Currency risk hedging during crisis periods : an empirical study beyond the traditional mean-variance space

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Amsterdam Business School

Master Business Economics: Finance track

Master Thesis:

Currency risk hedging during crisis periods:

An empirical study beyond the traditional mean-variance space

By Tristan Wanders Student ID: 11156260 July 2016

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II

Statement of Originality

This document is written by Student Tristan Wanders who declares to take full responsibility for the contents of this document.

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

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

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III

Acknowledgements

There are a few people who I would like to thank for helping and supporting me during the past months in the completion of my thesis.

First of all I want to thank my supervisor Esther Eiling for the excellent supervision. From the start she provided me with good feedback and constructive criticism. During the entire time of writing the thesis she was available through email and responded very quickly. The feedback sessions always went according to schedule and every time she thoroughly read my work in progress and provided good feedback.

Secondly I would like to thank my parents for supporting me in every step of this Masters program and the rest of my education. They were always there for me when I needed someone to talk to or share my thoughts with. Especially my father who was always available to help me verify the calculations or economic reasoning used in this paper. This was extremely helpful and contributed to the quality of my thesis.

Finally I want to thank my girlfriend for supporting me every step of the way. She was always very understanding towards me and helpful so I could finish my second Master’s degree. In times when my motivation was low she was there to give me a push and make sure that I gave everything to finish my thesis.

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IV

Abstract

This paper analysis the effect of currency risk hedging within international portfolios during crisis periods and compares this with non-crisis periods. In addition to the distinction between crisis and non-crisis periods this paper does not only assess the traditional mean-variance space but also analyses the higher moment of portfolio returns. Within this paper the effect of currency risk hedging is examined for the entire sample period, non-crisis periods and crisis periods. The performance indicators are the first four moments of portfolio return and the Sharpe ratio. We find that currency risk hedging does not improve the performance of an international portfolio and if investors have preferences over more than just variance it is better to leave the portfolio exposed to currency risk. The unhedged portfolio outperforms an hedged portfolio during the entire sample periods, non-crisis and crisis periods. It is true that in all cases currency risk hedging reduces the variance of the portfolio. However this reduction comes at the cost of lower mean returns and Sharpe ratios. For the higher moments it is difficult to draw a solid conclusion because the effect of currency risk hedging is in most cases non-significant. However, performances of unhedged and hedged portfolios do converge during crisis periods. Despite the fact that the hedged portfolio is outperformed by the unhedged portfolio we find that a hedged portfolio on itself performs better during crisis periods than non-crisis periods.

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V

I. Introduction

Broadening investments by including foreign stocks and bonds in a portfolio is a common practice. Especially with regard to a long-term portfolio this diversification can be beneficial (Campbell et al., 2003). The idea behind this diversification is founded within the modern portfolio theory. It states that if assets with low correlation are combined within a portfolio at the right ratio, risk can be reduced regardless of the volatility of the underlying stocks and bonds. This makes investing in foreign securities even more interesting because early studies already documented the relatively low level of correlation among national equity markets (Grubel, 1968).

However including foreign investments within a portfolio also exposes it to risk. There are three main risks involved with an international portfolio, namely political risk, local tax implications and exchange rate risk. Exchange rate risk or currency risk is the risk is very important for investors. This is due to the fact that the returns on a foreign stock must first be converted to the currency used by the investor. These fluctuations can be beneficial and enhance the returns but they can also negatively influence the return and reduce it (Adler & Dumas, 1984).

Despite these risks associated with foreign investments, the investor has the possibility to reduce the risk of losses caused by fluctuations in the exchange rate. This is called currency risk hedging. An unhedged position in international securities can be seen as a long position in foreign currency equal to the securities value. In contrary a fully hedged position equals a net zero position in foreign currency (Campbell et al., 2010). Hedging the currency risk can be accomplished by using currency forwards or options. By using these methods investors can lock in the current exchange rate for expected cash flows in foreign currency they will receive in the future.

Since foreign investments are inherent to currency risk, a question that arises within finance literature is whether currency risk should be hedged or not. Currency risk hedging used to be described as a “free lunch” (Pérold and Schulman, 1988), meaning the portfolio’s expected return remains unaffected while variance is reduced. This suggests that the risk return trade-off of international portfolios are improved at no cost which means hedging currency risk would always be the best option.

However recent literature states that empirical evidence is found of the existence of a currency risk premium (Lustig and Verdelhan, 2007). If this premium exists and currency risk is indeed priced, hedging currency risk may affect the expected return on the portfolio. De Roon et al. (2012) states that currency hedging reduces the portfolio variance as expected but also lowers the average portfolio returns. There results imply that exposure to currency risk improves portfolio performance, suggesting that there is no need to hedge currency risk

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- 2 - Assuming, due to the strong evidence, that currency risk hedging is no free lunch and does effect the portfolio’s returns, the following question arises. Which of the two has a greater influence on the investors preference, the reduced variance of a hedged portfolio or a higher expected return of a unhedged portfolio? This risk-return trade-off can be analysed by determining and comparing the Sharpe ratios of the unhedged and hedged portfolios. De Roon et al. (2012) find that in some cases exchange rate risk may actually improve the performance of international portfolios suggesting it’s better to leave the portfolio unhedged. However in periods of economic collapse this may change because reducing variance and risk can become more important than high returns. The idea behind this is that during periods of economical downfall ex post returns are in most cases very low and possibly negative while the volatility (variance) increases. So when returns are already low investors should focus on minimizing their variance and risk which will help prevent even larger losses. Therefore it could be the case that during crisis periods the risk-return trade-off is better for hedged portfolios than unhedged portfolios. On the other side Lustig et al. (2014) find evidence that the risk-return trade-off of currency risk premia shows countercyclical behaviour and improves during crisis periods. This might suggest that the ex-ante return during crisis periods is higher and exposure to currency risk is better than hedging.

Until now all literature with regard to currency risk hedging use a large sample which includes both crisis and non-crisis periods. The effects of currency risk hedging during crisis periods are not yet assessed or compared with the effects of currency risk hedging during non-crisis periods. So to the best of my knowledge no research has yet been done with regard to the following research question:

“What is the effect of currency risk hedging within international portfolios during crisis periods and how does this compare with non-crisis periods?”

The sample that will be used in this paper consists of stock returns on the MSCI World index during the period July 1975 till December 2015. Perspectives of the seven largest market are taken, namely the United States, Canada, Australia, Switzerland, Euro-zone, Japan and the United Kingdom. Therefore the returns on the MSCI World index will be denominated to all seven home currencies. The MSCI World index, an international equity portfolio, will be used as the base portfolio. For the construction of the hedged portfolios the minimum variance hedging strategy is used. In order to compare the performances of unhedged and hedged portfolios during crisis and non-crisis periods an overview all major crises during the sample period must be constructed. For this overview data from the IMF (Laeven and Valencia, 2013) is combined with that of the NBER (business cycle database ; Reinhart and Rogoff, 2008).

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- 3 - To test for changes between the unhedged and hedged portfolios this paper does not only focus on the traditional mean-variance space but also assesses the higher moments of portfolio return. These higher moments, skewness and kurtosis, are important to include because currency returns are not normally distributed and hedging might have an impact on them (de Roon et al., 2012). This paper starts by examining these differences between the performances of unhedged and hedged portfolios during the entire sample period. So far the objectives of this paper are similar to those of existing literature. Many studies (Campbell et al, 2010 ; Schmittman, 2010) already discuss these changes. This paper however uses a larger sample period with more recent data and includes the higher moments of portfolio returns. Only de Roon et al. (2012) take these higher moments into account.

However, the main contribution and objective is to assess if currency risk should be hedged within international portfolios during crisis periods and compare this with non-crisis periods. This will be done by assessing the variance and expected return (Sharpe ratio) as well as the higher moments, skewness and kurtosis. The objective is to conclude if there is a significant difference between hedged and unhedged portfolios during crisis periods. The results will then be compared to the performances of hedged and unhedged portfolios on the same criteria during non-crisis periods.

In this paper I find that if international investors have preferences over more than just variance it is better to leave the portfolio exposed to currency risk, which is in line with the results of de Roon et al. (2012). We find that an unhedged portfolio outperforms an hedged portfolio during the entire sample periods, non-crisis and crisis periods. In all cases currency risk hedging reduces the variance of the portfolio, but this reduction comes at the cost of lower mean returns and Sharpe ratios. For the higher moments it is difficult to draw a solid conclusion because the effect of currency risk hedging is in most cases non-significant. However results show that performances of unhedged and hedged portfolios do converge during crisis periods suggesting that a hedged portfolio on itself performs better during crisis periods than non-crisis periods.

The outline of this paper is as follows. Section II discusses the related literature along with theory related to the large field of currency risk hedging. The following topics will be assessed within this section: principles of currency risk hedging, remarks on the minimum variance hedge, explanation of higher moments and the relation of crisis periods towards currency hedging. Section III will describe the methodology used in this paper and gives a clear explanation which steps were taken during the research. This is followed by a discussion of the Data used along with some summary statistics of unhedged returns and the overview of crisis periods in section IV. Section V will give the main empirical results which is followed by some robustness checks in section VI. These robustness checks involve adding a carry trade and taking the 2007 global financial crisis as subsample period. Finally the conclusion will be given in section VII.

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II. Literature review

This section discusses the academic finance literature related to field of currency risk hedging. It starts by examining literature and theory related to the principles of currency risk hedging. Important insights as well as crucial formulas will be examined. Next I discuss the minimum variance hedge into detail and give some remarks with respect to the possibility of nonzero currency returns. In the third part of this literature review the higher moments of portfolio returns are taken into account. Background information, investors preferences and results from existing literature are discussed using the Sharpe ratio, Skewness and Kurtosis. Finally the last section examines the relation of crisis periods towards currency hedging by explaining well-known phenomena such as carry trades and crash risk.

A. Currency Risk Hedging

Until now most research has been done on the topic whether currency risk should be hedged or not. As already mentioned before the key question is the existence of a currency risk premium. If there is no premium, currency risk can be described as a free lunch (Pérold and Schulman, 1988). This can only be the case if currencies have zero expected returns and positive volatility, leading to an international portfolio with reduced variance and unaffected expected returns (Glen and Jorion, 1993).

If currency risk is indeed priced as recent evidence suggests (Dumas and Solnik, 1995 ; Lustig and Verdelhan, 2007), hedging currency risk not only affects the variance but also the returns of international portfolios. Combined with the fact that according to international asset pricing models investors need to be compensated for bearing risk (Adler and Dumas, 1984), two things can be concluded. First of all currency risk hedging is not costless in every situation and may negatively affect the portfolios expected return. Secondly, bearing exchange rate risk can also influence the performance of an international portfolio in a positive way. Campbell et al. (2010), Schmittman (2010) and de Roon et al. (2012) all find that currency risk hedging indeed reduces the portfolio’s variance. De Roon et al. (2012) also examines the effect of currency risk hedging on the mean returns and finds that the reduction of the portfolio’s variance results in lower average returns.

As described earlier investors holding foreign assets are exposed to currency risk. In order to get a better understanding about this exposure and currency risk hedging in general, it will be clarified by means of an example. This example will walk through every step of currency risk hedging as described within corresponding literature. The perspectives used can be found within existing literate with regard to hedging currency risk (de Roon et al, 2012 ; Campbell et al., 2010 ; Schmittman, 2010)

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- 5 - Suppose a European investor who invests in a United States stock portfolio. Where 𝑃𝑡$ is the

stock price at time t in US Dollar and 𝑆𝑡 the spot exchange rate for one US Dollar expressed Euros at

time t. The Euro return on investment is then given by the following equation. 𝑅_𝑡+1€ =𝑃𝑡+1 $ _𝑆 𝑡+1 𝑃_𝑡$𝑆𝑡 − 1 = (1 + 𝑅_𝑡+1$ _{)(1 + 𝑅} 𝑡+1𝑐 ) − 1 (1)

Where 𝑅𝑡+1$ is de return on the stock price in US dollar and 𝑅𝑡+1𝑐 the currency return which equals

the return on the Euro US dollar exchange rate. 𝑅_𝑡+1$ = 𝑃𝑡+1

$

𝑃_𝑡$ − 1 , 𝑅𝑡+1

𝑐 ₌𝑆𝑡+1

𝑆_𝑡 − 1

From these equations it can be concluded that the return of an investor investing in foreign assets is dependent on both the return of the asset in the foreign country and the return on the corresponding exchange rate.

This example clearly explains in which way investors are exposed to currency risk. Therefore the following step is to explain how the investor can hedge against this risk. The most common way to do this is by engaging in so called currency forward contracts (Glen and Jorion, 1993). A currency forward contract locks in the exchange rate for the purchase or sale of a currency on a future date. This takes away the investor’s sensitivity to changing exchange rates. From the investor’s perspective it is very important to know the forward rate because this effects his hedged return.

The forward rate can be determined by the interest rate differentials of the currency pair. This is based on the covered interest rate parity, which is a no-arbitrage condition in foreign exchange markets (Stein, 1965). The forward rate (𝐹𝑡) depends on three variables: the spot

exchange rate (𝑆𝑡), the domestic interest rate (𝑖𝑑) and the foreign interest rate (𝑖𝑓). Using the

example the domestic and foreign interest rate will respectively be the European an United States interest rates.

𝐹_𝑡 = 𝑆_𝑡∗(1+𝑖𝑑)

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- 6 - When the forward rate is constructed this will need to be compared to the exchange rate in order to determine the currency forward return (Schmittman, 2010)). The idea behind this is that when an investor takes a position in a forward contract this only beneficial if the exchange rate moves against the investor. In the example this will the case if 𝑆𝑡 (Euro per US dollar) goes down

resulting in a positive currency forward return. However if 𝑆𝑡 goes up it would be better if the

investor had nog hedged his position using a forward contract. In this case the currency forward return in negative. The currency forward return is calculated as followed.

𝑓𝑡=𝑆𝑡+1_𝐹

𝑡 − 1 (3)

Finally the hedged return of the European investor, using the currency forward return (𝑓𝑡), will be:

𝑅_𝑡+1ℎ _{= 𝑅} 𝑡+1 € _{+ 𝑤}

𝑡ℎ𝑒𝑑𝑔𝑒∗ 𝑓𝑡+1 (4)

To assess the hedged return it is important to determine the optimal hedge ratio (𝑤_𝑡ℎ𝑒𝑑𝑔𝑒). Within the finance literature this is an often discussed topic. The choice of hedging strategy has a lot to do with the preferences of investors. Some like to hedge all of the currency risk while other like to remain unhedged. The most commonly used hedging strategy used within the field of currency risk hedging is that of Solnik (1974). He states that when the assumption is made that the expected returns on currencies are zero, the optimal hedging strategy is the one which minimizes the

portfolio’s variance. Solnik (1974) shows that this optimal strategy is a full hedge when currency and equity returns are uncorrelated. A full hedge equals 𝑤_𝑡ℎ𝑒𝑑𝑔𝑒= −1. However this full hedge would not be the best strategy if currency and equity returns are indeed correlated. In this case the full hedge does not necessarily minimize risk and instead the optimal strategy is the minimum variance hedge. The minimum variance hedge can be calculated by

𝑤_𝑡ℎ𝑒𝑑𝑔𝑒= −𝐶𝑜𝑣(𝑅_{𝑉𝑎𝑟(𝑅}€,𝑅_𝑐₎𝑐) (5) Calculating the minimum variance hedge can be achieved by regressing the unhedged portfolio returns on the currency forward returns(de Roon et al, 2012). The minimum variance hedge will then be the slope coefficient of the OLS regression.

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- 7 - B. Remarks on the Minimum Variance Hedging Strategy

An important assumption that backs up the minimum variance hedging strategy is that currency returns have zero expected returns. However due to the increasing evidence of the existence of a currency risk premium (Dumas and Solnik, 1995 ; Lustig and Verdelhan, 2007) this assumption might be flawed. If currencies indeed have nonzero expected returns this implies that currency risk hedging does not only affect the variance but also the expected return.(Schmittman, 2010).

Therefore a remark that needs to be made with regard to the minimum variance strategy is that it is only optimal under the assumption that expected currency returns are zero. It is not designed to take into account any impacts on the expected return. Meaning investors using this strategy mostly solely focus on minimizing risk. If the assumption of zero returns on currency is violated this has consequences for investors using this strategy.

If currencies have nonzero expected returns they can also be held for pure investment or speculative reasons, rather than only hedging motives (de Roon et al., 2012). Strong evidence on the benefits of speculative currency investing are provided by the carry trade literature as mentioned before. This strategy has historically delivered a very attractive risk-return trade-off (Brunnermeier et al., 2008). As a consequence the Sharpe ratio might be positively influenced by these carry trades instead of the hedging of currency risk.

C. Sharpe Ratio and Higher Moments

To give a complete analysis on the effects of currency hedging it is important to extend this analysis beyond the traditional focus of volatility and expected return. In order to assess the risk-return trade-off the Sharpe ratio is included within this paper. Furthermore there are the higher moments of portfolio return which may give another view on the effects of currency hedging (Arditti and Levy, 1975). These higher moments need to be taken into account because currency returns are typically not normally distributed. Therefore portfolio skewness and kurtosis are also included.

The Sharpe Ratio is the most commonly used method for calculating risk-adjusted returns It represents the excess return per unit of volatility or total risk (Sharpe, 1994). Overall the attractiveness of the risk-adjusted return increases with a higher Sharpe ratio. Secondly skewness is a statistic that describes the asymmetry of a set of data with regard to the normal distribution. It can be negative if the data points are skewed to the left of the data average or positive if the opposite goes (Harvey and Siddique, 2000). For investors it can be important to know which way the returns are skewed because this way a better estimate can be given whether future returns will be more or less than the mean. The fourth moment, Kurtosis (“fat tails”), is a statistical measure used to describe the distribution of data around the mean. In the statistical field kurtosis describes excess means and

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- 8 - outliers. A higher kurtosis means that the variance is the result of sudden extreme deviations instead of frequent modestly sized deviations (Dittmar, 2002).

Before assessing the effects of currency risk hedging the preferences of the investors with regard to the higher moments mentioned above are discussed. Every investors would like to reduce variance and at the same time let portfolio returns be unaffected, which would be the case if a ‘’free lunch’’ exists. This can be assessed by using the Sharpe ratio, a measure for calculating the risk adjusted return. Skewness describes the asymmetry with regard to the normal distribution and is disliked if negative due to potential large losses (Kraus and Litzenberger, 1976). Investors do not have clear preferences over kurtosis but a combination with negative skewness is disliked (Scott and Horvath, 1980)

De Roon et al. (2012) is one of the first papers that examines the effect of hedging currency risk beyond this traditional focus on volatility. They confirm that currency risk hedging reduces portfolio variance for almost all currencies, as documented by Campbell et al. (2010). However they also discover a downside with regard to currency hedging. It can be concluded that hedging in most cases fails to improve the portfolios risk-return trade-off and decreases the Sharpe ratio. With regard to the higher moments they state that currency risk hedging worsens the skewness of international portfolios (a decrease of 37%). They furthermore find that the kurtosis is significantly higher for hedged portfolios than for unhedged portfolios.

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- 9 - D. Crisis Periods

This research aims to examine the effect of currency risk hedging during crisis periods. A financial crisis is broadly defined by a period in which a financial institution or asset suddenly loses a large part of their value. This can be associated with stock market crashes, banking panics and currency crisis (Allen and Gale, 1998). The first question that needs to be answered is why crisis periods are interesting with regard to currency risk hedging. This will first be done by relating the effects of a crisis on the mean return, variance and the Sharpe ratio. By doing this we can give better insight into the possible effects of currency risk hedging on the performance of an international portfolio during crisis periods.

Crisis periods are accompanied by low or often even negative mean returns and high volatility (Frankel and Saravelos, 2012). Currency risk hedging is a strategy that reduces the variance of a portfolio (de Roon et al., 2012 ; Campell et al., 2010) and can therefore be very interesting during times of crisis. De Roon et al. (2012) find that currency risk hedging decreases the average return of a portfolio. So in order to assess the risk-return trade-off the Sharpe ratio must be taken into account. During a large sample period de Roon et al. (2012) find that the Sharpe ratio of an unhedged portfolio is better than that of a hedged portfolio. However during times of crisis this might change. Since mean returns are already lower during times of crisis it could be the case that a currency risk hedging strategy has a better risk-return trade-off due to its reduction in variance. The opposite can also be true because crisis periods might lead to an increased currency risk premium suggesting that currency risk hedging causes the mean returns to drop even worse during crisis periods (Lustig et al., 2014). This makes it very interesting to analyse the performances of unhedged and hedged portfolios with regard to the minimum variance framework.

As already mentioned currency returns are typically not normally distributed. Therefore to assess the total risk not only the variance but also the higher moments need to be analysed. According to Chaudhury (2011) the 2007 global financial crisis lead to a weaker negative skewness and lower kurtosis of equity returns. De Roon et al. (2012) find that for a large sample period currency risk hedging worsens portfolio skewness and increases Kurtosis. If this is also the case for currency risk hedging during crisis periods this would suggest it is better to leave the portfolio unhedged. In order to give better insight into the effects of currency risk hedging on the higher moments during crisis periods an empirical analysis has to be performed.

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- 10 - Secondly I will further discuss the effects of crises on the currency risk premium. This is important because recent literature suggests that the existence of this premium causes currency risk hedging to effect expected returns (Dumas and Solnik, 1995 ; Lustig and Verdelhan, 2007). The currency risk premium is a violation of the uncovered interest rate parity which states that higher foreign interest rates should depreciate over time by the difference between the foreign and home interest rate (Froot and Thaler, 1990). However empirical evidence shows that higher foreign interest rates almost always predict high excess returns for an investor in these currency markets (Lustig and Verdelhan, 2007). The question that needs to be examined within this paper is how this currency risk premium behaves in crisis periods.

So the currency risk premium states that an investor obtains an excess return for holding foreign currency relative to domestic currency (Carlson and Osler, 2003). Currency risk hedging implies that the investor no longer holds any foreign currency and therefore decreases his excess return. Lustig et al. (2014) find that currency risk premia show countercyclical behaviour, suggesting that risk premia increase in periods of economic downfall. They find that the expected excess returns on a long position in foreign currency, meaning exposure to currency risk, is high during crisis periods for the US. However during non-crisis periods the excess return can be low or even negative (Lustig et al., 2014). This suggests that even during crisis periods it is better to leave your portfolio unhedged and exposed to currency risk. Nevertheless we have to keep in mind that this paper analyses portfolios containing multiple currencies. This means that one currency can have a positive currency risk premium while the other has a negative risk premium. Therefore, the portfolio’s overall risk premium depends strongly on the different currencies within the portfolio itself.

Next, literature that relates currency returns to crash risk is discussed. An example of a strategy that uses currencies to generate returns is a carry trade. A carry trade is a speculative currency strategy which consists of selling low interest rate currencies (funding currencies) and investing in high interest-rate currencies (investment currencies) (burnside et al., 2012). Carry trades are profitable due to a phenomena referred to as the ‘’forward premium puzzle’’ (Froot and Thaler, 1990). Brunnermeier et al. (2008), state that carry trade returns are negatively skewed which means that the profitability of the carry trade depends on crash risk.

Jurek (2014) combined the facts mentioned above with the currency trades’ positive exposure to equity market downside risks. He suggests that the excess returns of currency carry trades have to do with exposure to this risk. This risk is related to rapid devaluations of currencies with relatively higher interest rates. Jurek (2014) concludes that crash risk premia account for at most one-third of the excess return to currency carry trades.

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- 11 - These sources state that the profitability of carry trades is caused by their exposure to crash risk. This means that during non-crisis periods their returns must be higher to compensate for the losses during crisis-periods. If currency risk hedging is applied to the portfolio the exposure to crash risk reduces. This suggests that the expected currency returns will also decrease.

Finally I will give some insight into which literature sources are used to construct the overview of crisis periods which will be used in the empirical analysis of this paper. As mentioned before a crisis is a period where financial assets suddenly lose a large part of their value. Examples are stock market crashes, banking panics and currency crises (Allen and Gale, 1998). To identity crisis periods, multiple sources will be combined in order to create a complete overview of all crises. First of all the IMF provides an updated international crisis database which includes all crises from 1970 until 2012 (Laeven and Valencia, 2013). This will be used as a guideline to determine the crisis periods that will be included within the empirical analysis. However, this database contains all crises for all countries within this period. also small crises are included which probably had little to no influence on the portfolio returns of the seven largest developed markets. Therefore only the major crises were used in this paper. To construct the final overview of crisis periods the data from Laeven and Valencia (2013) was combined with that of the NBER (business cycle database ; Reinhart and Rogoff, 2008).

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III. Methodology

This section will give an overview of the methodology used to answer the research question of this paper. It will start by discussing the construction of hedged portfolios. Next I provide the methodology behind the identification of crisis periods. This is followed by a description of the method used for testing changes between unhedged and hedged portfolios in the first four moments of portfolio returns and the Sharpe ratio. This method can be applied for testing changes in the entire sample period, non-crisis and crisis periods. Finally I will discuss the visualization of the performances of unhedged and hedged portfolios within the entire sample period with highlighted crisis periods.

A. Portfolio Hedging

In order to compare hedged portfolios with unhedged portfolios and to examine the differences during crisis periods first of all a base portfolio needs to be constructed. This base portfolio will be an unhedged international equity portfolio, the MSCI World. The returns of this international portfolio are given in US dollars. Therefore the second step is to determine the unhedged returns for each of the seven countries used in this analysis. Since the MSCI World index is already given in US dollar the unhedged return for a US investor equals that of the return on the MSCI World. For the investors from a different countries perspective the return on the MSCI World needs to be adjusted by the return on the exchange rate. To achieve this formula (1) described in section II can be used.

As mentioned before an international equity portfolio can be hedged by buying forward contracts. Forward rates can be calculated by using formula (2). For each of the seven countries used in this analyses forward rates need to be constructed with regard to the remaining six. For example, taking a Japanese investor’s perspective this means that 6 forward rates need to be constructed for all countries vis a vis the Yen. Every time the exchange rate (𝑆𝑡) and the foreign interest rate (𝑖𝑓)

changes while the domestic interest rate (𝑖𝑑) equals the home currency1. When all forward rates are

determined the return on currency forwards can be constructed by using formula (3)

The optimal amount of forward contracts for each country can be determined by using the minimum variance hedge. By means of an OLS regression this minimum variance hedge can be calculated. This will be done by regressing the unhedged portfolio returns of a country on a constant and on the six corresponding currency forward returns. The calculated slope coefficients will then equal 𝜔ℎ𝑒𝑑𝑔𝑒 .

𝑟𝑢_{= 𝑎 + 𝑏 ∗ 𝑟}𝑐_{+ 𝜀.} ₍₆₎

With 𝑟𝑢= return on unhedged international portfolio, 𝑟𝑐=return on N currency forwards, -b=𝜔ℎ𝑒𝑑𝑔𝑒 (de Roon et al., 2012).

1

So for the six forward rates vis a vis the Yen the exchange rate and foreign interest rate changes six times but the domestic interest rates remains the interest rate of the Yen.

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- 13 - In order to construct an out-of-sample analysis with regard to the currency returns the minimum variance hedge will be determined by using the past 60 months of returns. This can be achieved by a rolling regression .

𝑟_𝜏𝑢_{= 𝑎 + 𝑏 ∗ 𝑟}

𝜏𝑐+ 𝜀𝜏 𝑓𝑜𝑟 𝜏 = 𝑡 − 1, . . , 𝑡 − 60. (7)

When the minimum variance hedge is determined the returns of the hedged portfolio can be calculated as followed

𝑟ℎ_{= 𝑟}𝑢_{− 𝑏 ∗ 𝑟}𝑐 ₍₈₎

With 𝑟ℎ= return on hedged portfolio

B. Identifying Crisis Periods

When the hedged portfolios are constructed the next step is to identify crisis periods. These can then be used to divide the sample into a crisis and non-crisis part. Each part, crisis and non-crisis, will then have a unhedged and hedged portfolio. As stated in the literature review crisis periods are defined and identified by combining the data of the IMF and NBER. From this data an overview of crisis periods is constructed.

In order to divide the sample into a crisis and non-crisis part the overview of crisis periods need to converted into two dummy variables. The first dummy variable takes the value 1 if the month is considered a crisis period and a missing value if the month is considered a non-crisis

periods2. The second dummy variable is the opposite and takes the value 1 if the month is considered a non-crisis period and missing if it is considered a crisis period. To divide the sample into returns made in crisis and non-crisis periods the returns only have to be multiplied by the dummy variables. This can be achieved by the following formulas.

For crisis periods:

𝑟𝑐𝑢 = 𝑟𝑢∗ 𝑑𝑢𝑚𝑚𝑦𝑐𝑟𝑖𝑠𝑖𝑠 and 𝑟𝑐ℎ= 𝑟ℎ∗ 𝑑𝑢𝑚𝑚𝑦𝑐𝑟𝑖𝑠𝑖𝑠 (9)

Where 𝑟𝑐𝑢 = unhedged return during crisis periods and 𝑟𝑐ℎ= hedged return during crisis periods

For non-crisis periods:

𝑟𝑛𝑐𝑢 = 𝑟𝑢∗ 𝑑𝑢𝑚𝑚𝑦𝑛𝑜𝑛𝑐𝑟𝑖𝑠𝑖𝑠 and 𝑟𝑛𝑐ℎ = 𝑟ℎ∗ 𝑑𝑢𝑚𝑚𝑦𝑛𝑜𝑛𝑐𝑟𝑖𝑠𝑖𝑠 (10)

Where 𝑟𝑛𝑐𝑢= unhedged return during non-crisis periods and 𝑟𝑛𝑐ℎ= hedged return during non-crisis

periods

2

The aim is to create a sample that only contains returns of crisis periods. In order to construct such a sample with only crisis periods the non-crisis periods have to be coded as a missing value. If they are coded with the value “0” the non-crisis periods are also taken into account when the empirical analysis are performed.

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- 14 - C. Testing for Changes between Unhedged and Hedged Portfolios

After the construction of the unhedged and hedged portfolios and the identification of the crisis periods the differences between the two can be compared by assessing the first four moments and Sharpe ratio. This will first be done by comparing the unhedged and hedged portfolios for the entire sample period. Next the changes between unhedged and hedged portfolios will be assessed within crisis and non-crisis periods. First the standard deviations and the mean returns of the portfolios will be compared. To test for differences in the relation between mean and variance the Sharpe ratio will be used. The usage of the Sharpe ratio is mainly due to the fact that it is a measure of risk-return trade-off. Finally changes between skewness and kurtosis are tested. Since returns are not necessarily normally distributed this paper follows the approach of de Roon et al (2012) and Lo (2002), using the method of moments methodology.

The following example shows the derivation and underlying formulas with regard to testing differences for the Sharpe ratio. Appendix A contains the derivation of the tests for the first four moments of portfolio return. Each of the different moments can be calculated as followed. Let 𝑟𝑡 be

the excess return and 𝑚𝑘 the kth moment 𝐸[𝑟𝑡𝑘]. In this case 𝑟𝑡 is the out-of-sample return on a

portfolio. Following this method the Sharpe ratios of the hedged and unhedged portfolios during crisis periods can be calculated by using the first two moments (Lo, 2002)

Sharpe ratio = _(𝐸[𝑟 𝐸[𝑟𝑡]

𝑡2]−𝐸[𝑟𝑡]2)1/2

=

𝑚1

(𝑚2−𝑚12)1/2

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To test for differences between the Sharpe ratios of unhedged and hedged portfolios we need to derive the limiting variance of the Sharpe ratios. The limiting variance is expressed by Ω(𝑆𝑅)𝐴𝐵 and

depends on the first derivative of the Sharpe ratio with regard to the first two moments. The first derivatives of 𝑚1 and 𝑚2 are:

𝜕𝑆𝑅 𝜕𝑚1= 1 𝜎+ 𝜇2 𝜎3 (12) 𝜕𝑆𝑅 𝜕𝑚2= − 𝜇 2𝜎3 (13) Where 𝜎 = 𝑠𝑡𝑑𝑒𝑣(𝑟𝑡).

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- 15 - To derive the limiting variance of the Sharpe ratio the following formula can be used

𝑉𝑎𝑟[𝑆𝑅] =1 𝑇 𝜕𝑆𝑅 𝜕𝑚Ω 𝜕𝑆𝑅′ 𝜕𝑚 = 1 𝑇Ω(𝑆𝑅) (14)

Within this formula 𝜕𝑆𝑅_𝜕𝑚 represents the vector (_𝜎1+𝜇_𝜎23 − 𝜇 2𝜎3) and

𝜕𝑆𝑅′

𝜕𝑚 is the same vector but

transposed. Ω denotes the covariance matrix of the first two moment 𝑚1 and 𝑚2 .

To test for the differences of two Sharpe ratios 𝑆𝑅𝐴 and 𝑆𝑅𝐵 the formula can be rewritten as

followed. 𝑉𝑎𝑟[𝑆𝑅𝐴− 𝑆𝑅𝐵] =1_𝑇(𝜕𝑆𝑅_𝜕𝑚𝐴 −𝜕𝑆𝑅_𝜕𝑚𝐵) Ω ( 𝜕𝑆𝑅′𝐴 𝜕𝑚 −𝜕𝑆𝑅′𝐵 𝜕𝑚 ) =1_𝑇Ω(𝑆𝑅)𝐴𝐵 (15)

In this case Ω is the covariance matrix of [𝑚𝐴1 𝑚𝐴2 𝑚𝐵1 𝑚𝐵2].

So if the true difference between the Sharpe ratios equals 𝛿 the limiting distribution will give

√𝑇((𝑆𝑅𝐴− 𝑆𝑅𝐵) − 𝛿) → 𝑁 (0 , Ω(𝑆𝑅)𝐴𝐵) (16)

After constructing the limiting variance the standard error can be calculated which can be used for determining the t-statistic.

The same method can be used for testing the differences between variance, skewness and kurtosis. Each of these limiting variances depend on the first derivatives of their moments. They can be expressed as followed Standard deviation = (𝐸[𝑟𝑡2] − 𝐸[𝑟𝑡]2)1/2= (𝑚2− 𝑚12)1/2 (17) Skewness = 𝐸[(𝑟𝑡_𝜎−𝜇)3 3]= 𝑚3−3𝑚2𝑚1+2𝑚13 (𝑚2−𝑚12)3/2 (18) Kurtosis = 𝐸[(𝑟𝑡_𝜎−𝜇)4 4]= 𝑚4−4𝑚3𝑚1+6𝑚2𝑚12−3𝑚14 (𝑚2−𝑚12)4/2 (19)

The derivation of all the limiting variances using the derivatives with regard to their moments can be found in Appendix A

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- 16 - D. Visualizing Performances of Hedged and Unhedged Portfolios during Sample Period Finally I will give an overview of the performances of hedged and unhedged portfolios during the sample period. This will be done by constructing five graphs containing the mean returns, standard deviations, Sharpe ratios, skewness and kurtosis for each of seven home currencies perspectives. Each graph contains a line which represents the unhedged portfolio and an line that represents the hedged portfolio. To give insight in the performance of hedged and unhedged portfolios during crisis and non-crisis periods each graph will contain highlighted periods which represent crisis periods. This will be done according to the overview of crisis periods constructed from the data of the IMF and NBER. The results for the US dollar perspective will be presented in chapter V while the graphs for the other currency perspectives can be found in Appendix B.

In order to construct the mean returns, standard deviations, Sharpe ratios, skewness and kurtosis within the sample period rolling windows are used. Each of the five performance indicators will be estimated by using the data of the past 12 months. For example the expected return will then be

𝐸[𝑟_𝑡] =1 𝑇 ∑ 𝑟𝑡

𝑡−1 𝑡−12

The other performance indicators can be calculated as before using this new expected return

Standard deviation = (𝐸[𝑟𝑡2]− 𝐸[𝑟𝑡]2) 1/2 Sharpe ratio = _(𝐸[𝑟 𝐸[𝑟𝑡] 𝑡2]−𝐸[𝑟𝑡]2)1/2 Skewness = 𝐸[(𝑟𝑡_𝜎−𝜇)3 3] Kurtosis = 𝐸[(𝑟𝑡_𝜎−𝜇)4 4]

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- 17 -

IV. Data Analysis

The initial data sample will consist of stock returns on the MSCI World index over the period July 1975 until July 2015. A long sample can be chosen due to the fact that in this case multiple crisis are taken into account (subprime crisis, dotcom crisis etc.). This paper will use the perspective of the seven largest developed countries, namely the US, Euro-zone, Australia, Canada, Japan, Switzerland and the UK. In order to calculate the unhedged returns for each country exchange rates need to be used. These are retrieved from the International Financial Statistics Database (IFS) from the IMF. For dates referring to the time before the Euro-zone was formed Germany’s exchange rates will be used because this was the largest market within the region. All exchange rates were retrieved in currency per US dollar.

In order to create a hedged portfolio first the forward rates need to be determined. For the constructions of the forward rate, short term interest rates of each country are needed. From Datastream the 1M deposit interest rate (Financial Times/ Thomson Reuters) was retrieved except for the UK where I used the ST deposit interest rate (Financial Times/ Thomson Reuters). After examining the interest rate data it turned out that for Australia and Japan some dates were missing. Datastream reported no 1M deposit interest rates of Australia before April 1997 and for Japan non before August 1978. To fill in the missing data I used the short term T-bill interest rate given in the IFS database. These forward rates are needed to determine the minimum variance hedge and construct a hedged portfolio. As explained before in the methodology the minimum variance hedge is calculated by using the past 60 months of data. In order to achieve this rolling regressions are used. These regressions based on the past 60 months of data ensure an out-of-sample analysis but also shorten the dataset with 59 months. This means that the sample which will be used for further analysis ranges from June 1980 until July 2015.

To give a comprehensive overview of the data used in this paper Table I will provide some summary statistics. Two samples are presented, first the initial raw data which ranged from July 1975 to July 2015. This data could contain errors and still needs to be corrected for the usage of rolling regressions which shortens the dataset by 59 months. Therefore the second sample will contain the correct and final dataset. In order to give a complete overview the table presents the mean, median, stdev, min, max, skewness, kurtosis and number of observations. Finally the table presents an correlation matrix containing the MSCI World index denominated in US dollar and the six currency forward returns vis a vis the US dollar.

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- 18 -

Table I – Summary Statistics MSCI World and Currency Returns

This table reports the summary statistics for the monthly equity returns of the MSCI world and the currency forward returns via a vis the US dollar. Panel A reports data from July 1975 to July 2015, a total of 481 months. Panel B reports the data for the adjusted sample of June 1980 to July 2015, a total of 422 months. The usage of rolling regressions to determine the minimum variance hedge caused a decrease of 59 months in the dataset. For this table the MSCI World index was used as a base portfolio. For the construction of the currency forward returns one month interest rate differentials were used. The corresponding exchange rates were retrieved from the IFS database. The exchange rate of Germany was used for the Euro-zone prior to the introduction of the Euro. This table reports monthly mean returns and standard deviations, the median, minimum, maximum, skewness, kurtosis and number of months. Finally panel C reports the correlations between the MSCI World and the currency forward returns.

Panel A: Unhedged returns MSCI World and currency forward returns vis a vis US Dollar Entire sample

MSCI 𝑟𝑐Can 𝑟𝑐Aus 𝑟𝑐Swi 𝑟𝑐Eur 𝑟𝑐Jap 𝑟𝑐UK

Mean (%) 0.68 0.71 2.13 -2.25 -0.78 -2.22 1.67 Median 1.03 0.61 1.91 -2.21 -1.10 -1.93 1.33 Stdev (%) 4.34 2.11 3.82 4.18 5.51 3.79 3.64 Min -18.81 -10.17 -11.72 -17.56 -14.16 -12.61 -10.65 Max 14.53 7.23 14.22 12.55 90.22 8.60 16.48 Skewness -0.49 -0.10 0.12 -0.17 9.36 -0.11 0.44 Kurtosis 4.78 4.01 3.33 3.45 155.41 2.64 4.36 N 481 481 481 481 481 481 481

Panel B: Unhedged returns MSCI World and currency forward returns vis a vis US Dollar Adjusted sample

Mean (%) 0.71 0.69 2.43 -1.87 -0.72 -2.24 1.46 median 1.16 0.62 2.28 -1.63 -0.88 -2.13 1.06 Stdev (%) 4.44 2.10 3.82 4.07 3.67 3.74 3.57 Min -18.81 -10.17 -11.72 -17.56 -14.16 -12.61 -10.65 Max 14.53 7.23 14.22 12.55 11.41 8.60 16.48 Skewness -0.51 -0.15 0.12 -0.12 0.09 -0.04 0.32 Kurtosis 4.77 4.26 3.23 3.49 3.25 2.75 4.28 N 422 422 422 422 422 422 422

Panel C: Correlations MSCI World and currency forward returns vis a vis US dollar MSCI 𝑟𝑐Can 𝑟𝑐Aus 𝑟𝑐Swi 𝑟𝑐Eur 𝑟𝑐Jap 𝑟𝑐UK

MSCI 1.00 𝑟_𝑐Can 0.26 1.00 𝑟_𝑐Aus 0.25 0.55 1.00 𝑟_𝑐Swi -0.01 0.34 0.41 1.00 𝑟𝑐Eur 0.01 0.36 0.41 0.91 1.00 𝑟𝑐Jap 0.08 0.25 0.41 0.64 0.60 1.00 𝑟𝑐UK 0.18 0.42 0.49 0.61 0.62 0.49 1.00

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- 19 - Table I provides summary statistics for the unhedged MSCI World and currency forward returns vis a vis the US dollar. Panel A reports the initial sample ranging from July 1975 to July 2015. These summary statistics are provided to give an initial overview of the data and check for possible outliers. Panel A shows that the MSCI World has an mean return of 0.68%, a standard deviation of 4.34%, is slightly negatively skewed and has a some excess kurtosis. The currency forward returns report different mean returns ranging from -2.25% to 2.13%.

If we take a closer look to the currency forward returns we find a very high skewness and an exceptionally high kurtosis for the Euro. The highest return observed is 90.22%. Compared with the other currency returns this is a very large difference. When a closer look is taken at the dataset it can be concluded that this return is realized in December 1998. This large outlier is the result from the changing exchange rate from Germany to the European Union which took place in Dec 1998 (IFS Database). Such a large outlier will have quite some effect on the higher moments and is therefore corrected within the data set.

The Results can be observed in Panel B which reports the adjusted sample ranging from June 1980 to July 2015. This is the final dataset which will be used for the empirical analysis in this paper. Panel B shows that the mean return and the standard deviation of the MSCI World are slightly higher within this sample period. The skewness worsens a bit and the kurtosis almost stays the same. Currency forward returns now range from -2.24% to 2.43% but no large differences are observed. However, panel B no longer reports the large outliers of Euro currency forward returns.

Panel C shows that all currency forward returns vis a vis the US dollar are positively correlated ranging from 0.25 to 0.91. This is in accordance to Campbell et al. (2010). The correlations of the MSCI World to the currency returns is a bit lower and even slightly negative for the Swiss Franc. Because the correlations between currencies differ and are not perfect this suggests that the minimum variance hedge is the best option instead of using a full hedge.

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- 20 - The aim of this paper is to assess the effect of currency risk hedging within international portfolios during crisis periods and compare this with non-crisis periods. In order to achieve this we have to identify crisis periods within the sample. To determine which periods in the sample should be identified as a crisis period the data from Laeven and Valencia (2013) was combined with that of the NBER (business cycle database ; Reinhart and Rogoff, 2008). This leads to the following overview of crisis periods.

Table II – Overview of Crisis Periods

This table presents an overview of all major crises that happened during the sample period ranging from July 1980 to July 2015. A total of ten crises were identified using the combined sources of the IMF and the NBER. For each crisis period in the table below the start and end date are presented along with a short description of the crisis.

Panel A: Crisis periods within sample

Start End Crisis

Oct 1987 Oct 1987 Black Monday , largest one-day decline in stock market history Jan 1990 Dec 1991 Japanese asset price bubble collapsed

Jan 1991 Dec 1993 Scandinavian banking crisis: Swedish and Finnish banking crisis Sept 1992 Dec 1993 Black Wednesday, speculative attacks on currencies in the European July 1997 Dec 1998 Asian Financial Crisis

July 1998 Sept 1998 Russian financial crisis Feb 2001 Nov 2001 Bursting of dot-com bubble Aug 2007 June 2009 Global financial crisis

Jan 2010 Dec 2010 European sovereign debt crisis June 2014 Dec 2014 Russian financial crisis

Table III shows that there were ten major crises during the sample period (June 1980 – July 2015). These eleven crises represent a total of 119 months within the sample meaning that there are 303 non-crisis months within the sample. From these identified crisis periods a dataset needed to be constructed. This was done by hand, creating a dummy variable which took the value 1 if the month was considered a crisis period according to the table above.

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- 21 - After the identification of all crisis periods and the construction of the crisis dummy variable we can take a look at the summary statistics with regard to the unhedged returns. The following table presents the summary statistics of all crisis periods taken together.

Table III – MSCI World and Currency Returns during Crisis Periods

This table reports the summary statistics for the monthly MSCI world and currency forward returns during crisis periods that occur within the sample of June 1980 to July 2015. All crisis periods add up to a total of 119 months. These statistics were acquired by multiplying the unhedged returns by the crisis dummy variable as described in the methodology. The crisis dummy variable was constructed by had using table III. This table reports, for all crisis periods combined monthly mean returns and standard deviations, skewness and kurtosis.

Panel A: Unhedged returns MSCI World and currency forward returns vis a vis US Dollar Crisis periods

Mean (%) -0.27 0.83 2.17 0.24 1.10 -0.95 2.38

Stdev (%) 5.96 2.59 3.81 3.77 3.65 3.69 3.90

Skewness -0.29 -0.54 -0.42 0.39 0.36 -0.17 0.19

Kurtosis 3.62 4.69 3.47 3.21 2.78 2.23 3.03

N 119 119 119 119 119 119 119

Panel B: Correlations MSCI World and currency forward returns vis a vis US dollar Crisis periods

MSCI 1.00 𝑟_𝑐Can 0.30 1.00 𝑟_𝑐Aus 0.26 0.69 1.00 𝑟_𝑐Swi -0.04 0.37 0.36 1.00 𝑟_𝑐Eur 0.01 0.39 0.33 0.85 1.00 𝑟𝑐Jap -0.04 0.30 0.32 0.59 0.52 1.00 𝑟𝑐UK 0.13 0.53 0.34 0.63 0.61 0.30 1.00

Table III provides the summary statistics for the unhedged MSCI World and currency forward returns vis a vis the US dollar during crisis periods. Panel A shows that the average return on the MSCI World during crisis periods is negative at -0.27%. The standard deviation during crisis periods has increased by 34% to 5,96% when compared to the entire sample period. When the higher moments are taken into account it appears that the skewness and kurtosis slightly improve within crisis periods. The currency forward returns now range from -0.95% to 2.38% and only one of them is negative. It seems that the return on currency forwards improves during crisis periods. The next chapter will include hedged portfolios into the analysis and discusses the differences between the unhedged and hedged portfolios.

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- 22 -

V. Empirical Results

So far the only statistics provided were with regard to unhedged portfolios. In this chapter I start my analysis by assessing the impact of currency hedging on the first four moments of portfolio return and Sharpe ratio for the entire sample period (June 1980 – July 2015). Next I examine the differences between hedged and unhedged portfolios on the same criteria within crisis periods and non-crisis periods. Finally I compare the performances of the portfolios during crisis and non-crisis periods

A. Impact of Hedging on the First Four Moments and Sharpe Ratio

We first analyse the impact of hedging for the entire sample period. This will be done by assessing the mean returns, standard deviation, Sharpe ratio, skewness and kurtosis.

Table IV – Currency Risk Hedging in International Portfolios

This table reports the out-of-sample results for currency hedging in an international portfolio for the entire sample period. All the unhedged returns are presented in local currencies by using the corresponding exchange rates from the IFS database. One month interest rate differential were used to construct forward rates. The exchange and interest rate of Germany was used for the Euro-zone prior to the introduction of the Euro. To construct the hedged portfolios an minimum variance hedge is added to the unhedged returns. This minimum variance hedge is constructed by using rolling regression based on the past 60 months of data. Panel A presents the impact of currency risk hedging on the standard deviations of the overall portfolio returns. It shows the standard deviations of both unhedged and hedged portfolios along with the corresponding t-statistics in parentheses. The last row of Panel A (t-stat(hedged-unh)) reports the t-statistics of the null hypothesis that the difference between the hedged and unhedged standard deviation equals zero. Panel B,C,D and E report the impact of respectively the mean returns, Sharpe ratio, skewness and kurtosis.

Home currency:

US$ Can$ Aus$ SwF Euro Yen BP

Panel A: Impact on portfolio standard deviation Unhedged stock portfolio

Stdev (unhedged) 4.44% 4.17% 4.50% 5.19% 5.01% 5.03% 4.62% t-stat (21.21) (22.40) (22.98) (22.47) (21.06) (19.75) (21.29) Add minimum variance hedge

Stdev (hedged) 4.02% 4.12% 4.26% 4.32% 4.38% 4.38% 4.11% t-stat (23.28) (25.38) (24.49) (26.01) (24.99) (26.02) (24.80) t-stat(hedged-unh) (-2.60) (-0.41) (-1.47) (-4.66) (-3.19) (-3.09) (-3.54)

Panel B: Impact on portfolio mean returns Unhedged stock portfolio

Mean (unhedged) 0.71% 0.73% 0.82% 0.62% 0.73% 0.60% 0.81% t-stat (3.23) (3.65) (3.73) (2.48) (3.04) (2.40) (3.52) Add minimum variance hedge

Mean (hedged) -0.79% -0.37% 1.12% -2.72% -1.74% -3.32% 0.07% t-stat (-3.95) (-1.85) (5.33) (-12.95) (-8.29) (-15.81) (0.35) t-stat(hedged-unh) (-5.09) (-3.83) (1.01) (-10.17) (-7.61) (-12.06) (-2.47)

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- 23 -

Panel C: Impact on portfolio Sharpe ratios Unhedged stock portfolio

SR (unhedged) 0.159 0.174 0.182 0.119 0.145 0.119 0.176

t-stat (3.11) (3.39) (3.59) (2.37) (2.86) (2.33) (3.45) Add minimum variance hedge

SR (hedged) -0.193 -0.089 0.264 -0.631 -0.397 -0.758 0.017

t-stat (-4.13) (-1.86) (5.18) (-12.37) (-8.11) (-14.42) (0.35) t-stat(hedged-unh) (-10.66) (-9.16) (2.56) (-15.25) (-12.24) (-17.23) (-4.86)

Panel D: Impact on portfolio skewness Unhedged stock portfolio

Skew (unhedged) -0.51 -0.49 -0.32 -0.45 -0.47 -0.74 -0.41 t-stat (-2.40) (-2.64) (-1.80) (-2.11) (-2.03) (-3.31) (-1.68) Add minimum variance hedge

Skew (hedged) -0.55 -0.45 -0.17 -0.24 -0.24 -0.25 -0.28 t-stat (-3.43) (-3.16) (-1.02) (-1.65) (-1.47) (-1.75) (-1.79) t-stat(hedged-unh) (-0.19) (0.24) (0.76) (1.14) (1.10) (2.30) (0.73)

Panel E: Impact on portfolio kurtosis Unhedged stock portfolio

Kurt (unhedged) 4.77 4.38 4.20 4.35 4.81 5.33 4.73

Kurt (hedged) 4.02 3.62 3.83 3.50 3.70 3.50 3.75

t-stat (0.05) (1.18) (0.50) (1.49) (0.79) (1.72) (0.76) t-stat(hedged-unh) (-1.14) (-1.56) (-0.81) (-1.99) (-2.24) (-2.94) (-1.62) Each column present the results for the unhedged and hedged portfolios in a different home currency. This means that the first column takes the perspective of a US investors and is based on returns on the MSCI World index denominated in US dollars. Let’s first take a look a Panel A which assesses the impact of currency hedging on standard deviations. It can be concluded that indeed currency risk hedging reduces the variance of a portfolio. All seven perspective show a decrease in standard deviation ranging from 1.2% to 16.8%. The risk reduction is statistically significant for five of the seven home currencies. Only the Canadian and Australian dollars show non-significant decreases. This is in line with the findings of de Roon et al. (2012).

As already mentioned in the literature review it is expected that hedging currency risk does effect the expected return of the portfolio due to the existence of a currency risk premium. Panel B in this table reports results that are in line with this expectation. We find that for all seven home currencies except the Australian dollar currency hedging negatively influences the expected return. The average return over all seven home currencies are respectively 0.63% and -1.11% for the unhedged and hedged portfolios. individual decreases in expected return add up to 650% (Japanese Yen perspective). For the six currencies that report a decrease in expected return these decreases are

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- 24 - all statistically significant. Only the difference between unhedged and hedged portfolios in Australian dollars, which reports an increase in expected return, is not statistically significant.

Panel C tests changes in the portfolios Sharpe ratio in order to assess the risk-return trade-off. The table again reports for all home currencies except the Australian dollar a decrease in Sharpe ratio. Despite the significant reduction in volatility it can be concluded that the significant decrease in expected return has an higher impact. Sharpe ratios decrease by 90% (UK Pound perspective) to 737% (Japanese Yen perspective). All the decreases in Sharpe ratio are highly significant. Only the Australian dollar shows an increase in Sharpe ratio of 45%. This increase in Sharpe ratio between the unhedged and hedged portfolio is also statistically significant

In order to analyse the changes in the higher moments of portfolio returns Panel D and E report the skewness and kurtosis. For Table V can be concluded that currency risk hedging improves the skewness for all home currencies except for the US dollar perspective. The changes in portfolio skewness range from a worsening of 7.8% (US dollar) to an improvement of 66% (Japanese Yen). However all changes, except for the Japanese Yen, are not statistically significant. Finally we assess the impact of currency hedging on the kurtosis of the portfolios. The average kurtosis over the seven home currencies decreases by 20% when a minimum variance hedge is added to the portfolio. However the change in kurtosis is only statistically significant for three of the seven country perspectives .

So it can be concluded that currency risk hedging indeed significantly decreases the standard deviation of the portfolio. However, this comes at the cost of a significant lower return. Therefore the Sharpe ratio needs to be assessed in order to analyse the risk-return trade-off. The Sharpe ratio is significantly lower for six of the seven home currencies suggesting currency hedging worsens the portfolio performance and it is better to be exposed to currency risk. Analysing the higher moments Table IV suggests that currency risk hedging improves the portfolio skewness and kurtosis. Especially the improvement of portfolio skewness can be seen as a positive consequence. However with regard to the skewness it has to be taken into account that these improvements are not statistically significant except for the Japanese Yes. The decrease of Kurtosis in only significant for the Swiss Franc, Euro and Japanese Yen.

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- 25 - B. Impact of Currency Risk Hedging during Non-crisis and Crisis Periods

Until now the impact of currency risk hedging was only assessed for the entire sample period. This paragraph will make a distinction between crisis and non-crisis periods using the crisis periods defined in Chapter IV. We first analyse the effect of currency risk hedging during non-crisis periods followed by the effect during crisis periods. The non-crisis sample consists out of 303 months while the sample containing crisis periods consists out of 119 months.

Table V – Currency Risk Hedging in International Portfolios during Non-crisis Periods

This table reports the same statistics as table V but for a different sample period which only contains non-crisis periods, a total of 303 months. In order to achieve this the sample must first be divided into crisis and non-crisis periods by making use of the non-crisis overview table, table II . These non-crisis periods are defined and identified by combining the data of the IMF and NBER. The identified non-crisis periods are then converted into a dummy variable which takes the value 1 if the month is considered a non-crisis period and a missing value if the month is considered a crisis period. To create a sample with returns made only in non-crisis periods the returns only have to be multiplied by the dummy variable. This table again compares unhedged and hedged portfolios with another and tests for changes in standard deviation, the mean returns, Sharpe ratio, skewness and kurtosis.

Home currency:

Panel A: Impact on portfolio standard deviation during non-crisis periods Unhedged stock portfolio

Stdev (unhedged) 3.61% 3.50% 3.98% 4.32% 4.14% 4.07% 3.80% t-stat (21.11) (23.09) (20.17) (23.10) (22.68) (22.57) (20.97) Add minimum variance hedge

Stdev (hedged) 3.58% 3.67% 3.93% 3.80% 3.76% 3.97% 3.66% t-stat (21.68) (23.28) (21.42) (22.70) (23.04) (23.26) (21.78) t-stat(hedged-unh) (-0.23) (1.56) (-0.30) (-2.86) (-2.19) (-0.58) (-1.02)

Panel B: Impact on portfolio mean returns during non-crisis periods Unhedged stock portfolio

Mean (unhedged) 1.09% 1.00% 1.10% 1.05% 1.07% 1.05% 1.09% t-stat (5.19) (5.00) (4.78) (4.20) (4.46) (4.57) (4.95) Add minimum variance hedge

Mean (hedged) -0.54% -0.21% 1.24% -2.99% -2.06% -3.36% 0.07% t-stat (-2.57) (-1.00) (5.39) (-13.59) (-9.36) (-14.65) (-0.33) t-stat(hedged-unh) (-5.60) (-4.16) (0.43) (-12.23) (-9.73) (-13.52) (-3.85)

Panel C: Impact on portfolio Sharpe ratios during non-crisis periods Unhedged stock portfolio

SR (unhedged) 0.30 0.29 0.28 0.24 0.26 0.26 0.29

SR (hedged) -0.15 -0.06 0.32 -0.79 -0.55 -0.85 -0.02

t-stat (-2.65) (-1.05) (5.50) (-11.61) (-8.81) (-12.27) (-0.35) t-stat(hedged-unh) (-10.39) (-9.25) (1.00) (-15.29) (-13.77) (-17.07) (-7.23)