Bachelor's Thesis and Thesis Seminar Finance for Business (6013B0520)

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Bachelor's Thesis and Thesis Seminar Finance for Business

(6013B0520)

AP 17: Currency Carry Trade Strategy Slot B

The Effect of Exchange Rate Volatility on the Excess Return of Currency Carry Trade Strategy

June 30, 2021

Supervisor: dr. Ben Tims Author: Wenyu Song

Student number: 11645350

Word count: 8671

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Statement of Originality

This document is written by Student Wenyu Song 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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Abstract:

This research paper exploits the profitability of a well-known speculative strategy called “Currency Carry Trade” and focused on the emerging market setting.

Following by adopting fixed effect regression, the research investigates the effect of FX exchange rate volatility on the excess return of carry trade. According to those results reported in this paper, the changing unit of exchange rate volatility across time will lead to a negative effect on the excess return. These findings again confirmed with earlier studies’ findings. Moreover, this research investigates the negative effect under high and low volatile time period and reported that this negative effect will be even worse when the FX market is under high volatile time period. Furthermore, a different set of currency include more developed countries was used in robustness check, and the result confirmed again with previous findings.

Last but at least, some suggestions for future research will be listed and discussed in

this research paper.

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CHAPTER 1: Introduction

In the currency market, the carry trade is a well-known speculative strategy. Using this strategy, investors can borrow in a low-yield country and invest in a high-yield country to exploit excess return from the interest rate differences between countries. According to the Uncovered Interest Parity, if an investor acts as risk-neutral and has rational expectations, the gain exploited from the interest rate differential will be offset by the depreciation in the exchange rate. Indeed, if the UIP is valid, the currency carry trade strategy will not generate any expected excess return.

However, some early literature research tested the hypothesis that the excess return from a speculative carry trade is zero. They have found that UIP does not hold and carry trade strategy can obtain both statistically and economically signiﬁcant positive excess returns. These early researches used the research sample of the period when the Bretton Woods system just collapsed while the exchange rate started floating. For example, Hansen and Hodrick (1980) using the exchange rate of selected major currencies from the early 1970s and reported rejection of such a hypothesis. Also, Fama's (1984) study, which is based on a similar time and currency background, confirmed the hypothesis's rejection, and the UIP failed once again. Some later research even looked back further using a research sample before the Bretton wood system collapsed while the exchange rate remained fixed. For example, Lustig and Verdelhan (2007) started their sample in the 1950s and investigated how the aggregate consumption growth risk affects uncovered interest parity's validity and leads to carry trade excess return. With respect to these researches, the profitability of currency carry trade has attracted excessive attention among academics and investors.

These previous researches have drawn my attention for several reasons. Firstly, I would like to look into the validity of uncovered interest parity in this paper, but take a more recent period of research sample that started from the 2000s into consideration. Because the financial market nowadays has become even more international, the openness in the financial market allows more choice of trade for the investor. The investors make their decisions depending principally on the relative rate of return of the investment portfolio and adjusting their investment portfolio according to the market fluctuation. Accordingly, in this paper I will be focused on the profitability of the currency carry trade strategy for the past 20 years.

Moreover, several kinds of research investigating the relationship between FX volatility and the performance of currency carry trade have drawn my attention. For instance, Clarida et al.

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(2009) and Christiansen et al. (2011) suggested that the currency carry trade strategy is profitable only when the FX volatility is low. Accordingly, the other dimension of this paper will be focused on the effect of FX volatility on the profitability of currency carry trade strategy to check if the excess return generated from currency carry trade is more under the low volatile period.

Furthermore, when considering the factor of volatility, the emerging market has also attracted my interest. In line with the characteristics of emerging markets, the market itself is volatile, with high rate of economic growth and investment potential. All these characteristics are closely related to their trading currency, which also contribute to the effect of FX volatility.

Accordingly, for this paper, I would like to test the validity of UIP in emerging markets, investigate whether the currency carry trade strategy is profitable and the effect of the FX volatility on the profitability of carry trade strategy. Respectively, the research question of this paper will be:

To what extent does the volatility of exchange rate effect the excess return of currency carry trade strategy in emerging market?

In most of the related literature, cross-sectional tests were popularly used. In this paper, some empirical methodologies will be based on the research written by Brunnermeier et al.(2008) and Lustig et al.(2011). The main difference compared to existing research will be that the risk factor of FX volatility will be determined at a monthly frequency, and the effect of volatility on the excess return of carry trade under high volatility period will be compared to the low volatility time period using a dummy variable regression. Accordingly, the contribution of this paper to related literature will be that a recent sample period will be taken into consideration, a closer look at the emerging market, and a new sight of the volatility as a risk factor on the excess return of currency carry trade in the forex market.

The rest of the paper is organized as follows. In the literature review section, we are going to review several factors that affect the validity of UIP, compare the empirical findings and define the research gap. In the methodology and data part, the choosing data set, the methodology applied in this paper and the descriptive statistics will be presented and discussed. Then, in the following result section, the main empirical results will be interpreted and discussed. Lastly, a conclusion includes significant findings of this research, limitations of the study, and further explorations will be deliberate.

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CHAPTER 2: Literature review

In this section, the critical literature related to the currency carry trade and factors that affect the violation of UIP will be reviewed. Given that the profitability of currency carry trade is primarily caused by the forward premium puzzle, a violation of the UIP makes the carry trade proﬁtable on average. A great number of scholars have conducted many kind of literature researches in an attempt to test the validity of uncovered interest parity, and identify factors that affect the direction of carry trade’s excess return across different background settings. These studies have found largely diverse results due to the various time horizon covered, different region’s fundamental factors, and different methodologies employed. However, these studies focused more on the carry component of currency carry trade and lack an empirical analysis of the factor of FX component in a longitudinal study. Meanwhile, most of the literature related to the volatility of exchange rate are using sample data only covered early years. This research paper can fill in the time gap by taking a recent 20 years panel dataset that covers both cross-sectional and longitudinal studies, and mainly focused on the volatility of exchange rate on the excess return of currency carry trade.

2.1 Time horizon

Many scholars have researched the validity of UIP in various research sample forms in terms of different time lengths, sample scales, and time scales. Some recent studies investigate the validity of UIP by taking the different time lengths (long-run versus short-run) and sample scales (large-sample versus small sample) into consideration. For instance, Lee(2013) took a sample scale of 36 countries but with a short time length of 5 years. Based on the ordinary least regression, Lee represents that the short-term UIP is validated, and the failure of UIP is mainly due to currency bias. This finding is confirmed by other scholars using a more extended time spanned. For instance, the research was done by Lothian in 2016, which is an extension of the work for UK-US by Lothian et al.(2013). The latter research constructed a multi-country panel of 17 countries with annual data that covers two centuries, which has been used to examine the validity of UIP. By applying panel regression and fixed-effect analysis, Lothian(2016) reported that the result is consistent with the earlier study, which indicates that the long-term bond yields are positively correlated with one another expressed in common currency, as the UIP predicts.

Moreover, some other recent studies take the time scale (frequency domain) into consideration. For example, Hacker et al. (2012) investigate the relationship between exchange

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rate and interest rate differentials of Sweden and other major currencies using a wavelet approach.

Based on wavelet decomposition, the results reported that the spot exchange rate is negatively related to interest rate differential at a shorter time horizon but positively correlated at a longer time horizon. Furthermore, Hacker et al. (2014) investigate the causal relationship between exchange rate and interest rate differential using the same data sample and wavelet approach.

According to the causality test, the result indicates that most of the country pairs exchange rate Granger caused interest rate differential at 4-month wavelet scale and at 2-quarter scale. They also reported that, while considering the impulse response effect of the interest rate differential on the exchange rate, there is some evidence of a negative relationship at lower wavelet scales and a positive relationship at higher scales.

2.2 Developed countries vs. emerging market

Several studies have investigated the validity of UIP, including emerging markets (EM) in the analysis, but obtain diverse findings. For instance, Bansal and Dalquist (2000) have constructed a study comparing the forward premium puzzle between developed and emerging economies.

According to the research, they conclude that the forward premium puzzle is confined to developed economies and reported that the violation of UIP is not very significant in the EM data.

Accordingly, they also concluded that the differences across economies are influenced by macroeconomic factors like GNP, inflation rate, and inflation volatility. This finding is also confirmed by Frankel and Poonawala(2010), who use the seemingly unrelated regression model to test the bias in the forward market for emerging currencies and recognize the difference compared to major currencies. Frankel and Poonawala(2010) have found that the emerging market economies, on average have slightly above zero coefficients, and even when negative, the coefficient is insignificant less than zero.

On the contrary, other researchers including the emerging markets have reported substantial violation of UIP in the emerging market data. For instance, in the study conducted by Flood and Rose (2002), they included 23 developed and developing countries during crisis-strewn 1990s in sample data. Using ordinary least squares regression, they compare the results of developed and developing countries and have found that the UIP works better for crisis countries, while not significantly different between developed and developing countries. This result is also confirmed by Burnside et al. (2007), who constructed two portfolios to test the adding of emerging market currency on the Sharpe ratio associated with the carry trade. Respectively, they have found

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that the inclusion of emerging market currency leads to a larger Sharpe ratio, and the validity of UIP does not hold in the emerging market data as well.

Further research conducted by Gilmore and Hayashi (2011) resolve these contradictory findings. According to Gilmore and Hayashi (2011), they take different measurement of transaction cost, and the transaction costs due to bid/offer spreads are far below the transaction cost calculated by other academic literature. They also took from US investors' perspective and confirmed that the positive risk premium could be obtained in the long-term by taking USD in short position. Moreover, they suggested that actively choosing currencies with high-interest differentials can increase the excess return on EM currencies and the interest differential of major currency is a better predictor of the EM currency.

2.3 Factors affect the validity of UIP

The validity or violation of UIP has also been explained by factors like currency crash risk and volatility of exchange rate. Several studies have found that the return of the carry trade strategy is negatively related to the FX volatility. For example, Brunnermeri(2007) investigated the link between currency crash risk and carry trade for eight major currencies using the US dollar as the investment currency. They have found that the carry trade portfolios have delivered a negatively skewed return. Meanwhile, they have documented that currency crashes are linked to the sudden unwind in carry trade, which is positively correlated with increases in implied stock market volatility.

Some research papers have focused on investigating the cross-section of excess return and country fundamentals in the currency carry trade strategy. For instance, Lustig and Verdelhan (2007) focus on the cross-sectional variation between the returns of high and low interest rate currencies and make the case that the return on currencies with high interest rates have higher loading on consumption growth risk. Based on this research, many follow on researches have been developed. For instance, the paper written by Menkhoff et al. (2011) took a look into the cross- section of excess return and found that high interest rate currencies are negatively related to the movement in global FX volatility. Indeed, the research addressed that in the time of unexpected high volatility, the excess return remains low since low interest rate currencies tend to hedge by yielding positive returns.

Some other scholars have similar findings by using different methods. For example, Ichiue and Koyama (2011) investigate the role of exchange rate volatility in UIP by applying the regime-

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switching models for a select set of currency pairs using monthly data between 1980 and 2009.

They set the U.S. Dollar (USD) as the home currency while the other four major currencies as the foreign currencies. According to their empirical findings, the low-yield currencies appreciate less frequently, but once the appreciation occurs, the appreciation will be faster than their depreciation.

The fast appreciation is also called currency crash risk, in order to bear the risk, investors may require a risk premium for taking the short position in low yield currency. They further report that the depreciation in low-yield currencies is mutually correlated to the low-volatility. Further, Moore and Roche (2012) expanded the sample data to forty-two countries and used simulation exercises which indicate that the slope of Fama regression is positively related to the monetary volatility, the Fama regression slope is positive during high monetary volatility and negative when the monetary volatility is low. This resulted in the validity of uncovered interest parity being determined by the degree of monetary volatility. In relation to the effect of volatility factor on excess return, Jordà and Taylor (2012) considered the country fundamentals as essential determinants of currency returns. They take the use of fundamental equilibrium exchange rate and resolve the problem of negative skewness and market volatility related to the currency returns.

Others have highlighted the relevance of the financial crisis and uncovered interest parity.

For instance, Dimitriou et al. (2017) explore the dynamic linkages through the uncovered interest parity in the G7 countries during the Global Financial Crisis and Euro-zone Sovereign Debt Crisis.

They encompassed the UIP hypothesis into the Error Correction Model and revealed that Canadian Dollar and Great British Pound were more severely affected by the US Dollar due to strong financial and economic ties, while Japanese Yen was less affected during the Global Financial Crisis. In contrast, during the Euro-zone Sovereign Debt Crisis, they have found an increasing linkage among the selected currencies above, however, the dummy coefficient of currency pairs are significantly negative. This empirical evidence implies that investors move to less risky currency under crisis, which violates the assumption of UIP with risk aversion behavior and the irrationality of expectation.

According to these previous studies, the main goal of this paper will be relating the volatility of exchange rate to the excess return in emerging market. To check if the excess return is negatively related to movement of FX volatility in emerging market. Based on previous literature, the hypothesis of this research is that the uncovered interest parity is violated under emerging market setting, the currency carry trade strategy will be able to achieve a positive performance,

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and the increasing in volatility of exchange rate will negatively affect the excess return of carry trade.

CHAPTER 3: Methodology

In this section, the choice of data, the equation of methodology, the regression model, and the descriptive statistics will be represented and discussed.

3.1 Data

In this research paper, the portfolio construction and empirical methodology will be based on the literature research written by Brunnermeier et al.(2008) and Lustig et al.(2011). The research dataset will be panel data which include daily spot exchange rate and one-month forward exchange rates relative to the U.S. dollar (e.g., Chinese Yuan per USD), and the ex-post data of bid-ask spread for monthly spot and forward rate obtain from FactSet for 20 years spanned from January 2000 to December 2020. Even though the daily data will be implemented to construct the proxy for FX volatility, the empirical analysis is carried out at the monthly frequency. Overall, the research sample will be mainly consisted by the following ten emerging markets: China(CNY), India(INR), Indonesia(IDR), Mexico(MXN), Poland(PLN), Singapore(SGD), Saudi Arabia(SAR), South Africa(ZAR), Thailand(THB) and Turkey(TRY), total 252 monthly observations for each country will be extracted.

3.2 Portfolio construction

In this research paper, the log of spot and forward exchange rate will be denoted as s and f. Based on the forward discount f-s at the end of each period t, all currencies will be equally allocated to five portfolios and the construction of portfolios will be rebalanced at the end of each period. Assuming covered interest parity hold for all these data, sorting on interest rate differential is identical to sorting on the forward discount. Accordingly, all these currencies are allocated to each portfolio based on the ranked from low to high forward discount. In portfolio 1, currencies with the smallest forward discount at the end of each period are included, and portfolio 5 contains the currencies with the largest forward discounts at the end of each period. In respect to the currency carry trade, the portfolio 1 is therefore the funding currency in short position and portfolio 2 to 5 are the investment currencies in long position. Each portfolio consisted of 504 observations range from January 2000 to December 2020.

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3.3 Currency excess returns.

According to the unconditional uncovered interest parity, the differences in interest rates between two countries will equal the expected change in the exchange rates between them while the UIP hold. Under the violation of UIP, the monthly excess returns of holding foreign currency x by borrowing domestic currency are computed using the following method:

𝒁 _𝒕+𝟏^𝒙 = 𝒊_𝒕^𝒙− 𝒊_𝒕− ∆𝒔_𝒕+𝟏^𝒙 (1)

Where the ∆𝒔_𝒕+𝟏^𝒙 = 𝒔_𝒕+𝟏^𝒙 − 𝒔_𝒕^𝒙 , represent the depreciation of the foreign currency.

As adopted by Lustig et al.(2011) and Menkhoff et al.(2011), the assumption of covered interest parity is hold for the dataset , the 𝒊_𝒕^𝒙− 𝒊_𝒕 ≈ 𝒇_𝒕^𝒙− 𝒔_𝒕^𝒙 , and the approximated monthly excess return can be measured as:

𝒁 _𝒕+𝟏^𝒙 = (𝒇_𝒕^𝒙− 𝒔_𝒕^𝒙) − ∆𝒔_𝒕+𝟏^𝒙 ≈ 𝒇_𝒕^𝒙 − 𝒔_𝒕+𝟏^𝒙 (2)

Where the 𝒇_𝒕^𝒙 indicate the one-month forward exchange rate at time t. For the UIP hold, the expected value of 𝒁 _𝒕+𝟏^𝒙 should equals to zero, this has been tested by a great number of researchers and many findings shows that the 𝒁 _𝒕+𝟏^𝒙 can be both positive and negative.

Furthermore, the FX transaction cost is higher for currency trading due to the characteristic of volatile and rapid growing emerging market mentioned above. In order to make the estimation more accurate, the bid-ask spread will be used to calculate the transaction cost and the net return for currency in the portfolio will be taken into consideration. Referring to the set up used by Lustig et al.(2011), the bid-ask spreads are deducted from the excess return when the currency enter or exit the portfolio. Accordingly, the net excess return for currency that enters a portfolio at time t and stays in the portfolio at the end of the month are computed as below:

For long position:

𝒁 _𝒕+𝟏^𝒍 = 𝒇_𝒕^𝒃− 𝒔_𝒕+𝟏 (3)

For short position:

𝒁 _𝒕+𝟏^𝒔 = −𝒇_𝒕^𝒂+ 𝒔_𝒕+𝟏 (4)

Where the net excess returns for portfolio 1 are adjusted for the transaction costs in short positions, while the net excess return portfolios 2–5 are adjusted for transaction costs in long positions.

Indeed, the net excess return for currency carry trade strategies that go long in portfolio k = 2, 3, 4, 5, and short in the first portfolio are computed as the equation (3) minus the equation (4), the net excess return is calculated as below:

𝒁 _𝒕+𝟏^{𝒄𝒂𝒓𝒓𝒚} = 𝒁 _𝒕+𝟏^{𝒌=𝟐,𝟑,𝟒,𝟓}− 𝒁 _𝒕+𝟏^𝒌=𝟏 (5)

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Lastly, by taking the equally weighted average excess return of all currencies in each portfolio k(=portfolio 1-5), the net excess return of each carry trade j are calculated as below:

𝒓𝒙_{𝒋,𝒕+𝟏} = ^𝟏

𝑿∑ 𝒁_𝒕+𝟏^{𝒄𝒂𝒓𝒓𝒚} (6)

Where X denote the number of currencies in each carry trade j. The motivation of adopting this methodology setup for excess return is that the replicative work can ensure the validity of results, and new regression model can be developed based on existing literatures.

3.4 Volatility Proxy

To compute the proxy for volatility on each month, this research paper follows the methodology used by Menkhoff et al. (2011). A straightforward measure which similar to the measure of realized volatility will be adopted.

First of all, the absolute daily log return for each currency on each day will be calculated as below:

| 𝒓_𝝉^𝒙| (= | △ 𝒔_𝝉| ) (1)

Then, calculate the average of the log return for all selected currencies available on each trading day:

∑ ^{| 𝒓}^𝝉^𝒙^|

𝑿_𝝉

𝒙𝝐𝑿_𝝉 (2)

Lastly average all these daily values up to the monthly and the global FX volatility proxy in month t is calculated as followed:

𝝈_𝒕^𝑭𝑿 = ^𝟏

𝑻_𝒕∑ [∑ ^{| 𝒓}^𝝉^𝒙^|

𝑿_𝝉 𝒙𝝐𝑿_𝝉 ]

𝝉𝝐𝑻_𝒕 (3)

where 𝑿_𝝉 represents the number of available currencies on day τ and 𝑻_𝒕 represents the total number of trading days in month t.

3.5 Regression Model

Taking the time-variant characteristics of volatility proxy into consideration and perform the Hausman’s specification test. The test indicated the null hypothesis of random effect model is consistent, the specification test carried out a p-value of 0.0007 which is less than 0.05, so the null hypothesis is efficiently rejected. Indeed, fixed effect model regression will be firstly performed to investigate the effect of volatility on excess return of carry trade.

The regression equation is stated as below:

𝒀_𝒊𝒕 = 𝜶_𝒊+ 𝜷_𝟏𝑿_𝒊𝒕+ 𝒖_𝒊𝒕 (1)

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Where the 𝜶_𝒊 (i=1….n) is the unknown intercept for each portfolios, 𝒀_𝒊𝒕 is the dependent variable (DV) which are carry trade net excess return and carry trade excess return without bid-ask spread, where i = portfolios and t = time, 𝑿_𝒊𝒕 represents one independent variable (IV) which is the volatility proxy, 𝜷_𝟏 is the coefficient for that IV, and 𝒖_𝒊𝒕 is the error term. Based on previous literature research, the hypothesis of this regression model is formulated as below:

𝑯_𝟎: The volatility proxy has a positive effect on the excess return, 𝜷_𝟏> 𝟎 𝑯_𝟏: The volatility proxy has a negative effect on the excess return, 𝜷_𝟏 < 𝟎

Furthermore, in order to investigate whether the effect of volatility on excess return is differed between the high volatility period and the low volatility period, a fixed effect regression model with dummy variable of volatility proxy will be applied. Based on the FX volatility proxy in each month t, dummy variable can be created. For the value of volatility in month t lower than the 50 percentiles, the dummy variable equals to 0 for low volatile period, and for the value of volatility in month t higher than 50 percentiles, the dummy variable equals value equals to 1 for high volatile period. The regression equation with dummy variable is formulated as below:

𝒀_𝒊𝒕 = 𝜶_𝒊+ 𝜸_𝟏𝑿_𝒊𝒕+ 𝜸_𝟐𝑿_𝒊𝒕+ 𝒖_𝒊𝒕

Where 𝜸_𝟏 is the coefficient for the independent variable volatility proxy when the dummy value=0 (indicating low volatility period) and 𝜸_𝟐 is the coefficient when the dummy value=1(indicating high volatility period). According to previous research, the null and alternative hypothesis of this test are stated as below:

𝐇_𝟎: The effect of volatility on excess return will be less negative under low volatility period, where the 𝜸_𝟏 > 𝜸_𝟐

𝐇_𝟏: The effect of volatility on excess return will be more negative under low volatility period, where the 𝜸_𝟏 < 𝜸_𝟐

On the other hand, there is another methodology broadly discussed by scholars and popularly implemented in research to test the validity of Uncovered Interest Parity and determine the excess return of carry trade. The standard test of uncovered interest parity which summarized by Flood and Rose in 1996, under the assumption of rational expectation and rearranging from the unconditional test model of UIP, they derived the following equation:

𝒔_𝒕+∆− 𝒔_𝒕 = 𝜶 + 𝜷(𝒊_𝒕− 𝒊_𝒕^∗) + 𝜺_𝒊

This equation has been used as the fundamental equation to test the validity of UIP for a wide range of literatures. The null hypothesis of UIP can be expressed as 𝐻₀: 𝛼 = 0 𝑎𝑛𝑑 𝛽 = 1, which

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has been rejected by a great number of literatures research. In this research paper, in additional to the unconditional test, a slightly different equation based on the standard test equation which change the term (𝑖_𝑡− 𝑖_𝑡^∗) to (𝑓_𝑡+∆− 𝑠_𝑡) which also used by Wu and Zhang(1995) will be adopted to confirm the violation of UIP in this data set (Fama,1984).

3.6 Descriptive Statistics

The following Table 1 provides a descriptive overview of calculated factors of the five currency portfolios from the perspective of a U.S. investor. For each portfolio k, 504 observations included to calculate the average of changes in the spot rate, the forward discounts, the currency excess returns, and the net currency excess returns adjusted by bid-ask spreads. The lower two panels reported the excess returns of carry trades investment strategies that go short in the first portfolio and go long in portfolio k = 2, 3, 4, 5. All exchange rates and returns are reported in relative to U.S. dollars. In order to calculate the Sharpe ratio of excess return, which is the ratio of the annualized mean to the annualized standard deviation, the average returns are annualized by multiplying 12 and the standard deviation is annualized by multiplying the √12, and the Sharpe ratio is represented in the last line of each panel.

From the Table 1, the mean of each portfolio’s excess return is differed from zero, according to the unconditional test of UIP, the null hypothesis of expected excess return should be zero is failed, and the violation of UIP is confirmed in this paper. According to Table 1, the mean of excess return without bid-ask spread for each carry trade portfolio are positive except the carry trade of short in portfolio 1 and long in portfolio 3. The carry trade 4 of long in portfolio 5 can generate the highest positive average excess return of 0.00573 with a Sharpe ratio of 0.4590, which indicate this carry trade has the highest performance. However, this excess return is affected when the transaction cost has been taken into consideration, the mean of carry trade excess return net of bid-ask spread is mostly negative for the short in portfolio 1 and long in portfolio 3, 4, and 5.

Another significant figure from the Table 1 is the high value of kurtosis. However, this large value of kurtosis in forward discount under portfolio 1 is due to the construction of portfolio 1 includes all the smallest forward discount in each monthly period, which won’t have large impact on the model as a whole. Lastly, due to the large sample of 504 observations for each portfolio has been selected, the normality of the regression model can be confirmed, and other assumption of panel data regression will be confirmed in the following section.

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Table1: Descriptive Statistics

Panel A: Portfolio 1 2 3 4 5 Spot change

Mean -.000772 .000168 .002799 .003087 .003925

Std.Dev .0146 .0236 .0313 .0330 .0442

Skew. -.2223 .4806 3.4024 .8995 .9900

Kurt. 7.5050 17.0771 36.3434 6.9195 7.5483

Forward Discount: f-s

Mean -.000945 .000396 .001912 .004194 .009482

Std.Dev .00256 .00094 .00136 .00141 .00745

Skew. -9.3545 .9266 .2199 .4670 2.8646

Kurt. 124 4.7850 3.0342 5.1286 12

Excess Return without b-a

Mean -.000173 .000228 -.000887 .001107 .005557

Std.Dev .01473 .02346 .03133 .03297 .04477

Skew. .3069 -.4508 -3.4142 -.8664 -.7793

Kurt.

SR

7.5417 -.0407

16.9703 .0337

36.8343 -.0981

6.8859 .1163

7.1747 .4299

Net Excess Return

Mean -.000968 -.000588 -.003302 -.00356 -.004661

Std.Dev .01466 .02365 .03206 .03301 .04412

Skew. -.2621 -.5559 -3.6273 -.9182 -1.0132

Kurt.

SR

7.5514 -.2287

16.6967 -.0861

38.8171 -.3568

6.9268 -.3736

7.5895 -.3659

Panel B:

Carry Trade 1 2 3 4

Carry Trade Excess Return without b-a

Mean .000401 -.000714 .00128 .00573

Std.Dev .02486 .03153 .03152 .04324

Skew. -.1627 -2.9396 -.7813 -.7818

Kurt.

SR

12.5415 .0559

30.8197 -.0784

7.0858 .1407

7.5228 .4590

Carry Trade Net Excess Return

Mean .00038 -.002334 -.002592 -.003693

Std.Dev .03045 .038111 .0402 .05002

Skew. -.5329 -2.4159 -.6746 -.7722

Kurt.

SR

9.0495 .0432

23.7834 -.2121

5.1879 -.2234

6.1319 -.2558

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CHAPTER 4: Result and Discussion

In this section, the result from conditional UIP test will be firstly presented. Then the regression results of exchange rate volatility proxy on excess return and net excess return will be reported and discussed. After taking a deep look into each carry trade, the result from a dummy variable fixed effect regression of exchange rate volatility on excess return and net excess return will be performed and discussed. Lastly, a robustness check will be included and discussed in detail.

4.1 Result and Discussion

In order to confirm the violation of UIP again using the conditional standard test, the following Table 2 represent the regression of the forward discount on the change of spot rate.

According to the Table (2), the slope coefficient indicates that for Carry Trade 1 and 3, the 1%

increase of the forward discount has a positive effect smaller than 1% on the change of spot rate for each carry trade. For instance, taken the log-term into consideration, the slope of forward discount in Carry Trade 1 is 0.2915, an 1% increase in forward discount will lead to a 0.2915%

increase in the change of spot rate. Indeed, according to the equation of excess return, 𝒁 _𝒕+𝟏^𝒙 = (𝒇_𝒕^𝒙− 𝒔_𝒕^𝒙) − ∆𝒔_𝒕+𝟏^𝒙 , when forward discount increase by 1%, and the change of spot rate increase by less than 1% will finally lead to a small increase on the excess return, however, the t-statistics reported in the table does not exceed the critical value of 1.96. Therefore, the small increase is not significant and the increase in excess return will not be statistically significant as well. We can also conclude that under emerging market setting, for most of time currency carry trade strategy can be able to achieve a positive excess return when the transaction cost is not taken into consideration, however, this positive excess return is not statistically significant. This finding again confirmed with the early findings by Frankel and Poonawala(2010), and the violation of UIP in carry trade is not very significant under emerging market setting .

Table 2: Regression of forward discount on change of spot rate for carry (j=1-4)

Intercept (𝛼 ) Slope (𝛽) R Square

Carry Trade Estimate t-stats Estimate t-stats

1 -.0004 -0.71 .2915 1.15 0.0026

2 -.0013 -1.19 3.8135 3.46*** 0.0233

3 .0026 1.06 .1231 1.12 0.0002

4 -.0021 -0.45 1.2330 1.18 0.0028

*** Significance level at 1%, 5% and 10% are indicated by ***, ** and *, respectively.

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For panel data regression, several assumptions need to be hold. Firstly, the assumption of homoskedasticity hold in this dataset since the log term of variables has been taken into consideration. In order to solve the problem of heteroskedasticity, the robustness standard error will be taken into consideration. Also, the using of panel data itself is a solution for heteroskedasticity as well. Secondly, the assumption of multicollinearity also has been tested by using Variance Inflation Factor, and according to rule of thumb, this assumption holds for the dataset as well since the VIF for each factor is below 10. Last but at least, the assumption of autocorrelation also has been tested using Wooldridge test, by testing the null hypothesis of no first order autocorrelation, the p-value of each dependent and independent variable is greater than significance level of 0.01 for all cases, and greater than significance level of 0.05 for most as well, except for dependent variable of carry trade net excess return and independent variable of volatility proxy (0.0318<0.05). Indeed, the assumption of little autocorrelation is validated in this panel dataset. (Detailed Table in Appendix)

After confirming the assumption of panel data regression hold, the first regression to test the general effect of the exchange rate volatility proxy on the excess return and net excess return will be performed and represented in the following Table 3:

Table 3: Regression Result of volatility proxy on excess return and net excess return Number of

obs. Intercept Coef. 𝜷_𝟏

(Volatility Proxy) t-value p-value 𝑅² F-test Rho(ρ) Excess

Return 2016 .0258 -6.85 -4.62*** 0.0191 0.0606 21.31 .0075 Net

Excess Return

2016 .0299 -9.10 -6.41*** 0.0077 0.0737 41.05 .0019

As presented in the Table 3, a number of 2016 observations have been included to test the effect of volatility proxy on each excess return and net excess return. According to the coefficient of volatility proxy, the negative value indicates that the change in volatility proxy will have negative effect on both excess return and net excess return. By taking the log-term into consideration, the across time one unit increase in volatility proxy will lead to 6.85% decrease on the excess return, and a 9.10% decrease on net excess return. These negative effects of volatility proxy on both excess return and net excess return are statistically significant due to the absolute t- value of both are larger than 1.96. Meanwhile, based on the one-sided test for the null-hypothesis,

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according to the P-value of volatility proxy on both dependent variables are less than the significance level of 5%, then the null hypothesis of the volatility proxy has a positive effect on the excess return is rejected, and the alternative hypothesis of volatility proxy has a negative effect on excess return is statistically supported.

Furthermore, by looking at the R-square and F-test, the comparably low R-square indicate that a 6.06% small amount of change in excess return can be explained by the volatility of exchange rate. This is not surprising because the excess return of carry trade is hard to predict, the early research’s result of predicting the excess return done by Gilmore and Hayashi (2011) also present a small R-square. Also related to other earlier research, there are many other factors like crash risk, different interest rate differential and other market volatility need to be taken into consideration while predicting the excess return. However, this paper focusing on the effect of exchange rate volatility, and the high F-test statistics indicate that the negative effect of volatility proxy is still significant and need to be take into consideration. As also represented in the table, a Rho (ρ) means that percentage of the unexplained error term variance is attributable to the carry trade level fixed effects. In other words, after controlling for the independent variables of volatility proxy, there is a small number of observed differences in excess return and net excess return, about 0.75% and 0.19% of this difference occurs between each carry trade rather than within each carry trade. Lastly, based on the Table 3, there is a noticeable difference between the effect of volatility proxy on excess return and net excess return. This difference can be explained by the involvement of bid- ask spread transaction cost, since the involved transaction cost will increase when the exchange rate is volatile, accordingly the net excess return will be even lower. To summarize the general effect of volatility proxy, a conclusion of exchange rate volatility proxy has a significant negative effect on both the excess return and net excess return of currency carry trade can be made.

Beside the general effect, it’s necessary to take a closer look into each carry trade. By regressing the volatility proxy on excess return for each carry trade, the following Table 4 have presented some interesting findings.

Table 4: Regression Result of volatility proxy on excess return for carry trade (j=1-4)

Excess Return Number of

obs. Intercept Coef.

(Volatility Proxy) t-value p-value 𝑅² F-test Carry Trade 1 504 .0133 -3.66 -4.03*** 0.0001 0.0314 16.25 Carry Trade 2 504 .0241 -7.04 -6.24*** 0.0000 0.0721 38.98

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Carry Trade 3 504 .0221 -5.92 -5.20*** 0.0000 0.0511 27.01 Carry Trade 4 504 .0436 -10.77 -7.03*** 0.0000 0.0896 49.40

As presented in the Table 4, each carry trade has 504 observations to test the effect of volatility proxy on excess return of each carry trade. The coefficient results from each carry trade are in consistent with the general interpretation of the negative effect caused by unit change in exchange rate volatility proxy, as well as the t-value and p-value represented a statistically significant support to the negative effect. However, the excess return of Carry Trade 4 has suffered most severely from the negative effect of unit change in exchange rate volatility proxy. The one unit increase in volatility proxy will lead to 10.77% decrease on the excess return, this result is not surprising since the Carry trade 4 short in the Portfolio 1 which is constructed by the lowest forward discount of each currencies and long in Portfolio 5 which is constructed by the highest forward discount of each currencies. When the exchange rate is more volatile, the change in spot rate will also be large, and according to the equation of excess return, the excess return will ultimately have severely decreased. Therefore, taking the highest minus lowest position of carry trade is more effected by the change of exchange rate volatility.

After checking the general effect of exchange rate volatility, a further investigation on whether the change of exchange rate volatility have same effect on excess return and net excess return under different volatility period has also been conducted in this paper. Starting by determine the high and low volatility period using the 50 percentile of volatility proxy and summarizing the excess return under both high and low volatility period, a summarized result represented that the mean of excess return and net excess return under low volatility period is larger than the mean under high volatility period. This finding is consistent with Menkhoff et al. (2011)’s finding about excess return remain low under high volatility period. Then, a dummy variable fixed effect regression will be performed to investigate the effect of exchange rate volatility on both excess return and net excess return under different volatility time period. The following Table 5 summarized the regression result.

Table 5: Regression Result: if volatility period=1 vs. 0 (high volatility vs. low volatility) Panel A: if volatility period=1 (High volatility)

Number

of obs. Intercept Coef. 𝜸_𝟏

(Volatility Proxy) t-value p-value 𝑅² F-test Rho Excess

Return 1008 .0305 -7.78 -5.85*** 0.0100 0.0622 54.04 .0092

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Net Excess

Return 1008 .0331 -9.85 -7.35*** 0.0052 0.0700 34.17 .0019 Panel B: if volatility period=0 (Low volatility)

Number

of obs Intercept Coef. 𝜸_𝟐

(Volatility Proxy) t-value p-value 𝑅² F-test Rho Excess

Return 1008 .0154 -3.34 -1.37 0.1695 0.0018 1.89 .0092

Net Excess

Return 1008 -.0024 2.67 1.64* 0.1990 0.0008 2.70 .0034

As presented in the Panel A, the one unit increase in exchange rate volatility proxy has a negative effect of 7.78% decrease on excess return and 9.85% decrease on net excess return when the time period is considered as high volatile, and these effects are statistically significant according to the absolute t-value of 5.85 and 7.35. These negative effects are consistent with the finding in Table 3 as discussed above. However, the result from Panel B indicates that under low volatile time period, the one unit change in exchange rate volatility will lead to a 3.34% decrease on excess return, and a 2.67% increase in net excess return. Under the low volatility period, the negative effect of exchange rate volatility on excess return is not statistically significant, however, the positive effect represents a small significance. Moreover, the large p-value of 0.1695 and 0.1990 indicate that the null hypothesis of the negative effect of exchange rate volatility will be lower under low volatile period of time is supported, where the 𝜸_𝟏> 𝜸_𝟐 . Moreover, it’s surprising that the changing in exchange rate volatility will eventually lead to a positive effect on net excess return, although this effect is only representing a little significance. This result might be caused by the concept of the net excess return is a compensation for bearing extra unit of risk under low volatile period, further research can be conducted to investigate this finding. By comparing the Panel A and Panel B, a conclusion based on the difference of the volatility coefficient between high volatile period and low volatile period can be formulated. As represented in the Table 5, the exchange rate volatility has different extent of effect on both excess return and net excess return, the exchange rate volatility has a much less statistically significant negative effect under low volatility period, and the excess return is more sensitive to the change in exchange rate volatility when the market is in high volatile period.

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4.2 Robustness Check

For the robustness check, a different set of currencies included several developed countries’

currency has been taken into consideration. This set of currencies include Australia (AUD), Canada (CAD), Japan (JPY), India (INR), Mexico (MXN), the UK (GBP), Saudi Arabia (SAR), South Africa (ZAR), Switzerland (CHF) and Thailand (THB). This set of currencies are more balanced comparing to the basket consisted of only emerging market currencies. The same methodology of calculating the excess return, net excess return and volatility proxy will be implied, but a different random effect regression model is used due to the result from Hausman test, the p- value is greater than 0.05. Starting by summarized the descriptive statistics, the following Table 7 represent the detailed statistics of carry trade excess return and net excess return.

Table 7: Descriptive Statistics for robustness check Panel B:

Carry Trade 1 2 3 4

Carry Trade Excess Return without b-a

Mean .0029 .0067 .0069 .0084

Std.Dev .0311 .0294 .0304 .0400

Skew. .0311 .4171 -.3463 -.3438

Kurt.

SR

8.9156 0.3230

7.8614 0.7894

4.0735 0.7863

4.1151 0.7275

Carry Trade Net Excess Return

Mean -.0041 -.0013 -.0026 -.0038

Std.Dev .0402 .0429 .0448 .0556

Skew. -.3368 -.8235 -.4371 -.7749

Kurt.

SR

4.0326 -0.3533

9.5663 -0.1049

5.0923 -0.2010

6.0081 -0.2367

By comparing the two descriptive statistics table (Table 1 and Table 7), the average mean of excess return is much higher when including more developed countries’ currency, and the higher Sharpe ratio also indicate that the higher risk compensation the carry trade investment offers. But at the same time, the net excess return is much less comparing to the only emerging market setting, the effect of transaction cost is more severe when more developed markets currencies added, this confirmed that the transaction cost between emerging and developed country are higher.

Meanwhile, the following Table 8 represent the regression of the forward discount on the change of spot rate. As the table presented, the slope coefficients are diversified from one and for most carry trade except Carry Trade 4, the 1% increase of the forward discount has a negative effect on the change of spot rate for each carry trade. Also, according to the t-value, this negative

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effect is statistically significant for Carry trade 2 and 3. As referring to the equation of excess return 𝒁 _𝒕+𝟏^𝒙 = (𝒇_𝒕^𝒙− 𝒔_𝒕^𝒙) − ∆𝒔_𝒕+𝟏^𝒙 , when the forward discount increase and the change of spot rate decrease, the excess return will ultimately increase, and this increase in excess return is statistically significant on Carry Trade 2 and 3. This finding again confirmed the finding from Bansal and Dalquist (2000), when involving more developed countries the violation of UIP is more statistically significant, and the positive excess return is more significant when a diversified group of currencies got selected.

Table 8: Regression of forward discount on change of spot rate for carry (j=1-4) for robustness check

Intercept (𝛼 ) Slope (𝛽 ) R Square

Carry Trade Estimate t-stats Estimate t-stats

1 -.0002 -0.16 -.4373 -1.02 0.0021

2 -.0001 -0.12 -1.6079 -1.78* 0.0063

3 .0009 0.67 -2.2651 -2.54** 0.0126

4 -.0035 -1.01 1.2252 1.34 0.0036

After confirming the assumption of multicollinearity and autocorrelation hold for this panel data using the same method, as mentioned above, in order to test the general effect of the exchange rate volatility proxy on the excess return and net excess return, a random effect regression will be performed. The following Table 9 report the random effect regression result:

Table 9: Random effect regression Result of volatility proxy on excess return and net excess return Number of

obs. Intercept Coef. β₁

(Volatility Proxy) z-value p-value 𝑅² Rho(ρ) Excess

Return 2016 .0109 -1.19 -2.11** 0.035 0.0022 .0032

Net Excess Return

2016 .0238 -6.7711 -8.74*** 0.000 0.0366 .0000

As the Table 9 represented, the negative effect of exchange rate volatility is still significant when more developed country currency got involved. However, by comparing to the only emerging market setting represented in Table 3, the negative effect of exchange rate volatility proxy decreases from -6.85 to -1.19 for excess return and decreases from -9.10 to -6.77 for net excess return. These results indicate that the negative effect of exchange rate volatility is much less when more developed country got involved. The changing of the negative effect might relate

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to the less volatile and mature currency market of the developed country, the small change in exchange rate will not switch investor’s expectation and the excess return is less effected.

Furthermore, after determining the volatility period according to the 50 percentiles of volatility proxy, a random effect regression of exchange rate volatility on excess return and net excess return for both high and low volatile period has been performed and represented as in the following Table 10:

Table 10: Regression Result: if volatility period=1 vs. 0 (high volatility vs. low volatility) Panel A: if volatility period=1 (High volatility)

Number

of obs. Intercept Coef.

(Volatility Proxy) z-value p-value 𝑅² 𝜎𝑒

Excess

Return 1008 .0057 -.2535 -0.30 0.765 0.0001 .0377

Net Excess

Return 1008 .0447 -10.46 -9.05*** 0.000 0.0753 .0513 Panel B: if volatility period=0 (Low volatility)

Number

of obs. Intercept Coef.

(Volatility Proxy) z-value p-value 𝑅² 𝜎_𝑒 Excess

Return 1008 .0246 -5.286 -2.46** 0.014 0.0059 .0274 Net Excess

Return 1008 -.0171 5.174 1.75* 0.080 0.0030 .0377

Referring to the Table 10, some new and interesting finding has been presented. The Panel A reported that under high volatile period, the negative effect of exchange rate volatility on excess return is small and no longer significant when more developed country currency added, but the negative effect on the net excess return is still statistically significant as similar reported under the only emerging market setting. Meanwhile, as reported in the Panel B, under low volatile period of time, the negative effect of exchange rate volatility is significant on excess return, again a positive effect of exchange rate volatility has been found on the net excess return, and this time the positive effect is more significant when including developed country currencies.

Lastly, according to Moore and Roche (2012), the slope of Fama regression is positively related to the monetary volatility. Hereby, a Fama regression has been conducted to confirm this finding, and the result reported that the slope is -0.1955 under high volatile period and -0.4785 under low volatile period. This result can confirm that the Fama regression slope is positively increasing when monetary volatility is high, however, further research of including more

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developed country currency can be conducted to confirm whether the Fama regression slope can be positive during higher monetary volatility.

To conclude the robustness test, the adding of more developed currencies can affect the sensitivity of both excess return and net excess return to exchange rate volatility, the negative effect of exchange rate volatility will be remitted when more developed country’s currencies involve in the carry trade, and again the confirmation of positive effect of exchange rate volatility prove that the increase of exchange rate volatility under low volatile period might be a good thing to investors, further researches can be conducted to investigate this positive effect.

CHAPTER 5: Conclusion

Based on the regression result reported in the section above, several important findings have drawn my attention. First of all, according to both unconditional and conditional model of Uncovered Interest Parity (UIP), the UIP is violated under the emerging market setting. However, when adding more developed country to the list, the violation is more significant. Meanwhile, following by the violation of UIP, the currency carry trade will deliver a positive excess return, but the carry trade’s net excess return adjusted by transaction cost is not ideal and is decreasing due to bid-ask spread. Moreover, the regression results of exchange rate volatility on excess return and net excess return in this paper indicate that the exchange rate volatility has a general significant negative effect on both the excess return and net excess return of currency carry trade. Beyond these regression results, this paper split the time period to high volatile and low volatile period of time. By comparing to high volatility period, the summarized result confirm that the average profitability of carry trade is higher during low volatile period of time. These results confirmed with earlier research’s findings. Furthermore, other than the general effect of exchange rate volatility, this paper conducted further investigation on the effect of exchange rate volatility on both excess return and net excess return under high volatile and low volatile time period. The reported regression result indicates that, the negative effects of exchange rate volatility on both excess return and net excess return are more severe when the market is under high volatile period of time. On the other side, when the market is under low volatile time period, the negative effect of exchange volatility is not significant on excess return, and even will bring some little significant positive effect on net excess return. These results confirmed again in the robustness check. Along

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with some new findings from robustness check confirmed that a mix of developed and emerging market currency can obtain higher excess return from currency carry trade. And under the setting of mixed group of developed and emerging countries, the negative effect of exchange rate volatility is remitted and less significant.

However, there are some limitations of this study. First of all, the transaction cost calculated in this study used a bid-ask spread. Despite the bid-ask spread, transaction cost can raise from lags in settling spot contracts, the FX swap, the administration fee, and other related cost.

The calculation of net excess return can be more accurate and other transaction cost need to be taken into consideration in forex trading. Beside the transaction cost, the exchange rate volatility calculated in this paper was adopting a straightforward measure for realized volatility. Instead of the straightforward measure, a more accurate measure of implied volatility can be better adopted for further research. After all, this paper is generated from the U.S investor’s perspective. However, carry trade as an important strategy in FX market, a broader perspective from international investor can be taken into consideration for further research.

Based on these results and limitations from this paper, there are some important suggestions for further research. Firstly, even though there is plenty of paper investigate the validity of UIP and profitability of carry trade. There is a lack of research on the liquidity risk in international FX market. Some further research can be more focused on how the carry trade strategy performance change under the increasing in international market liquidity risk. Next in order, as mentioned in the result and conclusion, the further research can investigate the positive effect of exchange rate volatility on net excess return under low volatile period of time. This can be a direction to start for further studies. Moreover, scholars and investors can have a look on the allocation of currency carry trade in emerging or developed market. And determine which countries are more profitable to adopted currency carry trade strategy. There might be some improvements in carry trade strategy, which might enable investors hedge profitable returns even under high volatility period. Furthermore, other future researches can also take further investigation into the different measurement methodology of exchange rate volatility and comparing the effect of different measurement of volatility on the excess return of carry trade, there might be some interesting findings and some improvements of measuring method can be delivered. After all, under the globalized finance market, there are many unexpected changes across time, it’s always interesting to dig deeply and finding unexploited things.