Testing the uncovered interest parity on the Swiss franc peg

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Testing the uncovered interest parity

on the Swiss franc peg

Date: 26/06/2018

Supervisor: Stan Olijslagers Academic year: 2017/2018

Bachelor's thesis Semester 2

Niels Pranger 11056274

Abstract

In this research the uncovered interest parity is tested on the Swiss franc peg. Because of pressure on the Swiss franc to keep appreciating the Swiss national bank decided in September 2011 to peg their currency against the euro for a rate of 1.20 CHF/EUR. In January 2015 the peg was removed. In this paper I will do an empirical research to test if the uncovered interest parity holds during the complete period 2007-2016 and also during the period of the peg. I will run OLS regressions with Newey-West standard deviations to account for autocorrelation. Results on the short run test give negative coefficients and in the long run test positive coefficients. The coefficients during the peg are larger than 1 and have a higher R2 than other papers found testing the UIP on floating exchange rate regimes.

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Statement of originality

This document is written by Niels Pranger who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are 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 supervision of completion of the work, not for the contents.

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1. Introduction

In the summer of 2007 a credit crisis evolved in the United States and spilled over to Europe. During this crisis the Swiss franc appreciated enormously. Investors searched for countries to safely invest their money in. Switzerland was seen as a safe country and investors parked their money here. This caused an enormous increase in the exchange rate of the Swiss franc to the euro (CHF/EUR). The spot rate appreciated from 1.60 CHF/EUR in January 2007 to around 1.10 CHF/EUR in the summer of 2011. The appreciation had negative consequences on the export of Switzerland and caused a threat of deflation. In September 2011 the Swiss national bank decided to peg the Swiss franc against the euro with a floor level of 1.20 CHF/EUR, to protect the economy. The currency was stable during the peg and never dropped below the floor level. In January 2015 the peg was removed. The currency appreciated again and circled around 1.10 CHF/EUR.

The uncovered interest parity (UIP) will be tested over this period. The UIP links exchange rate depreciation with the interest rate differential and states that this must be a one-for-one. The UIP has been tested on many different cases. Froot & Thaler (1990), Chinn and Meredith (2004) and Bui (2010) all came to the same conclusion: with short term maturities the coefficient on the interest rate differentials is negative. But with long term maturities the coefficient is positive.

I will test if the UIP holds over the complete period 2007 to 2016. This will be done with weekly data for short- and long-term bonds of Switzerland and triple A euro zone bonds. I run OLS regressions with Newey-West standard deviations to account for autocorrelation. The short run results give negative coefficients and the long run results positive coefficients. This is in line with other studies.

This paper also tests the UIP during the different periods of the peg, with a focus on the period during the peg. Weekly data with different maturities of Swiss franc- and euro-Libor rates are used. The results were surprising. The coefficients during the peg were larger than 1. The R2 statistics of the different regressions are larger than found in other papers and in the test over the complete period.

Section 2 contains the theoretical framework with information about Switzerland, the Swiss franc and the model. Section 3 describes related literature. Next is section 4 with information about the data. In section 5 the results are discussed and the conclusion of the paper can be found in section 6.

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2. Theoretical framework 2.1 The Swiss Franc

The Swiss franc started to appreciate during the debt crisis. At the start of 2007 the spot exchange rate was around 1.60 Swiss franc per euro (CHF/EUR). Exactly 4 years later the spot exchange rate was 1.25 CHF/EUR. We can see this trend in graph 1 in the appendix. The line smoothly decreases, meaning an appreciation of the Swiss franc.

In the summer of 2011 the European debt crisis became even worse. Investors reconsidered their risky assets and found the assets too risky to hold. The risky assets were sold and investors moved their money to safe havens (Hui, Lo, & Fong, 2016). A safe haven is a place where investors invest in risky financial times (Hossfeld & MacDonald, 2015). Investors regard safe havens as places where money is safe. Switzerland was one of these safe havens during the crisis. Hossfeld & MacDonald (2015) have empirical evidence on the Swiss franc (CHF) being a safe haven currency. This implies that the returns of the currency and the returns of the global stock market are negatively correlated in risky financial times.

Being considered a safe haven can have negative consequences for countries. The currency of the safe haven appreciates because investors invest in assets in this currency. This is exactly what happened in Switzerland from the start of the European debt crisis until September 2011 (Lera & Sornette, 2016) (graph 1). Investors resorted their money in Switzerland, increasing demand in the Swiss franc and causing downward pressure on the CHF/EUR exchange rate. In the summer of 2011 the Swiss franc appreciated dramatically. The lowest spot rate was reached in the week of 8 August 2011, with an average of 1.085 CHF/EUR. The downward pressure on the spot exchange rate

threatened the Swiss economy and the overvaluation of the Swiss franc caused risk of deflation (SNB, 2011). The relatively expensive Swiss franc led to a decline in aggregate demand of foreign countries in Swiss' products. A decline in the demand lowers the price level, eventually causing deflation.

2.2 The Swiss economy

The Swiss economy suffered from the appreciation of the Swiss franc because exports are a big part of the Swiss economy. Most of the exports go to countries within the Euro zone (Lera & Sornette, 2016). The strong exchange rate worsened the competitive position of Switzerland. Switzerland became (relatively) more expensive for euro zone countries, the exports decreased. Graph 2 shows the change in export growth compared to the previous period. The Swiss export decreased enormously the last quarter of 2008 and the first quarter of 2009. In this period the Swiss franc did not appreciate very much. The decrease in export is the consequence of the start of the crisis. However, in the second and third quarter of 2011 the export decreased compared to the previous period, with a decrease of 5.7% in the third quarter (SNB, 2011). In this period the debt

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crisis worsened, but also the Swiss franc appreciated. The appreciating Swiss franc is a threat to the exports.

The SNB also faced the threat of deflation. When prices decrease, consumers expect prices to drop further and postpone their consumption. This leads to more deflation. It is a self-fulfilling prophecy: consumers expect deflation, postpone consumption and prices decrease further. This is dangerous for the economy, the demand decreases more and firms get in trouble. Graph 3 shows that the inflation forecast for 2012 is negative. Deflation very often is the consequence of a huge decrease in aggregate demand, which causes producers to lower their prices in order to restore equilibrium on the market (Bernanke, 2002). The decrease in aggregate demand can be explained by the appreciation of the Swiss franc, which led to a decrease of exports.

The decrease in exports and threat of deflation were a danger to the Swiss economy. The exchange rate approached 1 CHF/EUR in September 2011 but passive monetary policies were no longer effective (Lera & Sornette, 2016). On 6 September 2011 the Swiss National Bank declared to peg the Swiss franc against the euro with a minimum exchange rate of 1.20 CHF/EUR. In a statement the SNB declared that it is willing to buy unlimited quantities of foreign currency, targets to keep the three-month Libor rate at zero and holds sight deposits above 200 billion CHF (SNB, 2011). The SNB will intervene when the CHF/EUR comes close to the minimum rate. The central bank then buys foreign currencies with its domestic currency, to increase the supply of the Swiss franc. With these measures the SNB is trying to keep the exchange rate at or higher than the floor level, to protect the Swiss economy. The foreign currency assets almost doubled in 4 years (SNB, 2015). During the peg the spot exchange rate is stable ranging between 1.20 and 1.25 CHF/EUR. Graph 4 shows the exchange rate during the peg.

On 22 January 2015 the ECB announced their quantitative easing programme to fight the deflation. Quantitative easing is a policy to increase the money supply. The ECB bought government bonds in exchange for euros, increasing the supply for euros. This caused additional pressure on the Swiss franc to appreciate. A higher euro supply lets the Swiss franc appreciate against the euro. To maintain the peg the SNB needed to buy even more euros. But before this would happen, the SNB decided to remove the peg. On 15 January 2015 the SNB announced the removal of the Swiss franc – euro peg. Besides the quantitative easing of the ECB, the recovering economy in the United States which increased the demand in Swiss francs was another reason for the SNB to unpeg the Swiss franc (Jo et al., 2016). The Swiss franc appreciated dramatically after the remove of the peg. Graph 5 shows the period after the remove of the peg. It reached 1 CHF/EUR the first week. But later the spot exchange rate converged to around 1.10 CHF/EUR and moved around this rate.

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Part 2.3 covers the interest rate parities. The parity shows the relation between the interest rates of a home and foreign country and the expected depreciation of the exchange rate between these countries. It states that there is a one-to-one relation between the interest rate differential and exchange rate depreciation. I will test if the parity holds over the complete period (2007-2016) and if the parity holds during different periods of the peg (before, during and after). During the peg the change in exchange rate between the Swiss franc and the euro is around zero, so the parity holds if the interest rates are equal. Before going to the results, the UIP and regression model are

explained and related literature is discussed. 2.3 Interest rate parity

I will test if the uncovered interest rate parity holds over the complete and during the different periods of the peg. First the uncovered and covered interest models are explained and the intuition behind it, after this the regression model will be explained.

Investors can choose between investing in the domestic country or in a foreign country. If investors can switch between bonds across borders instantaneously, then the only difference between the two investments is the interest rate and the currency of denomination (Pillbeam, 2013, p.149). The expected depreciation of the currency is important to investors who invest in a foreign country because this effects the return. If the home currency appreciates against the foreign currency, the return on the foreign investment decreases. This is called exchange rate risk. The covered interest parity (CIP) and the uncovered interest parity both show the relation between the interest rate in the domestic and foreign country and the exchange rate change. The CIP protects investors from exchange rate risk, the UIP doesn't.

2.3.1. Uncovered interest rate parity

In the UIP model investors are not protected against exchange rate risk. The UIP shows the relation between the home interest rate, the foreign country interest rate and the expected depreciation:

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Here r is the interest rate in the domestic country, r* is the interest rate in the foreign country, Et(St+1) is the expected spot rate at time t+1 and St is the spot rate at time t. S is defined as domestic currency units per unit of foreign currency (CHF/EUR). A rise in the exchange rate means a

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currency. The parity requires the return in the domestic country to equal the return in the foreign country. Equation (1) can be rewritten to:

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Rewrite equation (2) in natural logarithm:

and for small values of r and r*. This gives:

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Where st+1 and st are spot rates in natural logarithm. Es. is a shortcut for writing Et(st+1) - st, this is the expected depreciation of the home currency over period t to t+1. The intuition behind equation (3): if r > r*, a depreciation of the domestic currency is expected to compensate investors for investing in the foreign country. The UIP condition implies that the interest differential (r-r*) between the domestic and foreign country equals the expected depreciation. There are two crucial requirements for the UIP condition to hold. First, capital has to be perfectly mobile so that investors can change their portfolio of foreign investments any moment (Pillbeam, 2013, p. 150). Second, the bonds have to be equally risky, if this does not hold then investors require a risk premium and the UIP condition no longer holds (Pillbeam, 2013, p. 150). When both requirements hold, the bonds are perfect substitutes. This implies that the UIP condition always holds. The UIP condition should always hold, otherwise there is an arbitrage opportunity. This research assumes both perfect capital mobility and that bonds in Switzerland and the Euro area are equally risky. The first assumption is reasonable, capital barriers between Switzerland and the euro (almost) don't exist. Because of the second assumption I don't have to take into account the risk premium.

The UIP works different when a currency is pegged compared to when a currency is free to float. If a currency is free to float, both countries can freely set their interest rate. The exchange rate between the two countries will adapt to the interest rates to hold the UIP. When a currency is pegged, as was the case for the Swiss franc during the period September 2011 to January 2015, UIP works differently. The expected depreciation is equal to (or close to) zero. The interest differential should also equal zero. That means that the country who set the peg cannot freely target their interest rate. Otherwise the expected depreciation would not equal zero. So in the case of

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Switzerland the expectation is that the interest rate follows the interest rate of the Euro zone during the peg.

2.3.2 Covered interest parity

Investors can protect themselves against exchange rate risk by entering a forward exchange contract. In the covered interest parity (CIP) the forward and spot market are linked to each other together with the domestic and foreign interest rate (Pillbeam, 2013, p.25):

(4) Where F is the forward exchange rate, S is the spot exchange rate, r is the domestic interest rate and r* the foreign interest rate. A forward exchange rate is an exchange rate buyers and sellers agree on to use at a specified date in the future. The forward ensures investors an exchange rate in the future. This protects the investor from exchange rate risk. The presence of arbitrageurs makes sure that the CIP condition holds constantly (Pillbeam, 2013, p. 25). The CIP formula can be simplified to the following approximation (the same mathematical method used to get from (1) to (3)).

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Where ft and st are in natural logarithm.

If we combine the equations (3) and (5) we get:

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2.3.3 The model

The interest differential and the expected depreciation do not always equal, hence the UIP doesn't always hold. We can test UIP using the following regression equation:

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The interest rates are now defined in weekly periods. The spot rate s is in natural logarithm. The w stands for weeks. However, equation (7) needs the expected spot rate Et(st+w). This is unobservable. But there are different ways to approach Et(st+w). In equation (6) the first approximation is showed.

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The forward rate ft can be an estimator of Et(st+1). This holds if we assume rational expectations and risk neutrality. ft - st can approximate the expected depreciation Es.. However, there is another estimator for Et(st+1). We need to assume rational expectations. This assumption states that economic agents know the relevant model to predict a variable so they don't constantly under- or overestimate the future value of the variable (Pillbeam, 2013, p. 202):

Where st+1 is the log of the spot exchange rate at time t+1, Et(st+1) is the log of the expected spot rate at time t+1 and ut+1 is a normally distributed error term with mean zero. So we can approximate the expected spot rate for time t+w by using the spot rate at time t+w:

Rewriting equation (7): (8)

The left side of the equation is the depreciation of the currency. The term between the brackets in the right side of the equation changes the yearly interest rate into the time-horizon rate. This will be done by multiplying the interest rate with the time horizon and dividing it by 52 weeks. For the 3-month bond rate the investment horizon is 13 weeks. The 3-3-month bond rate will be multiplied by 13 and divided by 52. In this way the yearly interest rate of the 3-month bonds are changed into 13-week interest rates. The interest differential is the difference between the interest earned in the domestic country and in the foreign country, where the interest rates are adjusted to their investment horizon. This should be equal to the depreciation of the currency over the same time horizon, according to the UIP. So the 13 week interest rate differential should equal the depreciation of the spot rate over 13 weeks. The idea is that an investor should be indifferent between

investments with the same time horizon, where one is denominated in domestic currency and the other in foreign currency. The coefficient β shows the relation between the interest rate differential and the exchange rate depreciation. The UIP states that there is a positive one-for-one relation between the two variables. If β is positive the relation is positive: if r > r* the currency depreciates, the foreign investors are compensated. This is in line with UIP. If β is negative the relation is negative and this is the opposite of the UIP.

The assumption of rational expectations is crucial in this model. Because of this assumption the expected spot rate for time t+w can be approximated by the spot rate at t+w. We can replace Et(St+w) in (8) by St+w. Past data of the spot exchange rate can be used. Basically, we assume that

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investors always expect the future rate right. Further I assume perfect capital mobility and equally risky bonds.

With equation (8) this paper tests if UIP holds in Switzerland for the complete period and the separate periods of the peg. UIP requires st+1 - st and (r - r*) to equal, it should be a one-for-one relation. In equation (8) st+1 - st and (r - r*) are written somewhat differently, but the relation between the variables is the same. For the UIP to hold α must equal 0 and β must equal 1. If this is not the case the UIP condition does not hold. Especially the β is important for the parities. It shows the relation between the interest differential and the expected depreciation. That's why I will have a closer look to β, keeping α in mind. In this research I will test if the UIP holds over the entire period and if it holds the period before, during and after the peg of the Swiss franc with the euro. Equation (8) is used to test this.

That brings me to the following hypothesis: versus

In the next paragraph is the literature review, based on the related literature I give my expectations.

3. Literate review

In this paragraph papers which tested the UIP hypothesis are summarized. First papers testing the UIP over a complete period, thereafter a paper testing a period during a peg.

In the paper of Chinn and Meredith (2004) the UIP hypothesis is tested with data from the Group of Seven countries (United Kingdom, France, Germany, Italy, Japan, Canada and the United States). Interest rates are used for both short-term and long-term estimates. United States is the base country for the exchange rate. Equation (8) is used for the regression. Rational expectations and risk neutrality are assumed. First the UIP is tested on short-horizon variables. The interest differential is taken from Eurocurrency yields with the same maturity. Data ranges from 1980 to 2000. The short-horizon estimates of the coefficient β give evidence of failure of the UIP model (Chinn and Meredith, 2004). The average of β is around -0.8. For most of the coefficients the null hypothesis is rejected. In some cases, the null hypothesis is not rejected but the standard deviations were so large that it is hard to reject almost every plausible hypothesis (Chinn and Meredith, 2004). Only three coefficients show a positive relation. These coefficients are not rejected to unity but have a very high standard deviation. The R2 of the regressions are low or even negative. These results are in line with other studies: exchange rates move the opposite way of interest differentials on short term. In the paper of Froot & Thaler (1990) is referred to a research of Froot on published coefficients. The average of 75

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coefficients was -0.88. Few coefficients were positive and not one equal to or larger than 1. Chinn and Meredith (1990) used for the long-horizon 5- and 10-year maturity government bond yields. For the 10-year maturity three of the six coefficients are not rejected against the null hypothesis. The R2 is higher for the regressions. For the 5-year maturity only Germany, United Kingdom, Canada and the United states are tested. The coefficients are positive, not rejected and the coefficient of Germany is close to 1. But again, all coefficients have large standard deviations. The conclusion is that longer-term data gives positive coefficients closer to 1.

Omer, de Haan and Scholtens (2014) tested the uncovered interest parity using the London Interbank Offered Rate (LIBOR). Rational expectations is assumed: E(st+i) = st+i. Equation (9) is used. The data of LIBOR was taken from 1 January 2001 to 31 December 2008 for 7 currencies (US Dollar, British Pound, Euro, Japanese Yen, Swiss Franc, Australian Dollar and Canadian Dollar). With 14 different maturities varying from 1 week to 12 months (Omer, de Haan & Scholtens, 2014). The data for the exchange rates with the US Dollar as base country are from the International Monetary Fund. The paper is different than other researches in that it uses more than only two or three maturities. The 1 week to 7-month maturities are all rejected against the null hypothesis. However, for the higher than 7-month maturities the coefficients cannot be rejected. UIP holds for industrialized markets with maturities above 7 months. The conclusion is the same: longer-term maturities give coefficients more in favour of the UIP. This research also shows that LIBOR can be used for testing UIP.

Jo (et al., 2016) tested UIP with equation (8). The data consists of daily interest rates and daily spot rates. The paper concluded that the parity can inform the trend or direction of the future spot rate, but not the exact rate.

In the paper of Bui (2010) equation (8) is used. In the paper UIP is tested with data from Australia and New Zealand. Bui tested whether the maturity of interest rates has an effect on UIP. The Australian and New Zealand dollar are defined as currencies per US dollar. Monthly data is taken and ranges from January 1985 till December 2009. 3-Month and 6-month bank accepted bills are used for the short term maturity. For the long term maturity 2-, 5- and 10-year treasury bonds are used. The Newey-West OLS regression is used. The coefficients show proof for the failure of the UIP in the short run, as do other studies. The four coefficients have negative signs and the average is -.90. β = 1 is rejected and R2 is very low for all regressions. In the long run the output shows positive signs for three of the four coefficients, but the estimates are closer to zero than to one. The null

hypothesis cannot be rejected for two of the four regressions, but this is because of the very large standard deviations. The R2 for the long run regressions are even smaller. The UIP might work better in the long run.

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tested UIP on different exchange regimes in east-Asia. In the paper the expected depreciation is equal to zero because the currency is pegged. The expected depreciation is removed out of equation (8) and tested is if the interest rate of the United States has an effect on the interest rate of Korea. The coefficient and R2 are expected to be higher during the peg than during the period where the currency floats. The results show a coefficient of 1.736 during the period of the peg compared to a coefficient of 0.179 after the peg. The adjusted R2_{is also higher.}

The conclusion for the UIP test on the complete period is that UIP holds better in the long run. In the short run the results show negative coefficients which are not in line with the UIP. The long run results show positive coefficients which comer closer to the value of 1. Further the papers found very high standard deviations and very low R2 statistics. The article that tested UIP on a pegged currency showed different results. The coefficient is higher during the peg and can be larger than 1. The R2 is also higher during the peg. I expect the same results in this research.

4. Data

The UIP requires three different variables: spot exchange rate, interest rate in the domestic country and interest rate in the foreign country. The spot exchange rate Swiss franc to euro

(CHF/EUR) is defined as Swiss francs per 1 euro. Data of the spot exchange rates are from the

European Central Bank. I use weekly data from 8-1-2007 to 26-12-2016, a total of 521 observations. To test if the maturity of the interest rates has influence on the performance of the UIP I use different maturities: 3-month, 1-year, 2-year and 5-year. The first 2 maturities are for the short term, the last 2 are used for the long term. For Switzerland the yield of government bonds are taken, provided by Thomson Reuters. The Euro zone has not a common bond, but the ECB provides data on the yield of triple-A rated government bonds within the Euro zone. If the rating of a triple-A rated country is downgraded the country drops out of the dataset.

Different data is used to test the UIP before, during and after the peg. Because the periods are short, short term data is necessary. For the bond yield only the 3-month and 1-year yields are available. Instead of bond yields, Libor rates are taken because there is more short term data available of it. I use the 3-month, 6-month and 12-month Libor rate of the Swiss franc and the euro to test the different periods. The data is provided by ICE benchmark Administration.

5. Results

The summarizing statistics of the exchange rate and interest rates in Switzerland, and the Euro zone can be found in tables 1 and 2. Table 1 shows the statistics of the Swiss bonds and the

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CHF/EUR spot rate. The longer maturity bonds give higher returns. However, the 2-year bond give a lower return than a 1-year bond. Apparently, a 2-year bonds was regarded safer than 1-year bond. The standard deviation of the 2-year bond was also lower in this period. The skewness and kurtosis statistics show the distribution of the rates. The average of the spot rate between the Swiss franc and the euro is 1.316. The lowest rate is 1.001 and this was on 26-1-2015, a few days after the unpegging of the Swiss franc. The summarizing statistics of the Euro zone are showed in table 2. The average of the government bond rate increases as maturity increases. Standard deviation is almost constant. The lowest values of the interest rates are all negative, this is to discourage savers. The summarizing statistics of the Libor rates can be found in table 3. The return increases as maturity increases.

In graph 6 scatter diagrams of the interest differential and exchange rate depreciation for the 3-month, 1-year, 2-year and 5-year periods can be found. It is not clear from these graphs what the relation between the deprecation and the interest different is exactly. To get clear results I will run an OLS regression on the full period. Thereafter follows an OLS regression on the three different stages of the peg.

There is a problem in using the OLS regression: autocorrelation. Because I use weekly data to research the effect of different monthly and yearly interest differentials on the exchange rate depreciation there are overlapping observations. Autocorrelation happens when the term of the exchange rate depreciation is larger than the term of the data (in this research 1 week) (Bui, 2010). For example there are overlapping observations between 1-1-2011 till 1-4-2011 and 8-1-2011 till 8-4-2011. The depreciation between these 3-month periods use the same spot rates between 8-1-2011 and 1-4-2011. Thus the left hand-side of the regression equation (10) has overlapping observations. This causes the error term to be a moving average error term and the OLS coefficient will be an inefficient and biased estimator (Bui, 2010). This problem should be dealt with. The

heteroskedasticity and autocovariance consistent (HAC) estimators of Newey and West solves this problem (Bui, 2010). In this research I will use the HAC estimators to run OLS, this will correct the standard deviations of the coefficients for the moving average correlation. The Newey-West OLS regression uses the HAC estimators. The number of lags need to be calculated to run the Newey-West OLS regression. Lags = integer(52*(N/100)1/4) gives an approximation of the number of lags, where N is the number of observations. Other approximations can also be used.

5.1 Testing UIP on the complete period

First UIP is tested on the complete period: 8-1-2007 to 26-12-2016. This will be done on four different time periods to test if the time horizon has influence on the performance of UIP. The periods are: 3-month, 1-year, 2-year and 5-year. For the 3-month regression the depreciation over a period of three months is needed and the interest differential between the 3-month Switzerland

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bond rate and 3-month triple-A Euro zone bond rate. The spot rate at time t = 0 and the spot rate 3 months later are required. Because it is weekly data this equals the spot rate at time t = 13. The last 13 weeks of 2016 drop out of the regression. The regression requires spot rates 13 weeks later, but I don't have any observations in 2017. The number of observations for the 3-month test is

521-13=508. The number of observations decreases for longer time periods, more future data is required. The number of lags of the residual autocorrelation needs to be calculated before the Newey-West OLS regressions can be done. For the 3-month period: Lags = integer(52*(508/100)1/4) = 78. Respectively for the 1-year, 2-year and 5-year: 77, 74, 66.

The results of the OLS estimation can be found in tables 3 and 4. In table 3 the results of the short run test are showed. There is evidence for the failure of the UIP in the short run. The estimated coefficients have negative 'wrong' signs, this is not in line with the hypothesis. The average of the estimated β is -1.49 and the relation between the depreciation and interest differential is negative. This is larger than in other papers. However, tested against the null hypothesis the estimated coefficients cannot be rejected. This is because of the extremely high Newey-West standard deviations (4.09 and 2.83 respectively), which makes it hard to reject any plausible hypothesis. This problem with very high standard deviations is also reported in other papers, but the standard deviations are even higher than in these papers. Over the complete period the exchange rate was very volatile, especially during the period of the peg and unpeg. This explains the higher standard deviations. The α of the 1-year period is rejected against α = 0. The adjusted R2 statistics are very low, but not negative.

The long run OLS estimation with Newey-West standard deviations are more in line with the UIP. Both regressions show a positive sign for the β. The coefficient of the 2- and 5- year regression are 0.68 and 0.85. The coefficients are closer to one than to zero, in other papers coefficients are mostly closer to zero. The null hypothesis cannot be rejected. The coefficient for the 2-year period can also not be rejected against H0: β = 0. This is because of the large Newey-West standard deviation. However, with a significance level of 10% the coefficient for the 5-year horizon can be rejected against H0: β = 0. The standard deviations (1.05 and 0.49 respectively) are much lower than in the short run and are more in line with other papers. Both alphas are rejected against H0: α = 0 and not in line with UIP. The adjusted R2 statistics are again very low, meaning that the interest rate only explains a little of the dependent variable.

My results show that the long run is more in line with the UIP than the short run. The β for both long run regressions are positive and cannot be rejected against the null hypothesis. The relation between the interest rate differential and the depreciation are positive (negative) in the long (short) run. The positive coefficients correctly explain the relation between the depreciation and interest differential. The uncovered interest parity works better in the long run, despite the alphas

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being rejected in the long run. This result is also concluded in other papers. The standard deviations are higher than in other papers. This can come because of the different periods (peg and no peg), which cause higher volatility.

5.2 Testing UIP on different periods of the peg

Now UIP will be tested on different periods of the peg between the Swiss franc and the euro. The first period is before the peg, the second period is during the peg and the third period is after the peg. Before peg: 8-1-2007 to 5-9-2011, during peg: 12-9-2011 to 12-1-2015 and after peg: 19-1-2015 to 26-12-2016. Data of the 3-month, 6-month and 12-month Libor rates of the Swiss franc and the euro is used. The stage where the peg is active is the most interesting. It is expected that the interest rate differential and the spot rate depreciation move closely during the peg and that β is close to one.

I start to test UIP on different periods of the peg with the 3-month rate. For the 3-month Libor rate the last 13 weeks before 5-9-2011 (end first period) and 12-1-2015 (end second period) are removed so there is no relation between the stages. Otherwise, the first period contains spot rates during the peg and the second period contains spot rates after the peg which are below 1.20

CHF/EUR. For the third stage, the last 13 weeks cannot be used because data in 2017 is needed. Thus the first period: 8-1-2007 to 06-06-2011, the second period: 12-09-2011 to 13-10-2014 and the third period: 19-1-2015 to 26-9-2016. In graph 2 the 3-month Libor rate interest differential and exchange rate depreciation are plotted over the complete period. The exchange rate depreciation and interest rate differential are relatively close during the peg.

To correct for autocorrelation I again use OLS with Newey-West standard deviation. Lags are respectively 64, 59 and 51. The results are shown in table 5. The results of OLS give extreme values for the coefficient β. The coefficient during the peg is 3.5755 and is rejected against the H0. This is a surprising result. I expected a β close to 1. The average interest differential and spot rate

depreciation during the peg for the 3-month Libor rate were respectively -0.093% and -0.152%. So the depreciation was not equal to zero during the peg. This is also visible in graph 2. The coefficient before and after the peg are extremely negative (-3.36 and -19.32 respectively), with very high standard deviations (2.85 and 9.3 respectively). The period after the peg has less than 100 observations, so it is not very reliable. However, the adjusted R2 is relatively high in this period (14.37%). This is also the case during the peg (12.9%). The better performance of the R2 during the peg can be explained by the two variables moving closer with each other. Hence, the interest differential explains more of the depreciation.

For the 6-month Libor rate the three periods are shorter. Instead of 13 weeks, the last 26 observations in every period are dropped. The results are shown in table 6. The coefficients for the

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period before and after the peg are again extremely negative and hard to interpret. The coefficient during the peg is 2.04 and H0 is not rejected. Alpha is also not rejected. So UIP holds during the peg with the 6-month Libor rate. The 12-month Libor rate results of the regression (table 7) give no proof for the UIP, the coefficient during the peg is -0.33 and with a significance level of 10% the H0 is rejected. The R2 is close to zero for the period during the peg. Due to few observations the period after the peg is not tested for the 12-month Libor rate.

Focusing on the most interesting part, the period during the peg, UIP performs best with the 6-month Libor rate. The coefficient decreases as the maturity of the Libor rate increases. Two of the three coefficients during the peg are larger than 1. In the regressions over the complete period as well as in other papers only very low and even negative R2 statistics are found. In two of the three periods during the peg as well as in other periods the R2 statistics are larger than 10%. The UIP seems to explain more during a peg, than when the currency is floating. While over the complete period the short run maturities gave negative coefficients, during the peg the coefficients are positive. This is a surprising result compared to the test over the complete period for short run maturities, where the coefficients were negative.

6 Conclusion

In this paper I tested the uncovered interest parity on different time horizons. Over the complete period there is strong evidence that UIP doesn’t hold in the short run. Although the null hypothesis is not rejected, the coefficients have ‘wrong’ signs and are very negative. The relation between the depreciation and the interest differential is wrong. It is only because of the very high standard deviations that the coefficients are not rejected. But in the long run the coefficients are positive and closer to 1. The coefficients are not rejected against the null hypothesis. The relation between the depreciation and interest differential is positive in the long run. The long run results are more in line with the UIP than the short term results. In the long run α is significantly different from 0. A nonzero alpha may give evidence for a constant risk premium (Chinn and Quayyum, 2013). I assumed risk neutrality, but the alpha might proof the existence of a risk premium. The R2 statistics are low in all regressions, which means that only a little of the variation is explained by UIP. I chose to take into account the extreme values of the depreciation around the peg and removal of the peg, to test the complete period over a currency-peg. A new research can remove the extreme values to test the complete period.

The test on UIP on different periods during the peg had different outcomes. The coefficients during the peg were positive and higher than 1. This result is in line with Keil and Cao (2008). The

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coefficient on the 3-month horizon was very high and positive and rejected against the null hypothesis. The 12-month horizon coefficient was close to zero and rejected against the null. However, the coefficient on the 6-month horizon is not rejected against the null hypothesis and the alpha is not significantly different from zero. These results are favourable for the UIP. The results before and after the peg were very negative and hard to interpret. Over the complete period the R2 statistics were close to zero. Tested on different and shorter periods on the peg the R2_{statistics were} larger than 10%. More research is needed on UIP during a peg to know how it performs during this period. The period during the peg was short and I could only use short term data. UIP works better with long term data, longer lasted pegs with longer maturity data should be tested.

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Swiss National Bank. (2012). Annual financial statements of the Swiss National Bank (parent

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Appendix

Tables

Table 1: Summary statistics of the Swiss bonds and the spot exchange rate.

The average, median, minimum, maximum and standard deviation of the Swiss bond rates are annual percentages. The average, median, minimum and maximum of the spot exchange rate represents the spot exchange rate, the standard deviation is in percentage.

3-month 1-year 2-year 5-year CHF/EUR

Average 0.353 0.630 0.423 0.731 1.316 Median 0.03 0.25 0.05 0.319 1.233 Standard dev. 1.172 1.218 1.1 1.136 0.196 Skewness 1.050 0.953 0.835 0.545 0.436 Kurtosis 2.990 2.885 2.783 2.252 1.825 Minimum -1.6 -1.15 -1.112 -1.026 1.001 Maximum 3.06 3.88 3.058 3.191 1.679 Number of obs. 521 521 521 521 521

Table 2: Summary statistics of the euro zone triple A bonds.

The average, median, minimum, maximum and standard deviation of the triple-A Euro zone bond rates are annual percentages.

3-month 1-year 2-year 5-year

Average 0.847 0.925 1.088 1.689 Median 0.166 0.210 0.487 1.527 Standard dev. 1.511 1.529 1.529 1.491 Skewness 1.313 1.235 0.990 0.306 Kurtosis 3.171 3.067 2.718 1.882 Minimum -0.907 -0.836 -0.813 -0.595 Maximum 4.296 4.502 4.622 4.642 Number of obs. 521 521 521 521

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Table 3: Summary statics Libor rates Swiss franc and euro

The average, median, minimum, maximum and standard deviation of the Libor rates are annual percentages. CHF3M is 3-month Swiss franc Libor rate, EUR3M is 3-month euro Libor rate.

CHF3M CHF6M CHF12M EUR3M EUR6M EUR12M

Average 0.439 0.522 0.715 1.272 1.427 1.624 Median 0.077 0.16 0.37 0.631 0.937 1.223 Standard dev. 1.139 1.152 1.163 1.695 1.676 1.652 Skewness 1.197 1.188 1.077 1.23 1.148 1.055 Kurtosis 3.155 3.122 3.003 2.991 2.892 2.788 Minimum -0.964 -0.884 -0.752 -0.334 -0.227 -0.086 Maximum 3.12 3.194 3.368 5.338 5.413 5.478 Number of obs. 521 521 521 521 521 521

Table 4: Short run OLS estimation of UIP

Regression formula:

. Newey-West standard deviation to

correct for the autocorrelation. Adjusted R2 found in normal OLS regression. P-value between brackets, tested against H0: α = 0 and H0: β = 0.

Estimates (p-value) Adjusted R2 Newey-West N α β Std. deviation β 3-months 508 -0.0123 -1.536 0.0024 4.0857 (0.103) (0.707) 1-year 469 -0.050* -1.442 0.0129 2.8286 (0.028) (0.610) *significant at 5% level

Table 5: Long run OLS estimation of UIP

Regression formula:

Estimates (p-value) Adjusted R2 Newey-West N α β Std. Error β 2-years 417 -0.0908** 0.6807 0.0099 1.0484 (0.001) (0.516) 5-years 261 -0.1748*** 0.8510 0.0115 0.4919 (0.000) (0.085) **significant at 1% level ***significant at 0.1% level

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Table 6: OLS estimation of UIP on different periods (3-month)

Regression formula:

Estimates (p-value) Adjusted R2 Newey-West N α β Std. Error β Before 231 -0.0294** -3.3552 0.0253 2.8521 (0.009) (0.241) During 162 0.0018 3.5755** 0.129 1.3222 (0.607) (0.008) After 89 -0.0264 -19.3172* 0.1437 9.2970 (0.055) (0.041) *significant at 5% level **significant at 1% level

Regression formula:

Estimates (p-value) Adjusted R2 Newey-West N α β Std. Error β Before 218 -0.0671** -4.7314 0.1011 3.0027 (0.003) (0.117) During 149 0.0033 2.04* 0.1241 0.9587 (0.647) (0.035) After 76 -0.0953*** -31.6474*** 0.6129 3.4245 (0.000) (0.000) **significant at 1% level ***significant at 0.1% level

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Regression formula:

Estimates (p-value) Adjusted R2 Newey-West N α β Std. Error β Before 192 -.1526*** -6.1342*** 0.4586 1.4129 (0.000) (0.000) During 123 -0.0011 -0.3307 0.0006 0.8322 (0.919) 0.692 ***significant at 0.1% level

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Graphs

Graph 1: Exchange rate CHF/EUR 2007-2011

Data of the exchange rate provided by the ECB.

Graph 2: Export growth Switzerland relative to previous period

Source: SNB (2011). Blue bar represents the exported goods, red bar the exported services and the black line represents the total export of Switzerland.

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1-1-2007 1-1-2008 1-1-2009 1-1-2010 1-1-2011 CHF/EUR

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Graph 3: Inflation forecast SNB

Source: SNB (2011). Blue line is het inflation, green dotted line forecast in September 2011 and yellow dotted line forecast in December 2011.

Graph 4: Exchange rate EUR/CHF during the peg

Data of the exchange rate provided by the ECB.

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 12-9-2011 12-9-2012 12-9-2013 12-9-2014 CHF/EUR

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Graph 5: Exchange rate EUR/CHF after removing the peg

Data of the exchange rate provided by the ECB.

0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 6-10-2014 6-10-2015 6-10-2016 CHF/EUR

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Graph 6: Scatter diagram of exchange rate depreciation and interest rate differential.

The 4 graphs show the scatter diagrams of the 5 different periods. S3M, S1Y, S2Y and S5Y stand for the depreciation in the specific period. Y3M, Y1, Y2 and Y5 stand for the interest differential of the specific periods. a) 3-month b) 1- year c) 2-year d) 5-Year -. 2 -. 1 0 .1 .2 S 3 M -.004 -.003 -.002 -.001 0 .001 Y3M -. 2 -. 1 0 .1 S 1 Y -.015 -.01 -.005 0 .005 .01 Y1 -. 4 -. 3 -. 2 -. 1 0 .1 S 2 Y -.04 -.03 -.02 -.01 0 Y2 -. 4 -. 3 -. 2 -. 1 0 S 5 Y -.1 -.08 -.06 -.04 Y5

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Graph 7: Interest rate differential 3 Month Libor rate and exchange rate depreciation -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 1-8-2007 1-8-2008 1-8-2009 1-8-2010 1-8-2011 1-8-2012 1-8-2013 1-8-2014 1-8-2015 1-8-2016