Uncovering the Interest Parity

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Bachelor Thesis

Economics

Uncovering the Interest Parity

Does the UIP hold between STIBOR and other Interbank

Offered Rates?

Hanna Marklund & Johan Thureson

May, 2014

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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.

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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

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

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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).

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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 six concludes.

1_{The Eurozone will in this paper be referred to as a country for convenience. We are aware}

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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).

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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}

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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)

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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 differential2 (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}

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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).

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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.

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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.

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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

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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:

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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.

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

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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

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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

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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.

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Table 5.4: 6-‐month Regressions

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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.

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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 6month 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.

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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

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8 Appendix

Table 8.1 Average 𝜷 − 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆𝒔