Is the Forward Exchange Rate Able to Predict the Spot Rate? - An Application to the Euro

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IS THE FORWARD EXCHANGE RATE ABLE TO PREDICT THE SPOT RATE? – AN APPLICATION TO THE EURO

Diogo Matos Almeida

Dissertation

Master in Economics

Supervised by João Loureiro, PhD

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Abstract

Since the beginning of floating exchange rates regime, the study of exchange rates and its prediction appeared to be a priority for many economists. Initially, the focus on spot exchange rates prediction came from efficiency studies. Starting from the theoretical and empirical literature regarding spot rates prediction made by several authors over the years, the objective of this dissertation is to understand to what extent the forward exchange rates are able to be used as a predictor of the spot exchange rates. From this first analysis, in which is concluded that the forward rates aren’t able to accurately predict the spot rates, is then analysed the possibility of news, the new relevant information that appear between the moment of the current forward rate and the moment of the future spot rate that is being forecasted, explain the forecast error between the rates. First, an interest rate differential with interbank market rates was used as news representative, and then, another differential was added based on german and greek Government Bonds interest rates. Estimations in which were used three month forward rates for both CHF/EUR and USD/EUR, news – relative to the interbank market rates differential – appeared to be significant. The rates differential concerning the Government Bonds interest rates was also significant with both three month and six month forward rates, for CHF/EUR. The Random Walk Theory was also tested, having been reject for both exchange rates.

JEL Codes: F31, G14

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Resumo

Desde o início do regime de câmbios flexíveis, que o estudo das taxas de câmbio e sua previsão se afiguraram como prioritário para muitos economistas. Inicialmente, o foco na previsão das taxas de câmbio spot partia do estudo da eficiência. Tendo como base o estudo teórico e empírico relativo à previsão de taxas spot feito por vários autores ao longo dos anos, o objetivo desta dissertação é perceber até que ponto as taxas de câmbio forward são capazes de ser usadas como previsor das taxas spot. Desta primeira análise, em que se conclui que as taxas forward são incapazes de prever devidamente as taxas spot, é depois analisada a possibilidade das news, informação relevante que surge entre o momento da taxa de câmbio forward atual e o momento da taxa de câmbio spot futura que está a ser prevista, explicarem o desfasamento entre as duas taxas de câmbio. Primeiramente, foi utilizado um diferencial taxas de juro do mercado interbancário enquanto representativos das news e, num segundo momento, um diferencial de taxas de juro de títulos de dívida alemã e grega. Nas estimações em que foram usadas taxas forward a três meses, as news – quando usadas taxas de juro do mercado interbancário - revelaram-se significativas em ambas as taxas de câmbio analisadas, CHF/EUR e USD/EUR. O diferencial relativo às taxas de juro de dívida pública demonstrou ser significativo no error de previsão da taxa de câmbio CHF/EUR, tanto com taxas forward a três meses como a seis meses. A Random Walk Theory também foi testada, tendo sido rejeitada para ambas as taxas de câmbio.

Classificação JEL: F31, G14

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List of Tables

Table 1: Estimation of Equation (3.3) from April 2000 to March 2019...18

Table 2: Results from Autocorrelation Test (with Levels and First Differences)...19

Table 3: Results from Estimation (3.4) with an LDV Included...20

Table 4: Estimation of Equation (3.6)...22

Table 5: Forecast Error Statistics...22

Table 6: Forecast Error for Increasing and Decreasing Spot Rate………...24

Table 7: Estimation of Equation (4.1) in Testing the Random Walk Hypothesis...25

Table 8: Random Walk Hypothesis Analyzed on Sub-Periods...26

Table 9: Results from Equation (5.1) for Determining Whether the Money Market Rates is News...29

Table 10: Results from Equation (5.2) for Forecast Error Estimation using Money Market Rates as “news”...29

Table 11: Forward Rate Prediction Ability Including “News” on Money Market and Sovereign Bond Rates...30

Table 12: Results from Equation (5.4) for Forecast Error Estimation with Interest Rate Differential of Government Bonds...31

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List of Figures

Figure 1: Forecast Error of CHF/EUR and USD/EUR………...………....21

Figure 2: Spot and forward exchange rates (Source: Own calculations based on the data collected from Thomson Reuters’s Eikon)………23

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1. Introduction

The forecasting of spot exchange rates is a topic that is commonly addressed in financial economics literature, given that economies are often heavily affected by the course of currencies. For both governmental decision-makers and for any firm that deals with different currencies, the fluctuations of the exchange rate are a crucial matter.

Due to the relevance of the exchange rate movements, financial analysts often attempt to create forecasting methods. A widely used method consists of using forward exchange rates as a predictor of the future spot rate. This possible prediction ability of the forward exchange rates has been tested many times for several time-spans and exchange rates, but only ambiguous results have been found to date. A large quantity of literature regarding the prediction of spot rates appeared in the 1960s and 1970s after the Bretton Woods System ended. This point marked the beginning of floating exchange rates.

Researchers who investigate the predictability of the spot rate based on the forward rate often try to explain the differences between the two rates. There is a wide array of approaches that have been used to justify the rate differential; these approaches include using official announcements made by the Government or Central Banks, testing the validity of established conditions such as Covered Interest Rate Parity (CIP), Uncovered Interest Rate Parity (UIP), or Purchasing Power Parity (PPP), and the use of government bond interest rates as a proxy of the investors’ feelings. In particular, this last approach of using government bond interest rates is adopted in this Dissertation.

If the forward exchange rate is confirmed to accurately predict the future spot rate, there are no arbitrage opportunities. The impossibility of excess returns is a base consideration of the efficient market hypothesis (EMH), which was first studied by Fama (1965). According to Fama and Malkiel (1970), the market is highly efficient in reflecting information due to the action of professional traders and no one can generate excess returns in the long term. Following their view, Malkiel (2011) believed that the arbitrage opportunities do not persist. Much of the theoretical and empirical literature dedicated to the prediction of the spot rate is based on articles concerning market efficiency and the EMH. The EMH has been tested on its various forms in several financial markets (Wickremasinghe, 2004; Beck, 1994; Laffont and Maskin, 1990), including the foreign exchange market, which is the largest and most liquid financial market; as a case in point,

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2 the market recorded an average trading of over 5 thousand billion dollars per day in April 2016 (BIS, 2016). Many of the studies have rejected the EMH and rational expectations hypothesis in the foreign exchange markets, given that these have produced indefinite results. However, these studies have not been able to explain the cause of inefficiency in an accurate way (Ibrahim et al., 2011).

This study intends to analyse the capability of the forward rates in predicting the future spot rates, and the exchange rates to be tested are the USD/EUR and CHF/EUR from 2000 to 2018. Both USD/EUR and CHF/EUR have had high volatility since the beginning of the euro, given that the US dollar and the euro are the currencies with highest turnover since 2001 (BIS, 2016). Moreover, the Swiss franc was used as a safe haven currency during the 2008 Great Recession, as many investors have shown confidence in the Swiss currency. During the Sovereign Debt Crisis in Europe, which had a severe impact on several European countries, there was a major confidence crisis in the euro, and there were even rumours that the euro could end. Such a background is the motivation for this study to conduct a separate analysis of the data; specifically, the full data sample was split in two equal sub-periods, with the first being from January 2000 until June 2009 and the second from July 2009 until December 2018. A crisis can have a negative impact on the efficiency. As suggested by Lim et al. (2008), this impact is mostly due to the chaos felt in financial markets and the consequent overreaction of the investors to the media about the market. This impact can arise in countless number during these phases, but the markets can ultimately recover. This paper is structured in the following manner. Chapter 2 presents relevant theoretical concepts and definitions as well as empirical literature. In Chapter 3, the forward rate is tested on its ability to predict the future spot rate. In Chapter 4, the study performs the same analysis as in the previous chapter but with an added variable, namely an interest rate differential, assuming that this variable can justify the error. Chapter 5 tests the hypothesis that spot rates can follow a random walk. Finally, Chapter 6 summarizes the results obtained in the previous chapters, and it offers some final remarks based on those same results.

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2. Literature Review

2.1. From market efficiency studies to exchange rates

forecasting

The EMH has been widely researched since it was first mentioned by Eugene Fama; according to Yen and Lee (2008), it has been one of the most frequently tested theories regarding financial economics. While the EMH has been applied mostly to the stock market, it can also be applied to the foreign exchange market (Ibrahim et al., 2011). Market efficiency has been defined in diverse ways by the various authors who have studied this topic. Tahir (2011) stated that a market is efficient when the prices of financial assets reflect all available information properly and with celerity. As for other authors, the most relevant feature— which ends up being a consequence of the previous characteristic—is the unattainability of excess returns in such markets (Brealy et al., 1988).

The EMH as defined in its strictest sense holds true when a market is entirely informationally efficient—where prices fully reflect the available information and where it is impossible to earn abnormal returns through their exploitation (Fama, 1970). Fama defined the concept of information efficiency by categorizing it based on the degree of the information subsets as generated into three forms, namely weak-form, semi-strong form, and strong form.

A weakly efficient market is the one in which asset prices already reflect previous returns, meaning that it is impossible to earn excess returns based on the same past prices, and the prices are not correlated with past information (Degutis and Novickytė, 2014; Fama, 1970). Regarding the semi-strong form, Fama (1970) refers to semi-strong efficiency when security prices reflect all present and past publicly available information. The tests are done to this mid-level degree of efficiency, and the tests are later named by Fama (1991) as event studies; these tests are based on specific events and their influence on the security prices and on whether the adjustment was efficient. Lastly, the highest degree of market efficiency is strong form, which encompasses both the previous two forms of efficiency. With this form, participants are not able to generate excess returns based on past prices and trading volumes, and neither can they do this with all publicly and privately available information (Fama, 1970).

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4 Clarke et al. (2001) provided important insight into the EMH and disproved some myths regarding it as well. In particular, their work refuted the belief that excess returns are impossible in an efficient market. Their explanation relies on the premise that the EMH does not state it is impossible to beat the market, there is still the possibility that someone is able to predict and outperform it. Still, in a global market with millions of investors, there may be someone who manages to outperform the market over time, but this does not threatens the EMH’s validity, as it is expected a priori that a small percentage of investors can attain to this (Clarke et al., 2001). This point was also addressed by Malkiel (2003); the basic notion is that every trend discovered by investors to be profitable—these usually being quantitative-based investment funds— will be exploited until it is no longer possible to earn excess returns from it. Thus, it is not impossible to generate excess returns out of a financial asset; however, this can only be done for a limited period and for a limited number of people.

The fiercest opponents to the EMH are institutional investors, whose investment decisions rely on trading rules based on extensive technical analysis. The reason is simple: if the markets are efficient, the prices of the assets are random. Therefore, the trading rules are useless, and abnormal returns are “lucky guesses”. Literature has pointed in both directions, where several studies have stated that the superior returns of filter and trading rules relative to the simple buy-and-hold strategy, and the opposite has been argued as well (see Neely, 2003; Neely et al., 1997 and Brock et al., 1992).

According to some authors, the high volatility of the prices is an indicator of the invalidity of the EMH, since prices should be stable (Shiller, 1981). This is a very refuted opinion, and others have stated that the high fluctuation of prices only confirms the fact that markets are informationally efficient and that these fluctuations are the result of the constant news being reported (Clarke et al., 2001; Földvári and Van Leeuwen, 2011).

As previously stated, most of the empirical work dedicated to the spot rate prediction was in fact a test to market efficiency. Concerning the foreign exchange market, Levich (1989) stated that in an efficient market, investors tend to form rational expectations, and thus the expected future spot rate based on the available information will likely be equal to the actual future spot rate. This notion is based on the weak-form of the EMH, and it has led to one of the most commonly used methodology in spot rate prediction, which consists of assessing and comparing a forward rate with the corresponding future spot rate.

In the work developed by Hallwood and McDonald (1994), the results lead to the common conclusion that the forward rate is a very poor predictor, in that it is limiting when

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5 following the spot rate trend. Still, the authors stated that the forward rates reflect the available information efficiently, and hence it does not mean that there is a rejection of the EMH. According to them, the forwards are an optimal predictor; it attributes the differences of the rates to the appearance of new information, the significant variances in risk premiums, or both. Nevertheless, in an efficient forward market, the deviations between a forward rate and its corresponding future spot rate have no serial correlation and zero mean. Levich (1979) defined two types of efficiency in this specific market, namely simple efficiency and general efficiency. Simple efficiency is where the forward rate is the expected future spot rate; in general efficiency, the forward rate is the sum between the expected future spot rate and a risk premium.

The estimations done by Levich – and as it will be also done in this dissertation – were made using the logarithm of the rates instead of the actual values; this was done in order to work around the Siegel’s paradox1_{as identified by Siegel (1972).}

Levich (1979) tested simple efficiency 𝐻 : 𝑎 = 0 ∩ 𝑏 = 1 ∩ 𝑐 = 0 based on the following regression:

ln 𝑆_, = 𝑎 + 𝑏 ln 𝐹_, + 𝑐 ln(𝑋 ) + 𝑒 (2.1)

in which 𝑆_, is the future spot rate, 𝐹_, is the n-period forward rate, and 𝑋 is any other variable to be chosen by the author of the study, having inconclusive the results. The first years of tests using this approach were right after the fall of the Bretton Woods System, which coincides with the beginning of the floating exchange rates regime. On these first tests, the simple efficiency hypothesis was not rejected. Later, in other studies using an altered version of (2.1), in which ,

, and ,

, was used instead of 𝐹, and 𝑋, , the simple efficiency

hypothesis was rejected (Hansen and Hodrick, 1980; Tryon, 1979).

In the empirical studies on the general efficiency hypothesis, authors allow 𝑋 to be tested by not imposing 𝑐 = 0, thus enabling the identification of variables that can produce a forecaster of the future spot rate superior to the forward rate. Bilson (1984) built a

1_{Siegel found that, if the rates are expressed as their actual values, then prediction of the future spot rate will} provide an unequal rate for the home and foreign country. Using actual values, the expected spot rate for home country is 𝑠 = 𝐸 (𝑠 ) and for the foreign country = 𝐸 . Both conditions can’t be

simultaneously correct. Using logarithms of the rates the expected spot rate for home country is ln (𝑠 ) = 𝐸 (ln 𝑠 ) and for foreign country ln ( ) = 𝐸

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6 forecasting equation by firstly using the current spot rate as the X variable and then by using a PPP forecast, the latter of which was proven to accurately predict the spot rates. However, this does not mean that the market is inefficient since the profits can correspond to the risk premium. In addition, the forecasts were done using past data – so the coefficients a, b and c were obtained before the predictions were made; performing a similar forecasting in order to predict future spot rates would not generate the same results, as coefficients a, b, and c could only be obtained at the end of the analysed period.

2.2. Review of methodologies and empirical results on spot

exchange rates prediction

2.2.1. Forward and spot exchange rates

Many researchers have attempted to use the forward premium as an optimal predictor, where the premium is a value that corresponds to the difference between the forward rate and spot rate when the forward is higher than its spot. Using an expression similar to (2.1), the hypothesis that a = 0 and b = 1 was rejected, which is meaningful given that the data sets are not the same (Gregory and McCurdy, 1984; Longworth, 1981). Fama (1984) even gave a value for b that is close to −1, which is the complete opposite of the tested value of +1; he had studied the rates of the Swiss franc versus the US dollar and decided on a value of −1.15. According to Hallwood and McDonald (1994), this suggests that when investors attempt to establish a forecasting procedure based on this sort of estimation, they will obtain a completely wrong estimation. This belief was shared by Taylor (1995); he stated that the forward premium mis-predicting the direction of the spot exchange rate—also known as the forward discount bias—may be due to the authors ignoring the constant term in the regression. In a more technical sense, this means that the more a foreign currency is at premium in the forward market at a given length, the less the home currency is predicted to depreciate over that length, but commonly empirical evidence shows otherwise (Taylor, 1995).

Taylor (1995) stressed some issues regarding the common use of regressions of the logarithm of the spot rate against the lagged logarithm of the forward rate. In the study, the series were not stationary, making it impossible to do a proper standard regression analysis.

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7 Aside from the non-stationarity, some exchange rates were also “extremely hard to distinguish from simple random walks”, and therefore the common simple efficiency tests were not viable, as this behaviour misperceives them. Due to these concerns, the author suggested a new test for simple efficiency based on the orthogonality of the forward rate forecast error. This is represented in (2.2) as follows:

𝑠 − 𝑓( )=ѱ𝐼_𝑡+ 𝜂_𝑡+𝑘 (2.2).

This new approach is based on the equality between two components, namely the difference between the log of a future spot rate and the log of its corresponding forward rate against a prearranged information set. It also tests ѱ = 0, as in testing whether the information set 𝐼 has an impact on the forecast error where 𝜂 is used as the error term. In tests using (2.2), the orthogonality tests for simple efficiency have also been rejected.

Dick et al. (2015) found a positive relation between a good exchange rate forecasting performance and interest rate forecasts, and through this he highlighted the importance of fundamental forecasts. Based on a sample of professional forecasters, Dick et al. (2015) noted that their ability to predict exchange rates is related to their ability to predict mainly short-term interest rates.

Narayan and Sharma (2015) studied the importance of time-frequency forward rate forecasting ability, and in their research they used daily, weekly, monthly, and quarterly data. Regressions using daily data generated different results compared to the other regressions, as the daily data regressions were seen to be far less consistent. Here, the relation between forward and spot exchange rate was frequency dependent.

Gottwald (2015) assessed the forecasting capacity of the forward exchange rates of the spot rate for USD/EUR. Relying on (2.1) and using ordinary least squares to forecast parameters, the regression analysis showed that the forward forecast undervalues the future spot rate. Furthermore, graphical analysis demonstrated the unreliability of the forward exchange rates as a forecaster.

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2.2.2. Spot rates prediction through theoretical conditions - CIP

and UIP

There are several ways to empirically assess market efficiency, and these ways can be used in spot exchange rates forecasting. There is a wide range of studies regarding market efficiency that focus mainly on the support of CIP and UIP.

The CIP is the condition of equilibrium between interest rates of two countries and the difference between the forward and spot exchange rates of those two countries; this guarantees the impossibility of arbitrage opportunities. In this case, considering a scenario where there are no obstacles in financial markets, the interest rate differential should be the same as the difference between the forward exchange rate and spot rate, while assuring the holding of the CIP as represented:

(𝑖 − 𝑖∗_{) − 𝑓}( )_{− 𝑠} _{= 0.} _(2.3)

n the existing literature using this condition, researchers use mainly two kinds of tests: simple deviations of condition (2.3) and regression analysis as follows:

𝑓 − 𝑠 = 𝛼 + 𝛽(𝑖 − 𝑖∗_{) + 𝑢} _. _(2.4)

The first type of test is based on (2.3), and it consists of assessing whether the obtained value diverges significantly from 0, with 0 being the value that assures the inexistence of arbitrage. However, due to transaction costs, the authors who rely on this type of analysis define a no-arbitrage band, and they test whether the obtained values are within the band. The results are quite ambiguous, and many authors have highlighted the importance of high quality data in this sort of experiment (MacDonald and Taylor, 1992). While Frenkel and Levich (1975, 1977) found that a vast majority of profit opportunities were in fact inside the neutral band, McCormick (1979) used higher quality data to demonstrate that in the GBP/USD rate, 70% to 80% of the deviations consisted of arbitrage opportunities.

Taylor (1987) did a similar study to McCormick’s using high-frequency contemporaneous data of the USD/GBP and USD/DEM. Taylor obtained opposing results to the McCormick’s findings, with only one arbitrage opportunity found in 3456 calculations. This led the author to conclude that these results “overwhelmingly support the market efficiency hypothesis by confirming the covered interest rate parity condition”. Two years later, Taylor (1989) conducted a similar analysis, but considering the periods of economic

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9 turmoil and contrary to the findings of Frenkel and Levich (1977), there were still very few arbitrage opportunities.

The other analysis based on CIP uses (2.4), and the analysis comprises testing 𝛼 = 0 and 𝛽 = 1. Although the results are not the same in all studies, there is a general agreement that the CIP is sustained, mainly because in most studies the value estimated for 𝛽 is insignificantly different from 1 (MacDonald and Taylor, 1992). According to Taylor (1987, 1989), this non-rejection of the hypothesis does not mean the inexistence of arbitrage opportunities—that is, the CIP not being verified during the period; instead, it could point to how the CIP was supported on average during the observed period. In this way, the tests based on (2.3) are considered to be more adequate.

The second condition as a validity for the analysis of the foreign exchange rate prediction ability is the UIP. According to this parity, holding capital in the domestic or foreign currency should not systematically provide different returns (Olmo and Pilbeam, 2011). This hypothesis states that interest rate differential should be equal to the expected rate of change of the exchange rate; it also states that if at a given time the equality does not hold, agents will mobilize their investments across financial markets to the most profitable options until the parity is achieved (Moosa and Bhatti, 1997). The proposition is summarized in the following:

(i − i∗) = ∆s . (2.5)

Olmo and Pilbeam (2011) reviewed some of the extensive literature regarding UIP and efficiency analysis. In most of the studies they reviewed, it is concluded that UIP is not verified empirically (see Froot and Thaler, 1990; Flood and Rose (2002) and Sarno et al. (2006)).

Macdonald and Torrance (1990) argued that the rejection may be due to expectational and risk factors. Taylor (1989) agreed that over-expectation in speculative bubbles can be one of the reasons for the failure of the UIP, and this hypothesis was also supported by Olmo and Pilbeam (2011). The rejection of the UIP is often attributed to time-varying risk premium, but authors who attempted to relate risk premium to the parity failed to reach significant results (MacDonald and Taylor, 1992).

Olmo and Pilbeam (2011) argued that many of the rejections seen in most literature regarding UIP are caused by misleading regressions. The authors proposed a new method

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10 based on profitability that consist of the comparison between different investments and the return of holding funds in domestic returns (i.e., US dollars). The investments used were an investment in a foreign currency, an investment in a currency at a forward discount and an investment in the currency with the highest yield in the previous period. The results were ambiguous, as two of the four currencies (i.e., Swiss franc and yen) were considered to be efficient.

More recently, Chinn and Frankel (2016) tested the relation between exchange risk premium and macroeconomic variables. The authors relied on VIX—which is a measure of market risk—while believing that many existing studies have flaws in the methodologies. Using survey data, the authors found a positive correlation between forward discount and expected depreciation as predicted by the UIP. The authors also noted the interest differential ability to reflect agents’ expectations of the exchange rates.

2.3. The effect of news in spot rates forecasting

The term news was firstly used and was made widespread by Jacob Frenkel, who used the word in referring to unanticipated events. Frenkel (1981) analysed a 6-year period (i.e., 1973 to 1979) in which he looked for the impact of unanticipated events in the exchange rate variation. This is a pertinent insight to this dissertation, since the sub-periods to be analysed are from the start of the euro until the beginning of the Great Recession (i.e., from 1999 to 2008) and from 2009 to 2018.

The impact of news is approached through different perspectives. It can be detected using different tests by analysing only at the single possibility of the randomness of the exchange rates or at the impact of certain events on the exchange rates. This can take place through the forecast error of a chosen forward rate that is relative to its corresponding spot (Levich, 1978) or through a simple expression that relates the forward rate to its corresponding spot rate with an added component of “news” that explains the difference in values.

One of the major contributions regarding efficiency was an article by Levich (1979), who looked at efficiency in the foreign exchange market along with an analysis on the role of news. Specifically, the author performed an in-depth analysis of the theoretical and empirical literature regarding this subject. A relevant consideration taken by Levich is the

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11 way in which the concept is specified; on this point, he stated that the concept should not be thought of as a hypothesis that can be accepted or rejected. In fact, efficiency should be seen as a process since market agents have a very broad range of opinions on different matters; this can lead to an impossibility of reaching full efficiency in the short run, and efficiency can only be attained to in the long run. Moreover, Levich pointed out several issues regarding the analysis on efficiency and news. A poor model choice for determining exchange rates can lead to an improper rejection of market efficiency, as the sole existence of different models hampers the rejection of market efficiency.

In crisis periods, uncertainty can reign in the market, as well as rumours and numerous alterations on the expectations of the economic agents which will in turn lead to fluctuations in asset prices. The high frequency of new (unanticipated) information in the years when a recession becomes deeper can lead to high volatility of the exchange rates, which will likely increase the inaccuracy of the forward rates. Frenkel (1981) based his work on the notion that the news may explain the difference between a forward exchange rate and a spot rate, and he related them together by adding the component news as represented by (𝑧 − 𝑧 ) in (2.6). The variables 𝑧 and 𝑧 represent future information and expected future information respectively; both can be measured through interest rates, surveys, or even actual news from media and social media.

𝑠 = 𝑎 + 𝑏 𝑓 + 𝑏 (𝑧 − 𝑧 ) + 𝑤 . (2.6)

If a researcher analyses the role of the news using (2.6) in a time where a great deal of information is available—as given between t and t+1—there may be a considerable variance of the forward forecasting error, the difference between a forward rate, and a future spot rate (Macdonald and Taylor, 1992).

Similar to the proposal made by Frenkel (1981), Macdonald and Taylor (1992) used an estimation for the forward forecast error based on 𝑧 , which contains all the news with relevance. This was used in order to determine the exchange rate 𝑧 , which is the news expectations. This estimation is based on the past information set and the news with a random error term 𝜂 .

𝑠 − 𝑓 = 𝛾(𝑧 − 𝑧 ) + 𝜂 (2.7)

The expression in (2.7) emphasises the notion that when there is a considerable amount of new data regarding fundamentals, 𝑠 and 𝑓 will not be close, given that the

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12 emergence of more new information leads to a higher difference between 𝑧 and 𝑧 (Macdonald & Hallwood, 1994).

Having determined the equation that researchers can base their work on, there are other choices to be made, such as the method used for obtaining the expected values. In the above-mentioned article by Frenkel (1981), the author analysed the impact of news on the forward rate forecast error for several exchange rates through interest rate differentials, and this was done using a time series to generate 𝑧 (where 𝑧 is an observed variable). However, it is nearly impossible to quantify the component of news with an acceptable level of precision. To tackle this challenge, Frenkel (1981) used a macroeconomic variable that reflects the news through the confidence of the investors in the currency—the interest rate. The author obtained significant results with this expression based on the interest rate differential, and this was found to be consistent with the idea that most of the exchange rates fluctuations are caused by this news component.

Other authors relied on time series as well, such as Bomhoff and Korteweg (1983) who implemented it in a dynamic manner. Specifically, the variables that they based the estimations for the news component on were allowed to vary over time. The researchers, who analysed roughly the same period that was analysed by Frenkel (1981), concluded that new information can explain 16% to 60% of the unexpected changes for several exchange rates.

Others relied on different estimation methods, such as Dornbusch (1982), who generated the news component based on OECD survey data, or MacDonald (1983) and Copeland (1984), who used autoregressive models (i.e., VAR and ARIMA). In such a study, Dornbusch arrived at interesting conclusions regarding exchange rates’ response to news with respect to three specific topics, namely current accounts, cyclical or demand factors, and interest rates. Unanticipated economic growth in the US seems to lead to a depreciation of the US dollar. When current account improvements were unexpected, there was a noticeable US dollar appreciation, which was a result that was also found by Branson (1983). Dornbusch (1982) discovered a positive coefficient regarding current accounts in the Japanese yen and German mark. In the end, unexpected increases in the short-term interest rate differential showed significant results for all exchange rates evaluated.

MacDonald (1983) used a similar expression as the one used by Frenkel (1981) as seen in (2.6), but the author took different sets of information instead of relying only on the past information of the variable intended to be predicted. The variables included in z were

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13 home and foreign money supply growth; other variables that were regressed against them were inflation rate, interest rates, budget deficit, or income. Relying on both ordinary least squares (OLS) and ZSURE estimators, the results here suggested that an unexpected increase in home money lead to an appreciation of the home currency. The author also found that lagged news were statistically significant; this was a result highlighted by Bomhoff and Korteweg (1983) as well.

In general, the empirical research regarding the impact of news supports the perspective that news is one of the explanations for unexpected exchange rates movements. However, the volatility of the exchange rates itself is much higher than the variables that were analysed in this sort of studies (Davidson, 1985; Mcdonald, 1994). McDonald (1994) presented some explanations for this, such as the importance of non-quantifiable news (e.g., political announcements) which alters the behaviour of agents. Frankel and Rose (1995) conducted a survey on the literature of these announcement effects, and they found that there are ways of working around this non-quantifiability. The researchers suggested that gathering official announcements, newspapers, and press releases can turn this disadvantage into an advantage; since with this way it is easy to identify the actual hour and date that the news were disclosed in order to study its effect on the exchange rate. However, the results until the date of that review have been disappointing.

Faust et al. (2007) looked for the effects of several macro announcements using high-frequency data from 1987 to 2002. As expected, US macro announcements that were better than expected led to the US dollar appreciation and also to a lower risk premium in holding foreign currency. A similar result was obtained by Andersen et al. (2007), who examined the US macroeconomic news effect on US, German, and British stock, bond, and foreign exchange markets. According to them, positive domestic shocks were observed to generate a positive effect on the dollar. News regarding US inflation do not generate any significant and systematic result (Andersen et al., 2007), a result which is different to the one obtained by Clarida and Waldman (2007), who also studied the US dollar. Negative news regarding inflation - when it is higher than expected – led to appreciation of the home currency (Clarida and Waldman, 2007). Goldberg and Klein (2005) obtained similar results regarding the euro from 2003 until 2005. They observing the period from 1999 to 2005, and they found that in the first 4 years, negative news about inflation led to euro depreciation, which is a trend that changed in the last 2 years of the observed time span (Goldberg and Klein, 2005).

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14 The high volatility of the exchange rates can also be due to the existence of speculative bubbles and overpricing of the assets or of a given currency. Another possible explanation that relies more on the technical side concerns either the use of the wrong economic model, the use of wrong variables used in the model to estimate exchange rates, or even both (Macdonald, 1994). Kallianiotis (2018) studied the role of the news component using an equation similar to (2.6) and found significant results. He concluded that in two of the four exchange rates he analysed, news had an impact on future spot rates. The author conducted the study using a perspective of efficiency analysis, in which he considered the pairings of the Canadian dollar to US dollar and the euro to US dollar as efficient; with this premise, the change in the interest rates are anticipated and have no impact on future spot exchange rates. In the opposite direction when testing for the US dollar to the British pound and the Japanese yen to US dollar, the interest rates changes appeared to be unanticipated, and thus they had an effect on the exchange rates.

2.4. The Random Walk of the Spot Rates

The random walk theory suggests that spot exchange rates follow a random walk, and as a result the rates do not have any correlation with its past prices. In general, equality has been observed between the expected future spot exchange rate and the current spot exchange rate, which confirms the random walk hypothesis (Kallianiotis, 2018). Thus, the difference between the actual future and current spot rates are the result of unexpected events that occur between t and t+1. Since these events are random, one way of testing this hypothesis is by assessing the mean error of coefficient 𝛽 as seen in (2.8), which should be around 0 according to this hypothesis:

𝑠 − 𝑠 = 𝛽 + 𝑢 (2.8)

A commonly used empirical test consists of using (2.9), and it further tests the hypothesis of 𝛽 = 0 and 𝛽 = 1. Here, (2.9) is similar to (2.1), but instead of using a forward rate as an explanatory variable, it uses past values of the same spot rate. The non-rejection of this hypothesis confirms that there is random walk followed by the evaluated exchange rate:

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15 In both (2.8) and (2.9), 𝑠 and 𝑠 represent the current and past spot exchange rates. In a spot rate prediction analysis, this type of empirical testing is used for checking the capability of the current spot rate to predict the future spot rate.

There have been empirical results supporting this theory, with Meese and Rogoff (1982) obtaining superior results in predicting future spot rates by relying on Random Walk being compared to widely used macroeconomic models (i.e., Modified Frenkel – Bilson, Modified Dornbusch – Frankel, Modified Hooper – Morton). More recently, Kallianiotis (2018) used (2.9) with data sets of several exchange rates; the author proceeded to perform the mentioned hypothesis tests, and the random walk theory was not rejected for both USD/EUR and USD/GBP.

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16

3. Testing the Forward Rate as a Predictor of the Spot Rate

3.1. Introduction

As mentioned, this dissertation assesses the effectiveness of the forward exchange rate in predicting the future spot rate. In this chapter, the study looks at the forward rate, particularly in how it can be a predictor of the spot rate.

To ensure a proper econometric analysis, a time series must be stationary (Milionis, 2004). In checking for stationarity, the study uses the augmented Dickey–Fuller (ADF) test, which is applied to all time series on levels. If the stationarity hypothesis is rejected, the test is then applied again to all time series on first differences. If using first differences and if a time series appear to be non-stationary, the test is then applied using second differences. This test will then determine how the time series will be used on the regressions. Aside from the spot rates, the 3-month and 6-month forward exchange rates are also used. Since the data are of monthly frequencies, there is data overlapping, and thus it is likely that there is error autocorrelation.

To test for serial correlation (or error autocorrelation), several tests can be used, such as the Breusch–Godfrey test or the Durbin–Watson (D-W) statistic. D-W takes values between 0 and 4, and the value must be as close to 2 as possible. Often, the values that indicate no error autocorrelation are between 1.5 and 2.5 (Haery et al., 2013).

Firstly, the regression that will be estimated is the same that is used by Frenkel (1981) and has been posteriorly replicated by many authors to different currencies and periods. The estimation is as follows:

𝑠 = 𝛽 + 𝛽 𝑓 + 𝑢 (3.1)

In addition, the tests establish the null hypothesis of 𝛽 = 0, 𝛽 = 1, and a joint hypothesis test that contain these two hypotheses is performed. If these hypotheses hold while assuring the regression is not serially correlated by correcting the data overlapping effect, the forward exchange rate is then an efficient predictor of the spot exchange rate (MacDonald, 2007).

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17 Posteriorly, an analysis of the forecast errors is made based on the work of Frankel (1979) using (3.2):

∆𝑠 − ∆𝑓 = 𝛽 + 𝑢 (3.2)

Here, the estimate has only one constant without explanatory variables, and a significance test should be applied to 𝛽 . According to Levich (1979), the mean errors of the forecast error tend to be small and statistically insignificant.

3.2 Data description

The data concerning forward and spot exchange rates were obtained through the Thomson Reuters’s Eikon, a software dedicated to the monitoring and analysis of financial data. The interest rates used later—namely LIBOR and Government Bond rates—were taken from Federal Reserve Economic Data (FRED) that is kept by the Federal Reserve Bank of St. Louis. All data are monthly, and the values correspond to the last day of the month; the data are from January 2000 to April 2019.

3.3 Empirical results and discussion

The first equation to be estimated is (3.3). It was applied to CHF/EUR and USD/EUR exchange rates; the study used OLS to run the regression, and the results are presented in Table 1.

𝑠 = 𝛽 + 𝛽 𝑓 + 𝑢 (3.3)

Here, 𝑠 is the logarithm of the future spot exchange rate, with n being either 3 or 6 months; 𝑓 corresponds to the logarithm current forward exchange rate of 3 or 6 months.

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18

Table 1. Estimation of Equation (3.3) from April 2000 to March 2019

Exchange Rate 𝛽 𝛽 𝑅 D-W p-value (𝛽 = 0 ∩

𝛽 = 1) CHF/EUR (3 months) 0.0008 (0.0029) 0.9923* (0.00865) 0.9832 2.33 0.3127 USD/EUR (3 months) -0.01416* (0.0053) 0.9291* (0.0224) 0.8839 0.5701 0.0064 CHF/EUR (6 months) 0.0021 (0.00539) 0.98205* (0.01597) 0.94456 0.6322 0.181 USD/EUR (6 months) -0.031* (0.0075) 0.8487* (0.0315) 0.7647 0.2583 0.0000

𝑅 = R-squared; D-W = Durbin–Watson statistic; * = significant at 5% level; ** = significant at 10% level; the value in parentheses below the coefficient is its standard error.

If the forward rates predicted the spot rates with 100% accuracy, 𝛽 would be 0, and 𝛽 would be 1. Thus, two hypotheses are created in which the null on the first case was 𝛽 =0 and 𝛽 =1 on the second; both were tested using a Wald test. Based on the p-values concerning the joint hypothesis test (i.e., in the last column) conducted at the commonly used 5% level of significance, the null hypotheses regarding the Swiss franc are not rejected, while the ones regarding US dollar are always rejected.

After the first estimation, the study conducted tests to assess stationarity and error autocorrelation. Here, (13.3) may lead to deceptive conclusions since the time series used are non-stationary. The use of non-stationary time series can lead to misleading results, as the methodologies that are used in the time series analysis assume stationarity (Milionis, 2004). To test for stationarity, the study conducted an ADF test. In this test, the null hypothesis is that there is a unit root, meaning that the sample is non-stationary and that the alternative is the complete opposite. The results are depicted in Table 2.

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19

Table 2. Results from Autocorrelation Test (with Levels and First Differences) Levels

Variable t-Statistic p-value

₣/€ (spot rate) -0.69732 0.844

$/€ (spot rate) -2.0768 0.2544

₣/€ (3 months forward rate) -0.72629 0.8367

$/€ (3 months forward rate) -1.77454 0.3925

First Differences

₣/€ (spot rate) -17.72878 0.0000

$/€ (spot rate) -14.56854 0.0000

As expected, when tested on levels, the non-stationarity hypothesis was rejected for all variables. When using first differences of the variables, the ADF test showed the inexistence of a unit root, so the variables are stationary.

Forecast errors are expected to be correlated, since there is an overlapping of the data; here, the forward rates have either 3 or 6-month maturities, and the data frequency is monthly. Accordingly, it is likely to observe serial correlation between error terms (McDonald, 1994). Through the D-W statistic, the study found that error autocorrelation occurs in almost all regressions; only the one using the Swiss franc/euro 3-month forward rate presents a D-W closer to 2. In order to extend this evaluation, the study proceeded to use a Breusch–Godfrey test to determine the actual order of error autocorrelation. The results demonstrate the need to use a lag of the dependent variable 𝑠 , which is the logarithm of the current spot rate and is obtained from 𝑠 . In a dynamic model such as the one presented, a lagged dependent variable is often the best choice for autocorrelation correction (Keele and Kelly, 2006). Using the current spot rate as an explanatory variable allows us to understand the explanatory power of the forward rates more accurately.

The results of the estimations including the lagged dependent variable are in Table 3. The regression is done using the Swiss franc/euro 3-month forward rate as the explanatory

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20 variable; since the regression exhibits no serial correlation, it will not be added to the lagged dependent variable, and the regression for this set of data is finalized as (3.3).

Equation (3.4) is based on (3.3) with an added lagged dependent variable (LDV) to correct for serial correlation, and variables are used as first differences in order to be stationary. As already mentioned, the first regression (CHF/EUR for 3 months) is calculated, as seen in (3.3).

∆𝑠 = 𝛽 + 𝛽 ∆𝑓 + 𝛽 ∆𝑠 + 𝑢 (3.4)

As stated, for the forward rate to be a perfectly accurate predictor of the future spot rate, 𝛽 should be 0, and 𝛽 should be 1. The joint hypothesis concerning this perfect predictability capacity of the forward rate (𝐻: 𝛽 = 0 ∩ 𝛽 = 1) was rejected for all data sets, as p-values of an absolute 0 were seen on every estimation.

Prior to the development of complex regressions, a simple analysis first used by Frankel (1979) was based on the forecast error. The forecast error is often taken as the mean absolute error (MAE) of 𝑠 − 𝑓 , which is the difference between the spot rate and its corresponding forward rate. The regression-type analysis of the forecast error, which is calculated without considering additional explanatory variables, consists of examining the residuals and its deviation from 0 and the statistical significance of 𝛽 with respect to (3.5) and (3.6). As Gottwald (2015) pointed out, aside from the regular coefficient and significance

Table 3. Results from Estimation (3.4) with an LDV Included

Exchange Rate 𝛽 𝛽 𝛽 𝑅 D-W p-value (𝛽 =

0 ∩ 𝛽 = 1) CHF/EUR (3 months) -0.00182 (0.00125) -0.1697* (0.06585) - 0.028799 1.993286 0.0000 USD/EUR (3 months) -0.000755 (0.001910) 0.082589 (0.066534) 0.028398 (0.066709) 0.007591 1.988935 0.0000 CHF/EUR (6 months) -0.001790 (0.001266) -0.037635 (0.066279) -0.169832* (0.066401) 0.030589 1.991203 0.0000 USD/EUR (6 months) -0.000743 (0.001909) 0.112840** (0.066823) 0.035306 (0.066688) 0.013660 1.977043 0.0000

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21 analysis, a graphical analysis is also helpful for understanding the relation between the two exchange rates. Figure 1 contains the error of every moment of the time sample.

-.20 -.15 -.10 -.05 .00 .05 .10 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 -.15 -.10 -.05 .00 .05 .10 .15 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018

(a) Swiss franc; spot and 3-month forward rates (b) US dollar; spot and 3-month forward rates

-.20 -.15 -.10 -.05 .00 .05 .10 .15 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 -.20 -.15 -.10 -.05 .00 .05 .10 .15 .20 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018

(c) Swiss franc; spot and 6-month forward rates (d) US dollar; spot and 6-month forward rates

Figure 1: Forecast Error of CHF/EUR and USD/EUR

Results of the forecast error regression are in Table 4, while Table 5 contains statistics concerning the mean error. When calculating the forecast error based on (3.5), the estimations exhibit serial correlation. As previously explained, the study added the LDV 𝑠 − 𝑓 in order to correct this issue. As a result, the equation used is given as (3.6):

𝑠 − 𝑓 = 𝛽 + 𝑢 (3.5)

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22 The valuesobtained in Table 4 for 𝛽 are all negative and are close to 0 as expected. This may indicate some level of overestimation by the forward rates.

The use of mean error statistics in the evaluation of exchange rates forecasting accuracy was firstly brought by Meese and Rogoff (1983). According to the authors, the root mean squared error (RMSE) is the main measure, but it may not be the most suitable in some cases. Accordingly, the MAE should also be included, as it could useful when exchange rates distribution has fat tails.

It is common for studies to properly draw conclusions from RMSE or MAE. Several authors based on Cheung, Chinn, and Pascual (2005) have calculated the quotient between RMSE (or MAE) of any given exchange rate determination model and the RMSE (or MAE) of the random walk model. Values above 1 demonstrate the superiority of the random walk model, while values below 1 demonstrate its inferiority. Mean absolute percentage error MAPE) does not require this sort of further calculations, as it is already a relative value. MAPE determines the amount of error in predictions when compared to the actual value (Khair et al., 2017).

Table 4. Estimation of Equation (3.6)

𝛽 𝛽 D-W ₣/€ (3 months) -0.000783 (0.002014) 0.603647* (0.053018) 1.974696 $/€ (3 months) -0.000614 (0.002048) 0.696786* (0.047127) 1.580827 ₣/€ (6 months) -0.000674 (0.002152) 0.801743* (0.039934) 2.160307 $/€ (6 months) -0.000531 (0.002066) 0.861364* (0.033835) 1.633740 𝑅 = R-squared; D-W = Durbin–Watson statistic; * = significant at 5% level; ** = significant at 10% level; the value in parentheses below the coefficient is its standard error.

Table 5. Forecast Error Statistics

MAE MAPE (%)

₣/€ (3 months) -0.00230 -0.23508

$/€ (3 months) -0.00106 -0.22692

₣/€ (6 months) -0.00427 -0.44823

$/€ (6 months) -0.00275 -0.52636

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23 Concerning Table 5, the MAPE values for all exchange rates and forward rate periods confirm the slight overestimation reflected in Table 4.

According to Table 3, in which the study tested the forward rate’s prediction ability of the future spot rate, this hypothesis is rejected as the study found p-values of 0.00 for all exchange rates and forwards used. Alongside the graphical representations of the spot and forward exchange rates (see Figure 2), this rejection seems to suggest that the latter limits follow the first with a lag of the period of the forward rate.

Figure 2. Spot and forward exchange rates (Source: Own calculations based on the data collected from Thomson Reuters’s Eikon)

To assess this possibility, the sample was split in two sub-periods, and two estimations using (3.5) were made; the results did not show serial correlation, and thus there

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24 was no need to use (3.6). One of the estimations contains all observations when the spot rate increased, and the other has the ones when the rate decreased; the results are presented in Table 6.

As expected, the obtained coefficients for 𝛽 are positive on the estimation and are restricted to periods when the spot rate increased; likewise, they are negative when the spot rate decreased. When the spot rate decreases, there is on average overestimation by the forward rate. While when it increases, there is underestimation. This may lead to the notion that the forward rate limits would follow the spot rate trend with a lag, and that they do not have any prediction capacity.

Table 6. Forecast Error for Increasing and Decreasing Spot Rate

𝛽 D-W ₣/€ (3 months) – increasing SR 0.006508 (0.001057) 2.279702 ₣/€ (3 months) – decreasing SR -0.010874 (0.002098) 1.500150 SR = Spot rate; D-W = Durbin–Watson

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25

4. Does spot rates follow a random walk?

The equation presented below has been widely used to test the random walk hypothesis since Fama (1965) first approached this theory. In reviewing empirical literature regarding foreign exchange markets, Mussa (1979) emphasised this notion stating that the natural logarithm of the spot rates followed a random walk.

∆𝑠 = 𝛽 + 𝛽 ∆𝑠 + 𝑢 (4.1)

The dependent variable in (4.1) is the variation of the spot rate at time t+1 and the explanatory variable is the variation of the spot rate at time t. The joint hypothesis tested is 𝐻: 𝛽 = 0 ∩ 𝛽 = 1, and if not rejected, it confirms the existence of random walk by the spot rates. If the actual coefficients of 𝛽 and 𝛽 are 0 and 1, the spot rate is a perfect predictor of the future spot rate. The results obtained are displayed in Table 7.

The coefficients with respect to the random walk equation are mostly statistically insignificant. Thus, the joint hypothesis was rejected for both exchange rates, as p-values of 0.00 were found for exchange rates.

Following the first stage of estimations and coefficient tests, regression (4.1) and respective tests were repeated for two sub-periods. This is done in order to detect possible effects of the 2008 Financial Crisis and the consequent confidence crisis by the investors in the euro on the spot rate’s capacity to predict the future spot rate. The sub-periods used are from 2000 until June 2009 and from July 2009 until March 2019. The results are displayed in Table 8.

Table 7. Estimation of Equation (4.1) in Testing the Random Walk Hypothesis

Exchange Rate 𝛽 𝛽 D-W p-value (𝛽 = 0 ∩

𝛽 = 1) ₣/€ -0.001789 (0.001251) -0.169635* (0.065974) 1.994185 0.0000 $/€ -0.000819 (0.001912) 0.027094 (0.066781) 1.998882 0.0000

𝑅 = R-squared; D-W Durbin–Watson statistic; * = significant at 5% level; ** = significant at 10% level; the value in parentheses below the coefficient is its standard error.

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26 The segregation of the periods did not show any significant changes on the spot rate’s prediction capacity of the future spot rate. The joint hypothesis tests (with the hypothesis being 𝐻: 𝛽 = 0 ∩ 𝛽 = 1) was rejected for all exchange rates on both time samples.

Table 8. Random Walk Hypothesis Analysed on Sub-Periods

2000:06 - 2009:06 𝛽 𝛽 𝑅 D-W p-value (𝛽 = 0 ∩ 𝛽 = 1) CHF/EUR -0.000576 (0.001235) -0.171409** (0.095054) 0.029494 1.958091 0.0000 USD/EUR -0.003387 (0.002933) 0.101063 (0.096171) 0.010215 1.978530 0.0000 2009:07 – 2019:04 𝛽 𝛽 𝑅 D-W p-value (𝛽 = 0 ∩ 𝛽 = 1) CHF/EUR -0.002939 (0.002141) -0.173222 (0.092241) 0.030007 2.006874 0.0000 USD/EUR 0.002057 (0.002489) -0.083344 (0.092980) 0.006938 1.986215 0.0000

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27

5. Investigating the Role of News in Forecast Errors

5.1 Introduction

The estimates realized until this point demonstrated the incapacity of the forward rates to accurately and consistently predict the future spot rates on the analysed exchange rates. According to Frenkel (1982), the observed deviation may arise from news—which as mentioned is defined as the information that comes up between time t and t+n—following the nomenclature of all equations calculated in this dissertation.

To evaluate this possible justification of the forecast errors, two types of estimates are used, which are based on equations that have already been calculated (see Section 3.3) with the added explanatory variable of the news component. Equation (5.1) is based on (3.3), which calculates the forward rate capacity to predict the spot rate; equation (5.2) is based on (3.5) and is applied when estimating the forecast error to see whether the inclusion of news actually helps to explain the errors.

The following estimates are intended to explain the deviations between the forward and corresponding spot exchange rate. This explanation is summed in the term “news”, and the variable that is used to represent news is given as (𝑖 − 𝑖€) − (𝑖 − 𝑖€) . It indicates

the change (i.e., the one between time t and t+n) of the interest rate differential of the n-month LIBOR rate and is based on the US dollar; the n-n-month LIBOR is based on euro when the analysed exchange rate is the USD/EUR. The same rate that is based on the Swiss franc is used when the analysed exchange rate is the CHF/EUR.

The study chose LIBOR as interest rate because money markets are highly liquid, and the LIBOR can quickly capture emerging new information relatively quickly.

∆𝑠 = 𝛽 + 𝛽 ∆𝑓 + 𝛽 [(𝑖 − 𝑖_€) − (𝑖 − 𝑖_€) ] + 𝑢 (5.1) 𝑠 − 𝑓 = 𝛽 + 𝛽 [(𝑖 − 𝑖_€) − (𝑖 − 𝑖_€) ] + 𝑢 (5.2)

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28 After the first attempt at explaining the forecast error based on Money Market’s interest rates, the study addresses another approach based on sovereign debt interest rates. During the European sovereign debt crisis, there was the risk that Greece (and other European countries) could go bankrupt, thereby threatening the survival of the euro and leading to a confidence crisis towards the euro (Chang and Leblond, 2015). This risk reflected the interest rates of Greece’s sovereign bonds; this situation was seen in many countries with very high sovereign debts (Nelson et al., 2010). Hence, following the same rationale as in the two previous equations, the study uses an interest rate differential and assesses whether this differential has indeed any significance on the forward rate inability to predict the future spot rate.

The interest rates used are the Greek year government bonds and German 10-year government bonds. The yield of Greece’s bonds sky-rocketed during 2011 and 2012; this reflects investors’ feelings towards Greece and is seen as a good representation of the bankruptcy fear that was slightly felt in all Europe. On the other side, the interest rates concerning German bonds were kept stable during this period, which demonstrates Germany’s financial well-being (Young and Semmler, 2011).

Equations (5.3) and (5.4) are then built from (5.1) and (5.2) respectively, having had the variable [(𝑖 − 𝑖 ) − (𝑖 − 𝑖 ) ] added. This variable is the change in interest rate differential between t and t+n.

∆𝑠 = 𝛽 + 𝛽 ∆𝑓 + 𝛽 [(𝑖 − 𝑖_€) − (𝑖 − 𝑖_€) ] + 𝛽 [(𝑖 − 𝑖 ) −

(𝑖 − 𝑖 ) ] + 𝑢 (5.3)

𝑠 − 𝑓 = 𝛽 + 𝛽 [(𝑖 − 𝑖_€) − (𝑖 − 𝑖_€) ] + 𝛽 [(𝑖 − 𝑖 ) − (𝑖 −

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29

5.2 Empirical results and discussion

Results regarding (5.1) are in Table 9.

∆𝑠 = 𝛽 + 𝛽 ∆𝑓 + 𝛽 [(𝑖 − 𝑖€) − (𝑖 − 𝑖€) ] + 𝑢 (5.1)

The CHF/EUR using a 3-month forward rate provided the most significant results. The coefficient for 𝛽 was also significant for the estimation of the USD/EUR when using 3-month forward rates. In other words, the news component indeed had an impact on the 3-month forward rate prediction capacity for both CHF/EUR and USD/EUR.

Since the exchange rate for CHF/EUR using the 3-month forward rate was the only that generated significant results, the forecast error estimation with the news component in (5.2) was solely calculated for that set of data. Results are depicted below in Table 10.

𝑠 − 𝑓 = 𝛽 + 𝛽 [(𝑖 − 𝑖_€) − (𝑖 − 𝑖_€) ] + 𝑢 (5.2)

Table 9. Results from Equation (5.1) for Determining Whether the Money Market Rates is News

𝛽 𝛽 𝛽 𝑅 D-W p-value (𝛽 = 0 ∩ 𝛽 = 1) CHF/EUR (3 months) -0.001943** (0.001232) -0.180603* (0.065216) 0.012372* (0.004902) 0.055770 2.01869 4 0.0000 USD/EUR (3 months) -0.000925 (0.001892) 0.070587 (0.066308) 0.007484** (0.004619) 0.018023 1.93686 6 0.0000 CHF/EUR (6 months) -0.001658 (0.001280) -0.041211 (0.067011) 0.004185 (0.003423) 0.008502 2.35240 4 0.0000 USD/EUR (6 months) -0.000808 (0.001909) 0.107337* * (0.067019) 0.001728 (0.002650) 0.014305 1.90893 2 0.0000

Table 10. Results from Equation (5.2) for Forecast Error Estimation using Money Market Rates as “news” 𝛽 𝛽 𝑅 D-W CHF/EUR (3 months) -0.001676 (0.001241) 0.011304* (0.004910) 0.023012 2.382757

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30 As seen in Table 9, the significance of 𝛽 indicates that “news” may explain some of the existing forecast error on the CHF/EUR exchange rate. Results from (5.3) are displayed in Table 11.

∆𝑠 = 𝛽 + 𝛽 ∆𝑓 + 𝛽 [(𝑖 − 𝑖_€) − (𝑖 − 𝑖_€) ] + 𝛽 [(𝑖 − 𝑖 ) −

(𝑖 − 𝑖 ) ] + 𝑢 (5.3)

Table 11. Forward Rate Prediction Ability Including “News” on Money Market and Sovereign Bond Rates

𝛽 𝛽 𝛽 𝛽 𝑅 D-W p-value (𝛽 = 0 ∩ 𝛽 = 1) CHF/EUR (3 months) -0.001945** (0.001228) -0.197754* (0.065097) 0.011909* (0.004865) -0.001284* (0.000605) 0.076823 2.062052 0.0000 USD/EUR (3 months) -0.001045 (0.001912) 0.069647 (0.067555) 0.007388** (0.004648) 0.000365 (0.000952) 0.018876 1.949224 0.0000 CHF/EUR (6 months) -0.001555 (0.001266) -0.119253 (0.078731) 0.004866 (0.003386) -0.001138** (0.000414) 0.046290 2.449384 0.0000 USD/EUR (6 months) -0.000875 (0.001929) 0.101571 (0.068633) 0.001643 (0.002668) 0.000490 (0.000630) 0.016502 1.931069 0.0000

𝑅 = R-squared; D-W = Durbin–Watson statistic; * = significant at 5% level; ** = significant at 10% level; the value in parentheses below the coefficient is its standard error

The CHF/EUR exchange rate with 3-month forward produced again the most significant results. The same exchange rate using 6-month forward rates also had a significant 𝛽 coefficient. Thus, both estimations for CHF/EUR indicate the impact of the change of the interest rate differential concerning sovereign bonds on the forward rate prediction capacity.

As observed in Tables 9 and 10, the set of data that generated significant results for all coefficients was the one using a CHF/EUR spot rate and a 3-month forward rate. Therefore, (5.4) will only be estimated with that data. Results are on Table 12.

𝑠 − 𝑓 = 𝛽 + 𝛽 [(𝑖 − 𝑖€) − (𝑖 − 𝑖€) ] + 𝛽 [(𝑖 − 𝑖 ) − (𝑖 −

(38)

31 Coefficient 𝛽 appears to be significant. This demonstrates the impact of the news component on the forecast error.

Table 12. Results from Equation (5.4) for Forecast Error Estimation with Interest Rate Differential of Government Bonds

𝛽 𝛽 𝛽 𝑅 D-W CHF/EUR (3 months) -0.001636 (0.001241) 0.010839* (0.004892) -0.001129** (0.000613) 0.023012 2.382757

(39)

32

6. Conclusion

This dissertation assessed the ability of the forward rate to predict the future spot rate. Given the failure of the forward rates to forecast the spot rates, the study examined the role of news, as in the information that emerges within the period of a forward rate and the future spot rate to be analysed. The Random Walk Theory, which states that there’s no correlation between a spot rate and to its past values, is also addressed.

Regarding econometrics, when time series were non-stationary, they were used as first differences in order for them to be stationary, which is the main condition for a proper analysis. When the regression appeared to be serially correlated, a LDV was added to correct this issue.

Firstly, the objective of the empirical work was to evaluate the forward rate capacity to predict the future spot exchange rate for USD/EUR and CHF/EUR. This ability can be assessed through several ways, either through (3.1) as a regression analysis (𝑠 = 𝛽 + 𝛽 𝑓 + 𝑢 ) and the corresponding hypothesis testing or through a calculation of the forecast error. The regression and the hypothesis tests applied (𝐻: 𝛽 = 0 ∩ 𝛽 = 1) showed the inability of the forward rates to predict the future spot rate for all data sets.

The forecast error evaluation encompassed two methodologies, namely through a regression analysis in (3.1) that analyses the value of 𝛽 and through the analysis of the MAE and MAPE. Both procedures demonstrated some level of overestimation by the forward rate.

A further evaluation made using the forecast error regression as seen in (3.1) involved estimating it, but using two sets of data. The two sets were established through splitting the data set of the CHF/EUR exchange rate with the 3-month forward rate between 2 periods: when the spot rate increased and when it decreased. As seen previously, the estimation that is limited to a decreasing spot rate showed an overestimation by the forward rate but at a higher level than when the whole data set was used for the calculations. In the opposite direction, the estimation using an increasing spot rate data showed an underestimation by the forward rate. This leads us to the conclusion that the forward rate is attached to the spot rate, and consequently its movements are highly dependent on the movements of the spot rate.