ERASMUS UNIVERSITY ROTTERDAM
ERASMUS SCHOOL OF ECONOMICS
MSc Economics & Business
Master Specialisation Financial Economics
International Diversification and the Currency Hedging Decision
The U.S. Perspective
Author:
K.V. Sigeris
Student number:
334959
Thesis supervisor:
Dr. A.P. Markiewicz
Finish date:
December 2010
International Diversification and the Currency Hedging Decision
Preface and Acknowledgements
Firstly, I would like to thank my thesis coach Agnieszka Markiewicz for her help and supervision on
the Master Thesis. Her seminal, International Investments, and especially the seminar’s investment
assignment, gave me the incentive to research this topic.
Secondly, I would like to thank Panagiotis Tegos for his comments on my thesis and for all these
years we spent together during our studies. Furthermore, I would like to thank Tasos Arampatzis and
Stamatis Angelinas for their grammatical corrections.
Last but not least, I would like from the bottom of my heart to thank my family, for their undoubtedly
and selflessness support throughout all these years of studies.
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International Diversification and the Currency Hedging Decision
NON-PLAGIARISM STATEMENT
By submitting this thesis the author declares to have written this thesis completely by himself/herself, and not to
have used sources or resources other than the ones mentioned. All sources used, quotes and citations that were
literally taken from publications, or that were in close accordance with the meaning of those publications, are
indicated as such.
COPYRIGHT STATEMENT
The author has copyright of this thesis, but also acknowledges the intellectual copyright of contributions made by
the thesis supervisor, which may include important research ideas and data. Author and thesis supervisor will
have made clear agreements about issues such as confidentiality.
Electronic versions of the thesis are in principle available for inclusion in any EUR thesis database and repository,
such as the Master Thesis Repository of the Erasmus University Rotterdam
Abstract
This thesis investigates how U.S. investors can benefit from international diversification and how
currency hedging affects internationally diversified portfolios. Based on data from 2004-2010,
international hedged and unhedged efficient frontiers are formatted. Two optimization processes
are performed, using twenty national stock index portfolios and fifteen currencies. Moreover,
three different hedging strategies are tested. The results show that hedging one individual
country index portfolio leads in general to lower levels of standard deviation (risk), but also to
lower level of excess returns. Furthermore, in the presence of short sales constraints, there is
evidence that U.S. investors, who diversify their portfolios in developed and emerging markets
simultaneously, should hedge their exchange rate exposure for low levels of risk, but not for
higher levels of risk. When comparing the unitary hedging strategy to the Black’s universal
hedging strategy, the unitary hedging strategy performs slightly better.
Keywords: International Diversification, Exchange Rate Risk, Currency Hedging
JEL class.: G11, G15
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International Diversification and the Currency Hedging Decision
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International Diversification and the Currency Hedging Decision
Table of Contents
Preface and Acknowledgements .................................................................................................................. ii
Abstract ........................................................................................................................................................ iii
Table of Contents .......................................................................................................................................... v
List of Tables ............................................................................................................................................... vii
List of Figures ............................................................................................................................................. viii
1. Introduction .............................................................................................................................................. 1
2. Literature Review ...................................................................................................................................... 3
2.1 International Diversification ............................................................................................................... 3
2.2 Emerging Markets ............................................................................................................................... 4
2.3 Currency Hedging ................................................................................................................................ 6
3. Methodology ........................................................................................................................................... 12
3.1 Country’s index portfolio dollar excess returns ................................................................................ 12
3.2 Hedging with Forward Contracts ...................................................................................................... 13
3.3 Black’s Universal Hedging Ratio ........................................................................................................ 14
3.4 Portfolio’s Dollar Return and Return Variance ................................................................................. 15
3.4.1 Unhedged Portfolio .................................................................................................................... 15
3.4.2 Hedged Portfolio ........................................................................................................................ 16
3.5 Optimization ..................................................................................................................................... 16
3.6 Sharpe Ratio ...................................................................................................................................... 18
4. Data ......................................................................................................................................................... 18
5. Results ..................................................................................................................................................... 20
5.1 Black’s Universal Hedging Ratio Computation .................................................................................. 20
5.2 Index Returns 2004-2006 .................................................................................................................. 21
5.3 Index Returns 2007-2010 .................................................................................................................. 23
5.4 Sharpe Ratio ...................................................................................................................................... 27
5.5 Analysis of Efficient Frontiers Derived from Internationally Diversified Portfolios .......................... 29
5.5.1 International Portfolio, 2004-2006 Testing Period .................................................................... 29
5.5.2 International Portfolio, 2007-2010 Testing Period .................................................................... 31
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International Diversification and the Currency Hedging Decision
5.6 Efficient Frontiers’ Sharpe Ratio ....................................................................................................... 33
5.7 Currency Trends and Results ............................................................................................................ 34
6. Conclusion ............................................................................................................................................... 36
References .................................................................................................................................................. 38
Appendix A: Black’s Universal Hedging Formula, Data Inputs .................................................................... 43
Appendix B: Correlation Tables................................................................................................................... 46
Appendix C: Optimal Portfolio Weights & Efficient Frontiers’ Sharpe Ratio .............................................. 47
Appendix D: Short Sales Optimization ........................................................................................................ 53
Appendix F: Correlation & Covariance Tables ............................................................................................ 58
Appendix E: Risk Free Rates and DataStream Codes .................................................................................. 64
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International Diversification and the Currency Hedging Decision
List of Tables
Table 1
Country Index Portfolios used in the Optimization Process…………………………………….
18
Table 2
World Average Values……………………………………………………………………………………………..
20
Table 3
STOCK INDEX PORTFOLIOS, 2004-2006……………………………………………………………………
24
Table 4
STOCK INDEX PORTFOLIOS, 2007-2010……………………………………………………………………
25
Table 5
Sharpe Ratio - STOCK INDEX PORTFOLIOS, 2004-2006…………………………………………….
27
Table 6
Sharpe Ratio - STOCK INDEX PORTFOLIOS, 2007-2010…………………………………………….
27
Tables 7-8
Exchange Rate Volatilities……………………………………………………………………………………….
42
Tables 9-10
Country Weights on World Market Portfolio……………………………………………………………
43
Tables 11-12 World Market Excess Returns and Return Volatilities in Different Currencies…………
44
Tables 13-14 Correlation Matrix – Local MSCI Index Return………………………………………………………….
45
Tables 15-20 Correlation & Covariance Matrix – Dollar MSCI Index Excess Return, 2004-2006…….
Portfolio
Tables 21-26 Correlation & Covariance Matrix – Dollar MSCI Index Excess Return, 2007-2010…….
Portfolio
Table 27
Proxy of Risk Fee Rate……………………………………………………………………………………………..
57
60
63
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International Diversification and the Currency Hedging Decision
List of Figures
Chart 1
Optimization 1: Efficient Frontiers, 2004-2006…………………………………………………………
29
Chart 2
Optimization 2: Efficient Frontiers, 2004-2006………………………………………………………..
29
Chart 3
Optimization 1: Efficient Frontiers, 2007-2010………………………………………………………..
31
Chart 4
Optimization 2: Efficient Frontiers, 2007-2010………………………………………………………..
31
Charts 5-7
Optimization 1: Optimal Portfolio Weights 2004-2006……………………………………………
46
Charts 8-10
Optimization 2: Optimal Portfolio Weights 2004-2006……………………………………………
47
Charts 11-13 Optimization 1: Optimal Portfolio Weights 2007-2010……………………………………………
48
Charts 14-16 Optimization 2: Optimal Portfolio Weights 2007-2010……………………………………………
49
Chart 17
Optimization 1: Efficient Frontiers’ Sharpe Ratio, 2004-2006………………………………….
50
Chart 18
Optimization 2: Efficient Frontiers’ Sharpe Ratio, 2004-2006………………………………….
50
Chart 19
Optimization 1: Efficient Frontiers’ Sharpe Ratio, 2007-2010………………………………….
51
Chart 20
Optimization 2: Efficient Frontiers’ Sharpe Ratio, 2007-2010………………………………….
51
Chart 21
Short Sales Optimization: Efficient Frontiers, 2004-2006………………………………………..
53
Chart 22
Short Sales Optimization: Efficient Frontiers, 2007-2010………………………………………..
53
Charts 23-25 Short Sales Optimization: Optimal Portfolio Weights, 2004-2006…………………………..
54
Charts 26-28 Short Sales Optimization: Optimal Portfolio Weights, 2007-2010…………………………..
55
Chart 29
Short Sales Optimization: Efficient Frontiers’ Sharpe Ratio, 2004-2006………………….
56
Chart 30
Short Sales Optimization: Efficient Frontiers’ Sharpe Ratio, 2007-2010………………….
56
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International Diversification and the Currency Hedging Decision
1. Introduction
The lower correlation between foreign assets is the main advantage of international investing and
the key point that led most investors adapt this investment strategy, which was first established in
the 1960s and 1970s. However, while international diversification leads to significant risk
reduction, namely idiosyncratic and systematic risk, it also leads to exposure to another source of
risk, foreign exchange rate risk. Currency fluctuations have a great impact on total portfolio
return and risk, thus it becomes very important on how this risk can be managed properly.
One way to control for currency exposure is through multicurrency diversification, where in total
currency fluctuations seem to cancel one another. An alternative way to achieve it is through
currency derivatives, were exchange rate fluctuations can be hedged away. It is well known that
the use of currency derivatives can reduce risk in internationally diversified portfolios and
improve the risk adjusted performance of a portfolio. However, Abken and Shrikhande (1997)
showed that currency hedging does not always reduce risk of efficient international portfolios.
The goal of this Master Thesis is to research how currency hedging affected international
efficient equity portfolios, for the sample period January 2004 until August 2010. To do so,
twenty national MSCI index portfolios and fifteen currencies are used. Among these countries,
thirteen are developed and seven emerging. The effect of currency hedging is examined by
comparing efficient frontiers, which are derived by optimizing these individual country index
portfolios. The comparison of the efficient frontiers is based on three hedging strategies;
unhedged, unitary hedged and optimally hedged using Black’s universal hedging formula.
Furthermore, the research is conducted by taking the view of an American investor, and for this
reason, the base currency is U.S. Dollar.
The whole sample period is split in two testing periods; the first lasts from January 2004 to
December 2006 and the second from January 2007 to August 2010. The two sub periods are
chosen in such a way, so as the first represents a period of positive market returns, while the
second the recent financial crisis period.
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The results show that simply hedging one individual country index portfolio not only leads to
lower levels of standard deviation (risk), but also to lower levels of excess returns. Only three
countries display higher excess return when hedged, during the first testing period, regardless of
the type of hedging.
Contrary to previous studies, this is one of the few that uses more than eight countries in the
optimization process of internationally diversified portfolios and also multicurrency
diversification. Furthermore, this is the first study suggesting that U.S. investors who diversify
their portfolio abroad, using both developed and emerging countries, should hedge their
exchange rate exposure for low levels of risk, but not for the higher levels of risk, if short sales
restrictions are posed. Results show that hedged international efficient frontiers dominate the
unhedged for the low levels of standard deviation, but not for the higher levels. Furthermore,
unitary hedged strategies perform better than the Black’s universal hedged strategies.
This Master Thesis is structured as follows: Chapter 2 provides the literature review of previous
studies, concerning diversification, emerging markets and currency hedging. Chapter 3 describes
the methodology used to calculate the index dollar excess returns for every country, how these
returns are hedged using forward contracts and how the Black’s universal hedging formula is
derived. Moreover, Chapter 3 provides the methodology used to calculate the international
portfolio return and return variance, the optimization process and the Sharpe ratios. Chapter 4
presents the data, which are used in this study, and Chapter 5 describes the results. Finally, the
last chapter concludes the findings of this research, and topics for future research are suggested.
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2. Literature Review
This chapter discusses the literature review used to conduct this thesis; concerning international
diversification, the case of emerging markets and finally the effect that currency hedging has in
international investment strategies.
2.1 International Diversification
Does international diversification improve the risk-return relation for investors? This question
has deserved much attention from academics and investors trying to exploit the benefits and
threats from such an investment policy.
The uncertainty of expected returns can be reduced through diversification (Markowitz, 1991).
This is the principle of Modern Portfolio Theory first established by Markowitz (1952), who
recommended the use of variance returns as a measure of portfolio riskiness, and also, using this
point as an assumption he states that the portfolio selection is driven by the risk-return relation
between the assets in the portfolio. He showed that a diversified portfolio not only can have riskreturn combinations that are not found in individual securities, but also that, in most of the cases,
will have higher expected return for the same level of variance (risk), or lower risk for the same
level of expected return than single securities. The only case that the variance will not be
decreased is if the returns of the portfolio securities are perfectly correlated.
The idea that diversification can improve the portfolio performance in terms of risk-return
tradeoff is well understood and is based on the fact that portfolio security returns are less than
perfectly correlated; the lower the correlation of security returns the better the diversification.
Thus, a reasonable investment practice is turning from local to international investing. This case
for international portfolio diversification was established in the 1960s and 1970s. Lessard (1976)
and Solnik et al (1996), state that the main advantage of international diversification is the low
correlation between countries. Grubel (1968) is the first who finds that US investors could have
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achieved a superior risk-return tradeoff by diversifying part of their assets in other countries
between 1959 and 1966. Levy and Sarnat (1970) demonstrated the gains from diversification in
developed and developing markets by analyzing international correlations. Moreover, Solnik
(1974) showed that more risk seduction can be attained with international diversification by
comparing domestic and international portfolios for the period 1966-1971. Finally, using the
international CAPM, De Santis and Gerard (1997) estimated that a U.S. investor can expect an
annual gain of 2.11 on average from international diversification and that the long-term gains
from international diversification remain economically attractive. Putting it in another way,
Fletcher and Marshal (2005), took the view of a U.K. investor for the period 1985-2000, and
found a significant increase in the Sharpe ratio by adding foreign equities in U.K. domestic
portfolios and significant diversification benefits even if short selling constraints are present.
As already stated, the key factor of international diversification is the low correlation between
foreign equities. However, correlations change over time affecting the risk reduction concept. In
the recent decades, globalization has taken place, thus rising correlations between foreign
markets. Although King, Sentana and Wadhwani (1994) tried to shed some light on this, they
couldn’t find strong evidence of a trend increase in correlations while Solnik et al. (1996) by
examining monthly data for stocks between 1959 and 1995, found that for the last 10 years the
correlations between foreign stocks markets and the U.S. stock market didn’t seem to increase,
unlikely with the whole data period. However, they state that international correlations increase
during periods of high market volatility and according to Forbes and Rigobon (2002), there is a
high level of international market comovements (interdependence) during stable periods as well
as during crises, which can lead to some benefits of diversification being lost.
2.2 Emerging Markets
To exploit more diversification benefits, emerging markets are also used in this study. Emerging
markets are characterized by rapid economic growth and have investment possibilities that offer
a risk-return tradeoff not easily found in developed countries, thus providing high incentives for
including them in the portfolio selection when constructing international portfolios. A key
characteristic of emerging markets is their lower correlation with other markets, thus offering
bigger diversification benefits. However, the volatility of their asset returns is higher when
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compared to developed markets, a fact which could mitigate the diversification benefits, but De
Santis and Imrohoroglu (1997) couldn’t find any empirical evidence that this market volatility
has increased due to liberalization.
Gilmore and McManus (2001) using the method of cointegration and examining weekly data for
the period 1995-2001 on three Central European emerging markets, namely Czech Republic,
Hungary and Poland, found that these markets are not integrated with the U.S. market and that
the low correlation between those markets with the U.S. market provide diversification benefits
for U.S. investors for both short and long horizon. Furthermore, Gupta (2006, 2008) found that
although world markets move towards integration reducing the benefits, there are still unrealized
gains to be made by Australian investors by incorporating emerging markets in their portfolios,
even if short sales constraints are present.
The drawback of investing in emerging markets though, is the restrictions on short selling. Short
sales and even transaction costs counter contrary on the return of a portfolio and mitigate the
benefits of diversification. Using mean-variance spanning tests, De Roon, Nijman and Werker
(2001) find that although there are significant diversification benefits by adding emerging
markets to the portfolio, these benefits disappear if short sales constraints or small transaction
costs are present. On the contrary, Li et al. (2001, 2002) found that emerging markets are still a
valuable opportunity for U.S. investors as they offer substantial diversification benefits when
imposing short sales constraints. They also argue that De Roon et al. findings are not sensible
because they are based on some individual Latin American or Asian countries and not on the
optimal combination of those emerging markets.
Diversification benefits are attained not only by developed countries, but also by investors from
the emerging markets. Bugar and Maurer (2002) concluded that Hungarian investors can
drastically reduce the risk of their domestic stock investment by diversifying their portfolio
globally. Furthermore, Goriaev and Prikhodko (2004) by taking the view of a Russian investor
for the testing period 1999-2003, when Russian stock market experienced exceptional returns
with an average of 40% per annum, found substantial benefits for Russian investors from
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international diversification, which remain statistically and economically significant even in the
presence of short selling constraints and transaction costs.
2.3 Currency Hedging
There are three important ways that international investments differ from national investments
(Lessard, 1976). First, the covariances among international markets are much lower than those in
domestic markets. Second, barriers imposed by taxation, currency controls or investor home bias
can lead to further segmentation of national markets causing assets to be priced in a domestic
rather than in an international milieu. Third, floating exchange rates between different currencies
may give rise to currency risk on international portfolios.
Fluctuations in exchange rates have become very important in international investing because
these changes may offset any benefits from diversification and have a significant effect on the
returns when translated into home country. Any depreciation of the foreign currencies included
in the portfolio, leads to lower return when translated back to the domestic. The importance of
the currency risk management can be pointed out by the fact that currency risk accounts for
about forty to fifty percent of the total risk of a single-country investment in multicurrency stock
portfolios (Eun and Resnick, 1988; Schmittmann, 2010).
For all the above reasons currency risk should be of major importance for international investors
and their strategies should be designed in order to control the adverse effects that the unpredicted
exchange rate fluctuations can have on foreign market returns.
One way to control exchange rate uncertainty is through multicurrency diversification, but it is
shown that exchange rate uncertainty is a largely nondiversifiable factor adversely affecting the
performance of international portfolios (Eun and Resnick, 1988). For that reason the most proper
and widely used instruments for managing currency risk are currency derivatives. Using
currency derivatives, hedging strategies can be designed and incorporated in the international
investment practice, as the primary objective of hedging is to reduce the risks produced from
price movements of assets by taking an offsetting position in the underlying asset.
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The three most common types of derivatives used to hedge currency risk are currency forwards,
currency futures and currency options. Currency forwards are private agreements between two
parties to buy or sell a currency at a pre-specified price and date. Futures on the contrary, are
publicly traded on exchanges and also standardized in quantity, delivery date and place.
Moreover, futures are characterized by daily marking-to-market which gives the right for
settlement prior to the delivery date. Finally, currency options give the owner the right, but not
the obligation to buy or sell currency at a predetermined price and time in the future.
Hedging the currency risk of foreign equity returns can reduce both systematic and unsystematic
risk for local investors who diversify their portfolio in foreign equity markets (Lee, 1988). Eun
and Resnick(1988) investigated the effects of floating exchange rates on multicurrency portfolios
by developing ex ante unhedged and fully hedged strategies from the U.S. investor perspective
for the testing period 1980-1985. They state that exchange rate uncertainty is largely
undiversifiable due to the high correlations among the exchange rate changes. For that reason,
they employed simultaneously multicurrency diversification and forward hedging to reduce
exchange rate risk. Their findings suggest that U.S. investors can substantially benefit by using a
hedging strategy in their international investments, as all hedging strategies performed far better
than the unhedged in out-of-sample periods.
One of the most important papers in the currency hedging debate is that of Perold and
Schoulman (1988). They claim that in the long run investors should take currency hedging as
having zero expected return, introducing the term “free lunch”, which means that hedging can
provide you risk reduction without any repercussion on expected returns. They based their results
by comparing historical volatilities of hedged and unhedged portfolios including US, UK, Japan
and West Germany stock and bond markets during the testing period 1978-1987 and concluded
that a “free lunch” exists at no significant costs.
This argument of Perold and Schoulman gave the incentive to many authors to investigate if
“free lunch” really exists. Froot (1993) claims that free lunch exists only in short term investing
and if exchange rates follow a random walk and are not mean reverting. The same evidence of no
“free lunch” existence is provided by Walker (2007) who takes the view of a global investor
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based in emerging markets and results that currency hedging increases volatility, and also by
Chang (2009) who finds that less risk is associated with lower returns. Moreover, De Santis et al.
(1999) claim that the inclusion of the euro-currency in international portfolios will lead to small
benefits, but also costs for investors.
As the evidence of “free lunch” in currency hedging appears to be weak -Froot (1993) and
Walker (2007) base their findings on the fact that the unhedged portfolios perform better than the
hedged ones- another controversial issue arises, which is the proper amount of currency exposure
that should be hedged in order to achieve the greatest possible risk reduction arising from
exchange rate fluctuations. A widely examined hedge policy in the literature is that of full or
unitary hedging. Eun and Resnick (1988) using this policy, conclude that hedging results in
lower variance and covariance, and furthermore Perold and Schoulman (1988) suggest that
although a full hedge strategy may not lead to the optimal risk reduction, it always leads to a
significant reduction of currency risk.
Fung and Leung (1991) tried to derive an optimal hedge ratio in a general utility framework, and
using 1-month, 2-month and 3-month forward contracts for the period 1979-1987, found this
ratio to be very close to one, and suggested that financial managers should adopt a unitary
hedging strategy, without having to spend time and resources for hedging currency exposure.
Moreover, Glen and Jorion (1993) provide statistical tests where full hedged strategies perform
better than the unhedged. The same results are provided by Bugar and Maurer (2002). In
addition, Abken and Shrikhande (1997) using the testing period 1980-1996, and splitting the data
into three sub periods 1980-1985, 1986-1990 and 1991-1996, conclude that U.S. investors,
through unitary currency hedging, can achieve a risk reduction in their international equity
portfolios only in the first period and not in the other two. Possible explanations for this can be
that during the 1980-1985 testing period, there was a large appreciation of the U.S dollar against
most major currencies, followed by a long lasting depreciation, and also the different structure of
security returns and exchange rate correlations for the 1986-1996 testing period.
Unitary hedging turns out to be beneficial for the risk-reward ratio in an international context,
however there is research to claim the opposite. Based on studies for UK investors covering the
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1802-1990 testing period and giving more attention on the last 20 years, Froot (1993) finds that
at long horizons (5 years for stocks, 8 years for bonds), the value of hedging disappears as
currency returns display mean reversion. His results indicate that in long horizon, complete
hedging does not reduce the return variance, but in some cases it even enhances it, thus he
proposes a zero hedge ratio. Contrary to Froot, Schmittmann (2010) couldn’t find any evidence
that over long horizons mean reversion provides a “natural hedge” and concludes that the
investment horizon should have small impact in the hedging decision.
In line with Froot’s paper, Valera and Naka (1997) do not favor hedging, as their results, based
on 1983-1988 testing period for U.S. investors diversifying in the U.K., Germany and France,
suggest that the risk-return trade-off of an unhedged strategy is better than a hedged, owing to
transaction and other costs associated with hedging. In addition, Morey and Simpson (2001) and
Simpson (2004) by following five different hedging strategies found that on average the
performance of an unhedged strategy is superior to the performance of a hedged strategy,
regardless of the time horizon. They also found that always hedging using futures contracts
produces the best efficient frontiers for small levels of risk.
Full hedging at one and no hedging at the other seems to be as the two sides of the same coin.
Black (1990) extenuated somewhat the large difference between these two policies. Based on the
assumption that all investors across the world have the same level of risk tolerance, he derives a
universal hedge ratio that should be applied to all investors, irrespectively of their country of
origin. The universal optimal hedge ratio should always be less than 100% (Black in his
examples found ratios between 0.30 and 0.77) because of Siegel’s paradox. Siegel’s paradox
shows that percentage changes in exchange rates are not the same for the local and the foreign
currency, thus investors try to bear some currency risk in their portfolios.
However, this universal hedge ratio was strongly criticized by Solnik (1993) because of the
unrealistic assumption that investors around the world have the same risk tolerance. Solnik
claims that although the hedge ratios are on average less than one, they are not universal,
depending on risk aversion and relative wealth of investors from different countries. Also, the
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ratio is a function of many parameters that are significantly unstable over different time horizons
(Gastineau, 1995).
By adopting the idea that the optimal currency hedging decision lies between zero and one,
Gastineau (1995) suggested a 50% hedge ratio driven by regret theory. He claims that a halfhedged half-unhedged investment policy is an improvement because it pays attention to stock
and bond allocations, as well as to currency allocations. The results of the research show a
significant increase in portfolio performance, especially in the long run, and suggest that 50%
hedge ratio will at least have a modest increase in the performance of portfolios with static
hedging, or provide a reasonable starting point for portfolios with active currency management.
Moreover, Gartner and Wuilloud (1995) point the advantage of a 50% hedge ratio in terms of
regret when another hedge policy performs better. However, they say that this strategy almost
never leads to maximum currency risk reduction, but it minimizes regret.
Regardless of the type of hedging used to reduce the adverse effects of unexpected exchange rate
fluctuations, at the end what matters is if the type of hedging policy chosen could indeed
improve the risk-return performance of the portfolio.
Glen and Jorion (1993) were the first to provide statistical tests for the portfolio performance, by
applying four different types of hedging. Their results show that for the 1974-1990 period used
for their tests, adding forward contracts to international bonds and stocks, improves performance
significantly. Furthermore, Kaplanis and Schaefer (1991) point the importance of currency
hedging, especially in periods of high exchange rate variability, to capture the benefits of
international diversification.
Eaker, Grand and Woodard (1991) investigate a different aspect of currency hedging, that is the
impact that currency hedging has to investors from different countries, and conclude that the
direction of the effect is the same but the magnitude is not. In addition, Schmittmann (2010)
takes the view of German, Japanese, U.K and U.S. investors for the testing period 1975 to 2009
and concludes that currency hedging reduces the volatility of international investments
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International Diversification and the Currency Hedging Decision
significantly. Moreover, trying to find the reason for currency hedging use, Allayannis and Ofek
(1998) suggest that firms use currency derivatives for hedging rather than for speculation.
Although evidence on international diversification and foreign exchange hedging appears to be
somewhat mixed, the existing literature in general favors both these investment policies. The
objective of this thesis is to shed more light on these aspects and how they affect international
investing in the last few years.
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3. Methodology
In this chapter, the methodology that was used to calculate the results is described. Firstly, it is
explained how the dollar excess returns are calculated for every country, how these returns are
hedged and how the Black’s universal hedging formula is derived. Then, the international
portfolio return and return variance is discussed, and finally, the optimization processes used to
format the efficient frontiers and the Sharpe ratio are explained.
3.1 Country’s index portfolio dollar excess returns
The purpose of this thesis is to investigate how currency hedging affects actual historical returns
of internationally optimized portfolios that generate an efficient frontier, which is a graph of
optimal portfolios that have the highest return for a given level of risk (standard deviation). An
investor will choose a portfolio on the efficient frontier according to his risk appetite. For the
construction of efficient portfolios, the equity index returns of twenty countries will be used.
These equity indices are the indices compiled by Morgan Stanley Capital Investment (MSCI).
The comparison of optimal universally diversified portfolios, both in cases of hedged and
unhedged, will be based in monthly excess returns. Kaplanis and Schaefer (1991) found that the
difference in portfolio risk is marginal, when comparing continuously hedged exchange risk with
monthly hedge adjustments; thus, the choice of monthly data intervals is based in that finding.
Excess return is the return of each individual country MSCI index above the risk free rate. In
order to compute the monthly excess return for every country, the specific country monthly risk
free yield is deducted from its MSCI index. Then, excess returns are translated into dollar excess
returns, by using the exchange rates, as the base country is United States. Finally, the monthly
mean dollar excess return and the standard deviation of the monthly dollar excess return for
every country is calculated and annualized.
12
K.V. Sigeris
International Diversification and the Currency Hedging Decision
This method applies for unhedged returns from currency risk. For the calculation of unitary
hedged exchange rate returns, the methodology is very similar. What changes is that instead of
using spot exchange rates, forward premiums are used. This is because unitary currency hedging
is used, which assumes that all currency risk is eliminated. When the Black’s universal hedging
formula is used, the method is a combination of the two above methods (unhedged – unitary
hedged), in the proportions of the hedge ratio.
Taking all these into account, the unhedged and hedged portfolio frontiers are derived from the
unhedged and hedged annualized dollar excess returns respectively. Using Microsoft’s Excel
Solver, the optimal portfolios, which constitute the efficient frontier, can be derived. These
frontiers can then be compared. Noteworthy is that the exchange rate uncertainty is controlled in
this research not only through currency hedging, but also through multicurrency diversification,
as in total 15 different currencies are used.
3.2 Hedging with Forward Contracts
The uncertainty that foreign currencies might depreciate against local currency leads investors to
short forward contracts to hedge. By doing so, exchange risk is eliminated because the foreign
currency is sold at the end of the contract for a certain price predefined by the contract. In that
way, protection against an appreciation of the local currency is provided to foreign investments
when translated back to the domestic currency, as the future spot exchange rate becomes certain
by shorting forwards.
For the purpose of hedging, forward contracts are assumed to be used. Because forward contracts
are private contracts not publicly traded on stock exchanges it is very difficult to find the prices
of these contracts. For this reason covered interest parity is assumed to hold.
1) f/s = (1 + rdc)/(1 + rfc)
Interest rate parity is a relationship linking spot exchange rates, forward exchange rates and
interest rates. Using the parity relation the forward premium (fp) is defined as:
2) fp = (f –s)/s = f/s – 1
13
K.V. Sigeris
International Diversification and the Currency Hedging Decision
For two currencies, the interest rate parity relation states that the forward premium/ discount
equals the interest rate differential between these currencies. Because we assume that 1-month
forward contracts are used, then the calculation of the forward premium/ discount can be defined
as the difference between the 1-month bond yields of the domestic and foreign country which
matches the maturity of the forward contract.
3.3 Black’s Universal Hedging Ratio
The Black’s universal hedging formula is:
3)
where
stands for the average expected excess return on the portfolio,
volatility of the portfolio and
for the average
stands for the average exchange rate volatility across all pairs of
countries. Historical data are used to create inputs for the formula. Using the above formula, the
optimal hedge ratio is computed, which applies to all country indices.
The steps for the calculation of the formula are:
1. Find country weights in the world market portfolio
2. Calculate excess return for every country and the average excess return of the portfolio
3. Calculate the return volatility for every country and the average volatility of the portfolio
4. Calculate exchange rate volatilities across all pair of countries and the average of these volatilities
Black’s universal hedging formula requires the use of one world market portfolio to get the
average inputs of it. For this reason, the country weights of the MSCI All Country World
Investable Market Index (ACWI IMI) are used. When comparing it to our portfolio, we observe
that our portfolio constitutes 90.15% of the MSCI ACWI IMI. Thus, our portfolio is assumed to
be the world market portfolio and the weights are adjusted from 90.15% to 100% using the
country weights of MSCI ACWI IMI.
The annual excess return for every country is calculated by deducting from every country’s
annual return its average risk free rate for that year. The return volatility for every country is
14
K.V. Sigeris
International Diversification and the Currency Hedging Decision
calculated as the standard deviation of the daily returns for these years. Then, these standard
deviations are annualized by multiplying with the square root of 260. Then, the average excess
returns and average return volatilities for every country are calculated by using the sum of the
weighted average of the excess return and the sum of the weighted average of the return
volatility of every country respectively.
Finally, exchange rate volatilities across all pairs of countries in our portfolio are needed.
However, because exchange rates are not available for all countries in the portfolio, these rates
are calculated using cross rates. Then for every pair the exchange rate volatility are calculated, as
well as the average of these volatilities.
3.4 Portfolio’s Dollar Return and Return Variance
3.4.1 Unhedged Portfolio
When someone invests abroad, he is exposed in two sources of risk: the volatility of local returns
and the exchange rate volatility. The local security index return (rlt) is calculated in this paper as
rlt = 100(lnpt –lnpt-1), with pt being the security index price at time t, while the exchange rate
return (et) is calculated as et = 100(lnst-lnst-1), with st being the spot exchange rate at time t.
Using these two, the unhedged portfolio dollar return can be defined as:
4)
= (1 + rlt)(1 + et) – 1 = rlt + et + rltet
where, after removing the rltet product, because is very small, it takes the simple form:
5)
rlt + et
The variance of the returns of the unhedged portfolio consisting of several multicurrency
securities is that derived from Eun and Resnick (1988):
6)
+
+2
15
K.V. Sigeris
International Diversification and the Currency Hedging Decision
with the first term being the security-return covariances, the second the foreign exchange rate
covariances and the third term the local return-foreign exchange rate covariances.
3.4.2 Hedged Portfolio
Similarly, the dollar return on a hedged portfolio can be defined as:
7)
rlt + fp
As already stated, the difference between unhedged and hedged returns is that the exchange rate
movement is replaced by the forward premium fp. This also holds for the variance of a hedged
multicurrency portfolio:
8)
+
+2
where the forward premium standard deviations and correlation coefficients replace those of the
foreign exchange rates that appear in equation 6.
3.5 Optimization
The final step, after having the dollar excess returns and standard deviations of the individual
country MSCI index portfolios, is to optimize these portfolios, for all the three hedging strategies
(unhedged, unitary hedged and universally hedged using Black’s formula). Optimization is
performed using Microsoft’s Excel Solver. Correlation and covariance matrices of dollar excess
returns across all pairs of countries are also computed, for the three types of dollar returns;
unhedged, unitary hedged and Black’s universally hedged returns (Appendix F).
In the portfolio optimization process some restrictions and assumptions are posed:
 The sum of the N index portfolio weights should equal to one:
=1
16
K.V. Sigeris
International Diversification and the Currency Hedging Decision
 No shortselling allowed. This means that one cannot sell an index short. In other words,
the index portfolio weights cannot be negative in the optimization process, nor bigger
than one:
0 ≤ wi ≤ 1
 Transaction costs are assumed to be zero
After that, for every testing period two optimization processes are performed, using the twenty
individual country index portfolios considered in this study.
Optimization 1:
 Minimize standard deviation for a given level of required return subject to the constraint
that country portfolio weights cannot be negative, nor bigger than one.
0 ≤ wi ≤ 1
However, in this process, there are no restrictions to individual portfolio weights, meaning that
this may lead for a given level of risk/return tradeoff to investment in only one specific country
index. Such a situation however can lead to exposure to one specific country and raise systematic
risk, and in practice may not be cost effective. This reason gave the incentives for the second
optimization process.
Optimization 2:
 Minimize standard deviation for a given level of required return subject to the constraint
that country portfolio weights are between 1% and 50%
0.01 ≤ wi ≤ 0.5
The maximum of 50% individual country index portfolio weight posed in this optimization limits
the exposure of systematic risk.
Furthermore, a third optimization process is performed allowing shortselling the national equity
portfolios. This optimization process is presented in Appendix D.
17
K.V. Sigeris
International Diversification and the Currency Hedging Decision
3.6 Sharpe Ratio
In addition, one should check if more return comes from taking more risk. Evaluating the
performance of the portfolio, both in cases of hedged and unhedged portfolios, based only on
returns ignores the risk in total. For that reason the Sharpe ratio is computed. The Sharpe ratio is
a ratio of reward (average excess return or risk premium) per unit of total risk. The ratio is
defined as:
9)
where rp stands for the portfolio return, rf for the risk free rate of return, and stands for σp the
standard deviation of the portfolio.
4. Data
All the data needed for this topic research are obtained from DataStream. Twenty countries are
used in this study and the performance is examined on a monthly basis. Taking the view of an
American investor diversifying his portfolio internationally, the countries considered are:
Table 1: Country Index Portfolios used in the Optimization Process
Developed
Emerging
Australia
Canada
France
Germany
Greece
Japan
Netherlands
Portugal
Singapore
Spain
Switzerland
United Kingdom
United States
Brazil
China
India
Mexico
South Africa
South Korea
Turkey
18
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Morgan Stanley Capital International (MSCI) provides stock indices that represent a welldiversified portfolio for every country. These indices are value-weighted, based on market
capitalization of all the listed firms, and include the reinvestment of dividends and capital gains
The data period examined in this study is from January 2004 to August 2010. This sample period
is split in two testing periods, from January 2004 to December 2006 and from January 2007 to
August 2010. All data, Morgan Stanley Capital International (MSCI) stock index values, spot
exchange rates, one-month forward rates and risk free rates, are at the last trading day of every
month of the sample period.
Spot exchange rates and one-month forward rates were carefully selected in order to be
expressed as the value of one foreign currency equals the U.S. Dollar. Because the study is based
on excess returns rather than returns, for every country the one-month excess returns are
computed by subtracting its one-month risk-free yield from its MSCI index return. However,
because not all countries issue one-month Treasury bills, wherever these weren’t available, one
or three-month Treasury bills or interbank rates are used as a proxy for the one-month risk-free
yield. The proxies of risk-free yield for every country can be found at Appendix E.
For the Black universal hedge ratio computation, the past two years’ daily data are used, again
obtained from DataStream. This means that the 2002-2003 data sample is used to compute the
hedge ratio of the 2004-2006 testing period, and the 2005-2006 data sample for the 2007-2010
testing period. The MSCI All Country World Investable Market Index (ACWI IMI) is used as
proxy of the world market portfolio and the country weights in the world market portfolio are
derived from it.
19
K.V. Sigeris
International Diversification and the Currency Hedging Decision
5. Results
In this chapter the results are shown. Firstly, the Black’s universal ratios are discussed, and then
the index returns and the Sharpe ratios of these returns are explained. Furthermore, the efficient
frontiers derived from the internationally diversified portfolios and the Sharpe ratios of these
frontiers are explained in detail and finally the effects of currency trends are discussed.
5.1 Black’s Universal Hedging Ratio Computation
Table 2 presents the world average values used as inputs for the ratio after adjusting our portfolio
to the world market portfolio. The hedge ratios for the 2004-2006 and 2007-2010 portfolios are
equal to 0.615 and 0.906 respectively. As already stated in the methodology part, for the ratio
calculation of the first portfolio data of 2002-2003 are used, while for the second portfolio, data
of 2005-2006 are used.
20
K.V. Sigeris
International Diversification and the Currency Hedging Decision
However, the weighted average excess return across all countries in 2002 is negative because
stock markets performed poorly that year. On the contrary, in 2003 the excess return is highly
positive. This leads as to the conclusion that the average of these two years cannot be used as an
indication of future excess return. A better estimate of future excess return would be to arbitrarily
use the half of the excess return of 2003, which is 12.09%. As Black (1995) states, the universal
hedging formula assumes that investors put into the formula their opinions about what other
investors around the world expect for the future, so the negative excess return of 2002-2003 is
clearly not a good indicator for the future as 2003 performed with flying colors.
Table 2: World Average Values
2002
2003
2005
2006
2002-03
2005-06
Excess Return
μm
Return Volatility
σm
Exchange Rate Volatility
σe
-25.40%
24.18%
13.63%
11.60%
-0.61%
12.61%
26.18%
18.85%
11.21%
13.52%
22.51%
12.37%
11.65%
8.75%
Appendix A presents all the computations performed to arrive the inputs of table 2 that are used
in Black’s universal hedging ratio.
5.2 Index Returns 2004-2006
Table 3 presents the average excess returns and standard deviations of all country stock indices
included in the portfolio for the 2004-2006 testing period. When dollar stock index returns are
unitary hedged against exchange rate exposure, their standard deviation is lower for all countries,
leading to an average decline in standard deviation of 14.29% across all countries. However their
mean excess return is also lower for all the country equity indices, except for Japan, Switzerland
and China. The overall unitary hedged average excess return across all countries is 19% lower
when is compared to the unhedged. This finding is consistent with previous findings (see Chang,
2009) and suggests that higher return comes by taking more risk when using just one equity or
index.
21
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Moreover, when the dollar unhedged returns are compared with the Black’s universal hedged
returns, the standard deviation is again lower for all country indices, leading to a 12.24% average
decline in standard deviation across all countries. The mean excess return is again lower for all
country indices, except for Japan, Switzerland and China, and results on average in a 12%
decline in excess return across all countries.
During the 2004-2006 period, the foreign exchange returns of all countries are positive, except
for Japan, South Africa and Turkey, meaning that if these returns hadn’t been hedged they would
have led to higher dollar excess returns when denominated back to the domestic currency.
Furthermore, the standard deviation of the U.S. equity portfolio excess return is substantially
lower than the standard deviation of the rest equity portfolios dollar unhedged returns, meaning
that the standard deviation of the exchange rate, which is on average 8% for all countries, has
added up to the variability of the non-U.S. equity portfolios.
Most of the currencies, except for Australia, U.K., Brazil, India, Mexico, South Africa, South
Korea and Turkey, are sold forward with premium, resulting in higher dollar hedged excess
returns compared to unhedged. The standard deviations of the forward premiums is very low and
substantially lower than that of the exchange rates, meaning that they do not have any substantial
impact on the variability of the hedged returns.
The formulas of Eun and Resnick (1988) used in this paper to compute the dollar excess returns
indicate that the unhedged portfolio’s standard deviation depends on the exchange rate variance
and on the excess local return-foreign exchange rate covariances, while the hedged portfolio’s
standard deviation depends on the forward premium variance and the excess local return-forward
premium covariances. The same holds when computing the dollar excess returns. For that reason,
Japan, Switzerland and China have higher hedged returns compared to unhedged, as their
forward premiums are the highest of all countries, while their exchange rate returns are hedged.
Furthermore, the standard deviation of the unhedged dollar excess returns is always higher from
that of the hedged dollar excess returns, partly because the correlation coefficient between local
excess return and foreign exchange return is positive for most of the countries, leading to higher
22
K.V. Sigeris
International Diversification and the Currency Hedging Decision
standard deviations of unhedged dollar excess returns, and partly because the correlation
coefficient between local excess return and forward premium is low or even negative.
5.3 Index Returns 2007-2010
Information about the second period country equity portfolios concerning dollar excess returns,
standard deviations, forward premiums and exchange rate returns can be found in Table 4. For
the 2007-2010 testing period the picture is totally different. Financial markets experienced the
biggest crisis since 1929 resulting in negative returns around the globe and significantly higher
market volatility. The correlation between local MSCI monthly Index returns is on average 0.75
for 2007-2010 period, 31.2% higher than the 2004-2006 period, when the average correlation is
equal to 0.57. This finding of higher international correlations during periods of high market
volatility is in line with Solnik et al. (1996), and also Schmittmann (2010) found that correlations
were higher during 2007-2009 testing period. Correlation matrices can be found at Appendix B.
The standard deviation of the unitary hedged dollar excess returns is lower than the unhedged for
all national equity indices in the portfolio, leading to an average decline in standard deviation of
21.46% across all countries. The same results arise when comparing Black’s universal hedged
excess returns with the unhedged, as the average decline in standard deviation is 20.06% across
all the countries included in this study. Only Japan and China display higher standard deviation
of their dollar excess returns when hedged, regardless of the type of hedging. However, this
standard deviation is again high, as it is on average equal to 24.83% when unitary hedged,
32.04% when it is unhedged and 25.33% when it is optimally hedged using Black’s universal
hedging formula.
The unhedged dollar excess returns of all countries are negative, except for Singapore, China and
India. The same holds when returns are hedged, regardless of the type of hedging, but now only
except for China and India. Hedging has a negative impact on national excess index returns, as
the returns on average decline by 30% across all countries when unitary hedging is used, and by
a 27.8% decline when returns are hedged using the universal hedge ratio. On average, the
unhedged dollar excess return across all countries is -7.21%, with the unitary hedged returns
being -9.41% and the universal optimally hedged being -9.21%.
23
K.V. Sigeris
International Diversification and the Currency Hedging Decision
The standard deviation of the U.S. equity portfolio excess return is again lower than that of the
rest equity portfolios unhedged return, leading to the conclusion that also in this period the
exchange rate standard deviation, which is on average 12.83% across all countries, has added up
to the variability of the non-U.S. equity portfolios. The only exception is Japan and China, which
exhibit strong negative correlation between local excess returns and foreign excess returns.
Furthermore, emerging markets, as well as Japan, display large depreciation of their currencies, a
fact that favors hedging the currency exposure. In total, all currencies in our portfolio depreciated
against U.S. Dollar, except for the euro and U.K. pound. Forward premiums are again
characterized by minor variability and their correlation with the local excess return is small, or
even negative.
24
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Table 3: STOCK INDEX PORTFOLIOS, 2004-2006
US
AUS
CAN
JAP
SING
SWI
UK
FRA
GER
GRE
NETH
PORT
SPA
BRA
CHI
IND
MEX
SAFR
SKOR
TUR
24.7
17.2
13.0
11.6
15.8
13.3
19.8
12.0
19.5
28.9
27.0
21.6
26.0
23.5
32.7
18.6
18.2
26.3
22.5
21.0
3.8
38.2
24.1
15.6
-9.3
12.4
11.2
-3.4
15.3
12.3
-7.3
19.2
10.4
-13.7
-4.6
22.7
-21.5
29.4
21.3
-1.5
22.5
20.9
-11.0
24.9
16.4
-11.5
15.2
16.2
-38.3
12.2
18.6
-11.7
-10.3
27.6
-27.9
Unhedged Stock Index Portfolio Dollar Excess Returns
Mean Excess Return
Standard Deviation
5.4
6.9
15.3
13.6
17.6
14.3
14.3
14.5
20.8
12.2
17.1
9.5
9.8
8.7
15.5
10.5
15.1
13.2
Fully Hedged Stock Index Portfolio Dollar Excess Returns
Mean Excess Return
Standard Deviation
% change in st.dev. of
hedged returns to
unhedged
5.4
6.9
0.0
11.0
8.5
-37.0
14.0
10.6
-26.1
22.6
13.4
-7.7
18.1
10.8
-11.6
19.6
9.1
-4.0
5.2
7.5
-14.1
14.9
9.0
-14.7
14.6
11.4
-13.5
Hedged Stock Index Portfolio Dollar Excess Returns using Black's Optimal Hedge Ratio
Mean Excess Return
Standard Deviation
% change in st.dev. of
hedged returns to
unhedged
5.4
6.9
0.0
12.7
9.9
-26.8
15.4
11.6
-19.2
19.3
13.3
-8.6
19.1
11.2
-8.3
18.6
8.3
-12.9
6.9
7.1
-19.0
15.2
8.9
-15.3
14.8
11.6
-12.2
24.4
15.9
-7.9
12.6
10.8
-7.0
15.5
12.2
-8.3
19.5
10.4
-13.1
4.0
24.6
-14.9
28.5
21.4
-1.0
23.9
21.8
-7.3
27.8
17.1
-8.1
16.3
18.8
-28.5
16.1
19.3
-8.2
-5.1
31.2
-18.2
1.1
0.2
0.08
2.6
0.3
0.22
-1.3
0.4
0.07
1.0
0.4
0.11
1.0
0.4
0.18
1.0
0.4
-0.04
1.0
0.4
0.18
1.0
0.4
0.09
1.0
0.4
0.14
-11.8
1.0
0.04
3.9
0.7
0.10
-1.8
0.4
-0.30
-4.7
0.6
0.06
-4.4
0.5
0.17
-0.5
0.5
0.09
-13.9
1.3
0.02
0.4
8.6
-0.42
3.0
7.7
-0.34
1.5
7.4
-0.18
1.5
7.4
-0.05
1.5
7.4
-0.01
1.5
7.4
-0.27
1.5
7.4
-0.16
1.5
7.4
-0.11
10.6
11.8
0.34
2.0
1.3
0.30
1.0
5.3
0.37
1.2
5.5
0.26
-1.8
17.7
0.21
8.6
6.3
0.26
-0.3
14.7
0.60
Forward premium
Mean
Standard Deviation
Correlation between local
excess return and
forward premium
-2.3
0.4
0.01
0.3
0.3
0.09
3.5
0.5
0.08
Foreign Exchange Returns
Mean Return
Standard Deviation
Correlation between local
excess return and foreign
exchange return
1.5
8.5
0.27
3.6
7.7
0.22
-3.5
8.1
-0.15
3.4
3.9
0.21
25
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Table 4: STOCK INDEX PORTFOLIOS, 2007-2010
US
AUS
CAN
JAP
SING
SWI
UK
FRA
GER
GRE
NETH
PORT
SPA
BRA
CHI
IND
MEX
SAFR
SKOR
TUR
-28.8
46.3
-10.6
30.0
-14.6
28.5
-10.8
32.8
-0.6
40.1
6.3
36.4
0.5
40.6
-7.2
31.2
-7.0
32.0
-2.9
38.1
-5.0
47.8
-28.6
39.0
-15.9
-10.6
23.6
-21.4
-14.6
21.9
-23.3
-10.2
24.2
-26.1
-11.7
27.7
-30.9
3.9
36.9
1.5
-2.2
34.6
-14.8
-7.7
22.6
-27.6
-12.1
18.3
-42.7
3.0
25.4
-33.4
-12.8
35.9
-24.9
Unhedged Stock Index Portfolio Dollar Excess Returns
Mean Excess Return
Standard Deviation
-9.0
20.1
-7.2
32.1
-0.1
30.3
-9.4
19.0
2.2
32.1
-5.3
20.8
-13.3
23.6
-13.0
28.3
-8.5
30.7
Fully Hedged Stock Index Portfolio Dollar Excess Returns
Mean Excess Return
Standard Deviation
% change in st.dev. of
hedged returns to
unhedged
-9.0
20.1
0.0
-13.5
17.7
-44.8
-3.4
19.3
-36.2
-17.1
22.7
19.1
-1.4
28.2
-12.3
-9.2
16.2
-22.1
-8.3
18.4
-21.9
-13.0
20.8
-26.4
-9.7
23.0
-25.2
Hedged Stock Index Portfolio Dollar Excess Returns using Black's Optimal Hedge Ratio
Mean Excess Return
Standard Deviation
% change in st.dev. of
hedged returns to
unhedged
-9.0
20.1
0.0
-12.9
18.8
-41.5
-3.1
20.2
-33.2
-16.4
22.1
16.1
-1.1
28.5
-11.3
-8.8
16.2
-22.0
-8.7
18.7
-20.8
-13.0
21.3
-24.7
-9.6
23.5
-23.5
-28.6
39.5
-14.7
-10.6
23.9
-20.2
-14.6
22.3
-21.9
-10.3
24.9
-24.1
-10.7
28.7
-28.4
4.1
36.9
1.4
-2.0
35.1
-13.5
-7.6
23.3
-25.4
-11.6
19.3
-39.7
2.4
26.3
-31.0
-12.1
36.9
-22.8
2.1
0.6
-0.14
0.9
0.4
-0.14
1.2
0.4
-0.12
-0.7
0.3
0.01
0.0
0.3
0.05
0.0
0.3
0.12
0.0
0.3
0.17
0.0
0.3
0.03
0.0
0.3
0.27
0.0
0.3
0.14
-7.5
0.8
0.25
1.8
1.3
0.15
-3.4
0.6
0.26
-4.6
0.7
0.17
-7.0
0.6
0.24
0.7
0.7
-0.2
-10.1
0.9
0.27
-0.4
13.4
-0.02
12.4
11.2
0.22
6.8
13.0
0.36
6.8
13.5
0.38
6.8
13.0
0.45
6.8
13.0
0.28
6.8
13.0
0.29
6.8
12.9
0.52
-14.2
16.4
0.65
-40.7
1.8
-0.2
-65.0
8.9
0.64
-50.5
12.0
0.60
-42.0
18.3
0.55
-85.5
18.4
0.52
-10.8
15.7
0.69
Forward premium
Mean
Standard Deviation
Correlation between
local excess return and
forward premium
-3.0
0.4
0.12
0.1
0.2
-0.04
Foreign Exchange Returns
Mean Return
Standard Deviation
Correlation between
local excess return and
foreign exchange return
-3.1
18.3
0.59
-1.7
13.2
0.73
-70.1
11.4
-0.57
-7.9
6.5
0.52
26
K.V. Sigeris
International Diversification and the Currency Hedging Decision
5.4 Sharpe Ratio
As already stated in the methodology, Sharpe is a portfolio performance ratio which takes into
account both the return and the risk of the portfolio. Thus it is interesting to see how is the
Sharpe ratio affected by the exchange rate fluctuations and also by hedging these exchange rate
fluctuations.
During the first period portfolio (2004-2006), the average across all countries local returns
Sharpe ratio is 1.21, with the unhedged and unitary hedged dollar returns Sharpe ratio being
slightly lower, 1.17 and 1.16 respectively, while Black’s optimally hedged dollar returns Sharpe
ratio is slightly better and equal to 1.22 on average. The return and return volatility of the
exchange rates had a negative impact on the unhedged dollar returns Sharpe ratio, as for 13 out
of 19 countries is lower when comparing them with the local returns Sharpe (see Table 5) .
As noted in the previous section, hedging results in lower standard deviations for all the country
indices, but also in lower returns for almost all the countries. The risk-return relation between
these two results in higher ratio for 11 out of 19 countries when comparing hedged with
unhedged dollar returns, irrespectively of the type of hedging. However, hedging in a few cases
results in negative ratios and the slightly lower average ratio of unitary hedged dollar returns to
local returns is mainly driven by the substantial shift in the ratio of Brazil and Turkey.
For the 2007-2010 portfolio the average across all countries Sharpe ratios are negative, the local
returns Sharpe ratio is -0.35, and the unhedged, unitary hedged and Black’s optimally hedged
dollar returns Sharpe ratios are -0.25, -0.41 and -0.39 respectively. The unhedged dollar returns
Sharpe ratio exhibits the best performance, meaning that the return and return volatility of the
exchange rates had a positive impact on the unhedged dollar returns ratio, as 14 out of 19
countries have a higher ratio when comparing them with the local Sharpe. Both types of hedging
lead in better Sharpe performance only for two countries, namely UK and Korea, when
comparing unhedged with hedged dollar returns Sharpe ratios (see Table 6).
27
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Table 5: Sharpe Ratio - STOCK INDEX PORTFOLIOS, 2004-2006
USA
AUSTRALIA
CANADA
JAPAN
SINGAPORE
SWITZERLAND
UK
FRANCE
GERMANY
GREECE
NETHERLANDS
PORTUGAL
SPAIN
BRAZIL
CHINA
INDIA
MEXICO
SOUTH AFRICA
KOREA
TURKEY
Sharpe RatioLocal Returns
Sharpe Ratio-Unhedged
Dollar Returns
Sharpe Ratio-Fully
Hedged Dollar Returns
Sharpe Ratio-Black's
Ratio Dollar Returns
0.78
1.60
1.29
1.38
1.56
1.83
0.88
1.55
1.19
1.46
1.01
1.15
1.75
0.42
1.16
1.18
1.89
1.27
0.69
0.15
0.78
1.13
1.23
0.98
1.71
1.79
1.12
1.48
1.15
1.43
1.12
1.19
1.65
0.67
1.25
1.11
1.76
0.69
1.07
0.10
0.78
1.29
1.32
1.68
1.68
2.15
0.69
1.67
1.28
1.54
1.11
1.24
1.85
-0.20
1.38
1.08
1.52
0.93
0.66
-0.37
0.78
1.28
1.33
1.45
1.71
2.25
0.98
1.71
1.28
1.53
1.17
1.27
1.86
0.16
1.33
1.10
1.63
0.87
0.83
-0.16
Table 6: Sharpe Ratio - STOCK INDEX PORTFOLIOS, 2007-2010
USA
AUSTRALIA
CANADA
JAPAN
SINGAPORE
SWITZERLAND
UK
FRANCE
GERMANY
GREECE
NETHERLANDS
PORTUGAL
SPAIN
BRAZIL
CHINA
INDIA
MEXICO
SOUTH AFRICA
KOREA
TURKEY
Sharpe RatioLocal Returns
Sharpe Ratio-Unhedged
Dollar Returns
Sharpe Ratio-Fully
Hedged Dollar Returns
Sharpe Ratio-Black's
Ratio Dollar Returns
-0.45
-0.61
-0.18
-0.83
-0.08
-0.64
-0.41
-0.62
-0.43
-0.74
-0.45
-0.67
-0.43
-0.17
0.06
0.04
-0.14
-0.30
0.09
-0.08
-0.45
-0.22
0.00
-0.49
0.07
-0.25
-0.57
-0.46
-0.28
-0.62
-0.35
-0.51
-0.33
-0.01
0.17
0.01
-0.23
-0.22
-0.08
-0.10
-0.45
-0.76
-0.17
-0.75
-0.05
-0.57
-0.45
-0.62
-0.42
-0.73
-0.45
-0.67
-0.42
-0.42
0.11
-0.06
-0.34
-0.66
0.12
-0.36
-0.45
-0.69
-0.15
-0.74
-0.04
-0.55
-0.47
-0.61
-0.41
-0.72
-0.44
-0.66
-0.41
-0.37
0.11
-0.06
-0.33
-0.60
0.09
-0.33
28
K.V. Sigeris
International Diversification and the Currency Hedging Decision
5.5 Analysis of Efficient Frontiers Derived from Internationally Diversified
Portfolios
Charts 1-4 display the efficient frontiers of internationally diversified equity portfolios for the
2004-2006 and 2007-2010 data periods examined in this thesis. For every data period two
optimization processes are performed.
Every chart shows three efficient frontiers presenting the unhedged, the unitary hedged and the
Black’s universal optimally hedged efficient portfolios. In addition, the excess return and
standard deviation of the U.S. equity portfolio is presented in every graph. The horizontal axis
presents for every point the standard deviation, while the vertical axis the dollar excess return,
both being in percent and on an annual basis. Every efficient frontier shows the possible optimal
outcomes that result from the twenty individual country index portfolios that are used in the
optimization process.
5.5.1 International Portfolio, 2004-2006 Testing Period
Charts 1 and 2 present the efficient frontiers for the 2004-2006 data period derived from
optimization processes 1 and 2 respectively.
Simply investing in U.S. MSCI index is not optimal, especially in optimization process 1,
because in that level of standard deviation, there is always a higher level of excess return attained
by diversifying internationally, irrespective if the international portfolio is hedged or not. In the
second optimization, the risk reward ratio of the U.S. equity index is not feasible due to the
maximum of 50% constraint posed in individual country index portfolio weights.
Moreover, although twenty country index portfolios entered the portfolio optimization, in the
first optimization process, at maximum eight consist the efficient frontier. However these
country indices are not the same, but change as the required level of excess return changes. The
picture of the second optimization process is the same, as at maximum only eight out of twenty
country indices have weights in the frontier more than the minimum 1%. The restrictions posed
29
K.V. Sigeris
International Diversification and the Currency Hedging Decision
in the second optimization have narrowed the investment opportunity set that is offered in the
first optimization.
As it can be seen from the country weights presented in the Appendix C, for low levels of risk
the U.S. equity portfolio dominates in the efficient frontiers, especially in the first optimization
process. This is because the U.S. equity portfolio, irrespective of the type of the hedging strategy,
displays the lowest standard deviation among the 20 country indices used in this thesis, but also
one of the lowest excess returns, when compared with other countries’ dollar excess returns. This
relatively low risk-return relation of the U.S. equity index is the key factor that led the weight of
the U.S. equity index to be very high in the frontiers for the low levels of risk, irrespective of the
hedging strategy. As the curve moves to the northeast, the risk increases, as also does the excess
30
K.V. Sigeris
International Diversification and the Currency Hedging Decision
return. At higher levels of standard deviation, the weights change and the frontier consists mainly
of emerging markets equity indices. Especially at the highest levels of standard deviation,
emerging markets such as China and Mexico are heavily weighted.
The evidence weather hedging produced better efficient frontiers is mixed. Clearly for low levels
of risk the hedging strategies dominate the unhedged, as their efficient frontiers are to the
northwest of the unhedged. For higher levels of risk the picture changes, as the unhedged
portfolios have higher excess return for the same level of standard deviation than the hedged
portfolios.
When comparing the two types of the hedged frontiers, the evidence shows that the difference of
the hedging outcome is minor; the unitary hedged frontiers perform in general slightly better than
the Black’s optimally hedged frontiers. One possible explanation for this is that the optimization
process is performed using 20 individual country portfolios and fifteen currencies. The optimal
allocation between the hedging outcome and multicurrency diversification is possible to have led
to almost similar types of hedged efficient frontiers.
5.5.2 International Portfolio, 2007-2010 Testing Period
Charts 3 and 4 present the efficient frontiers for the 2007-2010 data period derived from
optimization processes 1 and 2 respectively.
The 2007-2010 efficient frontiers advocate the great impact that the crisis had on equity returns.
The curves represent mainly negative excess returns for different levels of risk. Only for the
highest levels of standard deviation the frontiers are above the x-axis. Attaining positive excess
returns seems very difficult for that period and these returns will be marginal.
Simply investing in U.S. MSCI index is again for this period not optimal, because international
diversification can always offer a higher excess return for the level of standard deviation that the
U.S. equity index has, irrespective if the international portfolio is hedged or not.
31
K.V. Sigeris
International Diversification and the Currency Hedging Decision
As for the 2004-2006 testing period, twenty country index portfolios entered to the portfolio
optimization for 2007-2010. However, for the first optimization process, at maximum only six
countries are enough at any level of required excess return to produce the efficient frontier. The
same holds also for the second optimization process, as at maximum only six out of twenty
country indices have weights in the frontier more than the minimum 1%. Again, as for 20042006, the investment opportunity set in the second optimization is less than in the first, due to the
restrictions in country portfolio weights.
At low levels of standard deviation, the efficient frontiers consist mainly of countries like
Switzerland, Japan, U.S., Canada, U.K. and South Africa. At higher levels of standard deviation,
the weights change and the frontier consists mainly of emerging markets equity indices and at
32
K.V. Sigeris
International Diversification and the Currency Hedging Decision
the highest levels of standard deviation, emerging markets such as China and South Korea
dominate the frontiers.
For the 2007-2010 testing period, again the evidence if hedging produced better efficient
frontiers is mixed. At low levels of risk the hedged frontiers perform better than the unhedged, as
they are to the northwest of the unhedged. However as the standard deviation rises the difference
disappears and at the higher levels of risk the unhedged frontiers dominate the hedged ones.
Furthermore, when comparing the two types of hedged frontiers, it is more apparent that the
unitary hedged frontiers perform better than the Black’s optimally hedged frontiers. However,
the difference between the two hedging outcomes is generally small. Using fifteen currencies and
20 individual country portfolios in the optimization process might have minimized the difference
between these two hedging outcomes, due to the optimal allocation between the hedging
outcome and multicurrency diversification.
5.6 Efficient Frontiers’ Sharpe Ratio
Appendix 2 presents also charts concerning the Sharpe ratio curves derived from the efficient
frontiers that are generated through the optimization process one and two. In every chart the
Sharpe ratio is functioned against the excess return. Excess returns in the charts are in percentage
and on an annual basis, while Sharpe ratios are straight numbers.
During the 2004-2006 testing period, the Sharpe ratio is maximized when the excess return is
around 20%, irrespective of the optimization process and whether the frontiers are hedged or not.
This means that the optimal risky portfolios, or tangency portfolios, lye in the frontiers for values
of excess return around 20%. Clearly investing only in the U.S. equity index portfolio is an
inefficient choice, as international diversification can offer much higher values or Sharpe ratios.
Moreover the Sharpe ratios of unitary hedged efficient frontiers are slightly better than those of
the Black’s universal optimally hedged efficient frontiers. Both these ratios have higher values
than the ratios of the unhedged efficient frontiers. However, for the highest levels of excess
returns, the unhedged frontiers display better ratios than the hedged ones.
33
K.V. Sigeris
International Diversification and the Currency Hedging Decision
During the 2007-2010 testing period, the Sharpe ratios are mainly negative, driven by the
negative excess returns that the frontiers had in this period. As the excess returns accelerate, the
ratios also accelerate until the point of the highest possible excess return. Furthermore, during
this period the unhedged Sharpe is slightly better for every level of excess return, while the
difference between the two types of hedged ratios appears to be close to zero.
What can be concluded from all the results is that if U.S. investors decide to invest their money
abroad then the decision to hedge their foreign holdings depends on their risk aversion. As no
international investment strategy examined in this study continuously dominates the others for
every level of risk, then results show that U.S. investors should hedge their exchange rate
exposure if they are risk averse, otherwise if they are seeking high returns they should not hedge.
Moreover, if they decide to hedge, then the unitary hedging strategy should be chosen. There are
two reasons that justify this argument. The first reason is that unitary currency hedging performs
slightly better, as its frontiers are slightly dominating the Black’s hedged frontiers, and the
second is that the computation of Black’s universal hedging ratio is time consuming as it requires
a lot of data to implement it. Furthermore, other disadvantages are also pointed in the past, as it
is based in the unrealistic assumption that all investor across the world have the same risk
tolerance (see Solnik, 1993).
5.7 Currency Trends and Results
One crucial point under consideration is how the appreciation/ depreciation trends of foreign
currencies relative to U.S. Dollar have affected the results. If the testing period is chosen in such
a way that all foreign currencies have appreciated or depreciated against the home currency,
favoring not hedging or hedging respectively, then is at least naïve to say that the evidence
provided by such an analysis is robust.
Abken and Shrikhande (1997) based their findings by splitting their testing period in sub periods
that in such a way that the U.S. Dollar depreciated or appreciated against all other currencies
during these periods. However, in this thesis, the choice of the testing periods was based in the
34
K.V. Sigeris
International Diversification and the Currency Hedging Decision
criterion that the first period to presents a prosperity period and the second the crisis period. No
trends in exchange rate fluctuations were considered for this choice.
During the 2004-2006 period all foreign currencies, except for Japanese Yen, South African
Rand and Turkish Lira, appreciated against Dollar, a fact that would not favor hedging. On the
contrary, during the 2007-2010 period the emerging markets currencies and the Japanese Yen
display large depreciation, a fact that would strongly favor hedging. In that period only Euro and
U.K. Pound appreciated against U.S. Dollar.
Based on these currency trends one would expect the unhedged frontiers to dominate the hedged
during the 2004-2006 testing period, while for the 2007-2010 testing period the opposite to
happen. However, for both periods, the evidence provided by the frontiers is the same; hedge for
low levels of risk and don’t hedge for the high levels.
This finding makes the advantage of multicountry-multicurrency diversification more obvious.
The currency risk and return is just one part of the total risk and return of the portfolio. The
efficient frontier consists in every level of risk of countries that produce the best risk-return
trade-off. In total, only the countries that display the best risk-return relation are used to form the
frontiers. The rest are omitted. This is why only less than half of the twenty countries are used
every time and for every level of risk to produce the efficient frontiers. However, this argument
should not be confused and naively say that appreciation/depreciation trends do not affect the
portfolios in total and the results. What can be concluded is that though this investment strategy,
these effects are diminished. As Gastineau (1995) felicitous stated: “No one can harbor illusions
that this study, or any similar effort, can completely eliminate currency-hedging controversies”.
35
K.V. Sigeris
International Diversification and the Currency Hedging Decision
6. Conclusion
This Master Thesis has examined how U.S. investors can benefit by diversifying their portfolios
internationally, and how exchange rate exposure affects their risk-return trade-off. For that
reason, internationally diversified equity portfolios were formatted and compared with the U.S.
equity MSCI index, both in cases when these portfolios are unhedged against exchange rate risk
and when hedged.
The internationally diversified equity portfolios were formatted using thirteen developed and
seven emerging country equity indices. Then, these indices entered the portfolio optimization
process, producing the efficient frontier which a figure presenting all the possible optimal
outcomes of the international portfolio’s dollar excess return against its standard deviation. Two
optimization processes were performed; the first by posing the restriction that individual country
portfolio weights are between 0% and 100%, and the second by posing the restriction that
individual country portfolio weights are between 1% and 50%. The two testing periods used to
derive the results are 1/12004-12/31/2006 and 1/1/2007-8/31/2010. For every testing period and
optimization process, three efficient frontiers are produced with each one derived from the
unhedged dollar excess returns, the unitary hedged dollar excess returns and the Black’s
universal hedged dollar excess returns during that testing period.
The results show that simply hedging one individual country index portfolio leads to lower level
of standard deviation (risk), but also leads to lower level of excess return. Only three countries
display higher excess return when hedged, in the 2004-2006 testing period, regardless of the type
of hedging.
Furthermore, regardless of the testing period and whether the international portfolios are hedged
against currency risk or not, simply investing in the U.S. equity index is not optimal for U.S.
investors, as for the same level of risk (standard deviation) there is always a higher level of
excess return attained by diversifying the portfolio internationally. This is true for the first
optimization process, while for the second the relatively low risk-reward ratio offered by the
36
K.V. Sigeris
International Diversification and the Currency Hedging Decision
U.S. equity index is not always feasible, when investing internationally, due to the constraints
posed to country portfolio weights.
When it comes to the hedging decision, the evidence is mixed, as for both testing periods and
optimization processes there is no hedging strategy that continuously outperforms the others for
every level of risk. However, at low levels of risk the hedged frontiers perform better than the
unhedged, as they are to the northwest of the unhedged frontiers. For higher levels of risk the
picture changes, because as the standard deviation rises the difference disappears and at the
higher levels of risk the unhedged frontiers dominate the hedged ones. This evidence proposes
that U.S. investors that are willing to bear high amount of risk in their portfolio, in order to gain
the higher possible dollar excess returns, should not hedge the exchange rate exposure, while the
rest should hedge it.
Moreover, if they decide to hedge their currency risk, the results show that if they have to choose
between the two hedging strategies used in this study, then they should use the unitary currency
hedging strategy as it performs better than Black’s hedging strategy.
This research does not take into account the transaction costs associated with hedging the
currency exposure. Although hedging is assumed to be rebalanced in a monthly basis and Perold
and Schoulman’s study (1988) indicates that transaction costs are very low, it is possible that
they can have a negative impact on results; thus, is proposed that further research can study the
effect caused by transaction costs. Moreover, currency risk is not the only risk that comes into
play when investing abroad. By simply taking into account only numbers that promise
exceptional returns totally ignores other sources of risk that might exist, suggesting that future
research should also examine this aspect.
37
K.V. Sigeris
International Diversification and the Currency Hedging Decision
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size, style and sector segments in 45 Developed and Emerging Markets”
42
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Appendix A: Black’s Universal Hedging Formula, Data Inputs
Exchange Rate Volatilities
Table 7: Exchange Rate Volatilities, 2002-2003
U.S.
Australia
Canada
Japan
Singapore
Switzerland
U.K.
Eurozone
Brazil
China
India
Mexico
South Africa
Korea
Turkey
U.S.
Australia
Canada
Japan
Singapore
Switzerland
U.K.
Eurozone
Brazil
China
India
Mexico
South Africa
Korea
Turkey
0%
10%
7%
9%
4%
10%
7%
9%
22%
0%
2%
9%
18%
7%
16%
10%
0%
8%
12%
9%
10%
9%
10%
22%
9%
10%
16%
22%
12%
17%
7%
8%
0%
10%
8%
10%
9%
9%
21%
8%
8%
12%
18%
10%
15%
9%
12%
10%
0%
7%
10%
9%
9%
21%
9%
9%
13%
23%
10%
17%
4%
9%
8%
7%
0%
15%
7%
8%
20%
4%
4%
14%
21%
6%
17%
10%
10%
10%
10%
15%
0%
7%
3%
22%
11%
11%
15%
22%
12%
17%
7%
9%
9%
9%
7%
7%
0%
6%
21%
7%
8%
12%
18%
9%
16%
9%
10%
9%
9%
8%
3%
6%
0%
24%
9%
10%
14%
22%
10%
17%
22%
22%
22%
21%
20%
22%
21%
24%
0%
20%
20%
22%
27%
23%
24%
0%
9%
8%
9%
4%
11%
7%
9%
20%
0%
4%
13%
22%
12%
17%
2%
10%
8%
9%
4%
11%
8%
10%
20%
4%
0%
13%
22%
12%
17%
9%
16%
12%
13%
14%
15%
12%
14%
22%
13%
13%
0%
24%
21%
21%
18%
22%
18%
23%
21%
22%
18%
22%
27%
22%
22%
24%
0%
24%
25%
7%
12%
10%
10%
6%
12%
9%
10%
23%
12%
12%
21%
24%
0%
20%
16%
17%
15%
17%
17%
17%
16%
17%
24%
17%
17%
21%
25%
20%
0%
Average Exchange Rate Volatility 2002-03
11.65%
Table 8: Exchange Rate Volatilities, 2005-2006
U.S.
Australia
Canada
Japan
Singapore
Switzerland
U.K.
Eurozone
Brazil
China
India
Mexico
South Africa
Korea
Turkey
U.S.
Australia
Canada
Japan
Singapore
Switzerland
U.K.
Eurozone
Brazil
China
India
Mexico
South Africa
Korea
Turkey
0%
8%
8%
9%
4%
9%
8%
8%
14%
2%
4%
7%
15%
7%
13%
8%
0%
8%
10%
7%
7%
7%
7%
13%
9%
8%
10%
13%
10%
13%
8%
8%
0%
9%
7%
7%
8%
8%
14%
8%
8%
9%
14%
9%
14%
9%
10%
9%
0%
6%
8%
7%
7%
14%
8%
8%
11%
18%
10%
14%
4%
7%
7%
6%
0%
7%
6%
7%
12%
4%
5%
7%
14%
6%
13%
9%
7%
7%
8%
7%
0%
5%
3%
15%
10%
9%
11%
13%
11%
14%
8%
7%
8%
7%
6%
5%
0%
5%
14%
8%
7%
10%
13%
9%
14%
8%
7%
8%
7%
7%
3%
5%
0%
15%
8%
8%
10%
13%
9%
13%
14%
13%
14%
14%
12%
15%
14%
15%
0%
13%
13%
12%
16%
15%
13%
2%
9%
8%
8%
4%
10%
8%
8%
13%
0%
4%
7%
15%
10%
14%
4%
8%
8%
8%
5%
9%
7%
8%
13%
4%
0%
8%
15%
10%
14%
7%
10%
9%
11%
7%
11%
10%
10%
12%
7%
8%
0%
13%
12%
12%
15%
13%
14%
18%
14%
13%
13%
13%
16%
15%
15%
13%
0%
16%
15%
7%
10%
9%
10%
6%
11%
9%
9%
15%
10%
10%
12%
16%
0%
16%
13%
13%
14%
14%
13%
14%
14%
13%
13%
14%
14%
12%
15%
16%
0%
Average Exchange Rate Volatility 2005-06
8.75%
43
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Country Weights on World Market Portfolio
Table 9: MSCI All Country World Investable Market Index (ACWI IMI)
Country Weights
Developed Markets
# of Securities Weight
Emerging Markets
Australia
Austria
Belgium
Canada
Denmark
Finland
France
Germany
Greece
Hong Kong
Ireland
Italy
Japan
Netherlands
New Zealand
Norway
Portugal
Singapore
Spain
Sweden
Switzerland
United Kingdom
United States
Total
236
33
50
306
43
46
182
164
57
134
21
146
1160
58
22
56
25
96
86
104
118
384
2494
3.37%
0.20%
0.44%
4.12%
0.41%
0.52%
4.24%
3.21%
0.31%
0.95%
0.19%
1.51%
9.14%
1.04%
0.07%
0.38%
0.14%
0.60%
1.83%
1.10%
3.03%
8.52%
42.41%
6021
87.73%
As of 30 September 2009
# of Securities
Brazil
Chile
China
Colombia
Czech Republic
Egypt
Hungary
Indonesia
India
Israel
Korea
Malaysia
Mexico
Morocco
Peru
Philippines
Poland
Russia
South Africa
Taiwan
Thailand
Turkey
Total
Weight
157
33
309
12
7
41
8
41
285
79
388
120
48
13
7
28
63
42
119
479
79
83
1.84%
0.17%
2.08%
0.08%
0.06%
0.08%
0.07%
0.23%
0.99%
0.32%
1.69%
0.34%
0.50%
0.04%
0.07%
0.06%
0.15%
0.69%
0.89%
1.54%
0.18%
0.20%
2441
12.27%
Data Source: http://www.mscibarra.com/
Table 10: Country Weights Assuming our Portfolio Is the World Market Portfolio
Developed Markets
United States
Australia
Canada
Japan
Singapore
Switzerland
United Kingdom
France
Germany
Greece
Netherlands
Portugal
Spain
Total
Weight
47.04%
3.74%
4.57%
10.14%
0.67%
3.36%
9.45%
4.70%
3.56%
0.34%
1.15%
0.16%
2.03%
90.92%
Emerging Markets
Brazil
China
India
Mexico
South Africa
Korea
Turkey
Total
44
K.V. Sigeris
Weight
2.04%
2.31%
1.10%
0.55%
0.99%
1.87%
0.22%
9.08%
International Diversification and the Currency Hedging Decision
World Market Excess Returns and Return Volatilities in Different Currencies
Table 11: World Market Excess Returns and Return Volatilities in Different Currencies, 2002-2003, 2005-2006
Country
2002
United States
Australia
Canada
Japan
Singapore
Switzerland
United Kingdom
France
Germany
Greece
Netherlands
Portugal
Spain
Brazil
China
India
Mexico
South Africa
Korea
Turkey
-26%
-17%
-18%
-19%
-19%
-27%
-30%
-37%
-47%
-42%
-38%
-32%
-33%
-18%
-19%
0%
-10%
-23%
-8%
-76%
Excess Return
2003
2005
26%
4%
22%
22%
31%
18%
11%
12%
31%
33%
1%
14%
26%
42%
78%
60%
33%
-2%
29%
50%
2%
15%
21%
43%
11%
31%
11%
21%
21%
25%
24%
8%
14%
14%
13%
33%
28%
31%
47%
33%
2006
2002
9%
12%
12%
6%
28%
15%
6%
14%
15%
15%
11%
26%
26%
13%
76%
40%
33%
23%
-3%
-22%
26%
12%
18%
23%
20%
28%
27%
34%
39%
19%
36%
21%
33%
27%
22%
17%
23%
21%
35%
45%
Return Volatility
2003
2005
17%
11%
10%
21%
19%
22%
19%
26%
31%
21%
29%
14%
22%
19%
23%
19%
15%
19%
28%
42%
10%
10%
12%
13%
10%
9%
9%
11%
12%
15%
11%
9%
10%
23%
16%
17%
17%
14%
17%
26%
2006
10%
14%
14%
19%
14%
13%
12%
15%
16%
19%
14%
10%
14%
24%
22%
26%
23%
24%
18%
33%
Table 12:
WEIGHTED World Market Excess Returns and Return Volatilities in Different Currencies, 2002-2003, 2005-2006
Country
2002
Excess Return
2003
2005
2006
2002
Return Volatility
2003
2005
2006
United States
Australia
Canada
Japan
Singapore
Switzerland
United Kingdom
France
Germany
Greece
Netherlands
Portugal
Spain
Brazil
China
India
Mexico
South Africa
Korea
Turkey
-12.03%
-0.64%
-0.81%
-1.97%
-0.13%
-0.90%
-2.79%
-1.75%
-1.69%
-0.14%
-0.43%
-0.05%
-0.67%
-0.37%
-0.43%
0.00%
-0.06%
-0.23%
-0.15%
-0.17%
12.13%
0.13%
1.00%
2.18%
0.20%
0.61%
1.02%
0.58%
1.10%
0.11%
0.01%
0.02%
0.53%
1.58%
1.39%
0.36%
-0.01%
0.29%
0.93%
0.00%
0.82%
0.55%
0.96%
4.35%
0.07%
1.03%
1.08%
0.99%
0.75%
0.09%
0.28%
0.01%
0.29%
0.29%
0.30%
0.36%
0.16%
0.31%
0.88%
0.07%
4.01%
0.46%
0.54%
0.60%
0.19%
0.51%
0.57%
0.66%
0.54%
0.05%
0.12%
0.04%
0.53%
0.26%
1.76%
0.44%
0.18%
0.23%
-0.05%
-0.05%
12.44%
0.47%
0.83%
2.29%
0.13%
0.95%
2.57%
1.61%
1.39%
0.07%
0.42%
0.03%
0.67%
0.55%
0.51%
0.19%
0.13%
0.21%
0.65%
0.10%
8.04%
0.40%
0.47%
2.11%
0.13%
0.74%
1.80%
1.20%
1.09%
0.07%
0.33%
0.02%
0.44%
0.38%
0.52%
0.21%
0.08%
0.19%
0.53%
0.09%
4.84%
0.39%
0.53%
1.30%
0.07%
0.31%
0.82%
0.52%
0.43%
0.05%
0.12%
0.01%
0.21%
0.47%
0.36%
0.19%
0.10%
0.14%
0.32%
0.06%
4.79%
0.51%
0.62%
1.91%
0.10%
0.43%
1.17%
0.69%
0.55%
0.07%
0.17%
0.02%
0.28%
0.44%
0.60%
0.26%
0.13%
0.18%
0.61%
0.00%
AVERAGE VALUES
-25.4%
24.18%
12.63%
11.6%
26.18%
18.85%
11.21%
13.52
45
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Appendix B: Correlation Tables
Correlation Matrix – Local MSCI Index Return
Table 13: Correlation Matrix - Local MSCI Index Return, 2004-2006 Portfolio
U.S.
Australia
Canada
Japan
Singapore
Switzerland
U.K.
France
Germany
Greece
Netherlands
Portugal
Spain
Brazil
China
India
Mexico
South Africa
Korea
Turkey
U.S.
1.00
0.64
0.67
0.37
0.58
0.58
0.57
0.66
0.77
0.54
0.57
0.31
0.63
0.51
0.61
0.51
0.72
0.56
0.57
0.42
Aus tra l i a
0.64
1.00
0.72
0.62
0.58
0.42
0.78
0.73
0.70
0.49
0.59
0.46
0.59
0.63
0.60
0.69
0.77
0.70
0.59
0.62
Ca na da
0.67
0.72
1.00
0.45
0.55
0.45
0.57
0.70
0.65
0.45
0.47
0.35
0.46
0.71
0.70
0.50
0.68
0.71
0.60
0.47
Ja pa n
0.37
0.62
0.45
1.00
0.28
0.56
0.53
0.55
0.55
0.31
0.50
0.44
0.35
0.46
0.20
0.50
0.60
0.47
0.54
0.47
Si nga pore
0.58
0.58
0.55
0.28
1.00
0.60
0.59
0.64
0.69
0.50
0.52
0.53
0.60
0.35
0.57
0.64
0.57
0.52
0.51
0.44
Swi tzerl a nd
0.58
0.42
0.45
0.56
0.60
1.00
0.66
0.77
0.81
0.62
0.74
0.44
0.65
0.26
0.32
0.58
0.56
0.44
0.63
0.40
UK
0.57
0.78
0.57
0.53
0.59
0.66
1.00
0.83
0.79
0.61
0.74
0.55
0.71
0.44
0.45
0.71
0.61
0.59
0.57
0.53
Fra nce
0.66
0.73
0.70
0.55
0.64
0.77
0.83
1.00
0.90
0.59
0.83
0.57
0.74
0.41
0.50
0.62
0.63
0.63
0.65
0.44
Germa ny
0.77
0.70
0.65
0.55
0.69
0.81
0.79
0.90
1.00
0.67
0.81
0.52
0.75
0.42
0.49
0.71
0.63
0.59
0.61
0.47
Greece
0.54
0.49
0.45
0.31
0.50
0.62
0.61
0.59
0.67
1.00
0.62
0.39
0.69
0.34
0.32
0.50
0.59
0.43
0.57
0.48
Netherl a nds
0.57
0.59
0.47
0.50
0.52
0.74
0.74
0.83
0.81
0.62
1.00
0.58
0.69
0.30
0.40
0.58
0.55
0.39
0.57
0.45
Portuga l
0.31
0.46
0.35
0.44
0.53
0.44
0.55
0.57
0.52
0.39
0.58
1.00
0.54
0.16
0.35
0.46
0.43
0.28
0.41
0.33
Spa i n
0.63
0.59
0.46
0.35
0.60
0.65
0.71
0.74
0.75
0.69
0.69
0.54
1.00
0.34
0.40
0.59
0.64
0.38
0.49
0.47
Bra zi l
0.51
0.63
0.71
0.46
0.35
0.26
0.44
0.41
0.42
0.34
0.30
0.16
0.34
1.00
0.73
0.43
0.66
0.66
0.47
0.66
Chi na
0.61
0.60
0.70
0.20
0.57
0.32
0.45
0.50
0.49
0.32
0.40
0.35
0.40
0.73
1.00
0.42
0.57
0.66
0.44
0.40
Indi a
0.51
0.69
0.50
0.50
0.64
0.58
0.71
0.62
0.71
0.50
0.58
0.46
0.59
0.43
0.42
1.00
0.59
0.60
0.58
0.52
Mexi co
0.72
0.77
0.68
0.60
0.57
0.56
0.61
0.63
0.63
0.59
0.55
0.43
0.64
0.66
0.57
0.59
1.00
0.65
0.75
0.58
South Afri ca
0.56
0.70
0.71
0.47
0.52
0.44
0.59
0.63
0.59
0.43
0.39
0.28
0.38
0.66
0.66
0.60
0.65
1.00
0.70
0.38
Korea
0.57
0.59
0.60
0.54
0.51
0.63
0.57
0.65
0.61
0.57
0.57
0.41
0.49
0.47
0.44
0.58
0.75
0.70
1.00
0.51
Turkey
0.42
0.62
0.47
0.47
0.44
0.40
0.53
0.44
0.47
0.48
0.45
0.33
0.47
0.66
0.40
0.52
0.58
0.38
0.51
1.00
Table 14: Correlation Matrix - Local MSCI Index Return, 2007-2010 Portfolio
U.S.
Australia
Canada
Japan
Singapore
Switzerland
U.K.
France
Germany
Greece
Netherlands
Portugal
Spain
Brazil
China
India
Mexico
South Africa
Korea
Turkey
U.S.
1.00
0.89
0.84
0.77
0.82
0.84
0.89
0.90
0.89
0.79
0.84
0.70
0.83
0.76
0.67
0.77
0.83
0.75
0.73
0.66
Aus tra l i a
0.89
1.00
0.78
0.73
0.73
0.85
0.89
0.89
0.86
0.74
0.84
0.71
0.80
0.73
0.69
0.71
0.67
0.71
0.73
0.65
Ca na da
0.84
0.78
1.00
0.73
0.84
0.69
0.81
0.76
0.73
0.66
0.73
0.62
0.67
0.81
0.69
0.74
0.76
0.76
0.69
0.52
Ja pa n
0.77
0.73
0.73
1.00
0.78
0.68
0.76
0.77
0.75
0.68
0.74
0.66
0.70
0.70
0.70
0.69
0.64
0.69
0.68
0.75
Si nga pore
0.82
0.73
0.84
0.78
1.00
0.71
0.76
0.80
0.79
0.73
0.82
0.72
0.78
0.80
0.80
0.83
0.78
0.75
0.81
0.75
Swi tzerl a nd
0.84
0.85
0.69
0.68
0.71
1.00
0.83
0.89
0.85
0.73
0.84
0.69
0.75
0.56
0.59
0.70
0.63
0.69
0.64
0.72
U.K.
0.89
0.89
0.81
0.76
0.76
0.83
1.00
0.93
0.88
0.73
0.87
0.72
0.81
0.74
0.70
0.73
0.75
0.78
0.67
0.66
Fra nce
0.90
0.89
0.76
0.77
0.80
0.89
0.93
1.00
0.95
0.79
0.92
0.80
0.87
0.73
0.65
0.77
0.75
0.72
0.76
0.76
Germa ny
0.89
0.86
0.73
0.75
0.79
0.85
0.88
0.95
1.00
0.73
0.88
0.74
0.84
0.69
0.68
0.77
0.76
0.66
0.77
0.77
Greece
0.79
0.74
0.66
0.68
0.73
0.73
0.73
0.79
0.73
1.00
0.76
0.77
0.82
0.73
0.58
0.70
0.64
0.65
0.72
0.72
Netherl a nds
0.84
0.84
0.73
0.74
0.82
0.84
0.87
0.92
0.88
0.76
1.00
0.76
0.79
0.71
0.64
0.76
0.71
0.70
0.75
0.75
Portuga l
0.70
0.71
0.62
0.66
0.72
0.69
0.72
0.80
0.74
0.77
0.76
1.00
0.81
0.72
0.61
0.77
0.68
0.62
0.75
0.71
Spa i n
0.83
0.80
0.67
0.70
0.78
0.75
0.81
0.87
0.84
0.82
0.79
0.81
1.00
0.71
0.68
0.73
0.78
0.67
0.77
0.77
Bra zi l
0.76
0.73
0.81
0.70
0.80
0.56
0.74
0.73
0.69
0.73
0.71
0.72
0.71
1.00
0.76
0.77
0.71
0.73
0.76
0.56
Chi na
0.67
0.69
0.69
0.70
0.80
0.59
0.70
0.65
0.68
0.58
0.64
0.61
0.68
0.76
1.00
0.80
0.56
0.71
0.70
0.72
Indi a
0.77
0.71
0.74
0.69
0.83
0.70
0.73
0.77
0.77
0.70
0.76
0.77
0.73
0.77
0.80
1.00
0.65
0.65
0.72
0.77
Mexi co
0.83
0.67
0.76
0.64
0.78
0.63
0.75
0.75
0.76
0.64
0.71
0.68
0.78
0.71
0.56
0.65
1.00
0.70
0.66
0.49
South Afri ca
0.75
0.71
0.76
0.69
0.75
0.69
0.78
0.72
0.66
0.65
0.70
0.62
0.67
0.73
0.71
0.65
0.70
1.00
0.65
0.58
Korea
0.73
0.73
0.69
0.68
0.81
0.64
0.67
0.76
0.77
0.72
0.75
0.75
0.77
0.76
0.70
0.72
0.66
0.65
1.00
0.76
Turkey
0.66
0.65
0.52
0.75
0.75
0.72
0.66
0.76
0.77
0.72
0.75
0.71
0.77
0.56
0.72
0.77
0.49
0.58
0.76
1.00
46
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Appendix C: Optimal Portfolio Weights & Efficient Frontiers’ Sharpe Ratio
Optimization 1: Optimal Portfolio Weights, 2004-2006
Note: Standard deviations on portfolio weight charts are not measured in equal intervals.
47
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Optimization 2: Optimal Portfolio Weights, 2004-2006
Note: Standard deviations on portfolio weight charts are not measured in equal intervals.
48
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Optimization 1: Optimal Portfolio Weights, 2007-2010
Note: Standard deviations on portfolio weight charts are not measured in equal intervals.
49
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Optimization 2: Optimal Portfolio Weights, 2007-2010
Note: Standard deviations on portfolio weight charts are not measured in equal intervals.
50
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Efficient Frontiers’ Sharpe Ratio, 2004-2006
51
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Efficient Frontiers’ Sharpe Ratio, 2007-2010
52
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Appendix D: Short Sales Optimization
The third optimization process performed in this thesis allows for shortselling the national equity
index portfolios up to 50%. This optimization is performed under the restrictions:
Short Sales Optimization:
 Minimize standard deviation for a given level of required return subject to the constraint
that country portfolio weights are between -50% and 100%
-0.5 ≤ wi ≤ 1
This means that individual country portfolio indices can be sold short up to 50% of their value,
but also bought up to 100% of their value.
Charts 21 and 22 present the efficient frontiers for the 2004-2006 and 2007-2010 testing period
respectively, derived from the short sales optimization process.
Simply investing in U.S. MSCI index is clearly not optimal, irrespective of the period, as can be
seen from all the international efficient frontiers. In this case, the positive effect that hedging has
on international efficient frontiers is clear. For both testing periods, the hedged portfolios’
efficient frontiers are to the northwest of the unhedged portfolios’. Only for the very low levels
of standard deviation the unhedged frontiers dominate the hedged ones. Furthermore, for the
2004-2006 testing period, the unitary hedged portfolio frontier produces better results than the
Black’s universal optimally hedged frontier, while for the 2007-2010 testing period the outcome
is almost the same.
This optimization allowing for selling short the national equity indices up to 50% of their value
advocates enthusiasm. This is because the excess returns derived from every efficient frontier for
every level of standard deviation are positive and substantially higher than those of the other
optimization processes. This fact is true not only for the 2004-2006 testing period, but also for
the 2007-2010 testing period, were the twenty individual country index portfolios that entered
the optimization process experienced large negative dollar excess returns in general.
53
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Unlikely the optimization process one and two, all the twenty individual country index portfolios
that entered the short sales portfolio optimization process have weights different than zero for
any level of standard deviation (risk). During the 2004-2006 testing period, for low levels of
standard deviation, countries like U.S., Australia, Singapore, Switzerland and U.K. are highly
positive weighted, and countries like Germany and emerging markets are highly negative
weighted. For high levels of risk, Greece, Spain, India, China and Mexico are highly positive
weighted and the rest mainly negatively weighted. During the 2007-2010 period Australia,
Japan, Switzerland, U.K. and Portugal are highly positive weighted for low levels of risk, and
Canada, Singapore, Brazil, China, India and Korea for high levels of risk. Large negative
weights display almost all emerging markets, as also Greece, Germany and Netherlands for low
54
K.V. Sigeris
International Diversification and the Currency Hedging Decision
levels of risk, and for high levels of risk, all the rest that weren’t positively weighted (Charts 2328).
Short Sales Optimization: Optimal Portfolio Weights, 2004-2006
Note: Standard deviations on portfolio weight charts are not measured in equal intervals.
55
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Short Sales Optimization: Optimal Portfolio Weights, 2007-2010
Note: Standard deviations on portfolio weight charts are not measured in equal intervals.
56
K.V. Sigeris
International Diversification and the Currency Hedging Decision
During the 2004-2006 and 2007-2010 testing periods, the Sharpe ratio is maximized when the
excess return is around to 35%, irrespective of the optimization process and if the frontiers are
hedged or not. This means that the optimal risky portfolios, or tangency portfolios, lye in the
frontiers for values of excess return around to 35%. Clearly investing only in the U.S. equity
index portfolio is an inefficient choice according to Sharpe ratios, as international diversification
can offer much higher values or Sharpe ratios.
Furthermore, during these testing periods the hedged Sharpe is generally higher than the
unhedged, while the unitary hedged Sharpe ratio appears to be better than the Black hedged
Sharpe, especially during the 2004-2006 testing period (Charts 29-30).
57
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Appendix F: Correlation & Covariance Tables
Correlation & Covariance Matrix - Unhedged Dollar MSCI Index Excess Return, 2004-2006
Table 15: Correlation Matrix - Unhedged Dollar MSCI Index Excess Return, 2004-2006 Portfolio
U.S.
Australia
Canada
Japan
Singapore
Switzerland
U.K.
France
Germany
Greece
Netherlands
Portugal
Spain
Brazil
China
India
Mexico
South Africa
Korea
Turkey
U.S.
1.00
0.60
0.58
0.37
0.59
0.76
0.59
0.78
0.84
0.63
0.75
0.46
0.73
0.52
0.60
0.52
0.75
0.60
0.62
0.50
Aus tra l i a
0.60
1.00
0.77
0.50
0.63
0.63
0.83
0.71
0.68
0.64
0.62
0.48
0.73
0.78
0.69
0.60
0.77
0.84
0.63
0.67
Ca na da
0.58
0.77
1.00
0.50
0.41
0.53
0.65
0.73
0.68
0.43
0.58
0.39
0.58
0.70
0.62
0.51
0.59
0.78
0.53
0.55
Ja pa n
0.37
0.50
0.50
1.00
0.24
0.42
0.33
0.39
0.42
0.33
0.35
0.41
0.32
0.50
0.22
0.46
0.57
0.61
0.57
0.50
Si nga pore
0.59
0.63
0.41
0.24
1.00
0.49
0.48
0.58
0.63
0.55
0.49
0.52
0.55
0.50
0.65
0.66
0.65
0.58
0.56
0.57
Swi tzerl a nd
0.76
0.63
0.53
0.42
0.49
1.00
0.76
0.80
0.86
0.76
0.74
0.47
0.72
0.54
0.56
0.45
0.68
0.63
0.61
0.39
UK
0.59
0.83
0.65
0.33
0.48
0.76
1.00
0.83
0.76
0.71
0.72
0.62
0.78
0.64
0.70
0.43
0.58
0.76
0.44
0.43
Fra nce
0.78
0.71
0.73
0.39
0.58
0.80
0.83
1.00
0.93
0.69
0.84
0.65
0.81
0.58
0.71
0.56
0.63
0.74
0.59
0.40
Germa ny
0.84
0.68
0.68
0.42
0.63
0.86
0.76
0.93
1.00
0.74
0.85
0.62
0.82
0.56
0.65
0.63
0.64
0.69
0.57
0.45
Greece
0.63
0.64
0.43
0.33
0.55
0.76
0.71
0.69
0.74
1.00
0.70
0.50
0.75
0.52
0.47
0.50
0.65
0.57
0.59
0.51
Netherl a nds
0.75
0.62
0.58
0.35
0.49
0.74
0.72
0.84
0.85
0.70
1.00
0.63
0.74
0.50
0.63
0.56
0.64
0.60
0.56
0.47
Portuga l
0.46
0.48
0.39
0.41
0.52
0.47
0.62
0.65
0.62
0.50
0.63
1.00
0.63
0.35
0.54
0.47
0.42
0.55
0.41
0.34
Spa i n
0.73
0.73
0.58
0.32
0.55
0.72
0.78
0.81
0.82
0.75
0.74
0.63
1.00
0.56
0.59
0.56
0.65
0.58
0.47
0.43
Bra zi l
0.52
0.78
0.70
0.50
0.50
0.54
0.64
0.58
0.56
0.52
0.50
0.35
0.56
1.00
0.69
0.57
0.73
0.76
0.53
0.75
Chi na
0.60
0.69
0.62
0.22
0.65
0.56
0.70
0.71
0.65
0.47
0.63
0.54
0.59
0.69
1.00
0.44
0.62
0.76
0.49
0.44
Indi a
0.52
0.60
0.51
0.46
0.66
0.45
0.43
0.56
0.63
0.50
0.56
0.47
0.56
0.57
0.44
1.00
0.63
0.54
0.58
0.61
Mexi co
0.75
0.77
0.59
0.57
0.65
0.68
0.58
0.63
0.64
0.65
0.64
0.42
0.65
0.73
0.62
0.63
1.00
0.74
0.77
0.76
South Afri ca
0.60
0.84
0.78
0.61
0.58
0.63
0.76
0.74
0.69
0.57
0.60
0.55
0.58
0.76
0.76
0.54
0.74
1.00
0.59
0.61
Korea
0.62
0.63
0.53
0.57
0.56
0.61
0.44
0.59
0.57
0.59
0.56
0.41
0.47
0.53
0.49
0.58
0.77
0.59
1.00
0.53
Turkey
0.50
0.67
0.55
0.50
0.57
0.39
0.43
0.40
0.45
0.51
0.47
0.34
0.43
0.75
0.44
0.61
0.76
0.61
0.53
1.00
Table 16: Covariance Matrix - Unhedged Dollar MSCI Index Excess Return, 2004-2006 Portfolio
U.K.
Greece
Netherlands
Portugal
Spain
Brazil
Mexico
South Africa
Korea
Turkey
50
36
57
76
76
60
42
61
104
89
85
96
108
90
133
104
81
99
102
121
150
98
87
119
304
203
190
195
301
179
345
Ca na da
57
150
206
104
71
72
81
109
129
107
97
74
100
288
191
170
158
295
158
303
Ja pa n
37
98
104
212
43
58
42
59
80
82
60
79
56
211
68
158
155
234
173
278
Si nga pore
50
104
71
43
148
57
52
74
101
115
69
84
80
175
170
189
147
186
142
265
Swi tzerl a nd
50
81
72
58
57
90
63
80
108
125
82
59
82
148
115
100
120
158
122
141
UK
36
99
81
42
52
63
77
76
88
107
73
72
82
162
132
88
95
174
81
144
Fra nce
57
102
109
59
74
80
76
110
129
124
103
91
102
175
161
139
124
203
130
159
Germa ny
76
121
129
80
101
108
88
129
174
169
130
108
130
213
185
194
156
238
159
225
Greece
76
150
107
82
115
125
107
124
169
298
140
113
156
260
173
203
209
260
215
334
Netherl a nds
60
98
97
60
69
82
73
103
130
140
135
98
104
168
159
152
137
184
138
208
Portuga l
42
87
74
79
84
59
72
91
108
113
98
176
101
133
156
146
103
191
114
171
Spa i n
61
119
100
56
80
82
82
102
130
156
104
101
144
194
153
157
145
184
120
200
Bra zi l
104
304
288
211
175
148
162
175
213
260
168
133
194
836
432
388
391
581
323
831
Chi na
89
203
191
68
170
115
132
161
185
173
159
156
153
432
466
225
248
432
222
364
Indi a
85
190
170
158
189
100
88
139
194
203
152
146
157
388
225
552
273
336
286
547
Mexi co
96
195
158
155
147
120
95
124
156
209
137
103
145
391
248
273
345
359
301
537
South Afri ca
108
301
295
234
186
158
174
203
238
260
184
191
184
581
432
336
359
690
328
612
Korea
90
179
158
173
142
122
81
130
159
215
138
114
120
323
222
286
301
328
442
428
Turkey
133
345
303
278
265
141
144
159
225
334
208
171
200
831
364
547
537
612
428
1461
58
K.V. Sigeris
India
Switzerland
50
98
China
Singapore
37
150
Germany
Japan
57
184
France
Canada
56
56
Australia
48
Aus tra l i a
U.S.
U.S.
International Diversification and the Currency Hedging Decision
Correlation & Covariance Matrix- Unitary Unhedged Dollar MSCI Index Excess Return, 2004-2006
Table 17: Correlation Matrix - Unitary Hedged Dollar MSCI Index Excess Return, 2004-2006 Portfolio
U.S.
Australia
Canada
Japan
Singapore
Switzerland
U.K.
France
Germany
Greece
Netherlands
Portugal
Spain
Brazil
China
India
Mexico
South Africa
Korea
Turkey
U.S.
1.00
0.64
0.67
0.37
0.57
0.57
0.57
0.65
0.76
0.55
0.56
0.30
0.62
0.51
0.59
0.50
0.72
0.56
0.57
0.42
Aus tra l i a
0.64
1.00
0.72
0.63
0.58
0.43
0.78
0.73
0.71
0.49
0.60
0.47
0.59
0.63
0.60
0.69
0.77
0.70
0.59
0.62
Ca na da
0.67
0.72
1.00
0.45
0.55
0.45
0.57
0.70
0.65
0.45
0.47
0.35
0.46
0.71
0.70
0.50
0.67
0.71
0.60
0.48
Ja pa n
0.37
0.63
0.45
1.00
0.28
0.56
0.54
0.56
0.56
0.31
0.50
0.45
0.36
0.45
0.20
0.51
0.59
0.47
0.54
0.48
Si nga pore
0.57
0.58
0.55
0.28
1.00
0.60
0.60
0.64
0.69
0.50
0.52
0.53
0.59
0.37
0.56
0.63
0.58
0.51
0.50
0.43
Swi tzerl a nd
0.57
0.43
0.45
0.56
0.60
1.00
0.67
0.77
0.81
0.63
0.75
0.45
0.65
0.26
0.32
0.58
0.55
0.45
0.63
0.41
UK
0.57
0.78
0.57
0.54
0.60
0.67
1.00
0.83
0.80
0.61
0.75
0.56
0.72
0.45
0.46
0.72
0.60
0.60
0.58
0.53
Fra nce
0.65
0.73
0.70
0.56
0.64
0.77
0.83
1.00
0.90
0.59
0.83
0.58
0.74
0.41
0.50
0.63
0.62
0.63
0.65
0.45
Germa ny
0.76
0.71
0.65
0.56
0.69
0.81
0.80
0.90
1.00
0.68
0.81
0.52
0.76
0.42
0.49
0.71
0.63
0.59
0.62
0.48
Greece
0.55
0.49
0.45
0.31
0.50
0.63
0.61
0.59
0.68
1.00
0.62
0.39
0.69
0.34
0.33
0.50
0.59
0.43
0.57
0.47
Netherl a nds
0.56
0.60
0.47
0.50
0.52
0.75
0.75
0.83
0.81
0.62
1.00
0.58
0.70
0.30
0.40
0.58
0.54
0.40
0.58
0.46
Portuga l
0.30
0.47
0.35
0.45
0.53
0.45
0.56
0.58
0.52
0.39
0.58
1.00
0.55
0.17
0.35
0.46
0.44
0.28
0.41
0.33
Spa i n
0.62
0.59
0.46
0.36
0.59
0.65
0.72
0.74
0.76
0.69
0.70
0.55
1.00
0.35
0.40
0.59
0.63
0.38
0.50
0.47
Bra zi l
0.51
0.63
0.71
0.45
0.37
0.26
0.45
0.41
0.42
0.34
0.30
0.17
0.35
1.00
0.74
0.43
0.65
0.66
0.47
0.65
Chi na
0.59
0.60
0.70
0.20
0.56
0.32
0.46
0.50
0.49
0.33
0.40
0.35
0.40
0.74
1.00
0.41
0.57
0.66
0.44
0.40
Indi a
0.50
0.69
0.50
0.51
0.63
0.58
0.72
0.63
0.71
0.50
0.58
0.46
0.59
0.43
0.41
1.00
0.58
0.61
0.58
0.53
Mexi co
0.72
0.77
0.67
0.59
0.58
0.55
0.60
0.62
0.63
0.59
0.54
0.44
0.63
0.65
0.57
0.58
1.00
0.64
0.74
0.56
South Afri ca
0.56
0.70
0.71
0.47
0.51
0.45
0.60
0.63
0.59
0.43
0.40
0.28
0.38
0.66
0.66
0.61
0.64
1.00
0.70
0.39
Korea
0.57
0.59
0.60
0.54
0.50
0.63
0.58
0.65
0.62
0.57
0.58
0.41
0.50
0.47
0.44
0.58
0.74
0.70
1.00
0.51
Turkey
0.42
0.62
0.48
0.48
0.43
0.41
0.53
0.45
0.48
0.47
0.46
0.33
0.47
0.65
0.40
0.53
0.56
0.39
0.51
1.00
Turkey
Table 18: Covariance Matrix - Unitary Hedged Dollar MSCI Index Excess Return, 2004-2006 Portfolio
Japan
Singapore
Switzerland
U.K.
France
Germany
Greece
Netherlands
Portugal
Spain
Mexico
South Africa
Korea
49
34
42
36
29
40
60
59
44
26
45
81
86
72
82
62
74
81
73
65
72
53
33
50
56
69
65
57
49
52
123
110
124
107
97
93
145
Ca na da
49
65
112
64
63
43
46
66
78
74
56
46
50
170
157
111
118
122
118
141
Ja pa n
34
72
64
180
40
69
55
67
86
65
76
74
50
138
58
142
130
103
136
177
Si nga pore
42
53
63
40
116
59
48
62
84
85
63
70
66
90
128
141
103
89
101
128
Swi tzerl a nd
36
33
43
69
59
83
46
63
84
89
77
50
61
54
62
111
83
66
107
104
UK
29
50
46
55
48
46
56
56
68
72
63
52
56
76
74
112
74
73
81
110
Fra nce
40
56
66
67
62
63
56
80
92
83
84
63
69
84
95
118
92
92
109
110
Germa ny
60
69
78
86
84
84
68
92
130
120
104
73
89
109
118
169
117
109
131
152
Greece
59
65
74
65
85
89
72
83
120
245
109
75
112
121
110
164
152
109
166
204
Netherl a nds
44
57
56
76
63
77
63
84
104
109
126
81
81
76
95
136
99
73
120
142
Portuga l
26
49
46
74
70
50
52
63
73
75
81
152
70
49
92
119
89
56
94
112
Spa i n
45
52
50
50
66
61
56
69
89
112
81
70
108
83
88
128
108
64
96
133
Bra zi l
81
123
170
138
90
54
76
84
109
121
76
49
83
515
357
202
244
244
198
404
Chi na
86
110
157
58
128
62
74
95
118
110
95
92
88
357
452
181
200
226
173
237
Indi a
72
124
111
142
141
111
112
118
169
164
136
119
128
202
181
437
199
206
227
308
Mexi co
82
107
118
130
103
83
74
92
117
152
99
89
108
244
200
199
270
170
227
255
South Afri ca
62
97
122
103
89
66
73
92
109
109
73
56
64
244
226
206
170
263
212
172
Korea
74
93
118
136
101
107
81
109
131
166
120
94
96
198
173
227
227
212
345
263
Turkey
81
145
141
177
128
104
110
110
152
204
142
112
133
404
237
308
255
172
263
760
59
K.V. Sigeris
India
Canada
38
38
China
Australia
48
Aus tra l i a
Brazil
U.S.
U.S.
International Diversification and the Currency Hedging Decision
Correlation & Covariance Matrix- Black’s Hedge Ratio Dollar MSCI Index Excess Return, 2004-2006
Table 19: Correlation Matrix - Black's Universal Hedged Dollar MSCI Index Excess Return, 2004-2006 Portfolio
U.S.
Australia
Canada
Japan
Singapore
Switzerland
U.K.
France
Germany
Greece
Netherlands
Portugal
Spain
Brazil
China
India
Mexico
South Africa
Korea
Turkey
U.S.
1.00
0.65
0.65
0.38
0.59
0.72
0.65
0.76
0.83
0.60
0.67
0.38
0.70
0.53
0.59
0.51
0.74
0.62
0.60
0.47
Aus tra l i a
0.65
1.00
0.79
0.56
0.61
0.51
0.83
0.73
0.70
0.56
0.60
0.46
0.67
0.76
0.69
0.67
0.81
0.83
0.62
0.67
Ca na da
0.65
0.79
1.00
0.48
0.50
0.50
0.67
0.75
0.69
0.44
0.53
0.36
0.53
0.75
0.69
0.52
0.67
0.82
0.59
0.56
Ja pa n
0.38
0.56
0.48
1.00
0.25
0.49
0.44
0.48
0.50
0.30
0.43
0.43
0.32
0.51
0.22
0.50
0.62
0.56
0.55
0.51
Si nga pore
0.59
0.61
0.50
0.25
1.00
0.58
0.58
0.63
0.67
0.52
0.50
0.52
0.58
0.45
0.60
0.64
0.63
0.56
0.52
0.51
Swi tzerl a nd
0.72
0.51
0.50
0.49
0.58
1.00
0.68
0.75
0.83
0.68
0.72
0.39
0.64
0.45
0.47
0.58
0.70
0.53
0.65
0.46
UK
0.65
0.83
0.67
0.44
0.58
0.68
1.00
0.84
0.79
0.66
0.73
0.56
0.75
0.64
0.64
0.66
0.68
0.72
0.55
0.55
Fra nce
0.76
0.73
0.75
0.48
0.63
0.75
0.84
1.00
0.91
0.61
0.82
0.57
0.74
0.55
0.63
0.64
0.69
0.71
0.64
0.46
Germa ny
0.83
0.70
0.69
0.50
0.67
0.83
0.79
0.91
1.00
0.69
0.81
0.52
0.76
0.53
0.58
0.70
0.68
0.66
0.61
0.49
Greece
0.60
0.56
0.44
0.30
0.52
0.68
0.66
0.61
0.69
1.00
0.63
0.40
0.70
0.45
0.40
0.51
0.65
0.51
0.58
0.51
Netherl a nds
0.67
0.60
0.53
0.43
0.50
0.72
0.73
0.82
0.81
0.63
1.00
0.56
0.68
0.43
0.52
0.60
0.63
0.49
0.58
0.49
Portuga l
0.38
0.46
0.36
0.43
0.52
0.39
0.56
0.57
0.52
0.40
0.56
1.00
0.54
0.28
0.45
0.48
0.46
0.40
0.41
0.35
Spa i n
0.70
0.67
0.53
0.32
0.58
0.64
0.75
0.74
0.76
0.70
0.68
0.54
1.00
0.50
0.51
0.60
0.69
0.48
0.49
0.48
Bra zi l
0.53
0.76
0.75
0.51
0.45
0.45
0.64
0.55
0.53
0.45
0.43
0.28
0.50
1.00
0.74
0.50
0.70
0.79
0.51
0.71
Chi na
0.59
0.69
0.69
0.22
0.60
0.47
0.64
0.63
0.58
0.40
0.52
0.45
0.51
0.74
1.00
0.43
0.60
0.76
0.46
0.43
Indi a
0.51
0.67
0.52
0.50
0.64
0.58
0.66
0.64
0.70
0.51
0.60
0.48
0.60
0.50
0.43
1.00
0.61
0.60
0.58
0.57
Mexi co
0.74
0.81
0.67
0.62
0.63
0.70
0.68
0.69
0.68
0.65
0.63
0.46
0.69
0.70
0.60
0.61
1.00
0.74
0.77
0.66
South Afri ca
0.62
0.83
0.82
0.56
0.56
0.53
0.72
0.71
0.66
0.51
0.49
0.40
0.48
0.79
0.76
0.60
0.74
1.00
0.68
0.53
Korea
0.60
0.62
0.59
0.55
0.52
0.65
0.55
0.64
0.61
0.58
0.58
0.41
0.49
0.51
0.46
0.58
0.77
0.68
1.00
0.53
Turkey
0.47
0.67
0.56
0.51
0.51
0.46
0.55
0.46
0.49
0.51
0.49
0.35
0.48
0.71
0.43
0.57
0.66
0.53
0.53
1.00
Table 20: Covariance Matrix - Black's Universal Hedged Dollar MSCI Index Excess Return, 2004-2006 Portfolio
Switzerland
U.K.
France
Germany
Greece
Netherlands
Portugal
Spain
Korea
Turkey
45
41
32
47
66
66
50
32
51
90
87
77
87
80
80
101
74
68
42
58
64
80
89
64
55
69
185
146
145
137
155
120
208
Ca na da
52
91
134
74
64
48
55
77
92
82
66
51
64
212
170
132
133
178
131
202
Ja pa n
35
74
74
177
37
54
42
57
76
64
62
69
45
167
63
144
140
140
142
213
Si nga pore
45
68
64
37
125
53
46
62
87
92
61
71
67
123
144
157
119
118
113
177
Swi tzerl a nd
41
42
48
54
53
69
40
55
79
89
65
40
55
93
83
105
99
83
105
119
UK
32
58
55
42
46
40
50
53
65
74
56
49
55
111
97
102
82
96
75
121
Fra nce
47
64
77
57
62
55
53
79
93
86
78
61
69
121
121
124
105
119
111
128
Germa ny
66
80
92
76
87
79
65
93
134
126
101
74
92
151
144
177
134
143
135
179
Greece
66
89
82
64
92
89
74
86
126
252
108
77
116
176
134
177
175
151
179
253
Netherl a nds
50
64
66
62
61
65
56
78
101
108
117
74
77
114
119
140
115
100
121
166
Portuga l
32
55
51
69
71
40
49
61
74
77
74
148
69
83
116
127
96
92
96
134
Spa i n
51
69
64
45
67
55
55
69
92
116
77
69
109
128
113
137
124
95
99
158
Bra zi l
90
185
212
167
123
93
111
121
151
176
114
83
128
605
387
270
294
366
243
546
Chi na
87
146
170
63
144
83
97
121
144
134
119
116
113
387
457
198
218
306
192
285
Indi a
77
145
132
144
157
105
102
124
177
177
140
127
137
270
198
474
226
247
245
389
Mexi co
87
137
133
140
119
99
82
105
134
175
115
96
124
294
218
226
292
238
254
353
South Afri ca
80
155
178
140
118
83
96
119
143
151
100
92
95
366
306
247
238
352
245
312
Korea
80
120
131
142
113
105
75
111
135
179
121
96
99
243
192
245
254
245
373
321
Turkey
101
208
202
213
177
119
121
128
179
253
166
134
158
546
285
389
353
312
321
976
60
K.V. Sigeris
South Africa
Singapore
35
91
Mexico
Japan
52
99
India
Canada
45
45
China
Australia
48
Aus tra l i a
Brazil
U.S.
U.S.
International Diversification and the Currency Hedging Decision
Correlation & Covariance Matrix- Unhedged Dollar MSCI Index Excess Return, 2007-2010
Table 21: Correlation Matrix - Unhedged Dollar MSCI Index Excess Return, 2007-2010 Portfolio
U.S.
Australia
Canada
Japan
Singapore
Switzerland
U.K.
France
Germany
Greece
Netherlands
Portugal
Spain
Brazil
China
India
Mexico
South Africa
Korea
Turkey
U.S.
1.00
0.88
0.86
0.79
0.84
0.82
0.90
0.91
0.90
0.81
0.89
0.77
0.82
0.77
0.67
0.78
0.89
0.84
0.82
0.73
Aus tra l i a
0.88
1.00
0.85
0.79
0.86
0.83
0.91
0.91
0.89
0.82
0.89
0.82
0.86
0.86
0.80
0.77
0.81
0.90
0.84
0.75
Ca na da
0.86
0.85
1.00
0.75
0.90
0.69
0.89
0.81
0.80
0.75
0.82
0.74
0.73
0.92
0.75
0.81
0.86
0.83
0.76
0.69
Ja pa n
0.79
0.79
0.75
1.00
0.82
0.76
0.82
0.81
0.80
0.74
0.82
0.75
0.77
0.69
0.66
0.71
0.78
0.80
0.75
0.72
Si nga pore
0.84
0.86
0.90
0.82
1.00
0.79
0.90
0.87
0.88
0.80
0.90
0.82
0.84
0.85
0.81
0.86
0.87
0.86
0.84
0.80
Swi tzerl a nd
0.82
0.83
0.69
0.76
0.79
1.00
0.82
0.90
0.90
0.76
0.86
0.78
0.83
0.64
0.61
0.71
0.78
0.78
0.78
0.65
UK
0.90
0.91
0.89
0.82
0.90
0.82
1.00
0.91
0.87
0.85
0.91
0.84
0.86
0.87
0.76
0.81
0.83
0.87
0.79
0.79
Fra nce
0.91
0.91
0.81
0.81
0.87
0.90
0.91
1.00
0.97
0.87
0.95
0.89
0.93
0.79
0.71
0.78
0.86
0.89
0.82
0.74
Germa ny
0.90
0.89
0.80
0.80
0.88
0.90
0.87
0.97
1.00
0.83
0.92
0.85
0.91
0.75
0.73
0.78
0.86
0.86
0.85
0.75
Greece
0.81
0.82
0.75
0.74
0.80
0.76
0.85
0.87
0.83
1.00
0.85
0.86
0.88
0.76
0.64
0.73
0.77
0.77
0.77
0.74
Netherl a nds
0.89
0.89
0.82
0.82
0.90
0.86
0.91
0.95
0.92
0.85
1.00
0.86
0.88
0.80
0.72
0.81
0.84
0.86
0.82
0.77
Portuga l
0.77
0.82
0.74
0.75
0.82
0.78
0.84
0.89
0.85
0.86
0.86
1.00
0.90
0.77
0.69
0.79
0.81
0.83
0.77
0.71
Spa i n
0.82
0.86
0.73
0.77
0.84
0.83
0.86
0.93
0.91
0.88
0.88
0.90
1.00
0.74
0.71
0.71
0.82
0.84
0.79
0.73
Bra zi l
0.77
0.86
0.92
0.69
0.85
0.64
0.87
0.79
0.75
0.76
0.80
0.77
0.74
1.00
0.80
0.80
0.76
0.81
0.75
0.68
Chi na
0.67
0.80
0.75
0.66
0.81
0.61
0.76
0.71
0.73
0.64
0.72
0.69
0.71
0.80
1.00
0.80
0.62
0.84
0.74
0.75
Indi a
0.78
0.77
0.81
0.71
0.86
0.71
0.81
0.78
0.78
0.73
0.81
0.79
0.71
0.80
0.80
1.00
0.72
0.82
0.77
0.80
Mexi co
0.89
0.81
0.86
0.78
0.87
0.78
0.83
0.86
0.86
0.77
0.84
0.81
0.82
0.76
0.62
0.72
1.00
0.80
0.74
0.62
South Afri ca
0.84
0.90
0.83
0.80
0.86
0.78
0.87
0.89
0.86
0.77
0.86
0.83
0.84
0.81
0.84
0.82
0.80
1.00
0.80
0.81
Korea
0.82
0.84
0.76
0.75
0.84
0.78
0.79
0.82
0.85
0.77
0.82
0.77
0.79
0.75
0.74
0.77
0.74
0.80
1.00
0.80
Turkey
0.73
0.75
0.69
0.72
0.80
0.65
0.79
0.74
0.75
0.74
0.77
0.71
0.73
0.68
0.75
0.80
0.62
0.81
0.80
1.00
Table 22: Covariance Matrix - Unhedged Dollar MSCI Index Excess Return, 2007-2010 Portfolio
Australia
Canada
Japan
Singapore
Switzerland
U.K.
France
Germany
Greece
Netherlands
Portugal
Spain
Brazil
China
India
Mexico
South Africa
Korea
Turkey
405
571
523
303
541
341
425
517
555
759
536
445
543
624
487
639
559
544
628
698
Aus tra l i a
571
1032
830
483
890
553
688
831
882
1217
855
750
903
1114
929
999
817
925
1024 1144
Ca na da
523
830
916
430
873
433
634
697
744
1054
744
643
722
1114
827
997
809
802
881
999
Ja pa n
303
483
430
362
501
302
366
435
471
650
470
407
478
528
460
550
463
488
545
659
Si nga pore
541
890
873
501
1032
524
680
794
865
1195
870
754
887
1094
942
1118
871
883
1029 1226
Swi tzerl a nd
341
553
433
302
524
431
400
530
572
729
534
462
568
534
460
601
508
518
617
UK
425
688
634
366
680
400
555
610
631
929
645
565
662
823
648
775
612
658
706
887
Fra nce
517
831
697
435
794
530
610
800
844
1145
809
717
865
891
733
894
756
806
887
1006
Germa ny
555
882
744
471
865
572
631
844
945
1189
853
747
915
925
811
976
821
851
1001 1108
Greece
759
1217 1054
650
1195
729
929
1145 1189 2147 1185 1143 1333 1414 1077 1373 1118 1135 1353 1628
Netherl a nds
536
855
744
470
870
534
645
809
853
1185
900
733
865
964
790
981
788
823
936
Portuga l
445
750
643
407
754
462
565
717
747
1143
733
814
840
877
721
920
718
760
838
968
Spa i n
543
903
722
478
887
568
662
865
915
1333
865
840
1073
966
841
949
838
881
991
1141
Bra zi l
624
1114 1114
528
1094
534
823
891
925
1414
964
877
966
1609 1161 1303
955
1040 1149 1301
Chi na
487
929
827
460
942
460
648
733
811
1077
790
721
841
1161 1324 1179
707
980
Indi a
639
999
997
550
1118
601
775
894
976
1373
981
920
949
1303 1179 1645
917
1059 1193 1553
Mexi co
559
817
809
463
871
508
612
756
821
1118
788
718
838
955
707
917
975
804
887
931
South Afri ca
544
925
802
488
883
518
658
806
851
1135
823
760
881
1040
980
1059
804
1024
980
1232
Korea
628
1024
881
545
1029
617
706
887
1001 1353
936
838
991
1149 1021 1193
887
980
1455 1467
Turkey
698
1144
999
659
1226
646
887
1006 1108 1628 1098
968
1141 1301 1300 1553
931
1232 1467 2282
U.S.
U.S.
61
K.V. Sigeris
646
1098
1021 1300
International Diversification and the Currency Hedging Decision
Correlation & Covariance Matrix- Unitary Unhedged Dollar MSCI Index Excess Return, 2007-2010
Table 23: Correlation Matrix - Unitary Hedged Dollar MSCI Index Excess Return, 2007-2010 Portfolio
U.S.
Australia
Canada
Japan
Singapore
Switzerland
U.K.
France
Germany
Greece
Netherlands
Portugal
Spain
Brazil
China
India
Mexico
South Africa
Korea
Turkey
U.S.
1.00
0.88
0.84
0.77
0.82
0.84
0.89
0.90
0.89
0.79
0.84
0.69
0.83
0.77
0.67
0.77
0.84
0.76
0.73
0.67
Aus tra l i a
0.88
1.00
0.78
0.73
0.73
0.85
0.89
0.89
0.86
0.74
0.84
0.72
0.80
0.74
0.70
0.71
0.68
0.72
0.73
0.65
Ca na da
0.84
0.78
1.00
0.73
0.85
0.69
0.81
0.76
0.74
0.66
0.73
0.62
0.67
0.81
0.70
0.75
0.77
0.76
0.69
0.53
Ja pa n
0.77
0.73
0.73
1.00
0.78
0.68
0.75
0.77
0.75
0.68
0.74
0.66
0.70
0.70
0.71
0.69
0.64
0.70
0.68
0.75
Si nga pore
0.82
0.73
0.85
0.78
1.00
0.72
0.76
0.80
0.79
0.74
0.83
0.72
0.79
0.80
0.81
0.83
0.79
0.75
0.80
0.75
Swi tzerl a nd
0.84
0.85
0.69
0.68
0.72
1.00
0.83
0.89
0.86
0.73
0.84
0.70
0.75
0.58
0.59
0.70
0.64
0.70
0.64
0.72
UK
0.89
0.89
0.81
0.75
0.76
0.83
1.00
0.93
0.88
0.73
0.87
0.72
0.81
0.74
0.70
0.74
0.76
0.78
0.67
0.67
Fra nce
0.90
0.89
0.76
0.77
0.80
0.89
0.93
1.00
0.96
0.80
0.92
0.80
0.87
0.74
0.65
0.77
0.76
0.73
0.76
0.77
Germa ny
0.89
0.86
0.74
0.75
0.79
0.86
0.88
0.96
1.00
0.74
0.88
0.74
0.84
0.70
0.69
0.77
0.77
0.67
0.77
0.77
Greece
0.79
0.74
0.66
0.68
0.74
0.73
0.73
0.80
0.74
1.00
0.76
0.77
0.83
0.74
0.59
0.70
0.65
0.65
0.72
0.71
Netherl a nds
0.84
0.84
0.73
0.74
0.83
0.84
0.87
0.92
0.88
0.76
1.00
0.76
0.79
0.72
0.65
0.76
0.72
0.72
0.75
0.76
Portuga l
0.69
0.72
0.62
0.66
0.72
0.70
0.72
0.80
0.74
0.77
0.76
1.00
0.81
0.73
0.61
0.77
0.69
0.64
0.75
0.71
Spa i n
0.83
0.80
0.67
0.70
0.79
0.75
0.81
0.87
0.84
0.83
0.79
0.81
1.00
0.71
0.68
0.73
0.78
0.67
0.77
0.77
Bra zi l
0.77
0.74
0.81
0.70
0.80
0.58
0.74
0.74
0.70
0.74
0.72
0.73
0.71
1.00
0.76
0.78
0.71
0.73
0.76
0.57
Chi na
0.67
0.70
0.70
0.71
0.81
0.59
0.70
0.65
0.69
0.59
0.65
0.61
0.68
0.76
1.00
0.80
0.56
0.72
0.71
0.71
Indi a
0.77
0.71
0.75
0.69
0.83
0.70
0.74
0.77
0.77
0.70
0.76
0.77
0.73
0.78
0.80
1.00
0.66
0.66
0.72
0.77
Mexi co
0.84
0.68
0.77
0.64
0.79
0.64
0.76
0.76
0.77
0.65
0.72
0.69
0.78
0.71
0.56
0.66
1.00
0.71
0.67
0.51
South Afri ca
0.76
0.72
0.76
0.70
0.75
0.70
0.78
0.73
0.67
0.65
0.72
0.64
0.67
0.73
0.72
0.66
0.71
1.00
0.65
0.59
Korea
0.73
0.73
0.69
0.68
0.80
0.64
0.67
0.76
0.77
0.72
0.75
0.75
0.77
0.76
0.71
0.72
0.67
0.65
1.00
0.76
Turkey
0.67
0.65
0.53
0.75
0.75
0.72
0.67
0.77
0.77
0.71
0.76
0.71
0.77
0.57
0.71
0.77
0.51
0.59
0.76
1.00
Table 24: Covariance Matrix - Unitary Hedged Dollar MSCI Index Excess Return, 2007-2010 Portfolio
U.S.
Australia
Canada
Japan
Singapore
Switzerland
U.K.
France
Germany
Greece
Netherlands
Portugal
Spain
Brazil
China
India
Mexico
South Africa
Korea
Turkey
U.S.
405
315
328
352
464
273
330
378
413
621
396
305
406
429
497
536
381
278
373
483
Aus tra l i a
315
315
267
293
364
243
290
330
353
511
350
278
343
362
456
435
275
234
328
416
Ca na da
328
267
373
320
460
215
287
305
327
495
334
263
313
434
500
498
336
269
337
367
Ja pa n
352
293
320
514
498
250
315
363
392
602
395
327
387
439
593
542
328
289
390
607
Si nga pore
464
364
460
498
794
327
396
469
513
808
548
442
536
628
838
811
502
388
576
762
Swi tzerl a nd
273
243
215
250
327
262
247
302
319
463
322
248
294
258
355
391
234
208
264
421
UK
330
290
287
315
396
247
339
356
373
524
378
291
361
380
475
469
317
264
315
442
Fra nce
378
330
305
363
469
302
356
434
458
646
454
366
438
426
502
557
359
278
405
575
Germa ny
413
353
327
392
513
319
373
458
529
660
476
373
469
448
584
616
400
284
450
639
Greece
621
511
495
602
808
463
524
646
660
1518
697
659
778
796
848
944
572
465
715
996
Netherl a nds
396
350
334
395
548
322
378
454
476
697
556
394
450
469
562
620
383
309
452
644
Portuga l
305
278
263
327
442
248
291
366
373
659
394
479
431
440
491
581
341
255
418
558
Spa i n
406
343
313
387
536
294
361
438
469
778
450
431
586
479
607
610
428
298
475
670
Bra zi l
429
362
434
439
628
258
380
426
448
796
469
440
479
767
775
746
447
372
535
565
Chi na
497
456
500
593
838
355
475
502
584
848
562
491
607
775
1365 1019
470
489
665
940
Indi a
536
435
498
542
811
391
469
557
616
944
620
581
610
746
1019 1196
513
419
633
955
Mexi co
381
275
336
328
502
234
317
359
400
572
383
341
428
447
470
513
511
293
384
410
South Afri ca
278
234
269
289
388
208
264
278
284
465
309
255
298
372
489
419
293
336
304
389
Korea
373
328
337
390
576
264
315
405
450
715
452
418
475
535
665
633
384
304
646
691
Turkey
483
416
367
607
762
421
442
575
639
996
644
558
670
565
940
955
410
389
691
1286
62
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Correlation & Covariance Matrix- Black’s Hedge Ratio Dollar MSCI Index Excess Return, 2007-2010
Table 25: Correlation Matrix - Black's Universal Hedged Dollar MSCI Index Excess Return, 2007-2010 Portfolio
U.S.
Australia
Canada
Japan
Singapore
Switzerland
U.K.
France
Germany
Greece
Netherlands
Portugal
Spain
Brazil
China
India
Mexico
South Africa
Korea
Turkey
U.S.
1.00
0.89
0.85
0.78
0.82
0.86
0.90
0.91
0.90
0.80
0.85
0.71
0.84
0.77
0.67
0.77
0.85
0.78
0.75
0.68
Aus tra l i a
0.89
1.00
0.80
0.76
0.76
0.85
0.90
0.90
0.87
0.75
0.84
0.73
0.81
0.77
0.72
0.73
0.71
0.77
0.75
0.67
Ca na da
0.85
0.80
1.00
0.75
0.86
0.71
0.83
0.78
0.75
0.68
0.75
0.65
0.68
0.84
0.71
0.76
0.79
0.79
0.71
0.56
Ja pa n
0.78
0.76
0.75
1.00
0.79
0.70
0.78
0.78
0.76
0.69
0.76
0.68
0.72
0.71
0.71
0.70
0.67
0.74
0.69
0.76
Si nga pore
0.82
0.76
0.86
0.79
1.00
0.74
0.79
0.81
0.81
0.74
0.84
0.73
0.79
0.82
0.81
0.84
0.80
0.78
0.81
0.76
Swi tzerl a nd
0.86
0.85
0.71
0.70
0.74
1.00
0.85
0.90
0.87
0.74
0.85
0.71
0.76
0.60
0.61
0.72
0.68
0.74
0.67
0.73
UK
0.90
0.90
0.83
0.78
0.79
0.85
1.00
0.94
0.89
0.75
0.89
0.75
0.83
0.77
0.71
0.75
0.78
0.82
0.70
0.69
Fra nce
0.91
0.90
0.78
0.78
0.81
0.90
0.94
1.00
0.96
0.81
0.93
0.81
0.88
0.75
0.67
0.78
0.78
0.77
0.78
0.77
Germa ny
0.90
0.87
0.75
0.76
0.81
0.87
0.89
0.96
1.00
0.75
0.88
0.75
0.85
0.72
0.70
0.78
0.79
0.72
0.79
0.78
Greece
0.80
0.75
0.68
0.69
0.74
0.74
0.75
0.81
0.75
1.00
0.77
0.78
0.83
0.75
0.60
0.71
0.67
0.68
0.73
0.72
Netherl a nds
0.85
0.84
0.75
0.76
0.84
0.85
0.89
0.93
0.88
0.77
1.00
0.77
0.80
0.74
0.66
0.77
0.74
0.75
0.77
0.77
Portuga l
0.71
0.73
0.65
0.68
0.73
0.71
0.75
0.81
0.75
0.78
0.77
1.00
0.82
0.74
0.62
0.78
0.71
0.68
0.76
0.72
Spa i n
0.84
0.81
0.68
0.72
0.79
0.76
0.83
0.88
0.85
0.83
0.80
0.82
1.00
0.72
0.69
0.73
0.79
0.71
0.78
0.77
Bra zi l
0.77
0.77
0.84
0.71
0.82
0.60
0.77
0.75
0.72
0.75
0.74
0.74
0.72
1.00
0.77
0.79
0.72
0.76
0.77
0.59
Chi na
0.67
0.72
0.71
0.71
0.81
0.61
0.71
0.67
0.70
0.60
0.66
0.62
0.69
0.77
1.00
0.80
0.57
0.75
0.72
0.72
Indi a
0.77
0.73
0.76
0.70
0.84
0.72
0.75
0.78
0.78
0.71
0.77
0.78
0.73
0.79
0.80
1.00
0.67
0.70
0.73
0.78
Mexi co
0.85
0.71
0.79
0.67
0.80
0.68
0.78
0.78
0.79
0.67
0.74
0.71
0.79
0.72
0.57
0.67
1.00
0.73
0.69
0.52
South Afri ca
0.78
0.77
0.79
0.74
0.78
0.74
0.82
0.77
0.72
0.68
0.75
0.68
0.71
0.76
0.75
0.70
0.73
1.00
0.69
0.63
Korea
0.75
0.75
0.71
0.69
0.81
0.67
0.70
0.78
0.79
0.73
0.77
0.76
0.78
0.77
0.72
0.73
0.69
0.69
1.00
0.77
Turkey
0.68
0.67
0.56
0.76
0.76
0.73
0.69
0.77
0.78
0.72
0.77
0.72
0.77
0.59
0.72
0.78
0.52
0.63
0.77
1.00
Table 26: Covariance Matrix - Black's Universal Hedged Dollar MSCI Index Excess Return, 2007-2010 Portfolio
U.S.
Australia
Canada
Japan
Singapore
Switzerland
U.K.
France
Germany
Greece
Netherlands
Portugal
Spain
Brazil
China
India
Mexico
South Africa
Korea
Turkey
U.S.
405
339
346
348
471
279
339
391
426
634
409
318
419
447
496
545
398
303
397
503
Aus tra l i a
339
353
305
314
405
260
317
360
385
561
380
306
379
414
500
480
312
278
373
466
Ca na da
346
305
409
334
495
232
313
335
359
540
365
291
344
487
531
539
372
307
378
414
Ja pa n
348
314
334
488
497
251
321
368
397
605
400
333
394
451
580
543
344
314
404
618
Si nga pore
471
405
495
497
813
340
420
494
540
838
572
465
563
668
848
836
533
429
611
801
Swi tzerl a nd
279
260
232
251
340
263
258
311
331
476
329
256
308
278
365
407
256
230
285
438
UK
339
317
313
321
420
258
349
374
390
556
397
311
383
412
492
494
338
293
346
476
Fra nce
391
360
335
368
494
311
374
454
479
678
473
385
464
461
524
583
389
316
437
606
Germa ny
426
385
359
397
540
331
390
479
553
695
497
394
497
485
605
644
432
326
488
673
Greece
634
561
540
605
838
476
556
678
695
1563
728
690
816
846
869
979
616
516
762
1046
Netherl a nds
409
380
365
400
572
329
397
473
497
728
573
411
475
507
583
648
413
346
484
678
Portuga l
318
306
291
333
465
256
311
385
394
690
411
496
455
472
512
607
368
291
444
588
Spa i n
419
379
344
394
563
308
383
464
497
816
475
455
618
516
629
637
459
341
511
705
Bra zi l
447
414
487
451
668
278
412
461
485
846
507
472
516
824
812
792
484
421
579
620
Chi na
496
500
531
580
848
365
492
524
605
869
583
512
629
812
1361 1034
493
536
698
974
Indi a
545
480
539
543
836
407
494
583
644
979
648
607
637
792
1034 1231
545
473
676
1005
Mexi co
398
312
372
344
533
256
338
389
432
616
413
368
459
484
493
545
543
330
421
448
South Afri ca
303
278
307
314
429
230
293
316
326
516
346
291
341
421
536
473
330
372
350
451
Korea
397
373
378
404
611
285
346
437
488
762
484
444
511
579
698
676
421
350
693
750
Turkey
503
466
414
618
801
438
476
606
673
1046
678
588
705
620
974
1005
448
451
750
1359
63
K.V. Sigeris
International Diversification and the Currency Hedging Decision
Appendix E: Risk Free Rates and DataStream Codes
Risk Free Rates
Table 27: Proxy of Risk Fee Rate
Country
Risk free rate used for every country
Brazil
BRAZIL CDB (UP TO 30 DAYS) - MIDDLE RATE
Canada
CANADA TREASURY BILL 1 MTH. (BOC) - MIDDLE RATE
France
FRANCE TREASURY BILL 1 MONTH - BID RATE
Germany
MNY MKT - 1-MONTH FRANKFURT BANKS - MIDDLE RATE
Japan
JAPAN GENSAKI T BILL 1 MONTH - MIDDLE RATE
Korea
SEOUL INTERBANK 1 MONTH - OFFERED RATE
Netherlands
NTHRLAND EU-GLDR 1M (FT/ICAP/TR) - MIDDLE RATE
Switzerland
SWTZRLAND EU-FRC-1M (FT/ICAP/TR) - MIDDLE RATE
UK
UK TREASURY BILL TENDER 1M - MIDDLE RATE
United States
US TREASURY BILL 2ND MKT 4-WK - MIDDLE RATE
Australia
AUSTRALIA DEALER BILL 30 DAY - MIDDLE RATE
Mexico
MEXICO CETES 2ND MKT. 28 DAY - MIDDLE RATE
Portugal
PORTUGAL LISBOR 1 MONTH - OFFERED RATE
South Africa
SOUTH AFRICAN JIBAR 1 MONTH - MIDDLE RATE
Turkey
TURKISH INTERBANK 1 MONTH - OFFERED RATE
Spain
SPAIN TREASURY BILL 1-3 MONTH - RED. YIELD
China
CENTRAL BANK BILL 3 MONTHS - MIDDLE RATE
Greece
GREECE TREASURY BILL 3 MONTH - MIDDLE RATE
India
INDIA T-BILL PRIMARY 91 DAY - RED. YIELD
Singapore
SINGAPORE T-BILL 3 MONTH - MIDDLE RATE
64
K.V. Sigeris
DataCode
BRCDBIR
CNTBB1M
FRTBL1M
BDMNY1M
JPTBG1M
KRIBK1M
ECNLG1M
ECSWF1M
UKTBT1M
FRTBS4W
ADBR030
MXCSM28
LISBO1M
SAJIB1M
TKIBK1M
ESTBL3M
CHBNK3M
GDTBL3M
INPTB91
SNGTB3M