Currency Risk Hedging in International Portfolios

Transcription

1 Master Thesis MSc Finance Asset Management Currency Risk Hedging in International Portfolios --From the Perspective of the US and Chinese Investors Student Name: Hengjia Zhang Student Number: Thesis supervisor: R.C. Sperna Weiland Date: June 2017 Faulty of Economics and Business Amsterdam Business School

2 Statement of Originality This document is written by Student Hengjia Zhang 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. Author signature: Hengjia Zhang Date: June 30, 2017

3 Abstract Whether to hedge currency risk is still under debate. In this paper, I show that currency risk hedging can indeed reduce the volatility of international equity portfolio for the US dollar and Chinese yuan. However, currency risk hedging also decreases portfolio expected average return and does not increase portfolio Sharpe ratio at the same time. Moreover, currency risk hedging leads to more negative skewness and higher kurtosis of the equity portfolio. The results suggest that currency hedging is not costless and may significantly influence portfolio performance. Keywords: Currency Risk Hedging, International Equity portfolio, Developed Market, Emerging Market i

4 Contents Abstract...i Section I Introduction... 1 Section II Literature Review... 5 Section III Data Section IV Methodology A. Hedging Position B. Test Changes in Portfolio Volatility, Returns and Sharpe ratio C. Higher Moments Section V Results A. Minimum Variance Hedging Ratio B. The Impact of Minimum Variance Hedging and Full Hedging for US Dollar C. The Impact of Minimum Variance Hedging and Full Hedging for Chinese Yuan D. Decompose Skewness E. Theoretical Analysis Section VI Robustness Check Section VII Conclusion A. Conclusion B. Limitation References ii

5 Section I Introduction With the ongoing globalization, many investors decide to include international assets into their portfolios. On the one hand, adding international assets to a portfolio might be beneficial from the perspective of diversification. On the other hand, it exposes investors to currency risk that could reduce or even offset the benefits from diversification. Whether to hedge currency risk or not is, however, still under debate, and crucially depends on whether currency risk is priced. If this is the case, a risk-return trade-off arises in which investors have to consider whether the decrease in risk is preferred to lower expected returns. Furthermore, currency risk hedging in international portfolios has been regarded as free lunch in both the academic and practitioner literature. In this case, holding currency hedging positions in global portfolios can reduce portfolios volatility without affecting portfolio expected returns. Therefore, currency risk hedging improves the performance of global securities at no cost. Indeed, more and more studies find evidence for currency risk being priced, meaning that currency returns are non-zero. For instance, Solnik (1974) plus Adler and Dumas (1983) find evidence to consider risks of exchange rate as a priced element in the IAPMs that is the international asset pricing model. As a result, currency risk hedging is not costless. For example, Lustig and Verdelhan (2007) show that currency risk premium indeed exists and they find that high interest rate currencies have positive excess returns that are up to 4 percentages. This result indicates that holding currency hedging position is not costless, as the reduction of return volatility comes at the cost of a decrease in the expected returns. Many previous such as Lustig and Verdelhan (2007), Brunnermeier, Nagel, and Pedersen (2009) studies on currency hedging still ignore currency return and suppose it to be zero. Thus, they hold the opinion that currency risk hedging is costless. In this thesis, however, I will investigate which hedging strategy is the optimal currency hedging strategy when taking into account that expected currency returns are non-zero and affect portfolio returns. Aside from advantages of currency hedging, there are also downsides to currency hedging. For instance, expected returns are lower when 1

6 currency returns are regarded as non-zero. Besides, after currency hedging, the portfolio Sharpe ratio remains unchanged, but the portfolio skewness worsens. Apart from the non-zero expected currency returns, another, possibly important, factor in deciding the optimal hedging strategy is the base country of the investor. At present, most research on currency risk (hedging) takes the perspective of a US investor. However, it is a priori not clear whether the results found for US investors translate one-to-one to that of investors based in other countries. For example, currency returns of emerging market countries might have different correlations with equity returns. Furthermore, transaction costs involved with currency hedging of emerging markets might be higher, making hedging more expensive. Therefore, an analysis from the perspective of Chinese investors who invest in international assets can be necessary. With rapid economic growth in China, China has played a more and more important role in the world economy. More and more Chinese investors take advantage of international diversification in asset management. Therefore, it is necessary to analyze currency hedging strategy from the viewpoint of investors in emerging markets. Furthermore, the different economic systems and situations could cause the different correlation of currency returns and equity returns between developed and emerging markets. And this would result in different currency hedging strategy when investors consider adding foreign assets into their portfolios. In this thesis, we will therefore also think about currency hedging from the perspective of US investors and Chinese investors. We focus on Chinese market since a lot of previous literature only focuses on developed stock markets and ignore emerging markets. Emerging equity markets, such as Chinese market, Indian market, Russian market, and South African market, develop rapidly in recent years and play more and more important role in world economy. Chinese market as one of the most important emerging markets should be paid more attention and consider the changes brought by investing in international assets. In addition, I also expect that correlation between expected stock portfolio returns and currency returns is positive in developed markets, while the correlation in emerging markets is negative. The data used in this thesis is from January 2000 to March 2017 at a monthly interval. The stock returns and exchange returns used in this thesis are returns from 2

7 the seven largest developed markets plus Chinese market. Following similar methodology with Esther, Bruno, and Pierre (2012), the benchmark portfolio that denominated in all eight home currencies consists of equally weighted global stocks. Subsequently, I add currency hedging positions to the benchmark portfolio, where I focus in particular on a minimum variance hedging strategy and a full hedging strategy. After adding hedging positions to an unhedged portfolio, I examine changes in the volatility, the expected mean return, portfolio Sharpe ratio plus portfolio higher moments to see whether currency hedging could improve the performance of a global portfolio. The moment method that does not rely on the normal distribution is used to derive the simple tests. The analysis starts with calculating minimum variance hedging ratios and constructing minimum variance hedging portfolio. In the light of minimum variance hedging strategy as well as a full hedging strategy, I find that for both US dollar and Chinese yuan, currency returns and international equity returns are positively correlated. In other words, if a US investor or a Chinese investor holds an international equity portfolio and he wants to hedge currency risk, he should take short currency hedging positions with positive equity returns in all the foreign currencies. The results are different from our initial expectation that currency return and equity return has a negative correlation. Both the US and Chinese investors should adhere to the same hedging positions. Next, I consider portfolio volatilities and the changes of portfolio volatilities because of minimum variance currency hedging and full hedging. I confirm that both minimum currency hedging and full hedging can indeed decrease portfolio variance for US dollar and Chinese yuan. The evidence of non-zero currency return indicates that currency risk hedging could affect the expected portfolio returns. Therefore, I test the changes of expected portfolio returns due to currency hedging and find that the expected returns indeed decrease. For both US dollar and Chinese yuan, the mean unhedged returns are significantly above zero. When adding minimum variance hedging positions or full hedging positions to an unhedged portfolio, the mean returns are no longer significantly different from zero. Moreover, the reduction in expected returns is statistically and economically significant when using full hedging. As a 3

8 consequent, the portfolio Sharpe ratios drop for both US dollar and Chinese yuan. In other words, neither minimum variance hedging nor full hedging improves risk-return trade-off of international equity portfolios denoted in US dollar and Chinese yuan. Then, I focus on higher moments of portfolio returns which are ignored by most previous literature. I test whether minimum variance hedging and full hedging exert effects on higher moments of portfolio returns. The results show that both minimum variance hedging and full hedging deteriorate the skewness of international equity portfolios for US dollar and Chinese yuan. When adding hedging positions into portfolios, the portfolio skewness is more negative for both US dollar and Chinese yuan. Moreover, the kurtosis is found to be higher for unhedged portfolio returns than both minimum variance hedging and full variance hedging equity portfolio. Although higher kurtosis may not be a bad signal, investors dislike negative skewness combined with fatter tails. Therefore, currency risk hedging not only poses an impact on portfolio volatilities and expected portfolio returns, but also exerts a significant effect on portfolio higher moments. It is necessary to take the effect into account when assessing the performance of minimum variance hedging and full hedging. Finally, to better understand the impact on the skewness of portfolio because of currency risk hedging, I decompose skewness into three components and test which component matters most. The change of skewness when using minimum variance hedging and full hedging almost has the same trend. The results exhibit that coskewness between currency hedging portfolio and unhedged equity portfolio poses a positive impact on the total skewness, which means it is the least important element of all the three elements. I perform a robustness check. The robustness check is performed by sub-sample analysis. Similar results are obtained when I divided the whole period into two halves. The rest of this thesis is organized as follows. Section II provides the literature review of currency risk hedging. Section III illustrates the data and reports statistical summary of equity and currency returns. Section IV introduces the methodology. Section V shows the main empirical results and theoretical analysis. Section VI focuses on robustness test, and the last section is the conclusion and limitation. 4

9 Section II Literature review When investors invest in international assets, their portfolio will be exposed to currency risk. Take a US investor as an example. Assume the US investor invests in a British stock portfolio. The expected dollar return of his investment can be expressed as $ R t+1 = P t+1 S t+1 P 1 t S t c = 1 + R t R t+1 1 (1) where S t is the spot exchange rate expressed in dollars per British pound at time t, P t c is the stock price expressed in British pound at time t and R t+1 = S t+1 S t 1 is currency return. Here, we assume that investors can only go long or short in forward contracts to hedge currency risk. Suppose that the investor enters into forward contracts to sell ω t edge /S t amount of US dollars for one British pound. Thus, the return of hedging portfolio is R t+1 $ = R t+1 ω t edge f t+1 (2) where f t+1 = (F t,t+1 S t+1 )/S t and F t,t+1 is the predetermined forward exchange rate expressed in US dollars for selling one pound at time t with delivery date t+1. When ω t edge = 0, it is for unhedged strategy and when ω t edge = 1, it represents full hedging strategy. From the expression (2), we see that it is essential to determine what is the optimal weight ω t edge. Perold and Schulman (1988) point out that in the long term, currency return is zero. Hence, currency risk hedging costs nothing. The reason is that hedging reduces portfolio volatility without affecting portfolio expected return. Eaker and Grant (1990) also show that, compared with unhedged international portfolios, there is a unitary forward hedge strategy that can decrease the volatility of the portfolio returns without a significant reduction in the mean returns. Solink (1993) proposes that the optimal hedging strategy is unitary or full hedge when equity returns and currency returns are not correlated. However, if currency return and equity return are positively or negatively correlated, which suggests that currency return is not zero. Therefore, the 5

10 optimal hedging strategy is not full hedging, but the minimum variation hedge. The hedging ratio can be obtained by ω edge = Cov(R$, R c ) Var(R c ) The calculation of the hedging ratio is to regress currency return on the unhedged portfolio return and hedging ratio is equal to the slope coefficient in the OLS regression. A negative correlation between equity return and currency return indicates that ω edge is below zero, which means that currency receives a positive weight in the hedged portfolio. Therefore, investors should take long positions in forward contracts. On the contrary, ω edge is larger than zero if currency and equity returns change in the same direction, which means foreign currency appreciates when an investment has positive returns. In this way, investors should go short in foreign currency with positive equity return to hedge risk. There is an extensive literature that focuses on whether to hedge currency risk when adding foreign assets into portfolios. Some of them are in favor of currency risk hedging, while others conclude that currency risk should not be hedged. According to the theoretical work of Levy and Lim (1994), and Bugar and Maurer (2002), if a portfolio is exposed to foreign exchange risk, the loss from currency risk could eliminate the benefits of international diversification. In other words, they think that the adverse impact on returns of portfolios brought by currency hedging overwhelms advantages resulting from international diversification when hedging currency risk. Consequently, it is necessary to hedge currency risk. Glen and Jorion (1993) point out that in international bond and stock portfolios, currency risk hedging is beneficial for both speculative and risk minimization motives. Moreover, they conclude that conditional hedging strategies increase Sharpe ratio of bonds and stocks portfolios. However, when investors only invest in equity portfolios, the results are insignificant. Some evidence argues against currency risk hedging in international portfolios. For example, Froot (1993) shows that, for US dollar and British pound, risk-minimizing currency positions increase as investment horizon becoming longer. He also studies that for long term stocks, currency returns are zero. Meanwhile, stocks do not display lower return volatility when currency risk is hedged than unhedged. Also, for investors who have small transaction cost and counterparty risk, the optimal hedge 6

11 ratio could be zero, which means it is better to not hedge. Campbell et al. (2003) hold that long-term investors who are conservative should hedge real interest rates and that they are supposed to hold more than half of their wealth in foreign currency. Statman (2004) concludes that there are not significant differences with and without currency hedge from 1988 to Hence, exposure to currency risk neither improves portfolio performance nor worsens portfolio performance. However, he only focuses on developed countries and ignores emerging economies. edge Opinions about optimal ω t are also divided. Black (1990) proposes a universal hedge ratio that should be slightly less than 100% to hedge currency risk, and he proposes that this hedging ratio should remain unchanged for all investors in spite of the different domestic currencies of their portfolios. In other words, investors with different nationalities should have the same hedging ratio and the optimal hedging strategy is to hedge part of currency risk rather than the entire currency risk. In this view, ω edge should be slightly lower than one. Adler and Prasad (1992) generalize Black (1990) s results and relax some prior assumptions, identifying five universal currency hedge ratio (UHR) definitions. They also find that investors can apply minimum variance hedging ratio that comes from the regression of unhedged portfolio on currency returns and a constant. Campbell et al. (2010) estimate the demand for different currencies within the sample and calculate unconditional hedge ratios through portfolio variance-minimization. According to the in-sample analysis, they propose that the decreasing of portfolio volatility by using the minimum variance hedging strategy is significant. Besides, full hedging strategy is also used in many papers. Campbell et al. (2010) argue that if unhedged international equity return is not correlated with currency return, full hedging could be the optimal hedging strategy. Much literature ignores currency return and regards it as zero. However, there is increasing empirical evidence that the assumption of zero currency return does not hold and that currency returns are non-zero. Brunnermeier, Nagel, and Pedersen (2009) show that holding high interest rate currencies and shorting sell low interest rate currencies simultaneously is quite profitable during the period until The existence of nonzero expected currency returns has consequences when applying minimum variance strategy since this hedging strategy is only appropriate if currency 7

12 returns are zero. The existing literature mostly focuses on decreasing volatility only, but little research considers impact both on currency returns and risk. Eun and Resnick (1988, 1994) find that unitary hedges increase average returns and Sharpe ratio of hedging portfolio. They believe that full hedging portfolios perform better than unhedged portfolio does. They also argue that, to a great extent, currency risk is non-diversifiable. If currencies expected returns are non-zero, investors might gain carry profit by holding hedging instruments. In other words, purchasing high interest rate currencies and simultaneously selling low interest currencies can generate significant benefits. Burnside et al., (2006, 2011) argue that this is a prevailed speculative strategy and deliveries an attractive balance between risk and return. However, Glen and Jorion (1993) analyze hedging as well as speculative positions in foreign currencies. They find that it is hedging component rather than the speculative component that improve the performance of global portfolio after including currency hedging. Meese and Rofoff (1983) study exchange rates and find that when investors hold foreign assets, they can make use of interest differential without suffering losses from exchange rates fluctuating because exchange rates fluctuate randomly. That is to say, it follows almost a random walk. Because of the random fluctuation of the exchange rate, the high-interest-bearing currencies could appreciate, while the other currencies depreciate. However, exchange rates are inclined to converge to their purchasing power parity in the long term. The previous literature on currency risk hedging most focuses on markets in developed countries, while ignore emerging markets. This thesis provides analysis from the perspective of investors in China. There are several reasons that analyzing currency risk hedging in the emerging market are valuable. First, in recent years, China plays a more and more important role in world economy. World Economic Outlook 2016 published by International Monetary Fund (IMF) says that Chinese economic growth is 6.7% 1, exceeds Indian economic growth, which ranks first in the world. Stock markets also develop rapidly in China. According to the Wall Street Journal, Chinese stock market capitalization has exceeded European stock market 1 World Economic Outlook 2016 published by International Monetary Fund (IMF) 8

13 capitalization in 2016, accounting for 16% 2 in the global stock market. Second, Many Chinese investors decide to hold foreign currency in their portfolios. In 2016, Chinese investors invest more than 2000 billion dollars assets in foreign countries. Of this total, about 20% capital is invested in stock markets. Furthermore, according to a survey by Asset Management Association of China, 75.6% Chinese investors consider to invest part of their investment portfolios in foreign stocks. 3 Third, China and U.S. have different economic system and policies, and these two countries are in different economic growth stages. Thus, it might be different in the exchange-rate regime and stock trading cost. For instance, it is true that the cost of currency hedging in emerging market is very high. The most obvious cost is the bid-ask spread. A forward contract that exchanges the US dollar to a currency of a developed country has a minimal spread, while a forward contract that exchanges the US dollar to the currency of an emerging market has a relatively large spread. It is interesting to see whether the correlation between exchange rates and equity returns is different between these two markets. This difference is important regarding the choice of the hedging strategy. Therefore, it is worthwhile to study currency hedging in Chinese stock market. It is natural to ask whether currency risk premium exists and whether currency return and equity return are positively correlated. Cho et al. (2010) analyze for eleven markets including six emerging countries markets and six developed countries markets from 2003 to They conclude that currency returns and equity price have a significantly negative correlation for emerging market investors who hold foreign assets. However, for investors in the developed market, currency returns are positively correlated with equity price. Thus, these differences in currency returns and equity prices correlation between developing and developed markets might bring about different currency risk hedging strategies. Whether currency risk premium exists in emerging markets is also a fundamental problem. A few papers focus on this issue. Harvey (1995) finds that high expected returns in emerging markets are high. Generally, high expected returns should be associated with large exposure to relatively high-risk factors. Whereas emerging market returns are exposed to low-risk factors. He finds that it is likely to result from currency risk. In other words, currency 2 The Wall Street Journal, February Asset Management Association of China 9

14 risk premium is not zero in emerging markets. Carrieri et al. (2004) conclude that currency risk in emerging markets is priced and currency risk premium is positive and economically significant. Total currency premium represents appropriate 40% of the emerging market risk premium. Furthermore, they confirm that hedging currency positions are predominant. Walker (2008) analyzes currency risk hedging from the viewpoint of emerging market investors who invest in global assets. For these investors, currency hedging is not free lunch, since currency hedging increases expected returns plus return volatility. He also finds that in some emerging markets, to a less significant extent, such as Chile, Mexico, Colombia, and Brazil, international portfolios consist of a large proportion invested in unhedged equity. This intuition means that emerging market currencies tend to appreciate when the international portfolio returns are negative. De Roon and Nijman (2001) investigate that when market friction and short sale constraints are excluded, a US investor could benefit from diversification when investing in assets from emerging markets. However, if investors are confronted with market friction, short sale constraints and a large portion of transaction costs, this benefit could disappear. A number of previous papers consider returns as normally distributed. However, this is not the case in reality. Jarque and Bera (1987) test the statistical significance fo stock market and confirm that the null hypothesis that the normal distribution exists should be rejected at a 5% significant level in all stock markets. As for bond markets, except for US bond market, rejecting the null hypothesis of normal distribution at a 1% level, all the other bond markets could reject the null hypothesis at a 5% level. Thus, the asymmetric distribution of international portfolio return indeed exists. Aggarwal (1990) argues that the distribution of currency forward return is not normally distributed, but negatively skewed and has a significantly positive kurtosis. Brunnermeier, Nagel, and Pedersen (2009) also illustrate that currency trade returns are negatively skewed that investors do not prefer. Therefore, in this thesis, except for the impact on expected return and portfolio volatility, I also study the effect of currency risk hedging on portfolio skewness as well as kurtosis. 10

15 Section III Data The calculation of the unhedged and hedged returns requires spot exchange rates, one-month forward exchange rates, the risk-free rate and equity return indices. All analyses are based on the period from January 2000 to March 2017 at a monthly interval. I consider seven developed markets and one emerging market: the United States, Euro-zone, the United Kingdom, Japan, Australia, Canada, Switzerland, and China. For equity returns on Euro-zone, I use a value-weighted average return of Germany, the Netherlands, France, and Italy. All the weights are based on market capitalizations of the selected markets. The forward contracts are one-month contracts for Japanese yen, British pound, Euro, Canadian dollar, Australian dollar and Swiss franc with respect to the US dollar and Chinese yuan. MSCI total return indices are used to measure equity returns in each stock market. For data of seven developed markets, I collect the spot and forward exchange rates from International Financial Statistic database (IMF), and the risk-free rates are from Datastream. For data of Chinese market, I collect spot and forward exchange rates from CEInet Statistics Database, and the risk-free rates are from CSMAR. 11

16 Table I Summary Statistics Table I presents the summary statistics of mean stock returns denoted in seven home currency and mean currency forward returns denominated in US dollars and Chinese Yuan. All the returns are annualized. Data are from January 2000 to March 2017 at a monthly interval. Stock returns of all the eight currency are constructed based on MSCI total return indices. The returns of Euro stock market are created as a value-weighted average of Germany, the Netherlands, France, and Italy. The spot and forward exchange rates of seven developed markets are from International Financial Statistic database (IMF). Risk-free rates are from Datastream. The spot and forward exchange rates of Chinese market are from CEInet Statistics Database, and the risk-free rates are from CSMAR. The table also reports standard deviations, skewness and kurtosis of stock returns and currency forward return. Panel A: Country-level stock returns in local currency US UK EUR JAN AUS CAN SWI CNY Mean (% p.a.) Stdev (% p.a.) Skewness Kurtosis Panel B: Currency forward returns(denoted in US$) US UK EUR JAN AUS CAN SWI CNY Mean (% p.a.) Stdev (% p.a.) Skewness Kurtosis Panel C: Currency forward returns(denoted in CNY ) US UK EUR JAN AUS CAN SWI CNY Mean (% p.a.) Stdev (% p.a.) Skewness Kurtosis

17 Table I reports summary statistics of annualized mean equity returns and currency forward returns for all the eight selected markets. Panel A is stock returns measured in home currencies. Panel B and Panel C are currency forward returns denoted in US dollar and Chinese Yuan, respectively. Annualized mean stock returns differ across markets. The average stock returns are lowest in Japan and Switzerland stock markets and highest in Canada and Australia markets, range from 2.76% to 6.50%. The standard deviation of equity denominated in Chinese yuan is 30.1% that is the highest, more than twice the standard deviation of the Australian dollar. The standard deviation of US dollar, British pound and Swiss franc are almost the same. Furthermore, all stock returns have negative skewness, ranging from to Thus, stock returns are not normally distributed. The kurtosis of all stock returns is positive and is greater than 3, which means a leptokurtic distribution. Currency forward returns denoted in US dollar are lower than stock returns. The British pound and the Euro have currency returns that are even below 1, while the Australian dollar and Swiss franc have currency returns more than 2. Furthermore, all currency forward returns have a lower volatility than stock returns, which is in the range of 9% to 13% except the Chinese yuan, giving a volatility of only 1.87%. Apart from Australia dollars, Canadian dollars, and Chinese yuan, all the other currency forward returns have positive skewness measures. When currency forward returns are denoted in Chinese yuan, Australian dollar, Canadian dollars, and Swiss francs have positive mean returns, while the other four currencies have negative average returns. Annual volatility is similar to that of currency returns denoted in US dollar, except the British pound exhibits a much lower volatility of only 2.90%. The British pound, the Euro and the Swiss franc returns have slightly positive skewness measures, while the others show negative skewness measures. Finally, we can observe positive kurtosis for all currency forward returns. 13

18 Table II Cross-country Return Correlations This table reports cross-country return correlations of currency returns and equity returns. All the equity returns are denominated in domestic currencies and all correlations are calculated using monthly returns. Panel A provides the correlations of equity returns between countries in the rows and columns. All possible correlations of currency pairs are included. Panel B reports the correlations of currency returns between countries in rows and columns. Panel C reveals the correlations between currency return and equity return denominated in home currencies. Panel D reports the correlations between forward currency return and equity return denoted in home currencies. US UK Euro JAP AUS CAN SWI CNY Panel A: Equity returns US 1.00 UK Euro JAP AUS CAN SWI CNY Panel B: Currencies US 1.00 UK Euro JAP AUS CAN SWI CNY Panel C: Currency Return and Equity Return US UK Euro JAP AUS CAN SWI CNY Panel D: Forward Currency Return and Equity Return US UK Euro JAP AUS CAN SWI CNY

19 Table II provides four correlations related to equity return and currency return. Panel A shows the correlation between monthly equity returns and Panel B exhibits the correlation between monthly currency returns between different currencies. In this table, all possible correlations of each currency pair are provided. Panel A displays that equity return correlations are all positive and relatively large. All correlations are above 0.40, and some correlations stand out as quite large. For instance, the Euro-zone stock market shows a high correlation of 0.86 with British stock market. The Euro-zone equity market has a high correlation with Swiss equity market (0.82). Furthermore, both Japanese and Chinese stock markets reflect relatively low correlations with all the other capital markets. It reveals that during an extended period Japanese stock market experienced low even negative equity returns, while the other equity markets had high investment returns. The stock market correlations suggest that international diversification could bring about benefits for investors. Panel B shows the correlations of currency returns between currencies in the row and column. In Panel B, we can find that currency return correlations are lower than equity return correlations. Except for Chinese yuan returns, all the other currency returns have a positive correlation with foreign currency returns. Chinese yuan shows negative correlations with US dollar, British pound, Euro and Japanese yen. Besides, Euro exhibits a high correlation with Swiss franc (0.81), and also with British pound (0.66), reflecting the European economic integration. Panel C reports the correlations between currency return and equity return. All the correlations are above zero, indicating that currency return and equity return are positively correlated. In other words, when equity return increases, currency return would also increase and currency would appreciate. Panel D shows the correlations between forward currency return and equity return. Except for Japanese yen, all the other currencies have negative correlations between forward currency return and equity return. Thus, when equity return goes up, forward currency return would decrease. 15

20 Section IV Methodology This section focuses on the method of constructing unhedged international portfolios and corresponding hedged portfolios. Then, I consider the changes in Sharpe ratio when adding currency hedging positions as a measurement of the effect on expected returns and volatility. I also test the differences in the first four moments of portfolio returns after currency hedging. The methodology is similar to the method that Esther, Bruno, and Pierre (2012) use. A. Hedging Position DeMiguel, Garlappi, and Uppal (2009) estimate the out-of-sample performance of the sample-based mean-variance model and find that the naive 1/N portfolio (equally weighted portfolio) performs best. Besides, the equally weighted strategy does not need to optimize over individual home currency returns. The out-of-sample analysis is used in this thesis. Therefore, the base portfolio consists of eight equally weighted stocks, which means that all investors invest in both domestic stocks and foreign stocks with equally weighted. Note that I consider seven developed markets plus Chinese stock market; therefore, I take an equally weighted average of all eight markets equity index returns. The excess return of the unhedged global portfolio is denoted as r t x. x r t+1 = 1 8 = i=1 8 i=1 ( P i t+1s t+1 P i 1) t S t i [(1 + R t+1 f r t+1 R t c = (S t+1 S t ) S t (4) c f ) 1 + R t+1 1] r t+1 (3) i i where P t is the stock price at time t denoted in currency i S t is the spot exchange i c rate. R t is equity return denoted in currency i and R t is currency return. r f t is risk-free rate denoted in home currency. Next, I add currency hedging positions to the predetermined portfolio and calculate hedged portfolio returns. I regress unhedged portfolio excess returns on currency forward returns to estimate the minimum variance hedging weights ω edge. 16

21 In order to obtain the minimum variance hedging weights, I use the past 60 months of excess returns and currency forward returns. r x τ = a + b t R c τ + u τ, τ = t 1, t 2,, t 60 (5) The minimum variance hedging weights ω edge = b. Consequently, returns of hedged international portfolio r t are calculated as: r t = r x c t b t R t (6) It is clear that when b = 0, it represents the unhedged strategy. The hedged portfolio returns r t are equal to unhedged portfolio returns r x t. When b = 1, it is for full hedging strategy. Because each investor invests his capitals in all the eight markets, there should be seven hedging ratios correspond to seven foreign currencies. Therefore, hedged international portfolios are constructed as: r t = r t x 7 c i=1 b ti R t (7) If currency return and equity return have a positive correlation, which reveals that currency would appreciate with increasing equity return. From equation (4), we could learn that, in this case, S t+1 would increase. As what is mentioned before, forward currency return f t+1 = (F t,t+1 S t+1 )/S t. Thus, the increasing spot exchange rate at time t+1 results in the decreasing forward currency return. Therefore, investors should take short positions in currencies with the positive equity return and go long in currencies with the negative equity return. For example, a US investor who holds the international equity portfolio needs to hedge risk of the British pound. In this case, investors are assumed to only use forward contracts to hedge currency risk. Going long in forward contracts means that investors have to buy one pound for F t,t+1 US dollars in the future. On the contrary, taking short positions in forward contracts means that investors have to sell one pound for F t,t+1 US dollars in the future. Therefore, if currency return and equity return have a positive correlation, the investor should take short positions in British pound forward contract with positive equity return. The intuition is that a positive correlation between currency return and equity return means British pound appreciates with equity return going up. Appreciated pound leads to a reduction in forward currency return. Hence, selling forward contracts gains negative return in currency and offset positive gains in equity. On the contrary, if equity return drops, British pound depreciates. Then, selling 17

22 forward contracts gain positive return in the pound and offset losses in equity. By doing so, investors could hedge currency risk and gain a stable total return. In summary, if currency return and equity return have a positive correlation, to hedging currency risk, investors should go short in foreign currencies. If currency return and equity return are positively correlated, investors should take long positions in foreign currencies. B. Test Changes in Portfolio Volatility, Returns and Sharpe ratio After calculating both unhedged and hedged portfolio returns, I use the moment method to examine the significance of differences in the first four moments between the unhedged and hedging portfolios. First, I test whether the volatility differences between unhedged and hedged portfolio returns are significant. Then, I examine the significance of the returns differences between unhedged and hedged portfolio. Next, I examine the changes of the portfolio Sharpe ratios. Sharpe ratio is the mean excess return earned by investors when they endure one unit of total risk. Thus, Sharpe ratio is a measurement of the trade-off between volatility and return. I start with the first two moments and allow non-normally distributed returns. Higher moments will be discussed in the next section. De Roon and Nijman (2001) argue that adding new assets to the benchmark portfolio does not move mean-variance frontier of the portfolio. In other words, investors who use mean-variance strategy cannot gain from only including new investments to their original portfolios. Therefore, a standard test for mean-variance spanning cannot be applied in this analysis, because when we compare the Sharpe ratios between the unhedged portfolio and hedged portfolio, unhedged Sharpe ratio is not a set contained within hedging Sharpe ratio and vice versa. Thus, I consider a straightforward examination for the changes in Sharpe ratio when adding currency hedging positions. The test is based on moment methodology and does not require x normal distribution. Denote r t the excess return of the portfolio and σ t the standard deviation of the portfolio. Let m k represents the kth non-central moment E[r x t ]. The Sharpe ratio can be calculated as: SR = r t x (8) σ t When expressing the Sharpe ratio in the term of the first and second moments, the 18

23 Sharpe ratio is rewritten as: SR = E[r t ] E[r t 2 E[r t ] 2 ) = m 1 (m 2 m 1 2 ) (9) The moments m k is estimated by 1 T T t=1 ( r k t m k ) = 1 T T t=1 u k,t = 0 (10) Denote the covariance matrix of m as Ω(m). Thus, the covariance between m a and m b is T 1 Cov u a,t, u b,t = T 1 Ω ab, with u t i = r t i m t i. Assume the true Sharpe ratio difference between the unhedged portfolio and hedged portfolio is λ. T SR un SR λ is normally distributed with a zero expectation. The limiting distribution is T SR un SR λ ~N (0, Ω SR un, ) (11) where Ω SR is the Sharpe ratios limiting variance that counts on Sharpe ratio s first derivatives with respect to the first two moments. C. Higher Moments Finally, I consider the impact of skewness and kurtosis on both unhedged and hedged portfolios and compare changes in skewness and kurtosis when adding currency hedging positions into predetermined portfolios. The skewness of returns r t is a function of the first three moments: skew = E[ r t μ 3 ] σ 3 = m 3 3m 1 m 2 + 2m 1 2 (m 3 m 1 2 ) 3/2 (12) It is standardized skewness that is expressed as the third central moment divided by the cube of the standard deviation. The kurtosis of returns r t can be denoted as: kurtosis = E[ r t μ 4 ] σ 4 = m 4 4m 3 m 1 6m 1 2 m 2 + 3m 1 4 (m 2 m 1 2 ) 3/2 (13) 19

24 Section V Results The empirical results of this thesis consist of three parts. Part one is mainly about construct minimum variance hedging portfolio and obtain minimum variance hedging ratio. Part two focuses on effects of currency risk hedging for US dollar and part three is about impacts of currency risk hedging for Chinese yuan. For each part, first, I test the impact of minimum variance hedging on portfolio returns, volatility, Sharpe ratio and higher moments. Then, I consider adding full hedging currency positions to base portfolios and examine the impact on portfolio returns, volatility, Sharpe ratio and higher moments. A. Minimum Variance Hedging Ratio The first step of constructing minimum variance hedging portfolio is to compute the minimum variance hedging ratio, which is also the optimal hedging ratio. Table II reports the results. I first calculate the minimum variance hedging ratios for US investors. Panel A of Table III provides the results of hedging ratios for different currencies. Each column indicates the hedging ratio for different currencies. For instance, the second column provides the optimal exposure to Euro. Panel A shows that all currency risk optimal hedging ratios positive for US dollar, which means that US domestic equity returns and currency returns are positively correlated. In other words, all foreign currencies appreciate when US domestic equity returns are positive. Therefore, to hedge foreign currency risk, short currency positions should be added to US investors base portfolios. For example, a US investor hold an international equity portfolio, his portfolio has a statistically significant exposure of 22.6% to Euro and an even much greater positive exposure to the Australian dollar. Panel A also illustrates that currency hedging ratios are relatively small, especially Chinese yuan hedging ratio. The optimal currency portfolio has an exposure of 0.5% to Chinese yuan, only one tenth of the exposure to the Australian dollar. The second row of Panel A is standard deviation, ranging from 0.77% to 12.35%. The last row is the t-statistics of the null hypothesis that minimum variance hedging ratio equals zero. For all currencies, the corresponding t-statistics of hedging ratio are above 1.96, thus, the null hypothesis is 20

25 supposed to be rejected. All hedging ratios are significantly above zero. Table III Minimum Variance Hedging Ratio Table III reports minimum variance hedging ratio, which is also the optimal hedging ratio. Panel A reports the optimal hedging ratios for US dollar. Panel B provides the results for Chinese yuan. Optimal hedging ratios are estimated as the slope coefficient in an OLS regression, which is the unhedged stock portfolio returns on the currency forward returns and a constant. The past 60 months data are used to calculate these ratios. The first row is the average value of optimal hedging ratio and the second row reports the standard deviation of all the optimal hedging ratio of all the eight selected markets. The last row provides the results of t-statistics of the null hypothesis that the optimal ratio equals zero. In every market, investors need to hedge all the other foreign currencies. Thus, for each foreign currency, it has a corresponding optimal hedging ratio. Panel A: Minimum variance hedging ratio for US investors US$ Euro BP Yen Aus$ Cd$ SwF CNY Mean Stdev t-stat (55.6) (44.2) (29.0) (33.1) (28.6) (37.1) (8.4) Panel B: Minimum variance hedging ratio for Chinese investors US$ Euro BP Yen Aus$ Cd$ SwF CNY Mean Stdev t-stat (14.1) (49.5) (43.7) (28.5) (152.2) (27.4) (40.3) 21

26 Table III Panel B reveals the results of minimum variance hedging ratio for Chinese yuan. The optimal hedging ratios are also above zero for all foreign currencies, which mean that for a Chinese investor, his domestic equity return has positive correlations with all the other foreign currencies. If he gains positive returns on the domestic investment portfolio, he would also gain positive forward currency returns. Thus, positions that are long all foreign currencies help Chinese investors hedging currency risk. For example, portfolio significantly exposes 30.9% to Swiss Franc. The standard deviations range from 1.53% to 12.43%, suggesting all optimal exposures are significantly positive. The last row indicates that the null hypothesis that the optimal hedging ratios are identical to zero should be rejected and all minimum variance hedging ratios are significantly different from zero. It is essential to understand the exact meaning of the numbers reported in Table III. The figures provided in the table are minimum variance hedging exposures, which are optimal amounts for the US and Chinese investors to hedge currency risks of their portfolios. Hence, the numbers are also the optimal currency hedging exposure. A US investor holding an equally weighted global portfolio would invest US dollars in the other foreign currencies for every dollar invested in the equity portfolio. Thus, one dollar invested in the long position in an equity portfolio, dollars are invested in short currency positions. For instance, among these US dollars, a US investor should enter into forward contracts to sell Euro worth dollars, as well as the British pound, Japanese yen, Australian dollar, Canadian dollar, Swiss franc and Chinese yuan worth 0.278, 0.220, 0.468, 0.231, and 0.005, respectively. Compared the minimum variance hedging ratios between US dollar and Chinese yuan, we could find that both US equity returns and Chinese equity returns are positively correlated. For investors from US and China, to hedge foreign currency risk, they should go short in currencies in their portfolios. For full hedging strategy, the hedging ratio is equal to one for all foreign currencies. B. The Impact of Minimum Variance Hedging and Full Hedging for US Dollar After calculating minimum hedging ratios, I examine whether minimum variance 22

27 hedging and full hedging can decrease equity portfolio volatilities. The results are provided in Panel A of Table IV. In this part, all the examination is from the perspective of US investors. The first column indicates the results from the view of a US investor and the returns are denoted in US dollars. Panel A introduces how many risk reductions are because of currency risk hedging. The results show that both minimum variance hedging and full hedging indeed decrease volatilities of international equity portfolios. The mean monthly standard deviation of unhedged US stock portfolios is 4.60%. When minimum variance hedging positions are added to international equity portfolios, monthly standard deviation drops to 3.26%, a reduction of 29%. The t-statistic of changes in monthly standard deviation is 1.997; therefore, the null hypothesis that the decreases in standard deviation are identical to zero is rejected at the 5% significant level. For the monthly standard deviation of full hedging portfolio is 3.25%, a 29% reduction in comparison with that of the unhedged portfolio. The volatility reduction is also statistically significant at a 5% level. Panel B of Table IV reveals the outcomes of impact on portfolio average returns. The table reports that currency risk hedging indeed lowers the mean returns of the international equity portfolio. The mean equity return denominated in US dollar is 0.46% per month before hedging. When adding minimum variance hedging positions, the average return drops to 0.30% per month. Thus, minimum variance hedging reduces mean return by 35%. Furthermore, the corresponding t-statistic of the unhedged portfolio is 1.976, which means the null hypothesis that average equity return of the unhedged portfolio is equal to zero should be rejected at the 5% significant level. In other words, unhedged portfolio return is significantly greater than zero. However, when adding minimum variance hedging positions into equity portfolio, the mean return of optimal hedging portfolio is no more significantly different from zero. The average return of full hedging equity portfolio is 0.26% per month, which is lower than minimum variance hedging equity portfolio. Same as the mean return of minimum variance hedging portfolio, the average return of full hedging portfolio is no longer significantly above zero. However, the change of mean return because of full hedging is significant, while the difference between unhedged 23