Analyzing whether the zero-lower-bound changed the degree of UIP violation

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Analyzing whether the

zero-lower-bound changed the degree

of UIP violation.

Jim Brands

Student number: 10094563

jimbrands@gmail.com

Supervisor: dhr. Prof. dr. F.J.G.M. Klaassen

Second reader: dhr dr. K. Mavromatis

Deparment of International Economics

University of Amsterdam

MSc. Thesis

Words: 14.315 (excluding tables)

August 25, 2015

Abstract

Scholars found that expected changes the in exchange rate and interest rate differentials between countries are negatively correlated. This means UIP is violated in the data. This is known as the for-ward premium puzzle. This thesis will analyze whether this degree of UIP violation changed during the zero-lower-bound that several central banks hit during the last decade. It will do so by regressing the depreciation on the forward discount and a interaction variable that measures the effect of the short-term nominal interest rates be-ing below 75, 50 or 25bps on the degree of UIP violation. The OLS regressions give some statistical proof of a change in the degree of UIP violation during the zero-lower-bound.

Keywords. Forward Premium Puzzle, Monetary policy, Zero-lower-bound, Carry Trade, UIP, Time-varying risk premium

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Statement of Originality

This document is written by Jim Brands who declares to take full respon-sibility for the contents of this document.

I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the su-pervision of completion of the work, not for the contents.

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List of Figures

1 Exchange rate between Australian Dollar and Euro . . . 27

2 Forward premium and four-week (annualized) LIBOR interest

rate differential between AUD and Euro . . . 28

3 (1 + it) −Ft St(1 + i ∗ t) and LIBOR . . . 28 4 (St+1 St ) − ( Ft St) and Zero-lower-bound . . . 28

5 Exchange rate between Japanese Yen and Euro . . . 31

rate differential between Japanese Yen and Euro . . . 32

7 (1 + it) −F_St_t(1 + i∗t) and LIBOR . . . 32

8 (St+1

St ) − (

Ft

St) and Zero-lower-bound . . . 32

9 Exchange rate between USD and AUD . . . 35

rate differential between USD and AUD . . . 36

11 (1 + it) −Ft St(1 + i ∗ t) and LIBOR . . . 36 12 (St+1 St ) − ( Ft St)) and Zero-lower-bound . . . 36

13 Exchange rate between USD and Euro . . . 40

rate differential between USD and Euro . . . 40

15 (1 + it) −F_St_t(1 + i∗t) and LIBOR . . . 40

16 (St+1

St ) − (

Ft

St) and Zero-lower-bound . . . 41

17 Exchange rate between Japanese Yen and USD . . . 43

rate differential between Japanese Yen and United States Dollar 43

19 (1 + it) −Ft St(1 + i ∗ t) and LIBOR . . . 44 20 (St+1 St ) − ( Ft St) and Zero-lower-bound . . . 44

List of Tables

1 Degree of UIP violation between the Australian Dollar and Euro 29

2 Degree of UIP violation between the Japanese Yen and Euro . 33

3 Degree of UIP violation between the United States Dollar and

Australian Dollar . . . 37

4 Degree of UIP violation between the Euro and United States

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5 Degree of UIP violation between the Japanese Yen and United

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1 Acknowledgements

First and foremost I’d like to thank my supervisor dhr. Prof. dr. F.J.G.M. Klaassen for being of enormous help in guiding me through the complete process of writing this thesis. Without his help I’d probably still be stuck with writing the introduction. I can imagine I wasn’t the easiest student to work with, and Franc has been nothing but patient with me during the whole process.

I’d also like to thank dhr dr. K. Mavromatis for his course in International Finance during the master. Not only did the course immensely increased my interest in the field of International Finance, it made me quickly realize I wanted to write my master thesis about the forward premium puzzle. Thanks for the very interesting course.

The acknowledgements wouldn’t be complete without mentioning my par-ents, who have been of enormous support during the five years I’ve spent studying at the University of Amsterdam. I couldn’t have done it without them.

Last but not least, I’d like to thank my fellow students: Arno de Jager, Frank van Moock and Mandy Malan in being of enormous help during my transition minor and MSc. program. Without them I’d still be stuck studying political science.

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2 Introduction

2.1 Introduction

One of the biggest puzzles in the field of international economics is the well documented empirical finding that expected changes the in exchange rate and interest rate differentials between countries are negatively correlated(Fama, 1986)(Fama & Bliss, 1987). This is puzzling as it means that uncovered

interest rate parity (UIP) seems to be violated in the data. UIP is the

hypothesis that interest rate differentials are offset by expected changes in the exchange rate. Imagine a two-country world that consists of a home and

foreign country. If the domestic interest rate (it) is higher than the foreign

rate (i∗_t), the domestic currency is expected to depreciate in the next period.

Excessive returns from trading between bonds with interest differences then become nonexistent. Keeping in mind that (s) is the log of the exchange rate (S) that’s defined as the amount of home units per unit of foreign currency, UIP is mathematically shown as: (Pilbeam, 2013):

Et[st+1] − st= it− i∗t (1)

Because currencies at a forward premium are expected to depreciate, it’s possible to borrow money by short-selling bonds at a discount, while lending this money by buying bonds at a premium. Trades as these are commonly re-ferred to as carry trade and have expected profitability that’s above expected market returns.

Violation of UIP is as much troublesome as it’s interesting for both the academic and non academic world. Academically, UIP is widely used in fi-nancial and open-economy general equilibrium models. Deviations should therefore be analyzed and hopefully, one day, completely understood. But understanding the deviations also holds relevance in the non academic world. Because of excessive forex returns, many financial intermediaries have been jumping on the profit-wagon of carry trade. Sadly, the profit-wagon of carry trade is very vulnerable yo forex volatility. Market agents engaged in carry trade risk losing money on both positions at the same time, which becomes particular problematic if the positions were leveraged. Contagious effects of financial intermediaries losing money from their balance sheets lead to major systemic risks for the financial system and the global economy. Economic externalities of carry trades gone wrong were seen globally during both the

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financial crisis in 2008 and the crisis in Iceland in 2011. Completely under-standing the mechanics of deviations from UIP may therefore possibly help in building a less volatile global economic and financial system.

During the financial crisis, central banks tried to stimulate aggregate de-mand and inflation by lowering short-term nominal interest rates up to a virtual zero. Economists call this situation the zero-lower-bound. As neg-ative interest rates are unlikely, the zero-lower-bound limits the amount of instruments available to policymakers. It could thus be seen as a structural break within monetary policy. This paper will add to the existing literature by looking at how the degree of UIP violation is influenced by this zero-lower-bound. Several scholars have already shown that structural breaks in systematic monetary policy change the degree of UIP violation(Bansal & Magnus, 2000)(Tambakis, 2012). The economic causality between the zero-lower-bound and the degree of UIP violation is argued to be found within the time-varying relative risk premium. It’s argued that the relative risk premium increases for the country with the central bank that reaches the zero-lower-bound. It’s therefore likely that the zero-lower-bound changes the degree of UIP violation. The research question is formulated as ”How did reaching the zero-lower-bound affect the degree of UIP violation on forex markets?”. The thesis will analyze this question by regressing the difference between the log of the next periods’s spot rate (st+1) and the log of the

cur-rent spot rate (st) on the forward premium and a interaction variable that

measures the effect of whether the short-term interest rates are below 25, 50 or 75bps on the degree of UIP violation.

Most of the relevance is found in the lack of literature revolving the zero-lower-bound and the forward premium puzzle. While the correlation be-tween monetary policy and the forward premium puzzle has been well doc-umented, the zero-lower-bound is yet to be a big subject in the forward

premium puzzle discussion. This was the first time that several central

banks hit the zero-lower-bound, making the general zero-lower-bound lit-erature scarce.(Krugman, 2015) Hopefully, this paper will be able to add something to the literature that looks at the causality between systematic monetary policy and the forward premium puzzle.

The structure of the thesis will be as followed. First I will describe the relevant literature, after which I will describe my own theory and the method-ology used. After that, the thesis will analyze the found results and link them to the theory. Concluding words will be about the policy implications, dis-cussion and possible further research.

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3 Literature review

The literature review is distributed in three sections. The first part describes the literature about the different methods ised to show UIP violation. After that, the theory describing the zero-lower-bound and it’s possible influence on the degree of UIP violation will be discussed. The last section will describe the literature that looks at the causality between the forward premium puzzle and systematic monetary policy.

3.1 Uncovered interest rate parity tests

Before describing how UIP is usually tested it may be useful to introduce a few important concepts from the literature. First remember that covered interest rate parity (CIP) implies that the log (indicated by lower-case letters)

of the current forward rate minus the log of the current spot rate (ft− st)

equals the interest rate differential (it−i∗t) for countries with otherwise similar

characteristics.1 Then consider that the forward rate (ft) can differ from the

expected future spot rate (Et[st+1]) by a risk premium (πt). Combing these

gives us equation (2)(Chinn & Meredith, 2004):

Et[st+1] − st = (it− i∗t) − πt. (2)

UIP refers to this last equation when the risk premium is zero. However, in the absence of observations on market expectations, equation (2) is untestable. Therefore, UIP is tested jointly with the assumption of rational expectations.

Rational expectations imply that Et[st+1] is a unbiased estimator of st+1.

This then leads to equation (3), where the error term is denoted as (ηt+1):

4st+1= (it− i∗t) − πt+ ηt+1 (3)

Combing equation (3) with the UIP null hypothesis that Et[st+1] equals

ft, leads to the ’risk-neutral-efficient-market-hypothesis’ (RNEMH)(Chinn & Meredith, 2005, pp.12). The standard regression for such a test is given by equation (4)

4st+1= α + β(ft− st) + ηt+1 (4)

1_{These conditions include identical default rate and tax treatment, the absence of}

restrictions on foreign ownership, and negligible transactions costs (Chinn & Meredith, 2004)

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With rational expectations and a non-existing risk premium, (ft − st) is

a unbiased predictor of (st+1 − st) Therefore, scholars have hypothesized

that β in (4) equaled unity. (Fama, 1984, pp.332). Astonishing and trou-bling enough, the data almost always reveals a value of β that’s significantly negative.(Fama, 1984, p.336). Not only is the joint hypothesis rejected, the data actually shows that the currency of the country with the highest interest rate is expected to appreciate.

Using rational expectations isn’t the only approach to tackle the problem of the unobserved investors expectations. Several scholars have used survey

market expectations as a measurement of Et[st+1]. However, it is still a

debate whether survey expectations actually are an unbiased estimator of Et[st+1] (Chinn & Meredith, 2005). An interesting consensus in the literature is that survey expectations work better for currencies with relatively higher inflation rates (Frankel & Chinn, 2002, p.3). When scholars only include currencies with relative low inflation rates, the null-hypothesis of unbiased survey expectations is usually rejected.(Frankel & Chinn, 2002). This is problematic for this thesis as the currencies that are used to test UIP are

often those of countries with relative low inflation rates.2 Because survey

expectations are hard to get by, and because the literature is still unsure whether this approach is unbiased, this thesis will stick to the risk neutral efficient market hypothesis.

Another difference in the literature is the different results for testing short-term-horizon UIP or long-term horizon UIP. Several scholars have argued that deviations from UIP are more prone on the short-term horizon. Scholars argue that this is because short-term exchange rate shock effects fade over longer horizons. These short-term exchange rate shock effects are argued to be causing UIP violation(Mussa, 1979). As this thesis is interested in reproducing the forward premium puzzle and testing whether the puzzle is influenced by the zero-lower-bound, it will only test for short-term (four-week interval) UIP. Another problem of testing for long-term (12 month+) horizon UIP is the overlapping sample problem. If someone doesn’t want to compensate for the moving average error term by using less observations, the only solution to the overlapping sample problem is using AR(1+) models. As this inherently means that equation (4) cannot be tested via a standard OLS 2_{UIP is often tested via forward rates, which means that the currency needs to have a}

forward market, which is often only found in countries with developed financial markets and therefore lower inflation rates. This is especially so in the older papers, such as Fama’s, as forward markets were rather rare in those days.

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regression, this thesis decided to stick to non overlapping data samples using short-term horizon UIP.

Equation (4) will be used by this thesis to test the degree of UIP violation. There’s several reasons to why this approach was chosen above others. First of all, it’s mathematically elegant and simple, making it easy to use and augment. Arguably even more important, it’s also the approach that most of the literature uses. This makes the results easier to compare and generalize to the work of other scholars.

However, a critical note has to be made. There’s a major problem with these joint tests of rational expectations and the non-existence of a risk pre-mium. Decisive rejections of these tests are no proof of either deviations from rational expectations or the non-existing risk premium. Only the joint hypothesis is to be rejected. Fama, who was the first to show the negative β coefficient in (4), concluded that the rejection of his hypotheses must have been due to a time-varying risk premium(Fama, 1986)(Fama & Bliss, 1987). Due this joint hypothesis problem, this thesis will not make any statements about rejecting either rational expectations or a non existing risk premium. It can however still test whether short-term nominal interest rates being below a certain threshold changes the degree of UIP violation.

3.2 Zero-lower-bound

The zero-lower-bound’s a situation in which a central bank cannot lower it’s short-term nominal interest rate without turning it negative. It became a major topic during the unwinding of the financial crisis in 2008 as this was the first time that several major central banks reached this bound. The zero-lower-bound becomes troublesome if central banks still wish to stimu-late aggregate demand, inflation or employment by lowering nominal interest rates(Romer, 2012, pp.308).

Admittedly, it’s still a discussion whether negative interest rates are as bad as some may think. The main argument against having negative rates is that it means people have to pay money to deposit their money. People may start to withdrawal deposits, as it’s more profitable to keep the money under a mattress than to hold it in a deposit account. Banks would then see a decrease in liabilities on their balance sheet, which could lead to ’fire sales’ and severe liquidity and solvency consequences for the financial sector. It’s also said that negative interest rate decreases the profit margins of banks, as they now have to pay interest on the asset side of their balance sheet.

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Overall, this could also decreases liquidity as banks become less willing to lend. Still, several central banks have recently decreased short-term nominal interest rates to a rate slightly below zero.

Summers also made an interesting argument against negative rates in a 2014 paper. Summers argued that close-to-zero or negative interest rates

are not sustainable because loans become too easy to roll over.

There-fore there’s very little incentive to to restructure inefficient or even zombie enterprises(Summers, 2014, pp.13). Taylor has also stated that actually hav-ing negative interest rates is not sustainable(Taylor, 2013). Paul Krugman, who’se been very active in the zero-lower-bound discussion, stated that inter-est rates could never go below the storage costs of money. According to Krug-man, there’s no chance these costs would be bigger than 1 percent.(KrugKrug-man, 2015)

It’s an interesting ’bound’ to study as it’s a structural break in the amount of instruments monetary-policymakers have. Sure, it could be argued that some banks have already lowered the rates below zero making the bound not as binding as economists thought beforehand. But it’s still highly un-likely that policymakers will continue to decrease these rates even further below zero. The European central bank was even willing to bend it’s own no ’bail-out’ clause by buying bonds on the primary market in the hopes of stimulating aggregate demand and inflation(Widder, n.d.). If Mario Draghi had thought decreasing the short-term interest rate even further was an real option, he’d probably preferred doing that.

For modeling purposes this thesis will define the zero-lower-bound as a situation in which the short-term nominal interest rate is below 50 bps. This value is chosen as it’s arguably the first value at which a significant interest rate decrease endangers the ability of policymakers of decreasing the interest again without turning it negative. However, to be sure, sensitivity analysis will be used to determine whether 50bps is valid. This will be done by also testing for the interaction effect if the zero-lower-bound is defined as 25 or 75bps.

3.3 Systematic monetary policy approaches to the

for-ward premium puzzle

A major part of the forward premium puzzle literature looks at the causality between monetary policy and the degree of UIP violation. The main

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ap-proach in doing so is by augmenting the UIP condition in equation (4) with

a monetary policy rule. Such a rule is best defined as: 0nothing more than

a systematic decision process that uses information in a consistent and

pre-dictable way.0(Poole, 1999, pp.1). Basically, it means scholars change (it) into

the ’optimal’ (it) as predicted by the monetary policy rule. The monetary

policy rules ’predicts’ this value by using and weighing other information such as output gaps, inflation - and unemployment rates. It can then be shown that systematic monetary policy does influence the degree of UIP violation. A very important implication of the papers is that there’s a very significant effect of structural breaks in monetary policy on the degree of violation. In general, this thesis will try to add to this literature by analyzing what hap-pens to the degree of violation when monetary policy loses the instrument of being able to significantly decrease the nominal short-term interest rates to reach policy objectives. Losing an instrument could be perceived as a structural break for monetary policy.

One of the earliest attempts in solving the forward premium puzzle by testing for causality between the degree of UIP violation and systematic monetary policy was done by McCallum in 1994. According to McCallum, scholars should augment the UIP condition with a monetary policy rule. He develops a model were policymakers have the objective of stabilizing the ex-change rate, using nothing but the interest rate. This model does a very good job at explaining the negative bias of UIP in the data. For some currencies, McCallum’s model even predicts positive correlation between the premium and the First difference exchange rate movement.(McCallum, 1994). Mc-Callum’s model is also one of the building blocks for the other systematic monetary policy approach papers. This thesis will also build on the insights given by McCallum’s paper in the sense that it will test whether the degree of UIP violation in equation (4) is influenced by policymakers losing the pos-sibility of lowering short-term interest rates without turning them negative. However, it will not augment the UIP condition with a monetary policy rule. A paper written by Tambakis in (2012) builds on McCallum’s findings. Tambakis also augments the UIP condition with a monetary policy rule. However, rather than modeling just one policy rule like McCallum, he mod-els six different policy rules. He differentiates between two groups, in every group there’s a ’Taylor-rule’ that responds to the output gap and the cur-rent inflation, a ’Strict-rule’ that maintains the inflation at a target level and a ’Forward looking rule’ that looks at the expected values of these vari-ables (Tambakis, 2012, pp.3). The main result is that the degree of UIP

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violation changes when there is a structural break in the monetary policy regime. If the central bank switches to inflation rate targeting this signifi-cantly decreases the degree of UIP violation.(Tambakis, 2012). Tambakis’s analysis also reveals that the degree of UIP violation is highest when the cen-tral bank has a ’forward-looking policy rule’. Apparently, UIP violations are quite sensitive to the persistence and volatility of the exchange and interest rate. Forward-looking policy rules tend to reduce this volatility. The papers does not give any economic reasoning to why UIP violations are sensitive to this volatility, it does however coincide with the fact that carry trade is most prone to currencies with low volatility. This has also been found by other scholars such as Bansal and Magnus(Bansal & Magnus, 2000). This thesis will also look at different central banks with different monetary policy rules. For example, the European central bank (ECB) has been thought to be much closer to a ’Taylor-rule’ in setting it’s shot-term interest rates. The Federal Reserve on the other hand is known to be more aggressive in setting its interest rates(Kool, 2005, pp.3). Analyzing the effects of losing the abil-ity to lower short-term interest rates without turning them negative could give an interesting perspective on the impact it has on the different sorts of monetary policy rules.

Steele and Wright also look at the degree of UIP violation under different monetary policy regimes. They hypothesize that investors have to ’adapt’ to new regimes, causing systematic forecast errors. Systematic forecast errors can arise either due to the existence of irrational traders or rational agents that make exceptional errors due to infrequent shocks to the economy. (Steele & Wright, 2002, pp.3) Several scholars have shown that systematic forecast errors lead to deviation from UIP.(Steele & Wright, 2002). Their study looks at five time periods, two without inflation rate targeting, one transition pe-riod and two pepe-riods were inflation rate targeting is completely implemented. The main finding of their paper is that the negative bias was especially sig-nificant when central banks switched to inflation rate targeting in the 1980’s, thus providing proof for their hypothesis. If the forward premium is in-deed substantiality caused by systematic forecast error arising from investors having to ’adapt’ to monetary policy changes this bias should be more pro-nounced for countries with unstable monetary policy. (Steele & Wright, 2002, pp.5)(Koutmos, 1998). This is very interesting, as this thesis will regress cur-rencies with central banks that target the inflation rate and central banks that do not solely target the inflation rate. Also, forex volatility during the financial crisis was higher than before, which could mean monetary policy

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was more ’unstable’ than normal.

3.4 Difference between short-term and long-term

un-covered interest rate parity

When testing for UIP violation, scholars often use ”short-term” UIP. This usually refers to time-horizons of four weeks. It’s when using this horizon that scholars often proof the forward-premium-puzzle, with large magnitudes of UIP violation.(Fama, 1986)(Chinn & Zhang, 2015)

More recently scholars have started testing long-term horizons. This usu-ally refers to time-horizons of a year instead of four weeks. Though, scholars have tested up until 10 years(Chinn & Meredith, 2005). When using this horizon, scholars often proof that the bias fades, and the found coefficients become close to unity. Meredith and Bansal argue that this is because short-term UIP is driven by stochastic market forces and monetary policy reaction functions. (Chinn & Meredith, 2004) According to them, the long-term hori-zon UIP is driven by economic fundamentals, and is therefore more consistent with UIP. Other scholars, such as Jiafeng Yu and Bansal, use other economic arguments, such as micro-economic adverse selection problems, though the conclusion is almost always that UIP holds better at the long-term horizon. (Yu, 2013)(Bansal & Shalisatovich, 2006)(Mussa, 1979)(Evans & Chakrabor-thy, 2012) For example, Ackerman and Pohl show that UIP holds a lot better if the forward and spot rates are substituted for interest rates with maturities up to 10 year. Even the bias on the short-term horizon then seems to fade according to the authors. (Pohl & Ackermann, 2013, pp12) Another inter-esting finding is that scholars have shown that the unbiasedness hypothesis holds even less if countries have experienced long periods with low interest rates. (Chinn & Zhang, 2015)

This is interesting for this thesis as this raises the question whether mon-etary policy influences the degree of UIP violation on a short-term horizon more than on a long-term horizon. An argument could for example be that in-vestors expect the zero-lower-bound to be a long-term problem, which would reduce it’s significance on the degree of UIP violation. Sadly, because of the econometric difficulties arising when using overlapping data-samples, this thesis will only analyze short-term horizon UIP violation.

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4 Methodology

The following section will describe and explain the methodological choices and difficulties that arise with these choices. First, it will describe which currencies are chosen, after which it will describe the differences between short-term and long-term horizon UIP. After that, it will describe the chosen measurement of short-term nominal interest rates. Concluding words will be about the econometric techniques used to analyze the degree of UIP violation.

4.1 Currencies

There’s a few criteria for picking the correct currencies to analyze. The most obvious, and arguably most important, is the availability of a forward market of the chosen currencies. This immediately limits the possibilities to curren-cies of countries with developed financial markets. Sure, covered interest rate parity should hypothetically allow the use of interest rates instead of the for-ward and spot rate, allowing scholars to regress the risk neutral efficient market hypothesis on underdeveloped financial markets. Another ’problem’ often found in developing countries is that UIP violation is a phenomenon that’s mainly found in developed countries (Bansal & Magnus, 2000). As this thesis aims to analyze whether the zero-lower-bound ’changed’ the degree of UIP violation, as opposed to analyzing whether UIP is violated at all, it will only look at developed countries.

Another criteria is that the currencies do not have a fixed exchange rate.

If they do, this may severely influence the regression between st+1− st and

ft− st. For example, if a currency were to switch from a fixed-exchange-rate

system to a float, such as the Swiss National Bank did in January 2015, the size of the ’shock’ could bias the OLS results due to high outliers. If currencies are systematically under (or over) valued due to heavy central bank interventions, investors may have an harder time predicting the next period’s spot rate.(Hog & Kim, 2015) This would increase the estimation error (ηt+1) and therefore reduce the explanatory power of the model.

Another criteria is that the currencies should not have capital controls. Domestic capital controls would prevent or hinder domestic investors from

buying foreign bonds and assets3, which would mean UIP reasoning does not

apply anymore. UIP is based upon a equilibrium between a domestic and 3_{And foreign investors from buying domestic bonds.}

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foreign currency, realized due to uncovered interest rate arbitrage. If part of the supply and demand is restricted by capital controls, this would hinder the arbitrage and thus hinder the mechanism from moving back to equilibrium values. This isn’t limited to violation of UIP, as capital controls could also violate CIP as it would hinder the covered interest arbitrage mechanism.

(Thorton, 2013)4

Next to good data availability, flexible exchange rates and the lack of cap-ital controls, it’s important to chose currencies that are subject to different sorts of monetary policy as several scholars have shown that different sorts of monetary policy lead to different degrees of UIP violation. (Tambakis, 2012)(McCallum, 1994)(Steele & Wright, 2002). Showing the different im-pacts the zero-lower-bound has on different monetary policy rules could give interesting results.

Last but not least, it’s important to chose currencies that had different zero-lower-bounds on different points in time. This rules out a part of the possibility that the significance of the zero-lower-bound is due to an spuri-ous relation. For example; if this thesis were to only regress the Euro and United States Dollar, it could be argued that the found effects are due to other changes in economic fundamentals after the 2008 crisis. This immedi-ately points out the first three candidates. Most discussed, as their bounds emerged only after the financial crisis of 2008, and due to their high economic dependency, are the Euro and the USD. A less discussed, but still very im-portant, currency that reached the zero-lower-bound is the Japanese Yen. Japan has been at, or near, the zero-lower-bound since the last decade of the last century.(Filardo & Hofmann, 2014) Adding Japan will therefore be inter-esting, as it will showcase the different effects reaching the zero-lower-bound has if the foreign central bank has already reached the zero-lower-bound in an earlier stadium.

Next to that, it’s important to add a currency that has not reached the zero-lower-bound at any point. A obvious choice is then the Australian dollar (AUD), a currency that’s commonly on the ”long-side” of carry trade, as the average Australian interest rates are higher than American, Japanese and European rates. The Australian dollar does not have any capital controls, which makes it a better candidate than other high interest rate contenders 4_{Let it be said that due to the Mundell-Flemming trilemma, having free capital flows}

and sovereign monetary policy directly implies that the currency has a flexible exchange rate (Gartner, 2009)

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such as Brazil and South Africa.

The ECB, FED, Bank of Japan (BoJ) and Reserve Bank of Australia (RBA) are significantly different in their policy goals. The ECB thrives to reach”medium-term inflation of close to but under 2 percent annually”(ECB, 2015). With that, its main goal is defined as price stability within the Eu-rozone. The FED on the other hand has a dual mandate, that targets both the employment - and the inflation rate. They define it as : ”The Board of Governors of the Federal Reserve System and the Federal Open Market Com-mittee shall maintain long run growth of the monetary and credit aggregates commensurate with the economy’s long run potential to increase production, so as to promote effectively the goals of maximum employment, stable prices and moderate long-term interest rates.”(FED, 2015)

The BoJ is also known to be inflation rate targeting. Its mandate is to achieve financial and price stability.(Bank of Japan, 2015). The BoJ is also known for having a major quantitive easing program, which seems to have been their answer on trying to stimulate the economy after reaching the zero-lower-bound. The RBA is also inflation rate targeting. Their goal is to reach inflation rates between 2 and 3 percent annually. They also have a interest rate target of 2.5 percent(of Australia, n.d.). This interest rate target is interesting for this thesis, as it has resulted in the RBA being the only one of the bunch that did not hit the zero-lower-bound.

The data used will be that from Reuters. It will cover the period of 2005 until 2015. This is a period that covers a few years before the financial crisis, the crisis itself and the aftermath. It’s chosen as such because this way it covers enough of the ’financial cycle’ that started the initial crisis that lead to the zero-lower-bound.

4.2 Durations

Analyzing the ”short-term” horizon UIP will be done by using spot rates that have a four-week interval. As such, the ’next-period’ is then defined as four weeks later. The rates are closing-rates on every fourth Friday. This is done because it’s the technique used by most scholars since Fama’s publication in 1986 (Fama, 1986). Logically, the forward rates will be those of the period equal to the interval.

During the analysis CIP will be tested by regressing the interest rate differential on the forward rate minus the spot rate. The interest rate dif-ferential is then defined as the one month London-Interbank- Offered Rate

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(LIBOR). This way there is no duration mismatch. The graphs showing the interest rate differential are annualized rates, based on the one month LIBOR rates.

There’s a common problem when using monthly or yearly intervals based on a dataset that has weekly data. Commonly this is referred to as over-lapping data. Overover-lapping observations create a moving average error term that causes a bias in the ordinary least squares regression. This is auto-correlation in the error terms. One solution would be to delete the weekly data, reducing the dataset to the necessary monthly data. The biggest draw-back of this technique is that it decreases the amount of observations by a magnitude of four. Next to that, several scholars have shown that simply deleting the observations still leaves a part of the moving average error term (Harri & Borsen, 2012, pp.2). The only other solution would be a time-series

AR(1+) regression with Newey-West5 _{error terms, that correct for auto}

co-variance and heteroskedasticity. Although the AR(1+) technique may seem more efficient, it has not been the common approach in the literature. As the goal of this thesis is to compare the results to the standard risk neutral efficient market hypothesis regressions results from other scholars, it will use a non-overlapping data sample OLS regression.

4.3 Short-term nominal interest rate

One of the biggest methodological questions for this thesis is about which interest rate to use as a measure of the zero-lower-bound. The most impor-tant thing is that it should be a short-term interest rate, as this is underlying in the definition of the zero-lower-bound. Second of all, it makes sense to use a interest rate that’s set by the central bank. Financial intermediaries and central banks have high correlation between their interest rates. If they wouldn’t, arbitrage opportunities could arise. Though, using the rate given by the central bank itself remains the most precise approach in measuring whether the central bank has hit the zero-lower-bound. Due to the relatively low amount of observations, caused by the overlapping-sample problem, it is of the utmost importance that every observation correctly indicates whether the zero-lower-bound has been hit. Keeping this in mind, this thesis will define the interest rate as the shot-term (3 month) deposit rate asked for by central banks.

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A major argument in using the deposit rate as opposed to the lending rate is that negatives rates are thought to be unsustainable because of the counterintuitive logic of negative rates on deposits. Negative lending rates seem more sustainable in that aspect, as cheaper money is always good for the borrower. Surely, this reasoning also follows from the fact that deposit rates are usually lower than lending rates, as this could otherwise be subject to arbitrage. It must also be said that the results between using the short-term deposit and lending rate shouldn’t differ to much, as they are highly correlated. (Mandler, 2010)

4.4 Econometric techniques

One of the biggest advantages of the ”risk neutral efficient market hypothesis” is that the standard test uses a a simple OLS regression. The dependent variable is the difference between the next period’s and current period’s spot

rate (4st+1). The independent variable is the forward premium (ft − st).

The standard regression looks like:

4st+1= α + β1(ft− st) + ηt+1 (5)

For the OLS estimation of equation (5) to be unbiased, it is important that

the error term (ηt+1) is orthogonal to the interest rate differential. As such, if

unbiased, the error term is merely the expectations error. (Chinn & Zhang, 2015)

Another important observation is that the intercept (α) does not have to equal zero even if risk-neutrality is assumed. Deviations from zero can also be explained by Jensen’s inequality, which implies that the expectation of a ratio is not equal to the the ratio of the expectations (Chinn & Meredith, 2005).

When using equation (5), the risk neutral efficient market hypothesis

ex-pects that β1 equals unity. When it does, there’s no statically distinguishable

violation of UIP. To add to this discussion, this thesis will regress (5) and look at whether the degree of UIP violation is significantly different from zero, and whether the risk neutral efficient market hypothesis is rejected at the 5, 1 or 0.1 percent level. If the found degree of UIP violation is within a confidence interval that covers both the null and alternative hypothesis, it will be concluded that the coefficient is statistically indistinguishable from both the null hypothesis and the implied unity value. Several scholars have

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shown that exchange rates have different conditional variance over time, as exchange rate volatility differs. This causes heteroskedasticity and this needs to be controlled for as it violates one of the Gaus-Markov OLS assumptions. This thesis will therefore use robust standard errors for every regression.

This thesis will add a independent dummy variable to equation (5) that

measures whether the domestic (λ) or foreign (λ∗) short-term nominal

in-terest rate is below 75, 50 or 25bps. It will also a interaction variables that

multiplies the independent variables with the forward premium (ft−st). This

leads to a linear regression with multiple regressors, as given by equation (6):

4st+1 = α + β1(ft− st) + β2λ + β3λ∗+ β4(ft− st)λ + β5(ft− st)λ∗+ ηt+1 (6)

As the Australian bank did not reach the zero-lower-bound on any definition

during the data-sample, the regression done between the Euro and AUD∗

and the USD and AUD∗ is given by equation (7):

4st+1 = α + β1(ft− st) + β2λ + β3(ft− st)λ + ηt+1 (7)

Equation (6) adds both zero-lower-bound to the same regression. Adding the independent variables will become problematic when the zero-lower-bounds are highly correlated, as perfect multicollinearity will arise. Within this data sample such correlation is found between the American and European zero-lower-bound.(Mandler, 2010)(Stock & Watson, 2011) Identification problems like these make it difficult to test for the individual effects of the bounds. As this thesis theorizes that the zero-lower-bound changes the degree of UIP violation because the relative risk premium increases if one of the central banks reaches the zero-lower-bound, the regression is done by subtracting

the independent variables (λ − λ∗) and multiplying these with the premium.

This results in the interaction variable: (ft− st)(λ − λ∗). In essence, this

interaction variable measures the period in which only one of the central banks reached the zero-lower-bound. This fits within the economic theory as this thesis theorizes that the zero-lower-bound changes the degree of UIP violation because the relative risk premium changes when one of the bank hits the bound. If both banks hit the bound, there’s no direct indication that the relative risk premium should change. The interesting periods are those where there’s fundamental changes within one of the banks, as this would be likely to change the relative risk premium. The regression is given by equation (8)

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For all three equations, the null-hypothesis is that the interaction vari-ables between the premium and the zero-lower-bound equals zero. The al-ternative hypothesis is then that the interaction variable coefficients do not equal zero. There’s not enough underlying economic theory for any of the three equations to hypothesize whether the coefficients should be positive or negative, the tests must therefore be two-sided. To make any statements about the direction of the degree of UIP violation, it will define a decrease in the sum of the premium and significant interaction coefficients as a in-crease in the violation of UIP, while a inin-crease in the sum of the coefficients is defined as a decrease in the degree. This may work counterintuitive, as some of the sums of coefficients will be positive and above unity, meaning that a further increase would actually be a increase in the degree of UIP violation. Though, it won’t be called as such, as the UIP violation is based on the empirical finding of the forward premium puzzle, in which the degree of violation is negative and often to high magnitudes.

4.5 Graphs

Next to analyzing the OLS regressions results, this thesis will use line graphs to look for outliers and interesting behavior between the premium, interest rate differential, CIP residual, UIP residual and exchange rate. For every exchange rate, six graphs will be plotted. First, the exchange rate s and

the first difference exchange rate st+1− st are plotted against time. Then,

the forward premium ft− stand annualized LIBOR (four week) interest rate

differential are plotted against time. Next, the CIP residual (1+it)−F_St_t(1+i∗t)

is plotted against time. The CIP residual uses the four week LIBOR interest rate differential against four week interval forward rates. After that the one month (annualized) LIBOR rates and three month deposit rates are plotted against time. The three month deposit rates graph shows all rates, and at which period in time they hit the zero-lower-bound. Last but not least, the

UIP residual (St+1

St ) − (

Ft

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5 Theory

5.1 Hypothesis

The hypothesis is that reaching the zero-lower-bound changes the degree of UIP violation. The economic reasoning behind this is that the zero-lower-bound has a causal relation with the risk premium. Extremely low interest rates near the zero-lower-bound are an indication of bad ’economic weather’. Bad ’economic weather’ refers to bad macro-economic fundamentals, such as recession and deflation. While economists definitely didn’t reach consen-sus about this, it has been shown that investors become more risk averse in bullish markets.(Verdelhan, 2006, pp.12) In terms of the zero-lower-bound, the relative risk premium is likely to increase due to several factors. First of all, default rates increase during recessions. If these default rates differ between countries and investors are risk averse, the relative risk premium will be time-varying. Moreover; the zero-lower-bound is a macro-economic problem on itself. Reaching short-term interest rates near zero hinders poli-cymakers from decreasing rates even further. As the conventional mechanism to stimulate aggregate demand and inflation is decreasing interest rates, the bound opposes a problem for policymakers. Hitting the zero-lower-bound will therefore worsen investors expectations and increase the asked risk premium. The mechanism behind bond risk also changes near the zero-lower-bound. Bonds lose their ’risk-free’ investment status as the downside of the bond price is significant larger than the upside(Gourio, 2012). One of the central banks within an exchange rate reaching the zero-lower-bound would therefore change the relative risk premium mechanism. This would mean that the risk premium is time-varying. From a more political economic perspective, bad economic weather is arguably positively correlated with political instability as voters become less satisfied. Political instability could increase economic uncertainty as politicians are likely to use economic policy to maximize their own chances on being re-elected. Potentially, this could increase the risk premium. A good example of a situation in which politics interfered with the risk premium is the current situation between Greece and the Eurozone. Uncertainty about whether Greece is to leave the Eurozone or even default increased bond and risk spreads on financial markets. So if there actually is a risk premium, it’s arguable that this premium increases close or at the zero-lower-bound. In other words, it’s likely that there’s an countercyclical risk premium (Verdelhan, 2006). If the risk-premium changes when

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inter-est rates are nearing the zero-lower-bound, it means it’s time-varying and therefore omitted in the standard OLS regression.

As pointed out by many scholars, a time varying risk premium would mean that the risk neutral efficient market hypothesis OLS regression results are biased, as the error term is then no longer orthogonal to the interest

rate differential (Fama, 1986). This correlation is argued to follow from

the fact that differentials between domestic and foreign interest rates are an indication of economic fundamentals. Extremely high interest rates, such as Russia in 2014, could indicate that the central bank is trying to fight

inflation or rapid domestic depreciation, thereby risking recession.6 _{On the}

other side of the spectrum, extremely low interest rates could indicate that the central bank is trying to to fight recession or deflation. Both recession and high inflation would be indicators of a high(er) risk premiums for the reasons summarized above. The correlation between the time-varying risk

premium and st+1− stfollows from the causality between forex volatility and

the risk premium. High volatility increases uncertainty, which means that if investors are risk averse, the risk premium increases. If this time-varying risk premium exists, and if the zero-lower-bound does indeed measure a part of the time-varying risk premium, it is likely that adding the zero-lower-bound as an interaction variable decreases the degree of UIP violation as measuring a part the unobserved risk-premium would decrease a part of the negative bias.

Though, even if the zero-lower-bound interaction variables are signifi-cantly different from zero, it will be hard to proof whether this is due to the time-varying risk premium or because of the (possible) causality between monetary policy and the degree of UIP violation. Namely, many scholars have also shown that monetary policy influences the degree of UIP violation (Steele & Wright, 2002)(Tambakis, 2012). For reasons explained before, the zero-lower-bound could be seen as a structural break in monetary policy. Proofing that reaching the bound changes the degree of UIP violation would therefore also be further evidence for the necessity of adding a measurement of monetary policy in the risk neutral efficient market hypothesis regression. The question that remains is what the actual causality between monetary policy, the zero-lower-bound, the possibility of a time-varying risk premium and the degree of UIP violation is. This thesis will add to the discussion by suggesting possible causalities such as those described above, yet it will only

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make statistical statements about whether the zero-lower-bound changed the degree of UIP violation as it’s found by the risk neutral efficient market OLS regressions.

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6 Analysis

The analysis will be done by regressing equations (5), (6) and (7) on the 10

year data-sample of five exchange rates. Line graphs showcasing s, st+1− st

it− i∗t and ft− st will be discussed to look for any outliers or observations

that could indicate failure on one of the models assumptions.

6.1 Australian dollar and the Euro

∗

Figure 1 and 2 show the first difference exchange rate, exchange rate, annu-alized LIBOR interest rate differential and the forward premium between the

AUD (domestic) and Euro (foreign). The forward premium (ft−st) is almost

always positive. This means that the forward rate has almost always been higher than the spot rate, indicating that under perfect UIP, the Euro was al-most always expected to appreciate. Via CIP, the positive premium indicates that the Australian dollar had a higher interest rate than the Euro, which is supported by the data. There seems to be one large outlier in September 2008 where the forward premium did turn negative. This is explained by sharp short-term nominal deposit rates declines by the RBA after the fall of Lehman brothers. The ECB followed shortly after with monetary loosening, which increased the interest rate difference again.

During this short period, the premium was at a negative value, while

the LIBOR interest rate differential (i − i∗) remained positive. This

indi-cates violation from CIP. Several scholars have shown that deviations from CIP are common during financial crises and are due to differences in rela-tive counterpart risk and a lack of short-term liquidity. A good example of short term liquidity problems are those that arose on financial markets after the collapse of Lehman brothers in September 2008. (Coudert, Couharde, & Mignon, 2011). Due to rapid ’fire sales’ and financial instability, uncertainty between financial intermediaries increased. This increased short-term lend-ing rates between banks, and thus inherently decreased the liquidity within the financial system.(Coffey, Hrung, & Sarkar, 2009). This doesn’t lead to deviations from CIP yet. Deviations were argued to be caused because Eu-ropean financial institutions were perceived to have a higher probability of default. Because of this, the credit risk premiums between the AUD, Euro, Yen and USD were argued to be unequal. As CIP is measured on risk free

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1.2 1.4 1.6 1.8 2 AUSEUR 1/1/2005 1/1/2010 1/1/2015 Date

(a) Exchange rate

−.1 0 .1 .2 FirstDiff 1/1/2005 1/1/2010 1/1/2015 Date

(b) First difference exchange rate

Figure 1: Exchange rate between Australian Dollar and Euro

rates, this leads to deviations from CIP7. Deviations from the LIBOR

differ-ential and ft− st were measured up to 260bps.(Jones, 2009). Acknowledging

that these deviations from CIP are caused by changing relative credit risk premiums inherently implies the existence of a time-varying risk premium.

(Vacek, 2010) Figure 3 shows (1 + it) −F_S_tt(1 + i∗t). This clearly shows (large)

deviations from CIP around the third quarter of 2008.

Deviations from CIP around the zero-lower-bound may cause a problem for this thesis, as the OLS estimates will be biased if the cause of the

devi-ation isn’t orthogonal to ηt+1. Correlation between st+1− st and the cause

of deviations from CIP wouldn’t be to surprising, as forex volatility also

increased during the crisis, thereby increasing the magnitudes of st+1− st.

This increased volatility means that there is heteroskedasticity in the sample, which is corrected for by robust standard errors on all OLS regressions. Just to show how well CIP did hold in the rest of the period, figure 2 shows the

interest rate difference and forward premium over time.8

Regressing equation (5) leads to the first output in table 1. The estimated

β1 coefficient is negative and statistically indistinguishable from both the null

and the alternative hypothesis −2.114. Statistically, there’s no proof for the significant negative bias that’s often referred to as the forward premium puzzle.

Adding λ∗ and the interaction variables λ∗(ft− st), thereby regressing

7_{As measured from the LIBOR}

8_{Note that testing the correlation does not directly proof how well CIP holds under}

all circumstances, though it does give an indication about whether CIP holds on average (Thorton, 2013, pp.56).

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−.001 0 .001 .002 .003 .004 premium 1/1/2005 1/1/2010 1/1/2015 Date

(a) Forward premium

.01 .02 .03 .04 .05 InterestDiff 1/1/2005 1/1/2010 1/1/2015 Date

(b) Interest rate differential

Figure 2: Forward premium and four-week (annualized) LIBOR interest rate differential between AUD and Euro

−.002 −.001 0 .001 .002 residual5 1/1/2005 1/1/2010 1/1/2015 Date (a) (1 + it) −F_St_t(1 + i∗t) 0 2 4 6 8 1/1/2005 1/1/2010 1/1/2015 Date LiborEUR LiborAUD

(b) Four-week LIBOR (annualized)

Figure 3: (1 + it) −Ft St(1 + i ∗ t) and LIBOR −.1 0 .1 .2 residual 1/1/2005 1/1/2010 1/1/2015 Date (a) (St+1 St ) − ( Ft St) 0 2 4 6 8 1/1/2005 1/1/2010 1/1/2015 Date InterestUS InterestAUD InterestEUR InterestJAP

(b) Short term deposit rates

Figure 4: (St+1

St ) − (

Ft

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Table 1: Degree of UIP violation between the Australian Dollar and Euro (5) (7) 75 bps (7) 50bps (7) 25bps Premium -2.114 -2.077 2.179 0.526 (4.540) (4.910) (4.635) (4.193) ZLB 0.000270 0.0169∗ 0.0155∗ (0.0244) (0.00738) (0.00718) Interaction 0.181 -3.711 -2.535 (8.991) (2.406) (2.177) Constant 0.00450 0.00412 -0.00802 -0.00331 (0.0123) (0.0139) (0.0130) (0.0117) Observations 130 130 130 130 R2 _0.002 _0.002 _0.032 _0.031

Standard errors in parentheses

∗ _{p < 0.05,}∗∗ _{p < 0.01,}∗∗∗ _{p < 0.001}

equation (7), does not significantly change the degree of UIP violation on any of the definitions. Sensitivity analysis does not give any reason to doubt whether the results are due to the wrong definitions, as both the coefficients and standard errors do not differ that much between the three definitions.

The financial crisis increased exchange rate volatility. This is shown by outliers in the first difference exchange rate line graph (Figure 1). The biggest outliers are during the third quarter of 2008. Before the financial crisis, the Australian dollar was trading at a positive forward premium, as the Australian interest rate was higher than the European. In terms of UIP, the Australian dollar was therefore expected to depreciate. But because the interest rate differential was minimized by sharp rate declines by both the ECB and the RBA in 2008, the Australian dollar was expected to minimize this expected depreciation. This follows from conventional UIP logic as:

Et[st+1] − st = (it− i∗t) (9)

Minimizing the interest rate differential during the financial crisis should thus

have led to an expected decline in st+1− st. Yet, the Euro appreciated more

than 30 percent in less than 3 months. Such an appreciation seems to be rather big in terms of conventional UIP.

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This may indicate the existence of a (time-varying) risk premium. Be-cause the financial crisis mainly hit American and European banks, it is easy to argue that this increased the probability of default for European and Amer-ican financial intermediaries more than Australian (Haslems, 2014). Not only was the Australian financial system hit less severe, the RBA also had higher initial interest rates, leaving more room for the central bank to fight liquidity and aggregate demand problems by lowering interest rates. This could’ve in-creased the European and American risk premium more than the Australian. If this relative risk premium exists, equation (8) becomes:

Et[st+1] − st = (it− i∗t) − πt. (10)

In equation (8) the risk premium (πt) is the Australian dollar risk relative

to the Euro. If investors deemed Australia to be safe haven, this could

explain why the Australian dollar still depreciated as much, as the increased foreign risk premium decreased the risk adjusted expected domestic returns

(it− i∗t − πt) needed for equation (9) to be in equilibrium.

If this is true, it must mean that πtis time-varying, and therefore biassing

the degree of UIP violation in the OLS regression of equation (5). This could

be an explanation as to why β1 isn’t close to, or at, unity. If there’s indeed a

time-varying risk premium, it is likely that it varied greatly at the start of the financial crises, thereby biassing the regression. This could also explain why the interaction coefficients for are statistically indistinguishable from zero.

Another interesting result is that the β0 coefficient is not significantly

different from zero. This is within expectations of the hypotheses of many

scholars(Fama, 1986).9_.

Concluding, it does not directly seem like the European zero-lower-bound changed the degree of UIP violation. There’s a few possible explanations as to why theinteraction variables are insignificant. Surely, the most obvious one would be that there’s no causal relation between the zero-lower-bound and the degree of UIP violation, thereby giving evidence for the null hypothesis. Another suspect is failure of CIP around the zero-lower-bound, which would

bias the regression if the cause of the failure isn’t orthogonal to ηt+1.

9_{Note that it was not hypothesized by this thesis, as scholars have shown that nonzero}

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100 120 140 160 180 JPEURSt 1/1/2005 1/1/2010 1/1/2015 Date

(a) Exchange rate

−.15 −.1 −.05 0 .05 FirstDiff 1/1/2005 1/1/2010 1/1/2015 Date

Figure 5: Exchange rate between Japanese Yen and Euro

6.2 Japanese Yen and the Euro

∗

The difference with the Japanese Yen and the Euro is that the Japanese economy has hit the zero-lower-bound years before the financial crisis started in 2008. Japanese short term deposit rates have occasionally been below

50bps during the last two decades. As the correlation between λ and λ∗is not

high enough to cause perfect multicollinearity, equation (6) is regressed.The causality between the Japanese zero-lower-bound and European is likely to be different. As policymakers have been dealing with close-to-zero short term nominal deposit rates for almost two decades, it is likely that the Japanese bound is less of a ’structural break’ in terms of both the time-varying relative risk premium and the instruments available to policymakers.

Figure 5 and 6 show the first difference exchange rate, exchange rate, LIBOR interest rate differential and forward premium over time. The image sketched by the forward premium is the complete opposite of that with the Australian dollar and the Euro, as the premium has been at a negative value, only turning positive at the end of 2014. The premium seems to be a good fit of the interest rate differential, though it does showcases a ’big’ outlier around September 2008 again. The interest rate differential decreased up to −0.4, while the forward premium only decreased up until −0.3 The same reasoning as between the AUD and the Euro can be applied here, as scholars have shown that due to relative differences in counterpart risk and the lack of short-term liquidity in financial crises, (large) deviations from CIP can

arise. Figure 7 shows the residual from (1 + it) −F_St_t(1 + i∗t). The graph shows

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−.004 −.003 −.002 −.001 0 premium 1/1/2005 1/1/2010 1/1/2015 Date

(a) Forward premium

−.04 −.03 −.02 −.01 0 InterestDiff 1/1/2005 1/1/2010 1/1/2015 Date

Figure 6: Forward premium and four-week (annualized) LIBOR interest rate differential between Japanese Yen and Euro

−.0005 0 .0005 .001 .0015 residual6 1/1/2005 1/1/2010 1/1/2015 Date (a) (1 + it) −F_St_t(1 + i∗t) 0 1 2 3 4 5 1/1/2005 1/1/2010 1/1/2015 Date LiborJP LiborEUR

Figure 7: (1 + it) −Ft St(1 + i ∗ t) and LIBOR −.15 −.1 −.05 0 .05 residual 1/1/2005 1/1/2010 1/1/2015 Date (a) (St+1 St ) − ( Ft St) 0 2 4 6 8 1/1/2005 1/1/2010 1/1/2015 Date InterestUS InterestAUD InterestEUR InterestJAP

Figure 8: (St+1

St ) − (

Ft

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As with the AUD and the Euro, deviations from CIP bias the regression

if the cause of the deviation isn’t orthogonal to ηt+1. The first difference

exchange rate movement shows increased volatility during the financial crisis. The interest rate differential turned closed to zero after the ECB reached the zero-lower-bound. Yet, the exchange rate volatility didn’t significantly decrease. As shown by figure 8 the Euro still appreciated by almost 40 percent

between 2013 and 2015. According to conventional UIP logic, this isn’t

within expectations. This may indicate that the zero-lower-bound changed the degree of UIP violation. It definitely indicates that even if one were to assume that the regression coefficients of equation (5) are unbiased, there’s

violation from unity in the β1 coefficient.

Table 2: Degree of UIP violation between the Japanese Yen and Euro

(5) (6) 75 bps (6) 50bps (6) 25bps Premium 2.893 -9.816 6.817 5.950 (3.113) (25.87) (4.792) (4.842) ZLBEUR 0.0131 0.0174∗ 0.0132 (0.00938) (0.00822) (0.00860) ZLBJP 0.0454 -0.00655 -0.00158 (0.0858) (0.00783) (0.00605) InteractionEUR 115.7∗∗∗ 90.54∗∗ 74.92∗ (33.99) (31.95) (35.34) InteractionJP 8.022 -8.965 -7.416 (26.12) (5.201) (5.243) Constant 0.00318 -0.0442 0.00494 0.00238 (0.00422) (0.0854) (0.00886) (0.00645) Observations 130 130 130 130 R2 _0.007 _0.084 _0.092 _0.078

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Table 2 shows the OLS regression results between the Japanese Yen and the Euro. The results from equation (5), as given by the first regression show a positive degree of UIP violation 2.893 insignificantly different from zero. As the correlation between the Japanese zero-lower-bound and the European zero-lower-bound is neglectable in terms of perfect multicollinearity, both bounds are added to the same regression, thereby regressing equation (6). The European zero-lower-bound interaction variable changes the degree of

UIP violation in all three regressions. During the zero-lower-bound, the

degree of UIP violation decreased, as there’s a very positive and significant

interaction coefficient.10 _{The significance of the interaction variable decreases}

as the short term nominal deposit rate that defines the bound decreases. The Japanese zero-lower-bound did not significantly change the degree of UIP violation on any of the zero-lower-bound definitions. This could be explained by the Japanese zero-lower-bound being less of a structural break in terms of monetary policy. As the Bank of Japan has had close to zero short term nominal deposit rates for the last 20 years, policymakers have been looking for other solutions to stimulate aggregate demand and inflation. An example would be the extensive quantitive easing program that the Bank of Japan has been pursuing for the last years. This could mean that the relative risk premium changes less, as the Japanese zero-lower-bound is more of a given than a fundamental change.

Sensitivity analysis does not give any reason to doubt whether the chosen definitions of the zero-lower-bound are the underlying problem. The coeffi-cients and standards errors for the interaction variable do not differ much between 75, 50 or 25bps. This goes for both the Japanese as European zero-lower-bound.

Concluding, it seems like the European zero-lower-bound changed the degree of UIP violation while the Japanese didn’t. There’s a few possible explanations. The economic explanation would be that the causality be-tween monetary policy and the degree of UIP violation works different for the Japanese bank, as its economic fundamentals are completely different. As said before, the Japanese short term nominal deposit rate has been very close to zero for the last two decades. Next to that, Japan has been using quantitive easing for a decade already. Scholars have shown before that the 10_{Admitted: as the interaction effects increase the distance between the found degree}

of UIP and the implied unity value, it could also be said that the degree of UIP violation increased.

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.6 .7 .8 .9 1 1.1 USAUS 1/1/2005 1/1/2010 1/1/2015 Date

(a) Exchange rate

−.3 −.2 −.1 0 .1 FirstDiff 1/1/2005 1/1/2010 1/1/2015 Date

Figure 9: Exchange rate between USD and AUD

degree of UIP violation is influenced by the sort of ’policy rule’ pursued by the central bank. (Tambakis, 2012). It could therefore very well be that the Bank of Japan has a different causality via the zero-lower-bound. It seems reasonable to assume that the Japanese zero-lower-bound was less of a structural break, as it has been ongoing for the last two decades.If the time-varying risk premium exists, it is likely that the Japanese one has less causality with the domestic short term deposit rates. As rates have been very low for a long time, investors may very well look for other determinants in deciding the relative risk premium. In that sense the results seem to be proof for the hypothesis that the zero-lower-bound changes the degree of UIP violation because it measures the omitted variable of monetary policy. An-other possible suspect is the failure of CIP around the onset of the financial crisis. This may have biased the regression.

6.3 United States Dollar and Australian Dollar

∗

Figure 9 and 10 show the first difference exchange rate, exchange rate, an-nualized (one month) LIBOR interest rate difference and forward premium between the USD (domestic) and AUD (foreign). The premium is always negative, which is indeed also the case for the LIBOR interest rate differ-ential. The correlation between the premium and interest rate differential

is estimated at 0, 836. The largest residuals from (1 + it) − F_St_t(1 + i∗t) were

between 2008 and 2009. Again, these deviations from CIP could bias the

regression if the cause of the deviation is not orthogonal to ηt+1.

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indistinguish-−.002 −.001 0 .001 .002 Premium 1/1/2005 1/1/2010 1/1/2015 Date

(a) Forward premium

−.05 −.04 −.03 −.02 −.01 0 InterestDiff 1/1/2005 1/1/2010 1/1/2015 Date

Figure 10: Forward premium and four-week (annualized) LIBOR interest rate differential between USD and AUD

−.002 −.001 0 .001 .002 residual 1/1/2005 1/1/2010 1/1/2015 Date (a) (1 + it) −F_St_t(1 + i∗t) 1 1.02 1.04 1.06 1.08 1/1/2005 1/1/2010 1/1/2015 Date LiborUScorr LiborAUDcorr

Figure 11: (1 + it) − Ft St(1 + i ∗ t) and LIBOR −.3 −.2 −.1 0 .1 residual 1/1/2005 1/1/2010 1/1/2015 Date (a) (St+1 St ) − ( Ft St) 0 2 4 6 8 1/1/2005 1/1/2010 1/1/2015 Date InterestUS InterestAUD InterestEUR InterestJAP

Figure 12: (St+1

St ) − (

Ft

(37)

able from both the null and alternative risk neutral efficient market hypoth-esis 2.350 . Adding the American zero-lower-bound as a interaction variable

does not significantly change the degree of UIP violation. The β1 coefficients

for 50 and 25bps do become significantly different from zero. This means that observations with short term nominal deposit rates above 50bps have

β1 coefficients that are different from zero and statistically indistinguishable

from unity. The risk neutral efficient market hypothesis is therefore not re-jected for these observations. This could indicate that the zero-lower-bound does indeed measure a period in which the risk premium is so time-varying that it causes a bias severe enough to change the degree of UIP violation from positive to negative. Keep in mind that the interaction effect is still insignificant. Comparing the differences between 75, 50 and 25bps with sen-Table 3: Degree of UIP violation between the United States Dollar and Australian Dollar (5) (7) 75 bps (7) 50bps (7) 25bps Premium 2.350 8.976 10.85∗ 10.56∗ (2.654) (5.081) (5.282) (5.199) ZLB -0.00589 -0.0258 -0.0241 (0.0168) (0.0202) (0.0171) Interaction -8.474 -15.33 -14.46 (7.268) (8.431) (7.478) Constant 0.00584 0.0101 0.0148 0.0141 (0.00707) (0.00761) (0.00820) (0.00783) Observations 130 130 130 130 R2 0.004 0.030 0.043 0.047

∗ _{p < 0.05,}∗∗ _{p < 0.01,}∗∗∗ _{p < 0.001}

sitivity analysis gives reason to doubt which definition is correct. There’s a very big difference in found coefficients. While the 50 and 25bps definitions have interaction effects that are comparable, the 75bps definition has a very insignificant T score.

While such a statement would definitely need more research, it could be argued that this shows the time-varying risk premium increases as interest

Analyzing whether the zero-lower-bound changed the degree of UIP violation