Currency risk hedging
A comparison between developed countries and emerging markets
Sharon Vijn
Bachelor thesis in Economics and Finance University of Amsterdam
Faculty of Economics and Business Amsterdam School of Economics Author: S. Vijn
Student number: 10640657 Date: June 29, 2016
Abstract
Over the past couple of years it has been demonstrated that portfolios containing both stocks of developed countries and stocks of emerging markets improves the risk-return performance especially when the correlations between developed and emerging markets are small or negative. Investing in foreign securities comes with exchange rate risk which can be hedged away to reduce overall risk. This might not be the best strategy when investing in emerging markets because the covariance between the local stock market and the exchange rate return are likely to be negative. This research has been done by forming portfolios of stocks from the six largest developed countries and the six largest emerging markets over the period 2005 to 2015. This study also includes two perspectives, one investor based in a developed country and one in an emerging market. Currency risk hedging improves the risk-return of all constructed portfolios but especially the investors base currency is what matters.
Keywords: Currency risk hedging, emerging markets, forwards, international diversification
Statement of Originality
This document is written by Sharon Vijn who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Table of contents
1. Introduction………..………..……….………5
2. Literature review………..………....……….…….….…6
3. Theoretical framework……….…10
3.1 International diversification...11
3.2 Currency risk hedging with forwards...12
3.3 Fully hedging...13
3.4 Optimal hedge ratio...14
4. Methodology……….15
4.1 Data………..15
4.2 Single-country portfolios………...………..16
4.3 Multi-country portfolios...16
5. Results………..18
5.1 Single-country portfolios – unhedged vs. fully hedged……….18
5.2 Multi-country portfolios – unhedged vs. fully hedged………..21
5.3 Optimal hedge ratios – single-country portfolios……….……….26
5.4 Optimal hedge ratios – multi-country portfolios………..………….28
6. Conclusion………...……….30
Index of tables and figures
TablesTable 01 – Covariance between local stock market returns……….….10
Table 02 – Covariances between exchange rate returns………..…...…11
Table 03 – Covariances between local stock market returns and exchange rate returns...…12
Table 04 – Returns and standard deviations single-country portfolios US perspective...19
Table 05 – Returns and standard deviations single-country portfolios Brazil perspective…....20
Table 06 – EQW portfolios – unhedged vs. fully hedged returns…………....…...…21
Table 07 – EQW portfolios – unhedged vs. fully hedged standard deviations…...….…22
Table 08 – Minimum variance hedge ratios – single-country portfolios………...…28
Table 09 – Minimum variance hedge ratios – multi-country portfolios……...…29
Table 10 – Constrained minimum variance hedge ratios ………...30
Table 11 Optimally hedged returns, standard deviations and Sharpe ratios…...……..30
Figures Figure 01 – Minimum variance frontier, developed countries, US perspective………...23
Figure 02 – Minimum variance frontier, emerging markets, US perspective……...23
Figure 03 – Minimum variance frontier, mixed portfolio, US perspective……...24
Figure 04 – Minimum variance frontier, developed countries, Brazilian perspective…...…24
Figure 05 – Minimum variance frontier, emerging markets, Brazilian perspective…...25
Figure 06 – Minimum variance frontier, mixed portfolio, Brazilian perspective……...25
List of abbreviations
USD US Dollar JPY Japanese Yen
EUR Euro
GBP British Pound CAD Canadian Dollar AUD Australian Dollar BRL Brazilian Real RUB Russian Ruble INR Indian Rupee
CNY Chinese Yuan Renminbi MXN Mexican Peso
ZAR South-African Rand
EME Emerging market economy US United States of America SA South-Africa
1. Introduction
Nowadays almost all financial markets are integrated and foreign investors have access to them all over the world. This is advantageous since investors are able to hold globally diversified portfolios which are known to reduce portfolio volatility. However since 1973 countries started to implement flexible exchange rate regimes and due to this, exchange rate risk has risen considerably. The increase in the volume of world trade contributed to this as well. Therefore the question arose whether to hedge this risk or not.
A lot of empirical evidence exists on the benefits of international diversification and currency risk hedging. Multiple studies say currency hedging is a free lunch, but since 2005 more studies researched the downside of currency risk hedging and stated that investors should stay unhedged. Other options would be half-hedging or optimally hedging. This is another point of discussion, should investors hedge all currency exposure or should they hedge only a part of it, and what part?
As there exists a lot of evidence on international diversification and currency risk hedging, less evidence exists on currency risk hedging and emerging markets. The largest part of the studies construct portfolios with stocks in developed countries from a US perspective. This study therefore will focus on different portfolios with stocks in both developed markets and emerging markets. Also different hedging strategies will be taken into consideration.
The rest of the paper is organized as follows: The following section reviews previous research on international diversification, emerging markets, different hedging strategies and investing in emerging markets. Section 3 provides information on hedging strategies, forward contracts. Section 4 describes the methodology, model specification and data used. The results and discussions are shown in section 5. Section 6 concludes and recommendations are given for further research on this topic.
2. Literature review
The advantages of international portfolio diversification have been examined by a large amount of empirical studies. Grubel (1968) was the first who extended existing literature to an international environment. He concluded that international portfolio diversification created complete new kinds of world welfare gains from the growing international economic relations. Levy and Sarnat (1970) presented estimates of potential gains from diversification. The inclusion of more countries in one portfolio improves the risk-return position especially when investing in countries whose economies are not highly correlated with that of the domestic country. Solnik (1974) showed that a portfolio consisting of foreign securities as well as domestic securities can reduce risk by a substantial amount due to low correlations between stock prices in different countries. Longin and Solnik (1995) however found more recently that these correlations are unstable over time but there is a pattern that during periods of high volatility the correlations are higher, for instance during the oil crises.
It is clear that international diversification is advantageous especially for investors who would like to lower their risks. However when investing abroad investors are exposed to an additional risk factor i.e. foreign currency risk, which can be described as the possibility of changing exchange rates. This risk can be hedged away, or an investor may choose to not protect himself against exchange rate fluctuations and speculate on currencies which can be quite profitable (Solnik, 1974). The question that arises is whether hedging the currency risk is necessary and to what extent.
Proponents of (fully) hedging the exchange rate risk like Eun and Resnick (1988) argue that investing in foreign securities is likely more risky due to fluctuating exchange rates, not only through its own variance but also through its covariances with the local stock market returns. The exchange rate changes against the US dollar are found to be highly correlated across currencies which means that currency risk is for a large part non-diversifiable. The outcome is therefore not surprising. The ex-ante investment strategies based on the minimum variance portfolio, equally weighted portfolio, tangency portfolio and Bayes-Stein investment strategies that incorporate hedging via the forward markets consistently outperform the corresponding unhedged ex ante investment strategies.
A lot more research has been done about hedging versus not hedging. When reviewing past studies, the conclusion is that results are conflicting. Campbell, Serfaty De Medeiros and Viceira (2010) investigated what role foreign currency should play in a diversified investment portfolio. They looked at seven major developed-market currencies such as the dollar, euro,
Japanese Yen, Swiss Franc, Pound Sterling, Canadian Dollar and Australian Dollar and found that optimal currency hedging substantially reduces risk for equity investors. They also show that risk-minimizing investors should short currencies that are more positively correlated with equity returns, like the Australian and Canadian Dollar and that they should seek exposure to currencies that are negatively correlated with equity returns like the US Dollar, the Euro and the Swiss Franc. The general conclusion of their study is that foreign currency plays a large role in a diversified investment portfolio.
Glen and Jorion (1993) came up with the same conclusion that optimal currency hedging substantially reduces risk for equity investors. They looked at stocks and long-term bonds as risky assets, just like Campbell et all (2010). Hedges are implemented using one-month forward contracts and they focus on the improvement in the Sharpe ratio that occurs when adding currency hedges to a portfolio of stocks and/or bonds. Another approach is to compare the return, volatility and Sharpe ratio of the portfolio with and without forward contracts. The conclusion is that hedging substantially reduces risk but it’s only beneficial when this risk reduction is not accompanied by an offsetting decrease in returns, in other words this means that currency risk is not a “free lunch”, which means that currency risk hedging reduces risk without any influence on the returns.
De Roon, Eiling and Gerard (2010) are in accordance with that. Although currency risk hedging is aimed at minimizing the variance of a portfolio, returns can be touched seriously as well. For instance, the monthly standard deviation for a US stock investor reduced with 17%. On the other hand the mean of the unhedged equity returns were 0.52% while the mean of hedged returns was only 0.31%. That is a reduction of 41%. In addition, the Sharpe ratios of unhedged portfolios are significantly above zero, the Sharpe ratios of hedged portfolios are never significantly different from zero. So actually being exposed to currency risk actually improves portfolio performance in terms of average returns and Sharpe ratios in their study. So we see that older studies were very positive about currency hedging but more recently the downside of currency hedging became known as well.
McCarthy (2003) considered both risk-return tradeoff and the minimum-variance model of Ederington (1979) to see whether hedging is effective. This model compares the variances of the hedged returns with the variances of the unhedged returns. Less volatility i.e. variance is preferred to more volatility. When looking at the risk-return tradeoff, the Sharpe ratio will be used just like Glen and Jorion (1993) did and their outcome is consistent with earlier studies. His general conclusion is that always hedging is preferable to remaining unhedged for an
discovered the same for the Australian Dollar since it is positively correlated with equity return. There is a difference though, Campbell et all. (2010) say the same about the Japanese yen: it has a positive correlation with equity return which means hedging would be better than no hedging. McCarthy (2003) however suggests that remaining unhedged is superior to always hedging for the JPY. This might be due to different timeframes. He ends his study with the conclusion that the method of comparing the outcomes did not significantly have an impact on his findings.
Schmittmann (2010) stated that for bond portfolios full hedging is the optimal strategy in almost all cases, this is confirmed by a significant amount of previous studies. The reason for this is that bond return volatility is dominated by exchange rate volatility. Equities total risk depends much more on correlations of equities and currencies.
All studies mentioned above used developed countries to study the benefits of hedging, but currently it is very attractive to invest in emerging equity markets due to larger diversification benefits. Christoffersen, Errunza, Jabocs and Langlois (2012) investigated why this is the case. They say that diversification benefits in developed markets are getting less due to higher correlations between countries in this globalized world but the benefits for emerging markets remain strong. This is due to the fact that crises in emerging markets are usually country-specific.
As mentioned earlier, currency risk hedging reduces risk when you want to invest in developed countries. The result for emerging countries is quite the opposite according to Hauser, Marcus and Yaari (1994). Hedging currency risk of (high-risk) emerging markets can decrease gains from international diversification. The benefit from hedging depends upon the contribution of currency risk to the overall volatility. The overall risk in portfolios of developed stock markets is for a large part due to currency risk. Therefore hedging currency risk can be very advantageous. However there is a negative covariance between changes in stock and currency prices in emerging markets. Hauser et. all (1994) did a survey and constructed six efficient frontiers: an unhedged and hedged frontier of developed markets, an unhedged and hedged frontier of emerging markets and an unhedged and hedged frontier combining developed and emerging markets. The results are not surprising. When investing in developed markets it is beneficial to hedge currency risk. However when investing in emerging markets it is better to not hedge at all due to the negative correlations between exchange rates and stock returns when measured in the local currencies of emerging markets. This study however lacks statistical proof of their findings.
Bugar and Maurer (2001) looked at the perspectives of an investor based in a developed country (Germany) and one investor in an emerging market (Hungary) to see whether it makes a difference. The results showed that for a German investor fully currency risk hedging reduced the volatility of returns in all stock markets. This was not the case for the Hungarian investor. Overall they concluded that it is beneficial to join the international flow of capital for both investors, perhaps even more to the Hungarian investor, and that the hedged portfolios performed better than the unhedged portfolios.
Again this study focused on investing in developed countries, interesting to know is whether currency risk hedging improves multi-currency portfolio performance, i.e. is currency risk hedging beneficial when investing in stocks from emerging markets?
3. Theoretical framework
3.1 International diversificationThe fact that international diversification is beneficial is well known. The diversification benefits result from low covariances between equity returns and exchange rate returns. EMEs and developed countries tend to move in the opposite direction and this, together with high expected returns, makes the investing in EMEs very popular. Table 1 presents the covariance between local stock returns of the twelve countries considered in this paper divided in developed countries and EMEs. Especially the Russian stock market has low a low covariance with all the other stock markets but there are no other remarkable numbers. Yet, the average covariance between developed stock price returns is approximately 0.32, yet that same covariance between emerging stock price returns is approximately 0.24. The average correlation between all countries is even lower, namely 0.21. This suggests that investing in emerging markets might create diversification benefits.
Covariance between local stock market returns
US JAP GER UK CAN AUS BRA RUS IND CHN MEX SA US Japan Germany UK Canada Australia Brazil Russia India China Mexico SA1 0.25 0.20 0.24 0.19 0.19 0.17 0.23 0.06 0.24 0.15 0.20 0.16 0.37 0.24 0.17 0.17 0.17 0.21 0.13 0.24 0.19 0.19 0.14 0.34 0.21 0.19 0.18 0.24 0.09 0.28 0.18 0.21 0.16 0.18 0.16 0.16 0.20 0.07 0.20 0.13 0.16 0.15 0.21 0.15 0.24 0.09 0.21 0.15 0.18 0.16 0.20 0.20 0.09 0.20 0.15 0.15 0.14 0.45 0.11 0.31 0.29 0.25 0.22 0.65 0.12 0.14 0.09 0.09 0.52 0.22 0.23 0.18 0.90 0.13 0.15 0.29 0.17 0.21 Table 1: Covariance between local stock market returns calculated using monthly data from 2005-2015. Covariances are given in percentages. 1 SA stands for South-Africa.
Table 2 shows the covariance between exchange rate returns against the US Dollar and the Brazilian Real. The covariances between exchange rate returns against the US Dollar are a lot lower than those against the BRL. Also, the variances of the currencies against the BRL are somewhat higher than those against the US dollar.
Table 3 shows the covariance between the local stock market return and the exchange rate return against either the US Dollar or the Brazilian Real. The covariances against the BRL are almost all negative except for the ZAR. This means for an investor based in Brazil, it could be beneficial to hold some exposure to some of the currencies mentioned. Also, the covariances
between developed stocks/currencies and emerging stocks/currencies are lower than between developed and developed. This confirms the theory that holding stocks from emerging markets has diversification benefits.
Taking a look at the covariance between local returns and exchange rate returns against the USD, it is striking that the Japanese yen has a negative relationship with all foreign stocks and the Renminbi has also very low covariances with foreign stocks. This is probably due to the peg between the US dollar and the Yuan Renminbi. Another observation is that these covariances are low in general. The average covariance is 0.15 which is a lot lower than the average correlation between local stock returns and the exchange rate returns. Where Russian, Australian, Indian and Chinese stocks have the lowest covariances with currencies, Brazilian stocks have the highest covariances.
Covariance between exchange rate returns against the US Dollar
USD JPY EUR GBP CAD AUD BRL RUB INR CNY MXN ZAR USD JPY EUR GBP CAD AUD BRL RUB INR CNY MXN ZAR 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.07 0.01 0.00 0.00 0.00 -0.01 0.00 0.00 0.00 -0.02 -0.01 0.09 0.06 0.05 0.09 0.06 0.07 0.04 0.00 0.05 0.08 0.08 0.05 0.07 0.06 0.06 0.03 0.00 0.05 0.07 0.08 0.08 0.08 0.07 0.04 0.00 0.06 0.07 0.16 0.13 0.11 0.06 0.01 0.09 0.13 0.20 0.09 0.07 0.00 0.10 0.12 0.21 0.04 0.01 0.09 0.08 0.07 0.00 0.05 0.07 0.00 0.00 0.00 0.10 0.10 0.22 Covariance between exchange rate returns against the Brazilian Real
USD JPY EUR GBP CAD AUD BRL RUB INR CNY MXN ZAR USD JPY EUR GBP CAD AUD BRL RUB INR CNY MXN ZAR 0.20 0.21 0.14 0.15 0.13 0.07 0.00 0.11 0.13 0.20 0.11 0.08 0.30 0.16 0.16 0.13 0.09 0.00 0.12 0.14 0.21 0.10 0.08 0.17 0.14 0.11 0.10 0.00 0.12 0.11 0.14 0.09 0.10 0.17 0.12 0.09 0.00 0.12 0.11 0.14 0.10 0.09 0.13 0.08 0.00 0.10 0.09 0.12 0.09 0.08 0.10 0.00 0.09 0.06 0.07 0.07 0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.23 0.09 0.12 0.10 0.07 0.13 0.13 0.09 0.08 0.20 0.11 0.08 0.11 0.08 0.18 Table 2: Covariance between exchange rate returns against the US Dollar and Brazilian Real respectively. Calculated using monthly data from 2005-2015. Covariances are given in percentages.
Covariance between local stock market returns and exchange rate returns against the USD
USD JPY EUR GBP CAD AUD BRL RUB INR CNY MXN ZAR US Japan Germany UK Canada Australia Brazil Russia India China Mexico SA 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03 -0.09 -0.04 -0.03 -0.02 -0.03 -0.03 -0.02 -0.04 -0.05 -0.02 -0.01 0.08 0.06 0.05 0.05 0.06 0.04 0.10 0.01 0.07 0.06 0.07 0.06 0.07 0.06 0.05 0.03 0.06 0.04 0.09 0.02 0.07 0.09 0.06 0.05 0.09 0.08 0.08 0.07 0.08 0.06 0.14 0.01 0.11 0.11 0.09 0.07 0.12 0.10 0.10 0.10 0.12 0.09 0.18 0.04 0.14 0.12 0.12 0.10 0.12 0.11 0.12 0.10 0.13 0.09 0.19 0.05 0.17 0.11 0.12 0.10 0.09 0.08 0.08 0.07 0.08 0.07 0.14 0.01 0.09 0.07 0.10 0.08 0.07 0.06 0.08 0.06 0.06 0.05 0.09 0.02 0.12 0.06 0.06 0.05 0.01 0.00 0.00 0.00 0.01 0.00 0.01 0.00 0.00 0.01 0.01 0.00 0.12 0.11 0.11 0.09 0.10 0.08 0.13 0.03 0.12 0.07 0.10 0.07 0.14 0.16 0.15 0.12 0.13 0.11 0.20 0.06 0.21 0.14 0.13 0.08 Covariance between local stock market returns and exchange rate returns against the BRL
USD JPY EUR GBP CAD AUD BRL RUB INR CNY MXN ZAR US JAP GER UK CAN AUS BRA RUS IND CHI MEX SA -0.12 -0.11 -0.12 -0.10 -0.13 -0.09 -0.19 -0.05 -0.17 -0.11 -0.12 -0.10 -0.15 -0.20 -0.16 -0.13 -0.16 -0.12 -0.22 -0.08 -0.21 -0.16 -0.13 -0.12 -0.04 -0.05 -0.07 -0.05 -0.07 -0.05 -0.09 -0.04 -0.10 -0.04 -0.04 -0.04 -0.06 -0.05 -0.07 -0.07 -0.07 -0.06 -0.10 -0.03 -0.11 -0.02 -0.06 -0.06 -0.04 -0.03 -0.03 -0.04 -0.06 -0.03 -0.06 -0.06 -0.06 0.01 -0.03 -0.04 0.00 -0.01 -0.02 -0.01 -0.02 -0.01 -0.01 -0.01 -0.03 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03 -0.03 -0.03 -0.03 -0.05 -0.03 -0.05 -0.07 -0.09 -0.03 -0.02 -0.03 -0.05 -0.05 -0.04 -0.05 -0.08 -0.04 -0.10 -0.03 -0.06 -0.04 -0.05 -0.05 -0.12 -0.10 -0.11 -0.10 -0.13 -0.09 -0.18 -0.05 -0.17 -0.11 -0.11 -0.10 -0.01 0.00 0.00 -0.02 -0.04 -0.02 -0.06 -0.03 -0.05 -0.04 -0.02 -0.03 0.02 0.05 0.03 0.01 0.00 0.02 0.00 0.01 0.04 0.04 0.02 -0.02 Table 3: each entry in table 3 denotes the covariance between the row local stock market return and the column exchange rate return against the USD and BRL using data ranging from 2005 until 2015.
3.2 Currency risk hedging with forwards
There are several instruments that can be used to hedge currency risk such as futures, options, swaps and forwards. A traditional way of hedging is when an investor borrows in foreign currency and lend the proceeds in his base currency. A fully hedged investor borrows the present value of the expected foreign investment proceeds, which looks like this:
1 + 𝐸(𝑅!) 1 + 𝑖!,!!!
Where 𝑖!,!!! is the foreign interest rate. The amount borrowed will then be exchanged at the
current spot rate into the base currency to invest at the domestic interest rate 𝑖!,!!!. At the
maturity date the foreign currency loan will be repaid. However this hedging strategy is imperfect because at time t-1 the expectation of the return might me different than the actual
currency risk away. Despite the impossibility to create a perfect hedge, lower transaction costs are possible when employing currency forward contracts.
Investors can eliminate exchange rate risk by selling the expected foreign currency gains via foreign exchange derivatives. A currency forward is an agreement between two parties to either buy (long position) or sell (short position) foreign currency at a future date at exchange rate F, which is the forward price. This forward price is determined at the time of transaction. Forwards usually have short maturities, the most common used maturity is one month (Maurer & Valiani, 2007). If the investor would like to hedge his currency risk using forwards, the return will then be defined as follows:
𝑅!,!"#! = 𝑅!,!"#+ ℎ! 𝑓!− 𝑒! = 𝑅!+ 𝑒!+ 𝑅!𝑒!+ ℎ! 𝑓!− 𝑒!
where 𝑓! is the forward premium or discount which can be calculated as Fi/Si-1, where Fi and Si
are the forward and spot exchange rates denominated in the domestic currency. ℎ! represents the hedge ratio which shows how much of the initial investment needs to be sold forward.
3.3 Fully hedging
When we set ℎ! equal to one in the above equation, we have the unitary hedge ratio or sometimes referred to as the full hedge ratio. From that equation as well it follows that even when using a full hedge, not all currency risk can be hedged away since we have the cross-term. The intuition behind this is because of the fluctuations in the exchange rate, the amount to hedge is unknown. This cross-term represents actually the remaining currency exposure but is in practice very small. When comparing the unhedged return with the hedged return, it becomes clear that by hedging the investor replaces the gain or loss on the exchange rate return with the forward premium or discount.
The full hedge or unitary hedge ratio is suboptimal because it ignores correlations between exchange rates and local returns as well as the speculative motives for taking currency positions (Glen and Jorion, 1993). Adjaouté and Tuchschmid (1996) add to this that the unitary hedge ratio is only optimal when the exhange rate returns and local returns are uncorrelated and when the forward exchange premium is an unbiased predictor of the future exchange rate returns, however this is very often not the case. The uncovered interest parity (UIP) implies that the difference between the domestic and foreign interest rate estimates the future exchange rate changes. A large amount of studies found that UIP does not hold in practice due to speculation. The failure of this parity is called the forward discount bias. It does not only mean
that fully hedging is not optimal, it also tells us that in some cases the mean returns of international investments can be affected by hedging (Schmittmann, 2010).
Bugar and Maurer (2001) go against this since their study showed different. The optimally hedge did not turn out to be better than the fully hedge approach, not when looking at risk reduction and not when looking at return improvement. Their explanation is that optimal hedging needs to estimate more parameters so there is higher estimation risk. Black (1989) says that hedge ratios are the same for all kinds of different investors and that they should never fully hedge, even when the above mentioned assumptions hold.
3.4 Optimal hedge ratio
As pointed out before, fully hedging might not be the most optimal strategy. Most studies look at the optimal hedge ratio as well, which is defined as the hedge resulting in the largest risk reduction. Therefore this ratio can be called minimum variance hedge ratio as well. The approach in this study to estimate the minimum variance hedge ratio will be the same as the one De Roon et all. (2010) and Schmittmann (2010) used. The hedge ratio can be calculated as the slope coefficient in an OLS regression of the unhedged returns on the exchange rate gain or loss minus the forward premium or discount, which looks like this:
𝑥
!𝑅
!,!= 𝛼 + 𝛽
!𝑒
!− 𝑓
!+ 𝛽
!𝑒
!− 𝑓
!+ ⋯ + 𝛽
!𝑒
!− 𝑓
!+ 𝜀
!
!!!
4. Methodology
Most studies take the viewpoint of an investor based in the United States, using the US Dollar as the numeraire currency. This study will take the same viewpoint but adds another viewpoint to it, namely the viewpoint of an investor based in Brazil with the Brazilian Real as the numeraire currency. The reason for this is that an investor’s base currency surely matters for drawing conclusions about whether to hedge or not. Both US and Brazilian investor will invest in three different portfolios: a portfolio consisting of developed market securities, a portfolio consisting of emerging market securities and one consisting of both developed and emerging market securities.
The methodology of this study is based on both Schmittmann (2010) and Bugar and Maurer (2001). They both studied the effect of international portfolio diversification from the perspectives of more than one investor.
4.1 Data
The sample data consists of stock index returns of twelve countries on a daily basis from January 2000 to December 2015. The six developed countries considered are the US, Japan, Germany, UK, Canada and Australia. The six stock markets selected are the largest countries in terms of market capitalization. The six emerging countries considered are the BRIC countries (Brazil, Russia, India, China), Mexico and South Africa. Again based on market capitalization. The stock indexes are obtained from the countries largest stock market indexes: the S&P500 (US), Nikkei 225 (Japan), DAX (Germany), FTSE100 (UK), S&P/TSX (Canada) and S&P/ASX 200 (Australia). For the emerging markets the following stock market indexes are used: the Bovespa Index (Brazil), MICEX (Russia), S&P BSE SENSEX (India), SHCOMP (China), IPC (Mexico) and FTSE/JSE (South-Africa). Each of the above mentioned indices are value weighted and consist of major companies based on market capitalization. They are adjusted for capital gains as well as dividend payments.
Next to these twelve market indices, the twelve currencies used are the Japanese Yen (JPY), US Dollar (USD), Euro (EUR), Pound Sterling (GBP), Canadian Dollar (CAD), Australian Dollar (AUD), Brazilian Real (BRL), Russian Ruble (RUB), Indian Rupee (INR), Chinese Renminbi (CNY), Mexican Peso (MXN) and the South-African Rand (ZAR). These currencies are obtained from Datastream, originally generated by WM/Reuters. For currency hedging one-month forward rates against the US Dollar and the Brazilian Real are used, generated by both WM/Reuters and Barclay’s Bank International. In order to calculate the BRL forward rates against any currency, the BRL forward rate against the US Dollar is divided
by the US Dollar against the third currency in question (Bugar & Maurer, 2001). The focus will not be on bonds in this study since almost all researchers have already agreed on fully hedging them.
4.2 Single-country portfolios
In the following section the US Dollar will be used as the base currency to explain notations, models and formulas. This base currency can be replaced and the same equation will still hold. Take Sit as the current US dollar price of foreign currency i at time t and take Pit as the foreign
currency stock index value of country i. The total unhedged return at the end of an investment period will then be:
𝑅!,!"# = 𝑆!"𝑃!"
𝑆!"!!𝑃!"!!− 1 = 1 + 𝑅! 1 + 𝑒! − 1 = 𝑅!+ 𝑒! + 𝑅!𝑒!
This means that the total unhedged return of an international investment depends on the return on the stock itself (Ri), the return on the foreign exchange rate against the US Dollar (ei) and a
cross-term (Riei). Note that an exchange rate gain means a depreciation of the investor’s home
currency towards the foreign currency. Most papers omit the cross-term since it is small in magnitude so the return is approximately:
𝑅!+ 𝑒! The variance of foreign investment returns will then be:
𝑣𝑎𝑟 𝑅!.!"# ≈ 𝑣𝑎𝑟 𝑅! + 𝑣𝑎𝑟 𝑒! + 2𝑐𝑜𝑣(𝑅!𝑒!)
McCarthy (2003) measured the performance of the unhedged alternative by the mean and variance of the monthly returns of the spot rate. This paper will use the same approach.
4.3 Multi-country portfolios
The above equations represent only one stock at a time, in order to look at the return when investing in multiple assets we can adjust the above equations to this:
𝑅! = 𝑥!𝑅!,!"# ! !!! 𝑅!! = 𝑥! ! !!! 𝑅! + ℎ!𝑥!(𝑓!−𝑒!) ! !!!
where 𝑅! is the return on a unhedged portfolio, 𝑅!! is the return on a hedged portfolio and 𝑥! is
the fraction of the total investment invested in asset i. It is important to mention that the investors used in this paper are risk averse, use the standard deviation or variance as a measure
of risk and a higher expected return and a lower variance of return are always preferred. The expected return of a hedged portfolio can be calculated with the following equation:
𝐸 𝑅!! = 𝑥!𝐸 𝑅! + ! !!! 𝑥! 1 − ℎ! 𝐸(𝑒!) ! !!! + ℎ!𝑥!𝑓!+ 𝐸(𝑅!𝑒!) ! !!!
The belonging variance of the portfolio return is then: 𝑉𝑎𝑟 𝑅!! = 𝑥!𝑥! 𝐶𝑜𝑣 𝑅!, 𝑅! ! !!! ! !!! + 2 𝑥!𝑥! 1 − ℎ! 𝑐𝑜𝑣 𝑅!, 𝑒! ! !!! ! !!! + 𝑥!𝑥! ! !!! 1 − ℎ! 1 − ℎ! 𝑐𝑜𝑣 𝑒!, 𝑒! + ∆𝑉𝑎𝑟 ! !!!
where ∆𝑉𝑎𝑟 = 𝑣𝑎𝑟 𝑅!𝑒! + 𝑐𝑜𝑣 𝑅!, 𝑅!𝑒! , which is the remaining risk which exists due to the
variance of the cross-term. These equations confirm the theory of the previous section, namely that when Ri and ej are negatively correlated, hedging can increase portfolio variance. Also,
when the correlation between Ri and Rj is lower, the variance will be lower. On the other hand,
when looking at the expected return, hedging can cause the expected return to increase if fi is
larger than ei (Bugar & Maurer, 2001 & Schmittmann, 2010).
In order to create the mean-variance efficient frontier, which is the set of portfolios that minimize risk for given levels of expected return, the following should be solved for portfolio weights and hedge ratios:
min 𝑉𝑎𝑟 𝑅!!; 𝑥 !, ℎ! 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜: 𝐸 𝑅!! = 𝐸 𝑔𝑖𝑣𝑒𝑛 𝑙𝑒𝑣𝑒𝑙𝑠 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡: 𝑥! = 1 ! !!!
This method of minimizing risk with a given level of expected return is called the minimum variance portfolio or sometimes called the optimal portfolio (Bugar and Maurer, 2001). This means we need N portfolio weights and N-1 hedge ratios because we do not need to hedge the home currency. The constraints are that the weights sum up to one which means the investors budget is completely invested in risky assets and none of it in the risk-free asset.
5. Results
In this section, empirical evidence about currency risk hedging in developed versus emerging markets will be presented for the sample period 2005 to 2015. First we will look at no hedging versus fully hedging for single-country portfolios and thereafter for multi-country portfolios as well. Both equally-weighted portfolios as optimal portfolios will be discussed. In paragraph 3 and 4 optimal hedge ratios will be discussed both unconstrained and constrained.
5.1 Single-country portfolios – unhedged vs. fully hedged
Table 4 presents monthly average returns and standard deviations of investing in single-country portfolios when the investor is based in the US. Both developed countries and emerging markets are considered and differences between those countries are visible. When looking at the average local returns, it can be found that the returns in emerging markets are usually higher than those in the developed countries. This however comes along with higher local standard deviations as well, especially Russian stocks and Chinese stocks carry a lot of risk.
Another remarkable difference between developed and emerging markets is the level of exchange rate loss. It can be observed that from an American point of view the exchange rate returns are almost all negative during this period (except for China) because of the appreciation of the dollar against all currencies mentioned during this time of period. These losses are even bigger when investing in an emerging stock market. Usually that would mean hedging can cause the average return to increase. This is the case for all developed countries except Australia. When looking at emerging markets this only holds for Russia, South-Africa and to a lesser extent for China. In these four countries it means hedging causes the average return to decrease because the forward discount is higher than the exchange rate loss.
In Australia and all emerging markets except China the loss on forwards is quite large. In other words this means the forwards are mispriced which could be due to the fact that derivatives markets in EMEs remain small and less developed compared with those in developed economies.
Average returns (% per month) – developed countries
US Japan Germany UK Canada Australia
Local Ei Fi Unhedged Fully hedged 0.40 - - - - 0.38 -0.12 0.14 0.17 0.43 0.70 -0.16 0.03 0.58 0.77 0.20 -0.19 0.04 0.04 0.27 0.26 -0.10 -0.01 0.23 0.32 0.20 -0.05 -0.24 0.24 0.05
Average standard deviations (% per month) – developed countries Local Ei Unhedged Fully hedged 5.02 - - - 6.09 2.70 5.19 6.13 5.82 3.09 7.26 5.79 4.28 2.76 5.68 4.23 4.58 2.88 6.63 4.51 4.45 3.99 7.19 4.37 Average returns (% per month) – emerging markets
Brazil Russia India China Mexico SA
Local Ei Fi Unhedged Fully hedged 0.40 -0.30 -0.74 0.29 -0.16 0.86 -0.73 -0.52 0.11 0.32 1.03 -0.32 -0.43 0.83 0.71 0.78 0.18 0.05 0.96 0.82 0.90 -0.33 -0.32 0.67 0.68 1.04 -0.76 -0.49 0.36 0.63
Average standard deviations (% per month) – emerging markets Local Ei Unhedged Fully hedged 6.74 4.53 10.12 6.66 8.10 4.58 9.12 7.94 7.21 2.61 9.07 7.22 9.54 0.59 9.53 9.57 5.40 3.24 7.62 5.32 4.58 4.68 7.73 4.61 Table 4: monthly average returns and standard deviations of single-country portfolios from a US perspective during the period 2005-2015.
Let us now turn to the standard deviations. Almost all unhedged standard deviations are higher than the local standard deviations due to exchange rate risk. For instance when looking at Brazil we see a local standard deviation of 6.74% and an unhedged standard deviation of 10.12% which is an increase of more than three percent. The standard deviation of exchange rate returns on the Chinese Yuan is quite low comparing to others because of the peg it had with the US dollar and since keeping the Yuan stable with respect to the US dollar has always been the focus of China’s currency strategy. This, together with a negative covariance between the Chinese Yuan and its stock market, causes the fully hedged standard deviation to be higher than the unhedged equivalent. The covariance between the Japanese Yen and the Japanese stock market is also negative which means that a higher hedge ratio may come along with a higher standard deviation, as is the case.
Table 5 presents monthly average returns and standard deviations of investing in single-country portfolios when the investor is based in Brazil. It is conspicuous that the forward premiums are a lot higher than those for an US-based investor especially for the developed
countries. Also, a Brazilian investor has positive exchange rate returns in all developed countries and China, in contrast to the American investor. Unless the positive exchange rate returns, the average return when fully hedging currency exposure is higher than the unhedged equivalent in all countries. This is because the forward premiums are higher than the exchange rate gains and hedging is beneficial.
Remarkable is the increase in the standard deviation after hedging in the US, Japan and China. The covariance between the Japanese stock market and the JPY against the BRL is -0.20 percent which is quite large comparing it to the average of -0.07 percent. A more detailed description of this follows when looking at multi-country portfolios. The other standard deviations are lower after hedging but these decreases are not overwhelming. Only the standard deviations of Canada and Australia decreased significantly because the covariance between the local return and the exchange rate return are approximately zero but the variance of the CAD and AUD are 0.10 and 0.13 percent respectively which is eliminated when the hedge ratio is equal to one.
Average returns (% per month) – developed countries
US Japan Germany UK Canada Australia
Local Ei Fi Unhedged Fully hedged 0.40 0.30 0.75 0.58 1.03 0.38 0.18 0.89 0.37 1.08 0.70 0.14 0.78 0.76 1.41 0.20 0.11 0.71 0.23 0.84 0.26 0.20 0.74 0.40 0.94 0.20 0.25 0.51 0.45 0.71
Average standard deviations (% per month) – developed countries Local Ei Unhedged Fully hedged 5.02 4.53 4.66 5.14 6.09 5.46 5.28 6.34 5.82 4.12 6.11 5.88 4.28 4.09 4.59 4.34 4.58 3.62 4.78 4.70 4.45 3.19 5.34 4.49 Average returns (% per month) – emerging markets
Brazil Russia India China Mexico SA
Local Ei Fi Unhedged Fully hedged 0.40 - - - - 0.86 -0.43 0.22 0.35 1.01 1.03 -0.02 0.31 0.96 1.29 0.78 0.48 0.80 1.15 1.47 0.90 -0.03 0.42 0.86 1.31 1.04 -0.46 0.26 0.55 1.28
Average standard deviations (% per month) – emerging markets Local Ei Unhedged Fully hedged 6.74 - - - 8.10 4.78 8.76 8.20 7.21 3.65 7.31 7.21 9.54 4.47 9.62 9.76 5.40 3.40 6.09 5.37 4.58 4.23 5.96 4.62 Table 5: monthly average returns and standard deviations of single-country portfolios from a Brazilian perspective during the period 2005-2015.
5.2 Multi-country portfolios – unhedged vs. fully hedged
Unhedged returns on multi-country portfolios depend on both local returns and exchange rate returns as well. Hedged returns however also depend on whether there is a forward premium or discount. Table 6 presents monthly hedged and unhedged returns and corresponding t-statistics and P-values. As can be seen, the differences are statistically significant for a Brazilian investor who invests in a developed or mixed portfolio. What is striking is that the returns are higher when hedging the exchange rate risk. This is contrary to other studies. Also, the other differences might not be statistically significant, they sure are economically. For instance a US investor expects a return of 0.37% per month in the case of not hedging, which is approximately 4.5% a year. He expects 0.41% per month when fully hedging, which is more than 5% a year and thus quite a lot more than not hedging. This difference is even larger when looking at a Brazilian investor. In all three cases he can expect higher returns when choosing to fully hedge his exchange rate risk.
EQW portfolios – unhedged vs. fully hedged expected returns (%) US perspective No hedge
Full hedge significance: Test of T-stat Test of significance: P-value Developed portfolio Emerged portfolio Mixed portfolio 0.25 0.44 0.33 0.35 0.41 0.39 0.43 0.22 0.10 61.71 80.82 89.67 Brazilian perspective Developed portfolio Emerged portfolio Mixed portfolio 0.55 0.75 0.63 1.09 1.17 1.00 4.69 1.79 3.98 0.00 19.35 0.00 Table 6: monthly returns of unhedged equally weighted portfolios versus fully hedged equally weighted portfolios. A t-test was performed to see whether the differences are statistically significant. The developed portfolio consists of equal weights in the S&P 500, Nikkei 225, German DAX, FTSE 100, S&P TSX and the S&P ASX. The emerged portfolio consists of equal weights in the Bovespa Index, MICEX, SENSEX, SHCOMP, IPC and the FTSE/JSE. The mixed portfolio consists of equal weights in all of the indices mentioned before.
EQW portfolios – unhedged vs. fully hedged standard deviations (%) US perspective No hedge (Sharpe) Full hedge (Sharpe) Test of significance: F-stat Test of significance: P-value Developed portfolio Emerged portfolio Mixed portfolio 7.03 (0.04) 9.00 (0.05) 6.86 (0.05) 6.27 (0.06) 6.64 (0.06) 5.69 (0.07) 2.62 4.48 3.67 0.04 0.00 0.00 Brazilian perspective Developed portfolio Emerged portfolio Mixed portfolio 6.36 (0.09) 5.06 (0.15) 6.04 (0.11) 6.45 (0.17) 4.90 (0.23) 6.23 (0.21) 0.62 0.39 0.61 22.15 43.27 19.18 Table 7: monthly standard deviations of unhedged equally weighted portfolios versus fully hedged equally weighted portfolios. An f-test was performed to see whether the differences between standard deviations are statistically significant. The Sharpe ratios are given in parentheses and the risk-free rate is based on the average return on a 4-week Treasury bill during the sample period. Of course these higher returns does not tell everything. We must look at the changes in standard deviation as well. Table 7presents monthly standard deviations of unhedged and fully hedged portfolios. The results for the two different perspectives are quite the opposite. Fully hedging for a US investor causes the standard deviation to decrease significantly in all three portfolios. For an investor based in Brazil fully hedging means that the standard deviation increases in two of the three portfolios. Unless the increase of the standard deviations, the Sharpe ratio is higher after hedging currency risk. This holds for both investors.
The portfolios used until now were equally weighted. Let us now take a look at minimum variance frontiers. Those portfolios are not equally weighted anymore but have weights that minimize the variance given some expected level of return. Figure 1 shows the minimum variance frontier for an American investor investing in developed countries. Below an expected return of one percent, the unhedged portfolio has a lower variance than that of the fully hedged portfolio. However the optimal portfolio, which maximizes the Sharpe ratio, is a lot higher when the currencies are fully hedged. The minimum variances are approximately the same for both strategies.
Figure 1: Minimum variance frontiers for two hedging strategies from the perspective of an investor based in the United States investing into six developed stock markets.
Figures 2 and 3 show the minimum variance frontiers for an American investor investing in respectively emerging markets and all countries. In both cases fully hedging is again the best strategy for an American investor. Figures 3 to 6 show the minimum variance frontiers for Brazilian investors investing in respectively developed countries, emerging markets and all countries in one portfolio. Again fully hedging is the best strategy except for low levels of expected return. Figure 2: Minimum variance frontiers for two hedging strategies from the perspective of an investor based in the United States investing into six emerging stock markets. 0,00% 0,50% 1,00% 1,50% 2,00% 2,50% 0,00% 0,50% 1,00% 1,50% 2,00% Po rco lio exp ect ed ret urn Porcolio variance
Minimum variance fronder - emerging markets
Op_mal por`olio - unhedged Unhedged por`olio Fully hedged por`olio Op_mal por`olio - fully hedged Minimum variance - unhedged Minimum variance - fully hedged 0,00% 0,50% 1,00% 1,50% 2,00% 0,00% 0,20% 0,40% 0,60% 0,80% 1,00% 1,20% 1,40% Po rtfo li o ex pected r etur n Portfolio varianceMinimum variance fronder - developed countries
Unhedged por`olio Fully hedged por`olio Op_mal por`olio - unhedged Op_mal por`olio - fully hedged Minimum variance - unhedged Minimum variance - fully hedgedFigure 3: Minimum variance frontiers for two hedging strategies from the perspective of an investor based in the United States investing into twelve countries both developed and emerging. Figure 4: Minimum variance frontiers for two hedging strategies from the perspective of an investor based in Brazil investing into six developed stock markets. 0,00% 0,50% 1,00% 1,50% 2,00% 0,00% 0,50% 1,00% 1,50% Po rco lio exp ect ed ret urn Porcolio variance
Minimum variance fronder - developed countries
Unhedged por`olio Fully hedged por`olio Op_mal por`olio - unhedged Op_mal por`olio - fully hedged Minimum variance - unhedged Minimum variance - fully hedged Local Por`olio 0,00% 0,50% 1,00% 1,50% 2,00% 0,00% 0,20% 0,40% 0,60% 0,80% 1,00% 1,20% Po rco lio exp ect ed ret urn Porcolio varianceMinimum variance fronder - mixed porcolio
Op_mal por`olio - unhedged Minimum variance - unhedged Minimum variance - fully hedged Local por`olio Unhedged por`olio Fully hedged por`olioFigure 5: Minimum variance frontiers for two hedging strategies from the perspective of an investor based in Brazil investing into six emerging stock markets. Figure 6: Minimum variance frontiers for two hedging strategies from the perspective of an investor based in Brazil investing into twelve countries both developed and emerging. 0,00% 0,50% 1,00% 1,50% 2,00% 2,50% 0,00% 0,20% 0,40% 0,60% 0,80% 1,00% 1,20% Po rco lio exp ect ed ret urn Porcolio variance
Minimum variance fronder - emerging markets
Unhedged por`olio Fully hedged por`olio Local Por`olio Minimum variance - unhedged Minimum variance - fully hedged Op_mal por`olio - unhedged Op_mal por`olio - fully hedged 0,00% 0,50% 1,00% 1,50% 2,00% 2,50% 0,00% 0,20% 0,40% 0,60% 0,80% 1,00% 1,20% Po rco lio exp ect ed ret urn Porcolio varianceMinimum variance fronder - mixed porcolio
Unhedged por`olio Fully hedged por`olio Local Por`olio Minimum variance - unhedged Op_mal por`olio - unhedged Minimum variance - fully hedged5.3 Optimal hedge ratios – single-country portfolios
Table 8 presents minimum variance hedge ratios for American and Brazilian investors investing in single-country portfolios. Remarkable is that all hedge ratios for American investors are statistically different from zero except China and Japan. China and Japan have ratios of -0.23 and -0.60 respectively due to negative covariance between 𝑅! and 𝑒!. To explain
this further let us take a look at the expected variance of a portfolio again: 𝑉𝑎𝑟 𝑅!! = 𝑥!𝑥! 𝐶𝑜𝑣 𝑅!, 𝑅! + 2 𝑥!𝑥! 1 − ℎ! 𝑐𝑜𝑣 𝑅!, 𝑒! + ! 𝑥!𝑥! !!! 1 − ! !!! ! !!! ! !!! ! !!! ! !!! ℎ! 1 − ℎ! 𝑐𝑜𝑣 𝑒!, 𝑒! + ∆𝑉𝑎𝑟
When investing in only one country the equation looks like this:
𝑉𝑎𝑟 𝑅!! = 𝑉𝑎𝑟 𝑅! + 2 1 − ℎ! 𝐶𝑜𝑣 𝑅!, 𝑒! + 1 − ℎ! !𝑉𝑎𝑟 𝑒! + ∆𝑉𝑎𝑟
So, the larger the hedge ratio h!, the lower the benefits of the negative covariance between the
exchange rate returns and stock market returns and the lower the hedge ratio h!, the higher the benefits of this negative covariance. As can be seen from the equation above, the variance of the exchange rate return itself is another risk factor. The variance of the Japanese yen is approximately 0.07 percent whereas the variance of the Chinese yuan renminbi is only 0.003 percent so when investing in the Chinese stock market more exposure to currency risk is allowed.
From an American perspective the risk minimizing hedge strategy for all other countries would have been to hedge more than 100 percent of currency exposure. Hedging more than 100 percent means taking a short position in the currency. For the Mexican stock market American investors should have hedged 192 percent of currency exposure. This is due to the large positive covariance of 0.2 percent between the Mexican stock in local currency terms and the Mexican peso exchange rate versus the US dollar. The higher ℎ! , the lower
2 1 − ℎ! 𝑐𝑜𝑣 𝑅!, 𝑒! and thus the lower total variance but the higher ℎ!, the higher 1 −
ℎ! !𝑐𝑜𝑣 𝑒!, 𝑒! and thus the higher the total variance. The hedge ratio when investing in the
Indian stock market is therefore a lot higher because the variance of the Indian rupee is only 0.06 percent whereas the variance of the Mexican peso is more than 0.1 percent. When investing in the Russian stock market the best strategy to minimize risk would be to hedge about 100 percent of currency exposure i.e. fully hedging is the optimal strategy because the
variance of the Russian ruble is approximately the same as the covariance between the local stock market and the ruble exchange rate against the US dollar.
Over-hedging i.e. taking short positions is not always possible. Many institutional investors and banks place a limit on leveraging through forward contracts. This would mean that the hedge ratio should be between zero and one. In the case of an American investor that would mean no hedging when investing in the Chinese or Japanese stock market but fully hedge in every other market.
In contrast to American investors, Brazilian investors should have retained some exposure to all the currencies mentioned. The ratios are all significant different from zero at the 5 percent significance level which means again that no hedging is not the optimal risk minimizing strategy. The covariance between the local stock market and its exchange rate return are negative for all countries except Australia. So the question is why the hedge ratios are below one but not negative. This is due to the fact that de variances of the currencies against the Brazilian real are all a lot higher than the variances of the currencies against the US dollar. For example the variance of the Japanese Yen against the US dollar is 0.07 percent but the variance of the Japanese Yen against the Brazilian real is 0.30 percent. This is because the Brazilian real is not as stable as the US dollar is.
It becomes evident that when investing in single-country portfolios, the base country of the investor makes a difference. Investors based in an emerging market such as Brazil face more exchange rate risk because their home currency is not as stable as those of developed countries but because of the negative covariance between the stock market return and its exchange rate return it is best to hedge some currency exposure but not all of it to minimize risk. American investors however should at least fully hedge their currency exposure in most cases.
Minimum Variance Hedge Ratios – Single Country portfolios US perspective Brazilian perspective Minimum variance hedge ratio Newey-West Standard error of hedge ratio Minimum variance hedge ratio Newey-West Standard error of hedge ratio US Japan Germany UK Canada Australia Brazil Russia India China Mexico South-Africa - -0.23 1.51 1.43 1.93 1.51 1.65 1.02 2.70 -0.60 1.92 1.38 - 0.17 0.16 0.13 0.11 0.08 0.16 0.16 0.16 1.35 0.13 0.11 0.38 0.29 0.58 0.56 0.53 0.90 - 0.71 0.55 0.43 0.86 0.89 0.10 0.12 0.13 0.08 0.15 0.13 - 0.20 0.20 0.21 0.14 0.13 Table 8: Minimum variance hedge ratios for monthly returns considering single-country portfolios. The ratios are obtained by regressing the unhedged return on the row stock markets on the associated exchange rate return minus the forward premium/discount. All regressions include an intercept. The Newey-West estimator was used to overcome autocorrelation and heteroscedasticity in the error terms.
5.4 Optimal hedge ratios – multi-country portfolios
Table 9 presents the minimum variance hedge ratios for equally weighted multi-country portfolios. Again, three portfolios are considered from two different perspectives. From an American perspective, fully hedging or over-hedging is still the optimal strategy to minimize risk except for Japan. The ratios are higher because the covariances between the six countries matters as well. In a single-country portfolio it was optimal to hedge -27 percent of the JPY, in an equally weighted developed portfolio it is optimal to hedge 405 percent of the JPY in order to minimize risk. These ratios are uncommonly high. Therefore we will consider constrained hedge ratios as well.
The constrained hedge ratios for a Brazilian investor can be found in table 10. The constrained hedge ratios for an American investor are not shown in table 10 since they are all equal to one, in every portfolio. This means for an American investor it would be optimal to fully hedge all currencies in the sample. A Brazilian investor however should not hedge all currencies in EMEs plus the Canadian Dollar and the Australian Dollar.
Minimum Variance Hedge Ratios – Multi Country Portfolios US perspective Brazilian perspective Minimum variance hedge ratio Newey-West Standard error of hedge ratio Minimum variance hedge ratio Newey-West Standard error of hedge ratio Developed US Japan Germany UK Canada Australia EMEs Brazil Russia India China Mexico SA1 All US Japan Germany UK Canada Australia Brazil Russia India China Mexico SA 0.00 4.05 2.65 2.21 5.76 -1.72 2.45 0.98 3.57 3.62 3.57 2.09 0.00 2.702 2.70 2.70 2.70 0.60 2.70 -2.34 2.70 2.70 2.70 1.78 0.00 0.16 0.16 0.15 0.21 0.16 0.11 0.09 0.21 0.73 0.26 0.06 0.00 0.11 0.13 0.12 0.16 0.15 0.11 0.07 0.13 0.59 0.16 0.09 1.84 0.99 -0.37 2.62 -3.40 0.02 0.00 0.71 -3.62 3.07 1.85 0.52 2.70 2.07 0.97 2.70 -2.70 -0.40 0.00 -2.70 -2.70 -2.70 1.28 0.15 0.25 0.17 0.17 0.17 0.21 0.17 0.00 0.09 0.18 0.16 0.21 0.10 0.57 0.11 0.13 0.12 0.17 0.16 0.00 0.08 0.13 0.58 0.16 0.10 Table 9: Minimum variance hedge ratios for monthly returns considering EQW multi-country portfolios. The ratios are obtained by regressing the unhedged return on the row stock markets on the associated exchange rate return minus the forward premium/discount. All regressions include an intercept. The Newey-West estimator was used to overcome autocorrelation and heteroscedasticity in the error terms. 2The hedge ratios are constrained in some case to prevent the hedge ratio from getting to large. 2.70 and -2.70 are randomly chosen numbers which are very large as well.
Table 10: Minimum variance hedge ratios for monthly returns considering EQW multi-country portfolios and the hedge ratio is constrained to be in between zero and one. These ratios are based on an investor living in Brazil. The hedge ratios for an American investor are not given since they are all one.
Lastly, the returns, standard deviations and Sharpe ratios of the unconstrained optimally hedged EQW portfolios. For an American investor optimally hedging would mean an improvement when comparing the Sharpe ratio with the strategy of fully hedging. For a Brazilian investor it would only be an improvement when investing in a mixed portfolio.
Optimally hedged returns, standard deviations and Sharpe ratios (%)
US perspective
Expected
return deviation Standard Sharpe Ratio Improvement?
1 Developed portfolio Emerged portfolio Mixed portfolio 0.73 0.24 0.36 5.77 2.66 4.34 0.13 0.09 0.08 Yes Yes Yes Brazilian perspective Developed portfolio Emerged portfolio Mixed portfolio 0.73 0.99 0.86 5.95 4.57 5.21 0.12 0.22 0.17 No No Yes
Table 11: expected returns, standard deviations and Sharpe ratios when hedging with the optimal hedge ratios.
1Improvement with respect to fully hedging.
Constrained Minimum Variance Hedge Ratios Brazilian perspective Minimum variance hedge ratio Minimum variance hedge ratio Minimum variance hedge ratio Developed US Japan Germany UK Canada Australia 0.68 1.00 0.00 0.95 0.00 0.00 EMEs Brazil Russia India China Mexico SA1
0.00 0.91 0.00 1.00 0.90 0.23
All US Japan Germany UK Canada Australia Brazil Russia India China Mexico SA
1.00 1.00 0.72 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
6. Conclusion
During the sample period almost all exchange rate returns were negative from an American point of view, these exchange rate returns were even bigger when investing in emerging stock markets. Therefore it is beneficial to hedge currency risk from an American point of view except for Australia since the expected forward discount is very high. The same holds for Brazilian investors but with a different reason. Their expected return increases after hedging because of high forward premiums.
From a US perspective, optimal hedging results in higher Sharpe ratios than fully hedging. From a Brazilian perspective this is only the case when his portfolio is mixed. Constrained optimal hedging means fully hedging for an American investor but for a Brazilian investor it means to retain exposure to a lot of currencies. What we can conclude is that an American investor would be better off to hedge currency risk, but for a Brazilian investor this is dependent on what the situation is. In general this study gives insights that the investors base currency has more impact on the effects of currency hedging than the differences between investing in developed countries or EMEs.
It would be interesting to look at out-of-sample data as well since this paper is based on an ex-ante analysis. Another interesting topic to research would be to simultaneously determine portfolio weights and optimal hedge ratios in order to create an optimal portfolio with optimal hedge ratios. Finally a closer look at mispriced forwards can improve the literature about currency risk hedging in emerging stock markets.
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