substituting equation (5) into equation (4) gives us an expression for the

realized change in exchange rate, the interest differential, risk premium and

an error term:

∆𝑠!,!!! = 𝑖!,! − 𝑖!,!∗ − 𝑟𝑝!,!!! + 𝜉!,!!! (6)

To be able to test whether the UIP holds the following equation is often used

for the regressions:

∆𝑠!,!!! = 𝛼 + 𝛽 𝑖!,! − 𝑖!,!∗ + 𝜀!,!!! (7)

where 𝛼 is the intercept, 𝛽 is the parameter which we will estimate and 𝜀!,!!!

is the uncorrelated error term. By comparing equation (6) and equation (7) we

see that under the assumptions of risk neutrality (no risk premium) and

rational market expectations the error term in equation (7) equals the white

noise term in equation (6).

6

Under the above-mentioned assumptions the 𝛽-estimate should equal

one. This means that the change in the realized spot exchange rate between

time t and t + k is due to the k-period interest rate differential and the error

term. Any other result than 𝛽=1 can only be explained by the existence of a

risk premium and/or non-rational expectations and also that these two

phenomena are correlated with the interest rate differential 2 (Chinn &

Meredith 2004).

If the expectations are rational and the error term is uncorrelated with

any known information at time t then according to equation (6) the risk

premium is essentially the difference between the interest rate differential at

time t and the realized change in spot exchange rate between t and t+k. A

finding of a 𝛽 > 1 then indicates the presence of a risk premium that has

declined over the period. This result is however rarely observed and in a

survey of 75 estimates none of the estimates are larger than one (Froot &

Thaler 1990). A more common finding is a 𝛽 < 1 and this suggest that a

increased interest rate differential also increases the risk premium. This

indicates that the risk premium also varies over time and that investors find

assets in countries with high interest rates riskier than corresponding assets in

countries with low interest rates (Froot & Thaler 1990). The most common

finding however is an estimate of 𝛽 <0. In the survey by Froot & Thaler

(1990) the average estimate is -0.88. An increase in the interest rate

differential then leads to an appreciation of the domestic currency instead of a

depreciation. This is sometimes explained by a higher variance in the risk

premium than in both the interest differential and the expected depreciation.

A negative covariance between the expected depreciation and the risk

premium then leads to a negative beta estimate (Fama 1984). Some studies

also test the null hypothesis that 𝛼=0. If however 𝛼 ≠0 this could be

interpreted as a constant risk premium of holding foreign assets, which is still

consistent with the UIP theory if the risk neutral assumption is relaxed (Chinn

& Meredith 2000).

2 This is called the unbiasedness theory but will in this paper be referred to as the UIP theory.

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3 Data

This paper aims to test whether the UIP holds between the Stockholm

Interbank Offered Rate (STIBOR) and the Interbank Offered Rates (IBORs)

in the following six countries: the United Kingdom, the United States, Japan,

Iceland, Norway and “the eurozone”. These countries are chosen because of

their mix of characteristics. The United States, the “eurozone”, Japan and the

United Kingdom all represent large economies while Sweden, Iceland and

Norway represent smaller economies. Large economies can have a greater

impact on other economies than small have. By including Norway and

Iceland we are able to see if our results differ when testing the UIP between

two small economies compared to testing between a small and a large

economy.

The interest rates used to test the UIP should, according to theory, be

risk-free interest rates. These rates are theoretical interest rates and reflect the

return an investor would get when investing in a risk-free asset. These

interest rates do not exist in reality but a number of interest rates are

considered proxies for the risk-free rate. The most commonly used proxies

are government short-term treasury bills (T-bills), especially the US T-bill.

Another commonly used proxy is the London Inter Bank Offered Rate

(LIBOR), which is the average interest rate the leading banks in London

would charge when lending to each other (Hull & White 2013).

The financial crisis in 2008 started a debate whether the LIBOR, or

other Interbank Offered Rates (IBORs), should be used as proxies for the

risk-free rates since the crisis showed that banks can default and also since

the LIBOR rate rose substantially compared to the rate of the US T-bill (Hull

& White 2013). However, the crisis also showed that countries can default as

well e.g. Iceland, which means that T-bills are not entirely risk-free either.

We will in this paper use the IBORs as proxies for the risk-free rates even

though the crisis showed that they bear some risk, especially under financial

instability. A great advantage with the IBORs is that there exists and

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extensive amount of data and that they all have the same maturity, which is a

condition for the UIP. The interest rates used in this paper are:

Stockholm Interbank Offered Rate (STIBOR)

Euro Interbank Offered Rate (EURIBOR)

London Interbank Offered Rate (LIBOR)

US dollar London Interbank Offered Rate (USD LIBOR)

Norway Interbank Offered Rate (NIBOR)

Reykjavik Interbank Offered Rate (REIBOR)

Tokyo Interbank Offered Rate (TIBOR)

The STIBOR represents the domestic interest rate in equation (7) while the

other IBORs represent the corresponding foreign interest rate. The chosen

maturities for the IBORs in this paper are 1-month (30 days), 3-months (90

days) and 6-months (180 days). We choose these three maturities to be able

to see if the results differ between different time periods. Another advantage

of the chosen maturities is that they are relatively short which means that we

are not left with too few observations.

Our data is collected from Thomson Reuters DataStream, where it in

turn has been collected from the respective countries central banks. Due to

the floatation of the SEK on November 19th, 1992 no data is collected prior

to January 1st, 1993. The data for the STIBOR, LIBOR, USD LIBOR and

NIBOR ranges from January 1st, 1993 to March 4th 2014, the TIBOR ranges

from December 1st 1995 to March 4th 2014, the REIBOR from July 29th 1998

to March 4th 2014, while the EURIBOR ranges from January 27th 1999 to

March 4th 2014.

9

Since we are testing the UIP between the IBORs in Sweden and the above-

mentioned countries, the currencies used in this paper are:

Swedish Krona (SEK)

Pound Sterling (GBP)

United States Dollar (USD)

Japanese Yen (JPY)

Icelandic Krona (ISK)

Norwegian Krone (NOK)

Euro (EUR)

Our data consists of historical spot exchange rates gathered from the Swedish

Central Bank’s (Riksbanken) website. The data ranges for the same period as

respectively corresponding IBOR. The exchange rates are expressed as one

unit of foreign currency in units of domestic currency.

According to equation (7) the change in the spot exchange rate from

time t to t +k should be due to the k-period interest rate differential. This is

tested by observing the IBOR differential and the spot exchange rate at time t

and then observing the spot exchange rate at time t+k. The data for both

IBORs and spot exchange rates are day-to-day data. To avoid problems with

overlapping we remove the data for all observations between t and t+k for

each period. In the cases where there is no data of the spot exchange rate at

time t+k (most commonly when not a business day) the nearest business day

spot exchange rate is chosen. This means, for example, that some of the 1-

month periods are 29 days, while others are 31 and that some of the 3-month

periods are 179 while some 181. The absolute majority of periods last the

correct amount of days and we have no reason to believe that the fluctuations

are not random. Both the interest rates and the exchange rates are

logarithmized to fit equation (7) and the IBORs are expressed as one plus the

IBOR in decimal form.

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4 Method In order to test if the uncovered interest parity holds between STIBOR and

our chosen IBORs regressions are performed using Ordinary Least Squares

(OLS). In accordance with equation (7) we observe the log k-period interest

rate differential and regress this differential on the realized change in log spot

exchange rate between time t and t+k.

When using OLS to perform a regression it is required that the

stochastic process is stationary. A stochastic process is stationary when its

joint probability distribution does not change over time. This means that

parameters such as the mean, the variance and the covariances do not change

over time and do not follow any trends. If the processes used in the

regressions are non-stationary the OLS-estimates might be invalid (Asteriou

& Hall 2011, pp. 267).

If a stochastic process has a unit root it is non-stationary. Before

performing any regressions we test all the variables (IBORs) for stationarity

using an Augmented Dickey-Fuller test (ADF-test). The ADF-test tests for

the presence of a unit root in a time series sample. The hypotheses are

following (Asteriou & Hall 2011, pp. 344-350):

𝐻! = 𝑇ℎ𝑒 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝑐𝑜𝑛𝑡𝑎𝑖𝑛𝑠 𝑎 𝑢𝑛𝑖𝑡 𝑟𝑜𝑜𝑡

𝐻! = 𝑇ℎ𝑒 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝑤𝑎𝑠 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 𝑏𝑦 𝑎 𝑠𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑟𝑦 𝑝𝑟𝑜𝑐𝑒𝑠𝑠

As OLS-regressions require stationarity we transform the variables that

contain a unit root. Taking the first difference of a stochastic process may

make it stationary, hence this is our approach to solving the problem with

non-stationarity. If our variables do not become stationary when taking the

first difference of the process, we take the second difference and so on until

the process becomes stationary. As the number of observations for some

variables are not as many as we wish, we chose to require a 1 % significance

level to reject the null hypothesis, thereby minimizing the risk for spurious

results.

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Two problems we are faced with whilst performing the regressions with OLS

is autocorrelation and heteroscedasticity in the residuals. They both violate

the OLS assumptions. If the variances of our residuals are not constant we

have heteroscedasticity, (𝑉 (𝜀!) ≠ 𝜎2). In the presence of heteroscedasticity

the OLS-estimator no longer has minimum variance and is no longer be

BLUE (Best Linear Unbiased Estimator). If our residuals are not temporally

independent our regressions show presence of autocorrelation

(𝐶𝑜𝑟𝑟 (∆𝑠!,!!!,∆𝑠!!!,!!!) ≠ 0), Consequences of using OLS in the presence

of autocorrelated errors include: 𝑅! which is often too high, residual variance

which often is underestimated, t-ratios which often are too large making us

reject the null hypothesis to often leading (Dougherty 2011, pp. 429-440).

Since we have reason to believe that the residuals from our

regressions show presence of heteroscedasticity and autocorrelation we use

the Newey-West estimator to correct for this while performing our

regressions.

In addition to the regressions we perform two t-tests of the 𝛽-estimates.

The first t-test has the following hypotheses:

𝐻!:𝛽 = 1

𝐻!:𝛽 ≠ 1

This test is performed to see if the estimates in the performed regressions are

in line with the UIP theory. The null hypothesis is therefore 𝛽 = 1. A

rejection of the null hypothesis means that we can reject the relationship

between the interest rate differential and the spot exchange rate as stated in

equation (7). Although being rejected this does not necessarily mean we can

say anything more about the relationship than that. Because of this we

perform another t-test, which has the following hypotheses:

𝐻!:𝛽 = 0

𝐻!:𝛽 ≠ 0

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This test is performed to see if there exists any relationship at all between the

interest rate differential and the spot exchange rate. The null hypothesis states

that there does not exists a relationship between the interest rate differential

and the change in spot exchange rate according to equation (7). A rejection

of the null hypothesis means that there exists a relationship and the 𝛽-

estimates show us in what way the variables are related.

An alternative method of testing the UIP is to use Generalized

Method of Moments (GMM) instead of OLS. Hansen & Hodrick (1980) use

GMM when testing the UIP. Instead of having one observation every 30 days

for the 1-month regressions GMM would enable us to use one observation

per day and avoid the overlapping problem. This would give us a

substantially larger number of observations. However, the GMM method is

criticized by Diez de los Rios & Sentana (2007) for not being robust when

the degree of overlapping is high. Due to this fact and as we are testing

IBORs with quite short maturities we believe that we have a sufficient

number of observations to be able to conduct these regressions using OLS.

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5 Results

5.1 Stationarity

In Table 5.1 we find the results from our stationarity tests. The stars signify

at what level we reject the presence of a unit root for each of the different

variables. None of the variables are stationary on a 1 % significance level.

The first difference of each variable is therefore taken. All of the variables

are first difference stationary on a 1 % significance level. We therefore use

the first difference of each variable while performing our regressions.

Table 5.1: Test for Unit Roots

Table 5.1 shows on what significance levels the processes are stationary (Stnry) or first difference stationary (F.D Stnry) for the three different rates.

(∗∗∗= 1 %,∗∗= 5 %,∗= 10 %)

5.2 Regression on 1-month IBORs

The results from the first set of regressions can be viewed in Table 5.2. The

𝛽-estimate for the Norway Interbank Offered Rate (NIBOR)3 is the only

estimate where we cannot reject the null hypothesis that 𝛽 = 1. With all of

the other estimates we can reject the null hypothesis on a 5 % significance

3 This is technically the STIBOR-NIBOR estimate. However, since all estimate include STIBOR we will refer to the estimates only with the name of the other IBORs. STIBOR-LIBOR will be referred to as LIBOR, STIBOR-TIBOR as TIBOR etc.

1 Month rates 3-month rates 6 month rates Stnry F.D Stnry Stnry F.D Stnry Stnry F.D Stnry

EURIBOR *** *** ***

REIBOR *** *** ***

TIBOR ** *** ** *** ** ***

NIBOR *** *** ***

LIBOR *** *** ***

USD LIBOR ** *** ** *** ** ***

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level, and in four out of these five cases we can reject the null on a 1 %

significance level as well.

Although the results strongly state that we can reject the UIP-theory,

we perform a second t-test to see if the 𝛽-estimates are significantly different

from zero. If we are unable to reject the second null hypothesis we cannot

rule out the possibility that our model is incorrect.

Table 5.2: 1-month Regressions

Table 5.2 shows the 𝛼 and 𝛽-estimates for the 1-month regressions with Newey west standard errors. The standard errors are below the estimates in brackets. N is the number of observations available for each of the regressions. The stars signify at what level we reject the null hypothesis that 𝛽 = 0 & 𝛽 = 1, (∗∗∗= 1 %,∗∗= 5 %,∗= 10 %).

With exception of the NIBOR estimate, all estimates are negative and most

of them even more so than unity. We find no significance for the NIBOR,

Reykjavik Interbank Offered Rate (REIBOR) and Tokyo Interbank Offered

Rate (TIBOR) estimates, which means we cannot reject the null hypothesis

that 𝛽 = 0. The US dollar London Interbank Offered Rate (USD LIBOR)

and Euro Interbank Offered Rate (EURIBOR) both hold at a 5 % significance

level while the London Interbank Offered Rate (LIBOR) estimate holds at a 1

% significance level. The EURIBOR is the most negative with a 𝛽 -

estimate = -2,473. This result implies that a 1 % higher interest rate in

Sweden than in “the eurozone” in time t, leads to an appreciation of the SEK

against the EURO with 2,473% in t + 1 month. The 𝛽-estimates show an

𝛼 𝛽 𝐻!:𝛽 = 0 𝐻!:𝛽 = 1 N

EUR

-0.0000 (0.0011)

-2.473 (1.070)

** *** 183

GBP

-0.0002 (0.0013)

-1.822 (0.592)

*** *** 255

ISK

-0.0007 (0.0027)

-1.784 (1.100)

*** 189

JPY

-0.0036 (0.0027)

-0.769 (0.550)

** 220

NOK

0.0001 (0.0012)

0.608 (0.412)

255

USD

-0.0007 (0.0021)

-1.361 (0.628)

** *** 255

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inverse relationship between the interest rate differential and changes in spot

exchange rate than that of the UIP theory.

All of our 𝛼-estimates are very small and close to zero. In addition to

this they have small standard errors, we therefore pay no further attention to

the signs before them.


In our second set of regressions, which can be seen in Table 5.3, the 𝛽-

estimates for both REIBOR and NIBOR are positive. We cannot reject the

null hypothesis that 𝛽 = 1 for these two estimates.

Table 5.3: 3-‐month Regressions


All of the 𝛽 -estimates, apart from LIBOR and REIBOR, have

decreased and have larger standard errors than their 1-month counterparts.

We can reject the null hypothesis that 𝛽 = 1 on a 5% significance level for

EURIBOR, LIBOR and USD LIBOR and on a 10% significance level for

TIBOR. The null hypothesis, that 𝛽 = 0, is rejected for EURIBOR on a 5%

significance level and for USD LIBOR on a 10% significance level. Both of

these significant 𝛽 -estimates are lower than negative unity. For the

𝛼 𝛽 𝐻!:𝛽 = 0 𝐻!:𝛽 = 1 N

EUR

-0.0008 (0.0041)

-3.848 (1.829)

**

** 61

GBP

-0.0005 (0.0042)

-1.182 (0.999)

** 85

ISK

-0.0097 (0.0085)

0.641 (0.529)

62

JPY

-0.0045 (0.0071)

-4.515 (2.832)

* 73

NOK

0.0005 (0.0034)

0.202 (0.722)

85

USD -0.0030 (0.0062)

-2.314 (1.368)

*

** 85

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remaining estimates we cannot reject the null hypothesis that 𝛽 = 0. Just like

the 1-month results, the 3-month results indicate that there is an inverse

relationship between the interest rate differential and the change in exchange

spot rates as to what the theory predicts.

The 𝛼-estimates for the 3-month regressions are very similar to the 1-

month 𝛼-estimates. All of the estimates are very close to zero regardless of

sign. The standard errors are also very small and close to zero.

The overall difference between the 1- and 3-month regressions is that

the latter seems to be less significant than their 1-month counterparts. This

can especially be seen in the LIBOR case. The 𝛽-estimate for the 1-month

LIBOR was significant at a 1 % level, and not even significant at a 10 %

level for the 3-month estimate.


As seen in Table 5.4 all of the 𝛽-estimates for the 6-month regressions are

negative. However, the null hypothesis that 𝛽 = 1 cannot be rejected for all

of the estimates. Even though having negative 𝛽-estimates the NIBOR and

EURIBOR standard errors are large enough to prevent us from rejecting the

null hypothesis, even at a 10 % significance level. The other estimates can be

rejected on at least a 5 % significance level. The significance however drops

for all estimates with the null hypothesis that 𝛽 = 0. As seen in Table 5.4

below, we can only reject the null hypothesis for the USD LIBOR and

LIBOR. None of them can be rejected at a higher significance level than 10

%. Just as for the earlier results, the statistically significant 𝛽-estimates are

lower than negative unity.

As for both the 1- and 3-month regressions the 6-month 𝛼-estimates

are all close to zero with small standard errors.

17

Table 5.4: 6-‐month Regressions


𝛼 𝛽 𝐻!:𝛽 = 0 𝐻!:𝛽 = 1 N

EUR

-0.0004 (0.0071)

-2.084 (2.529)

30

GBP

-0.0012 (0.0079)

-1.967 (1.018)

* *** 43

ISK

-0.0229 (0.0187)

-0.529 (0.740)

*** 31

JPY

-0.0054 (0.0154)

-2.609 (1.727)

* 37

NOK

0.0010 (0.0056)

-0.276 (0.802)

43

USD

-0.0053 (0.0154)

-2.303 (1.728)

*

*** 43

18

6 Conclusion

The main result from our regressions is that we in most cases can reject the

UIP theory of 𝛽 = 1. This result is found for all maturities, although slightly

weaker for the 3-month regressions. As stated in the UIP theory, any

deviations from the result of an estimated 𝛽 = 1 must be due to the existence

of a risk premium and/or non-rational expectations that are correlated with the

interest differential. Having in mind that our time horizon for the performed

regressions covers the financial crisis in 2008 and the instability that followed

makes the existence of a risk premium plausible. Our use of the Interbank

Offered Rates as proxies for the risk-free rate makes this explanation even

more plausible since the financial crisis showed that even the largest banks

can default. When assuming the existence of a risk premium it is also likely

that this has risen during the financial crisis. Our largely negative

𝛽 −estimates would then be consistent with the theory that the risk premium

has a higher variance than both interest rate differential and expected

depreciation (Fama 1984). Even though we find the existence of a risk

premium plausible, as stated by Froot & Thaler (1990) these explanations

have the debating advantage of being hard to disprove since the risk premium

is not directly observable. It is beyond this paper to conclude if the failure of

the UIP theory is due to the existence of a risk premium and/or non-rational

expectations. In consistency with Froot & Thaler (1990) we therefore think

future studies also should investigate expectational errors due to the

possibility of market inefficiency.

Despite the fact that the UIP theory (𝛽 = 1) in most cases can be

rejected, we have trouble rejecting the null hypothesis that 𝛽 = 0 for most

variables. By not being able to reject this hypothesis we can not rule out the

possibility that our model is incorrect and that the interest rate differential

does not explain any of the realized change in the exchange spot rate as stated

in equation (7). We can only reject the null hypothesis that 𝛽 = 0 for half of

19

the 1-month 𝛽 −estimates and the results for the 3- and 6-month estimates are

even less significant. One explanation for this could be that the standard

errors for the 𝛽 −estimates get larger with longer maturities. This might be

caused by the fact that we have fewer observations for the longer maturities.

In some cases the standard errors are even larger than the estimates and this,

of course, makes it impossible to rule out the null-hypothesis that 𝛽 = 0.

The 𝛼-estimate can, as stated by Chinn & Meredith (2000), be viewed

as a constant risk premium for investing in assets in other countries. Our

results imply an absence of such a risk premium since all of our 𝛼-estimates

are, regardless of maturity, very close to zero with small standard errors. It is

our belief that the absence of this risk premium can be explained by today’s

globalized economy and also by the fact that most economies are closely

linked together. It is no harder for an investor to invest globally than it is for

him to invest domestically, in addition to this the fact that information

instantly travels all over the world makes a constant risk premium of holding

foreign assets unlikely.

In all the cases where the null hypothesis that 𝛽 = 0 can be rejected

our 𝛽 −estimates are negative and smaller than negative unity. The average

𝛽 −estimates for the 1-, 3-, and 6-month regressions are -1.89, -3.08, and -

2.14 respectively4. These findings can be compared to those of Froot &

Thaler (1990), where the average 𝛽-estimate is -0.88. The estimates between

STIBOR and the IBORs from the larger economies, except the TIBOR, show

stronger statistical significance than the estimates represented by the smaller

economies. The single strongest estimate is found for the 1-month regression

of LIBOR. The regression show a 𝛽 −estimates of -1.822 and the null-

hypothesis of 𝛽 = 0 can be rejected on a 1 % significance level. The USD

LIBOR estimate is the only one for which we can reject the null-hypothesis

that 𝛽 = 0 on at least a 10 % level for all maturities.

The REIBOR and NIBOR estimates are less negative than the 𝛽-

estimates for the large economies and sometimes even positive. This is true

for all maturities except the 1-month estimate for REIBOR. Although the

statistical significance for the NIBOR and REIBOR estimates are weak this 4 For calculations see Appendix Table 8.1

20

implies the UIP in assets between two small economies are more in line with

the UIP theory than assets between a small and a large economy. Since most

research on UIP is been made using assets in at least one large economy

(most often tested between two large economies) we think future research

should further investigate if the UIP holds better when testing for assets

between two small economies.

21

7 References Asteriou, D. and Hall, S.G. (2011). “Applied Econometrics”, 2nd edition, Palgrave MacMillan Chinn, M. and Meredith, G. (2000). “Testing Uncovered Interest Parity at Short and Long Horizons”, Hamburgisches Welt-Wirtschafts-Archiv (HWWA), Discussion Paper 102 Chinn, M. and Meredith, G. (2004). “Monetary Policy and Long-Horizon Uncovered Interest Parity”, Int. Monet. Fund Staff Papers, Vol. 51, No. 3, pp. 409-430 Diez de los Rios, A. and Sentana, E. (2007). “Testing Uncovered Interest Parity A Continuous-Time Approach”, Bank of Canada Working paper, 2007-53 Dougherty, C. (2011). “Introduction to econometrics”, 4th edition, Oxford University Press, Fama, F. (1984). “Forward and Spot Exchange Rates”, Journal of Monetary Economics 14, pp. 319-338. Froot, K. and Thaler, R. (1990). “Anomalies: Foreign Exchange”, The Journal of Economic Perspectives, Vol. 4, No. 3. (Summer, 1990), pp. 179-192. Gottfries, N. (2013). “Macroeconomics”, Palgrave MacMillan Hansen, L. and Hodrick, R. “Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis”, The Journal of Political Economy, Vol. 88, No.5 (Oct, 1980), pp. 829-853 Hull, J. and White, A. (2013). “LIBOR vs. OIS: The Derivatives Discounting Dilemma”, Journal Of Investment Management, Vol. 11, No. 3, pp. 14-27. Taylor, M. (1995) “The Economics of Exchange Rates”, Journal of Economic Literature, Vol. 33, No. 1, pp. 13-47 Yu, Jianfeng. (2013). “A sentiment-based explanation of the forward premium puzzle”, Journal of Monetary Economics 60, pp. 474-491.

22

8 Appendix

Table 8.1 Average 𝜷− 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆𝒔 Average Significant 𝛽 −estimates Average All 𝛽 −estimates

1-‐Month

−2.473 − 1.822 − 1.361

3= −1.89

−2.473 − 1.822 − 1.784 − 0.769 + 0.608 − 1.361

6= −1.27

3-‐Month

−3.848 − 2.314

2= −3.08

−3.848 − 1.182 + 0.641 − 4.515 + 0.202 − 2.314

6= −1.836

6-‐Month

−2.303 − 1.967

2= −2.14

−2.084 − 0.529 − 0.276 − 2.303 − 2.609 − 1.967

6= −1.628

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