Dynamic Hedging Turned Friendly Fire: Perils of Hedging Foreign Currency Risks
Jin-Wan Cho ☆ Korea University Business School 1, 5-Ka, Anam-Dong, Sungbuk-Ku Seoul S. Korea 136-701 82-2-3290-2602
[email protected]
Taeyong Kim Morningstar Associates Korea 4F Dabo Bldg., 140 Mapo-Dong, Mapo-Gu Seoul S. Korea 121-714 82-2-3771-0771
[email protected]
Woojin Kim Korea University Business School 1, 5-Ka, Anam-Dong, Sungbuk-Ku Seoul S. Korea 136-701 82-2-3290-2834
[email protected]
August 2010
☆
We would like to thank Hyun Suk Lee, Jae Uk Khil and other seminar participants at 2010 Joint Conference Allied Korea Finance Associations (Dogo, Korea, May 2010), Hanyang University – Ansan Campus, and Korea University for helpful comments. We would also like to thank Hyunil Lim for excellent research assistance. All remaining errors are ours.
Dynamic Hedging Turned Friendly Fire: Perils of Hedging Foreign Currency Risks
Abstract This paper examines the effect of dynamic currency hedging on the performance of open-ended mutual funds that invest in overseas risky assets. Using a unique sample of 27 ‘Siamese Twin’ international mutual fund pairs in Korea which hold identical underlying foreign assets but offer different currency hedging alternatives, we find that hedged portfolios are more volatile than nonhedged portfolios when there is a negative correlation between the value of the foreign currency and the underlying asset. Moreover, we show that under this negative correlation dynamic hedging may adversely affect even the value of the hedged portfolios. Our findings strongly suggest that strategies for hedging foreign currency risk should be designed conditional on the correlation structure between the underlying asset and the currency returns.
Key Words: Dynamic Hedging, Foreign Currency Risk, Open-Ended Funds, International Mutual Funds, Korea
I. Introduction
The world-wide trend of liberalizing capital movement across the borders since a few decades ago has provided the investors around the world opportunities to invest not only in domestic assets but also in overseas (risky) assets. Accordingly, the mutual fund industry has also witnessed a rapid growth in international portfolios both in terms of the number of funds and the value of the funds’ holdings. 1 At the same time, as the global capital markets had to navigate through a number of financial crises, such as the Asian currency crisis in 1997 and the recent global crisis originated from the U.S. sub-prime mortgages, maintaining appropriate risk management strategies proved to be critically important not only at the financial intermediary level but also at the economy-wide level.
In particular, hedging currency risks in volatile
overseas exposures is regarded as one of the most important aspects of risk management. As the financial derivatives such as forward contracts on various currencies become readily available, most international mutual funds employ some type of hedging strategies to manage currency risks. Hedging currency risks is generally considered as desirable at least for the following two reasons. First, if currency risks are not properly hedged, changes in exchange rates could increase the volatility of the total return from an international investment, since the total return includes not only the return from the underlying assets but also those from the fluctuations in relative currency values. Therefore, hedging currency risks could reduce the overall volatility of the fund return. Second, by unbundling currency returns from an international investment, fund managers can provide their investors with the ‘uncontaminated’ returns from the underlying assets alone net of the changes in exchange rates. The investors can then make their own portfolio decisions without having to worry about the interactions between underlying assets and currencies. 1
According to 2009 Investment Company Fact Book (www.icifactbook.org) published by Investment Company Institute, the number of global/international equity closed-end funds in US increased from 65 in 2001 to 93 in 2007. During the same period, the net asset value of these funds increased from $8.8 billion to $58.6 billion. The proceeds raised from the issuance of international equity funds in 2007 ($19.9 billion) actually surpassed those of domestic equity funds ($6.0 billion) by more than three times. -1-
In practice, however, these seemingly plausible benefits of hedging are not always attainable due to a number of factors. First, with regard to the possible reduction of total return volatility, previous research shows that if the value of the underlying overseas assets and corresponding foreign currencies are strongly negatively correlated, hedging currency risks may actually increase the volatility of the hedged portfolio.
For example, Campbell, Serfaty-de
Medeiros, and Viceira (2010) show that the values of U.S. dollar, the Euro and the Swiss franc are negatively correlated with their respective stock markets and hence suggest that riskminimizing global investors should take long (rather than short) positions in these currencies. 2 Cho, Choi and Kim (2010) also show that for emerging markets the currencies tend to have positive correlation with their stock markets, while for developed markets, the converse is true. Therefore, they argue that in order to reduce total return volatility, an emerging market investor investing in a developed market should not hedge the currency risks, while a developed market investor investing in an emerging market should. The second benefit of hedging, namely providing an unbundled return to investors, is actually not that easy to implement in practice. Unlike a fixed amount of a single cash flow (e.g. proceeds from export denominated in foreign currency) that can be easily hedged by using a forward contract, fund managers of open-ended mutual funds have to deal with the cash flows in and out of the fund as well as the accumulated gains or losses from their holdings every day. A typical hedging strategy employed by fund managers is the so-called “dynamic hedging” technique in which a fixed proportion of net asset value is kept hedged every day. This involves adjusting forward positions each day in response to changes in net asset value. Unfortunately, this dynamic hedging scheme may successfully unbundle currency returns from a non-hedged international investment only under certain conditions. More importantly under dynamic hedging, the negative correlation between a foreign asset and its corresponding
2
Note that a typical currency hedging strategy takes a short position in the currency when they invest in a foreign asset. -2-
currency not only affects volatility in an adverse way, but may also reduce the value of the fund itself even when the expected changes in currency value is zero. .The intuition is that under negative correlation between the underlying and currency value, dynamic hedging scheme mandates a fund manager to sell additional forward contracts in response to increases in net asset value at lower currency values. Conversely, in response to a decrease in net asset value, the manager needs to unwind the short position at higher currency values. In short, dynamic hedging forces the managers to buy-high and sell-low under such negative correlation, leading to a reduction in fund value even when there no changes in currency values over a longer term. . In this paper, we investigate the effects of dynamic hedging on the volatility as well as the value of an open-ended international mutual fund. Specifically, we first derive a number of testable empirical implications from a simple analytical exercise. The derived hypotheses are as follows; holding the composition of underlying assets fixed, (i) the more negative the correlation between underlying asset and foreign currency returns, the higher the volatility of the hedged portfolio compared with the non-hedged portfolio, and (ii) dynamic hedging under this negative correlation adversely affects the value of the fund even after eliminating the effect of changes in currency values . We then test these hypotheses using a unique sample of international mutual funds offered in Korea. There are several reasons why we focus on the Korean market. First, Korean mutual fund industry offers a wide variety of international mutual funds to investors that invests in overseas risky assets. According to Lee (2010), the net asset value of international mutual funds increased almost three times from KRW 21.9 trillion in 2006 to KRW 60.6 trillion in 2009. 3 During the same period, the relative proportion of international funds out of all mutual funds increased from 8.4% to 22.2%. Vast majority of these international funds are regionspecific so that it is relatively easy to disentangle the effect of currency on the portfolio value.
3
These numbers are largely comparable to the size of global/international equity closed-end funds in U.S. reported in footnote 1.. -3-
More importantly, a subset of international mutual funds in Korea provides the investors with the same underlying foreign assets but offers different alternatives with respect to currency risk hedging.
That is, investors can voluntarily choose either to hedge or not hedge their
international portfolio. Therefore, any differences in fund characteristics between these hedged and non-hedged portfolios can solely be attributed to currency hedging activities. This feature allows us to cleanly separate and observe the effects of dynamic hedging on the volatility and value of the hedged portfolios. Finally, most of the major foreign currencies denominated in Korean Won exhibits a negative correlation with the corresponding foreign stock market during recent years. Since the necessary condition for dynamic hedging scheme to have an adverse effect is such negative correlation, Korean market would appropriately serve our purpose. Using a sample of these 27 ‘Siamese Twin’ international mutual fund pairs, we find results that are consistent with our hypotheses. Specifically, during our sample period when there was a negative correlation between the value of the foreign currency and the underlying foreign asset, hedged portfolio returns exhibit larger volatility than those of non-hedged portfolios by roughly 5% points in annualized standard deviations. Cross-sectionally, this effect is more pronounced as the correlation becomes more negative. Moreover, when such negative correlation is combined with higher volatility of the underlying asset and the currency, dynamic hedging actually reduces the value of the hedged portfolios. These findings provide a clear warning against adopting casual hedging strategies that do not take into account the correlation structure between the underlying asset and the currency returns. The results also complement Campbell et al. (2010)’s macro level implications by providing micro evidence at the mutual fund level. The rest of this paper is organized as follows. The next section provides a more detailed description of dynamic hedging and its implications on fund value which leads to our main
-4-
hypotheses. Section III describes the data and the sample and section IV reports the results from the empirical analyses. Section V concludes.
II. Dynamic Hedging and Its Effect on Fund Value
Traditionally, the goal of risk management or hedging has been identified as the reduction in volatility of the investment portfolio. From a financial engineer’s perspectives, on the other hand, the goal of hedging may be to unbundle away a part of bundled returns so that his/her clients can obtain only the part of the returns that they want to take. For example, for an international mutual fund, a fund manager can hedge away the currency portion from an international investment to provide only the returns from international underlying assets net of the currency returns to their investors. Unfortunately, the latter goal may prove to be incompatible with the former one since unbundling the currency return may in fact increase the volatility of the hedged portfolio. Mutual fund managers find these seemingly simple and plausible goals to be quite difficult to achieve in practice. This is because determining the types and maturities of hedging instruments is not so clear-cut in most cases. In addition, as investors buy and redeem shares of the fund and at the same time per share value of the underlying fluctuates, previously set hedge will no longer be effective especially for open-ended funds. As a way of compromising these difficulties, fund managers typically adopt the “dynamic hedging” scheme in which a (fixed) proportion of net foreign asset value (hereafter ‘NAV’) is supposed to be kept hedged, usually by taking short positions in forward contracts on the corresponding foreign currency. 4 Purchases and redemptions of shares of the fund as well as changes in per share underlying asset value cause the NAV to change. This implies that under dynamic hedging, the 4
Our definition of net asset value is not normalized by number of shares. Hence, it represents the value of the total assets under management rather than the value per share. -5-
manager has to sell proportionate amount of foreign currency forward when there is a new inflow into the fund even when the underlying asset value stays unchanged. By the same token, if an investor redeems shares of the fund, the manager has to buy back proportionate amount of the forward contract. In this section, we formally analyze the effect of dynamic hedging and investigate the implications of correlation structure between underlying asset and currency on the return and volatility of the hedged fund value. We first derive an expression for the hedged portfolio’s value in domestic currency as a function of the net foreign asset value denominated in foreign currency and the changes in exchange rates over time. Let α denote the target hedge ratio. 5 Then, α fraction of the initial net asset value, NAV0, would be hedged initially by taking a short position in the foreign currency in the amount of α × NAV0.
As NAV changes, however, the fund manager sells and buys forward contracts to
maintain the target hedge ratio. In order to steer away from the complications arising from the effects of risk free rates and to focus on NAV and currencies, we make a simplifying assumption that the risk free rates are the same for the countries involved. This assumption makes the forward price of any maturity equal to the spot price, and allows us to circumvent the effects of shortened maturity of the existing forward contracts. In addition, this in effect assumes away basis risks associated with hedging activities. Without loss of generality, we also assume that the international mutual fund invests in a single foreign market. Under these assumptions, we can express the cumulative value of the hedged portfolio denominated in domestic currency at time t, HFVt,as follows. HFVt = NAVt S t − α
∑
t −1 i =0
NAVi ( S i +1 − S i ) ,
5
(1)
For example, if the fund aims at hedging the fund fully against the currency risk, then α would be set to unity -6-
where Si is the value of foreign currency denominated in domestic currency at time i and NAVi is the net asset value of the underlying foreign asset denominated in foreign currency.
The
derivation is provided in the Appendix.
Equation (1) shows that the value of hedged fund consists of two components. The first term, NAVt × St, represents the value of non-hedged fund at time t, while the second term,
α
∑
t −1 i =0
NAVi ( S i +1 − S i ), captures the cumulative gains/losses from dynamic hedging. Equation (1) shows that the overall ‘unconditional’ volatility of hedged fund value
depends on both contemporaneous and serial correlations between NAV and exchange rates. To derive a tractable expression for the volatility of the hedged portfolio, we make few simplifying assumptions and approximations. We first obtain an expression for the return of a hedged fund in which dynamic hedging can successfully unbundle the currency return from the return on an international investment. 6 If the net cash flows in and out of the funds are executed at the prevailing underlying asset price, the return of per share non-hedged fund from t-1 to t, rnht, can be approximated as follows. rnht = (1 + rat) (1 + et) – 1 ≈ rat + et.
(2)
where rat is the return on the underlying asset in foreign currency and et is the return from the foreign currency. 7 We also assume that the profits and losses arising from hedging activities are not reinvested. This will be the case if the hedging is done by using only the forward contracts until the liquidation of the fund. Under this assumption, the hedged fund return from t-1 to t, can simply be measured by dividing the right hand side of Equation (1) by NAVt-1 × St-1 rather than HFVt-1, which includes the second term of Equation (1), namely the cumulative gains/losses from 6
Hence, these assumptions and approximations can be regarded as conditions under which dynamic hedging successfully provides unbundled asset returns. 7 Eun and Resnick (1994) also assume away the product terms between returns from the underlying asset and currency in their mean-variance analysis, -7-
dynamic hedging up to time t-1. This approximation helps not only in gaining tractability, but also in appropriately comparing the returns between hedged fund and non-hedged fund on a fair basis. Since the change of value due to dynamic hedging is –α NAVt-1 × (St – St-1) as shown in Equation (1), we can express the return on a share of hedged fund as follow. rht = (1 + rat ) (1 + et) – 1 – α et = rnht – α et ≈ rat + (1– α) et.
(3)
Equation (3) shows that if the fund adopts 100% target hedge ratio, the dynamic hedging scheme erases the currency return and provides the investors with a return net of the currency return. Note, however, that this is possible only when the interactions among currency return and underlying asset return – namely, the product of rat and et - are ignored, and the profits and losses from hedging activities are assumed not to be reinvested. 8 Hence, in practice, dynamic hedging can hardly unbundle the currency return. To obtain the relationship between volatilities of each these return, we define σnh, σh, σa and σe as the standard deviations of returns on non-hedged fund, hedged fund, underlying asset, and foreign currency, respectively. Then, from Equation (2), the return volatility of non-hedged fund is approximately
σ nh2 = σ a2 + σ e2 + 2 Cov ( rt a , et )
(4)
Likewise, from Equation (3), the return volatility of hedged fund is approximately
σ h2 = σ a2 + (1− α ) 2 σ e2 + 2 (1 − α ) Cov ( rt a , et )
(5)
Note that if the target hedge ratio is 1, the volatility of hedged fund is independent of the currency risk, implying that the currency risk is fully hedged. This, however, does not necessarily mean that the volatility of hedged fund is less than that of non-hedged fund. Note that reduction in volatility due to dynamic hedging can be expressed as follows. σnh2 – σh2 = α (2–α) σe2 + 2 α Cov (rat, et) 8
Another important assumption we used is that the hedges are not exposed to the basis risks. -8-
(6)
Since α is a number between zero and one, the first term in Equation (6) is always positive. If the second term, i.e. the correlation between underlying asset return and foreign currency return is positive, the right hand side of Equation (6) should always be positive, implying that dynamic hedging would reduce return volatility. If, however, this second term is significantly negative, so 2
that it is less than (α/2–1) σe , the right hand side of Equation (6) can become negative. In this case, dynamic hedging actually increases volatility of the fund return. Campbell et al. (2010) also point out that some currencies, such as the U.S. dollar, the Euro and the Swiss franc, are negatively correlated with their respective stock markets, and therefore, volatility minimizing investors should take a long position in the currency when they invest in equities traded in these currencies. Based on equation (6), we develop our testable hypothesis with respect to the effects of dynamic hedging on a fund’s return volatility as follows:
(H.1)
the more negative the correlation between underlying asset return and foreign currency return becomes, the less effective dynamic hedging becomes in reducing the volatility.
As mentioned earlier, there is an additional potential side effect of dynamic hedging. Dynamic hedging not only affects the volatility of the fund, but also the value of the fund itself. Equation (1) shows that if the foreign currency appreciates over time, dynamic hedging can reduce the fund value in the ex post sense. This is straight forward since hedging is accomplished by taking short positions in the foreign currency. With the appreciating foreign currency, the hedged fund value in local currency decreases over time from the forward currency position. However, this ex post loss from hedging should not be considered a cost of dynamic hedging since the fund manager would not know ex ante whether the currency will appreciate or depreciate which is precisely the reason why he/she hedges in the first place. In other words, value of the dynamically hedged portfolio, HFVt, should be compared with NAVt × S0 (value of a
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perfectly unbundled portfolio) rather than NAVt × St (value of a non-hedged portfolio) since the latter reflects the effect of changes in currency value. To circumvent such confounding effects due to changes in currency values, we consider the case where the expected change in currency value is zero. That is, E(ΔSt+1).= 0. This allows us to ignore the first term in equation (1) and isolate the pure effect of dynamic hedging on fund value by focusing on the second term. The expected value of time i component of this term can be written as E [NAVi × ΔSi+1] = Cov(NAVi , ΔSi+1) + E (NAVi) E(ΔSi+1).
(7)
Therefore, if the expected value of ΔSt+1 is zero, then E [NAVi × ΔSi+1] = Cov(NAVi , Si+1) – Cov(NAVi , Si)
(8)
The negative correlation between asset value and currency will make the right-hand side of Equation (8) become larger.
Since covariance also depends on the magnitude of standard
deviations of the two variables, large standard deviations in underlying asset and currency value will also contribute to the increases in right hand side of equation (8). Combining equation (8) with equation (1), we can see that this negative correlation causes the hedged fund to lose value. This is the case in which dynamic hedging can actually decrease fund value in the ex ante sense. To illustrate this, consider the following situation. 9 Suppose that at time 0, the value of a European asset is €100, and the price of Euro is $1. In order to hedge the currency risk, a fund manager takes a short position in a forward contract in the amount of €100. Further assume that the U.S. and Euro interest rates are the same, making the forward price be identical to the spot price. In other words, the forward price is also $1. At time 1, the asset appreciates to €110, while the Euro depreciates to $0.9 due to the negative correlation between the underlying asset and the currency. The fund manager now has to take an additional short position in Euro forward in the amount of €10 at $0.9. Finally, at time 2, the asset loses its value to €100, while the Euro
9
The example is originally drawn from Park (2009). - 10 -
bounces back to $1. 10 Then, even though the US$ value of the foreign asset remains to be at $100, the fund will lose $1 from the short position in €10 forward contract due to dynamic hedging. This is because the terminal position in forward contract is €110 of which €100 was contracted at $1, and €10 at $0.9. This example shows that dynamic hedging can be detrimental when underlying and currency tend to fluctuate in the opposite directions. What is interesting is the fact that the negative correlation between the foreign asset and the currency is again one of the main reasons behind this loss. Note that the precise reason why this happens is that after the fund manager took a short position in €10 forward contract, the Euro value moves higher next period. This positive ‘cross-autocorrelation’ between foreign asset and currency is generated because the foreign asset and currency values are negatively correlated and the expected return on the currency is assumed to zero. Therefore, if the foreign asset returns and the currency returns are negatively correlated, dynamic hedging may not only increase the volatility of the hedged portfolio, but also reduce asset values when the expected value of currency return is zero. Since a reduction of fund value occurs even when the expected return on the currency equals zero, we argue that this is a case of dynamic hedging turned into a ‘friendly fire’ We summarize this observation in the following hypothesis:
(H.2)
if non-hedged fund return and foreign currency return are negatively correlated, dynamic hedging causes the fund to lose its value in the absence of changes in currency values
In reality, expected return on the currency estimated through historical data may well be non-zero. In fact, foreign currency returns are highly positive in our sample. Hence, in our empirical specification, we eliminate the effect of currency return from the non-hedged return and compare this hypothetical ‘implied’ return against the dynamically hedged return.
10
Therefore, the expected return on the currency is kept at zero. - 11 -
Now that we have a set of testable hypotheses, we will proceed to the next section to investigate empirically the effects of dynamic hedging on fund value and return volatility.
III. Data and Sample
1. Correlation between Currency and Stock Market: A Global Perspective
To motivate our argument that hedging mechanism can actually turn out to be volatilityincreasing and value-decreasing, we first establish that negative correlation between currency and underlying are non-trivial. Table 1 presents the pair-wise correlation between the destination country’s weekly stock index returns and the weekly currency returns based on home currency price of the destination currency for eleven selected countries around the world, including emerging markets such as BRICs nations and developed markets such as the U.S. and the U.K. between 1996 and 2009. 11
Panel A reports the results for the full 14 year period and panels B
and C present the results for two 7 year sub-periods. Each panel reports 110 such pair-wise correlations. Note that the structure of the table is non-symmetric and diagonal cells are all empty by construction. The results from panel A indicate that out of 80 significant correlations, 46 (57%) are negative. The negative correlation is more pronounced for emerging market investors investing overseas. 12 From their perspectives, out of 45 significant correlation, 34 (76%) are negative. This finding confirms the findings from Cho, Choi and Kim (2009) in which the currency returns are reported to provide natural hedges for emerging market investors, while they are volatilityincreasing for the developed market investors. In particular, from the perspectives of investors in Brazil or Korea, negative correlation exists in all destination countries under investigation. Even 11
We obtain the data on equity indices and exchange rates from Datastream The following 6 countries are classified as emerging markets: Brazil, China, India, Korea, Russia, and Taiwan.
12
- 12 -
for investors originating from developed markets, except for Japan, at least 2 to 4 destinations provide negative correlation, For example, U.K. investors investing in China, Hong Kong, Japan or Russia should care about such negative correlation. In addition, as destination markets, the U.S., Japan, H.K., and Russia are the ones in which investors from other nations find the currencies to provide the most natural hedges. In fact, all foreign investors investing in the Japanese market are subject to such negative correlation. These findings suggest that negative correlations are non-trivial and thus should raise concerns for investors all around the world who invest overseas. Moreover, these correlation structures seem to remain stable over time. In Panels B and C, there are 39 correlations that are significant in both panels. Out of these 39 significant pairs, 28 (72%) pairs have the same signs. If we investigate all 110 pairs, 72 (65%) have the same signs. This stability is important in that the negative correlation, if any, can largely be expected ex ante. Hence, when fund managers design their hedging strategies, the expected negative correlation can be taken into account in advance. When we compare panels B and C, we observe that the correlation is more significant during the recent years. In panel C, 93 pairs are significant our of which 43 (46%) are negative, while in panel B, only 48 pairs are significant, out of which 24 (50%) are negative. At any rate, the proportion of negative pairs remain somewhere around 50% in both sub-samples. The results from table 1 also suggest that Korea is one of the home countries that have experienced persistent negative correlations between the returns from destination stock markets and corresponding currencies, Figure 1 provides a more detailed description of the correlation structure for Korea as a home country. In panel A, U.S. is the destination market and the currency value of US$ are denominated in Korean Won. In panels B and C, the destination markets and corresponding currencies are Hong Kong and Japan, respectively. The results from all 3 panels indicate that there is a strong negative correlation between the destination stock market index and destination currency value through the whole 14 year period. When the - 13 -
destination stock index rises, value of the Korean Won appreciates, offsetting the gains from the underlying. In fact, this is precisely the reason offered in the popular media for hedging currency risks, On the other hand, when the foreign stock market plunges, Korean Won depreciates providing a natural hedge. Taken together, these results suggest that Korea is well suited to serve the purpose of investigating the effects of negative correlation on dynamic hedging and its ramifications.
2. Development of International Mutual Funds and Currency Hedging in Korea Investing in global assets is a relatively a recent phenomenon in Korea. In the earlier days, most of the available international funds were offshore funds, which are created and managed abroad. Since 2006, however, both the number and assets under management (hereafter, ‘AUM’) of onshore overseas funds increased at a rapid pace. According to Korea Financial Investment Association (KFIA), the AUM by onshore overseas funds increased from approximately $2 billion in 2004, to $6 billion in 2005, $25 billion in 2007 and almost $100 billion in 2008. One of the reasons behind this rapid growth is the new tax advantages that the Korean government gave to these onshore overseas funds. According to this tax initiative passed on June 1, 2007, the investors in the onshore overseas funds were tax-exempt of their capital gains until 2009. The Korean government adopted this scheme in order to promote outbound international investments with the objective of curbing the sharp appreciation of Korean Won. 13 The first generation offshore funds did not provide hedging mechanism against currency risks. But as the Korean Won strengthened, distribution channels, such as commercial banks and investment banks, started demanding fund managers to provide hedges against currency risks. In response, most of the subsequent onshore overseas funds decided to provide hedges for 100% of their NAV’s against currency risks. The typical hedging strategy that these funds adopted was dynamic hedging scheme. 13
In 2006, the Korean Won gained 19.5% against the US dollar. - 14 -
3. Sample Construction Unlike most of these onshore funds that offered only hedged portfolios, some foreign currency denominated funds made themselves available to the investors in two separate forms: one with hedged option and the other without the hedging option. These two types of funds share the same underlying foreign currency denominated assets and hence the same portfolio weights, as well as the same management fees. 14 Therefore, the literal difference between them is whether they are hedged or not, and we believe that these ‘Siamese Twin’ funds provide an ideal environments to investigate empirically the effects of foreign currency hedging on fund’s return distribution. The results from this empirical analysis can then be used to infer the effect of hedging in the remaining majority of funds that only provide hedging alternative. There are initially 29 fund pairs available between March 2007 and July 2009 that offered both hedged and non-hedged classes. We obtain weekly per share return series on these funds from Morningstar Korea Financial Investment Association. From the original 29 fund pairs, we filter out those pairs where the number of weeks with valid returns is less than 15 or the discrepancy in availability of returns between the two classes is more than two weeks. Two fund pairs are excluded through this filter leaving us with a final sample of 27 fund pairs. In our sample of funds, the financial instruments used for hedging consists of both futures and forward contracts. Relatively smaller funds with AUM of less than KRW 2 billion (roughly US$ 2 million) used only futures contracts, while most of the larger funds used a mixture of forward and futures roughly on a 50:50 basis. Typical maturities of forward contract ranged from three to six months, while those of futures contracts lasted for two to three months. The most important factors in determining the maturity seemed to be the liquidity of the contracts. Table 2 presents the descriptive statistics of the mutual funds in our sample. The sample includes all foreign currency denominated mutual funds available in the Korean market that 14
For hedged funds, however, the fees for implementing hedging strategies are additional. - 15 -
provided both hedging and non-hedging options for retail investors with at least 15 weeks of valid return information available. These funds are all onshore funds. None of the offshore funds provided the option to hedge or not hedge. The sample period begins in March 2007 when these ‘Siamese Twin’ international mutual funds were first introduced and ends in July 2009.. For each fund in the sample, the first six columns report the type, its masked ID, the number of paired weekly returns available, the total AUM separately for non-hedged assets and hedged assets, and the currency that the fund targets to hedge (for hedged assets). There are 18 regional funds, and 9 sector funds out of which 7 are energy funds. On average, weekly returns are available for 70 weeks, or one year and four months. This reflects the fact that funds with options to hedge or not hedge became available only recently. The average AUM for hedged funds is about three times larger than that of non-hedged funds. This implies that investors’ demand for hedging options was much more stronger than for non-hedging options during the sample period. Note, however, that even the average AUM of the hedged funds was KRW 16 billion (roughly US$15 million), which by the U.S. standard is classified as small. With regard to the target currency to be hedged, there were 14 funds that targeted to hedge the U.S. dollar, 6 funds targeting the Hong Kong dollar, 2 funds targeting the Japanese Yen, 2 funds targeting the Euros, and the remaining 3 targeting a basket of currencies. For the last three funds that targeted a basket of currencies, we develop a matching currency index using the weights declared by the funds. The final two columns present the correlation between weekly currency return based on KRW denominated price and weekly underlying asset return, which is the key explanatory variable in our hypotheses. Since the underlying return is not directly observable, however, we need proxies for the true underlying return. We employ two different proxies for this purpose. Our first candidate is the hedged return itself. Although dynamic hedging may not be able to perfectly unbundle the currency return and hence replicate the true underlying return, it could be used as a reasonable proxy for the purpose of estimating the correlation structure. In our second - 16 -
approach, we infer the “implied” underlying return by removing currency return from the nonhedged return, both of which are directly observable. Note from Equation (2) that 1 + rnht = (1 + rat) (1 + et). Therefore, the “implied” underlying asset return rat can be estimated by rˆt a =
rtuh − et 1 + et .
(9)
One drawback of this approach is that this measure may mechanically underestimate true Cov (et , rta ) by subtracting observed et.from observed rnht to obtain rˆta .
As can be seen from the final two columns of table 2, the correlations between the underlying return and currency return are all negative, regardless of which measure is used to proxy for the true underlying return. This is consistent with the graphical results reported in figure 1. The average correlation is -0.479 when hedged return in used as the proxy for the true underlying and -0.639 when implied underlying is used instead. The prevalence of negative correlation indicates that dynamic hedging may increase return volatilities as well as adversely affect the value of the hedged funds. Moreover, the correlations ranges from -0.086 to -0.70 based on hedged returns and from -0.242 to -0.911 based on implied underlying returns. This allows us to examine not only the direction but also the magnitude of the effect of negative correlation by exploiting the cross-sectional variations in correlations. For all 27 fund pairs, however, the correlations based on implied underlying is unilaterally more negative than correlations based on hedged returns, suggesting a potential underestimation of true covariance structure when implied underlying is used. In what follows, we use the correlations obtained from hedged returns as the baseline since they exhibit less extreme values. Nevertheless, our basic results are robust to using correlations based on implied underlying returns instead.
IV. Empirical Analyses 1. Effect of Dynamic Hedgind on Return Volatility
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The first hypothesis (H.1) developed in section II summarizes the effects of correlation between underlying foreign asset return and the corresponding currency on volatility of hedged return. If the correlation is negative, dynamic hedging can actually increase the volatility of hedged fund return.
From Table 2, we observed that for all the funds in our sample the
correlation between underlying assets and the corresponding currency is negative, regardless of which proxy is used for the underlying. Hence, we expect to find evidence that volatility of a hedged fund is larger than that of the non-hedged counterpart. Table 3 presents a comparison of return volatilities between foreign assets that hedge against the foreign currency risk and those that do not hedge. The first four columns repeat the type, its masked ID, and the number of paired weekly returns available reported in table 2. The next two columns present the standard deviation of the weekly returns for both hedged assets and non-hedged assets in each of our sample funds. The final column presents the difference in volatility between the hedged group and the non-hedged group. The last four rows show the means and medians as well as the corresponding test statistics. As expected, volatility is generally greater in hedged assets than non-hedged assets. For 23 out of 27 funds, dynamic hedging increases return volatility. The average increase in weekly standard deviation is 0.67%, and the corresponding median increase is 0.63% both of which are statistically significant. These differences in weekly standard deviations translate into 4.5% to 4.8% per annum. These differences also amounts to approximately a 15% increase from nonhedged mean and median volatility. In order to investigate the magnitude of the effect of negative correlation on volatility of hedged funds, we first plot the relationship between correlation and differences in return volatilities in figure 2. In both panels A and B, the horizontal axis measures the correlation between the underlying return and the currency return, while the vertical axis measure the differences in standard deviations between non-hedged and hedged assets using weekly returns for each of the 27 fund pairs in our sample. In panel A, the underlying return is proxied by - 18 -
hedged return for the purpose of calculating correlation with the currency return. In panel B, we directly infer “implied” underlying return by subtracting currency return from the non-hedged return and dividing it by one plus currency return as in equation (9), and use this measure to obtain correlation with the currency return.. Each dot in the figure represents one mutual fund pair. The results from both panels A and B strongly suggest that hedged fund return volatility increases relative to non-hedged volatility as the correlation between the underlying asset and the corresponding foreign currency becomes more negative. In fact, those 4 funds for which the volatility of the hedged funds was lower than non-hedged funds in table 3 are the 4 funds that showed the least negative correlation in absolute terms in table 2. 15 Table 4 reports the results from cross-sectional analyses that formally test the first hypothesis (H.1) controlling for other fund characteristics. We report the OLS regression results where the dependent variable is the difference in volatility between hedged asset and non-hedged asset measured as standard deviation of weekly returns from hedged fund minus that from nonhedged counterpart. Correlation between the underlying and the currency return are calculated for each mutual fund using weekly return, where underlying return is proxied by hedged return. 16 We take the natural log of assets under management (KRW million) to control for potential size related effect. In order to examine if the results are affected by the currency itself, we use a dummy variable to control for the differential effects depending on whether the target currency is US dollar or non-US dollar. The estimates with ‘*’ indicate that the null hypothesis is rejected at a significance level of 10%, whereas ‘**’ at 5%, and ‘***’ at 1%.
The results from table 4 clearly indicate that more (less) negative correlation leads to larger (smaller) volatility of the hedged return relative to the non-hedged return. Even though the 15
These 4 fund’s masked ID’s are 2, 3, 17, and 19. Our results are virtually unaffected when we use the correlations based on ‘implied’ underlying return from equation (9) rather than hedged return. 16
- 19 -
sample size is only 27, for all the models, correlation between underlying asset and currency returns turns out to be the most important factor in explaining the differences in hedged and nonhedged return volatilities. R2 value in specification (1) where we only include the correlation and a constant amounts to 0.458, implying that close to half of the variation in volatility differences are explained by the correlation between the underlying and currency.
These results are
consistent with those reported in figure 1, and provide strong evidence in support of our first hypothesis (H.1). Overall when the underlying foreign asset and target currency returns are negatively correlated, dynamic hedging increases return volatility. We argue that this is a case of ‘friendly fire’ of hedging. But, the adverse consequence of negative correlation does not stop here. Since mutual funds typically engage in a day to day dynamic hedging, as the second hypothesis (H.2) suggests, negative correlation accompanied by large standard deviations of underlying and currency can cause the fund value to decrease under dynamic hedging. This is the worse case of ‘friendly fire’ of hedging, which will be discussed next.
2. Effect of Dynamic Hedgind on Fund Value
The second hypothesis (H.2) developed in section II addresses the effect of dynamic hedging on value of hedged assets. The first order effect of dynamic hedging on fund value comes from appreciation or depreciation of the target currency. Therefore, if the foreign currency appreciates, for example, the hedge will turn out to be costly ex post. But since hedging is not speculating, even if the fund may lose value with an appreciation of the foreign currency, we do not argue that this is a case of ‘friendly fire’ of hedging. The fund manager would not know ex ante whether the currency will appreciate or depreciate, and this uncertainty is precisely why he/she needs hedging.
- 20 -
Even when the realized return on target currency is zero, dynamic hedging can be costly. This is when the asset and currency returns fluctuate heavily in the opposite direction. When the expected return on target foreign currency is zero, the negative correlation between currency and the underlying asset combined with large standard deviations in both currency and underlying will generate this large fluctuations in the opposite direction. Our hypothesis (H.2) formally characterizes this relationship, In table 5, we report the geometric averages of weekly returns for each of the mutual fund pairs in the sample. We resort to geometric averages rather than arithmetic averages since our hypothesis is about the ultimate value of the fund rather than expected returns. 17 The first column presents the masked ID as in the previous tables. The next four columns present the geometric averages of weekly returns for the hedged asset, non-hedged asst, corresponding currency, and implied underlying asset. Implied underlying returns are obtained from equation (9). The last two columns present the difference between hedged and non-hedged returns as well as those between hedged returns and implied underlying returns. The last four rows show the means and medians as well as the corresponding test statistics. The estimates with ‘*’ indicate that the null hypothesis is rejected at a significance level of 10%, whereas ‘**’ at 5%, and ‘***’ at 1%. The results from the the second to last column ‘(A) – (B)’ indicates that hedged funds in general yielded lower return than the non-hedged counterpart. In all but for four sample funds, hedged fund returns are lower than those of non-hedged funds. The average of weekly return difference is 0.33%, and statistically significant at 1%. Weekly return of 0.33% translates into roughly 19% per annum when compounded weekly. However, this seemingly large difference is mostly due to the appreciation of the target foreign currencies. Over the sample period, most of the target currencies gained against the Korean Won, and therefore, the hedged funds must have incurred large losses from short
17
We obtain very similar results in all of our subsequent analyses when we replace the geometric averages with the arithmetic averages. - 21 -
positions on the target currency. Column (C) reports the geometric averages of weekly returns on the corresponding currencies in the sample. The average of weekly currency return is 0.30%, implying 17% per annum on a compounded basis. As mentioned before, our concern is not on the losses directly attributable to ex post appreciation of target currencies, but rather on the losses attributable to tendency of underlying and currency returns’ fluctuating in the opposite directions of each other after controlling for the effect of changes in currency. This second order effect of dynamic hedging on fund return can only be tested with the true underlying asset return. But as we discussed in the previous section, the true underlying asset return is unobservable. Therefore, in order to proxy the ‘unobservable’ true underlying asset return, we generate underlying return series implied in non-hedged and currency returns by using Equation (9). This in essence is the return on a non-hedged fund net of currency return, and is presented in Column (D). Therefore, the last column, ‘(A) - (D)’ can be regarded as measuring the second order effects of dynamic hedging on hedged fund return laid out in Hypothesis (H.2) Even after eliminating the effect of currency returns, the hedged return is still in general lower than the implied underlying asset return.
The average and the median of weekly
differences are -0.03% and -0.07%, which are in turn 1.5% and 3.6% per annum, respectively, although the mean difference is not statistically significant.
One could argue that these
differences may simply be driven by fees on hedging activities which are only imposed on hedged portfolios, and hence there is no real difference in returns except for the fees. However, we have not exploited the cross-sectional variation in correlations or standard deviations of the underlying and currency and its impact on returns yet. In table 6, we regress the difference between hedged and implied underlying return on the correlation between the underlying and currency, controlling for other fund characteristics in a similar manner as in table 4. The difference in return is measured as the geometric average of the hedged portfolio weekly return minus the geometric average of the implied underlying weekly return. We also include the standard deviation of the underlying, proxied by hedged return - 22 -
standard deviation, and standard deviation of the currency return which could amplify the fluctuations of these two series. 18 The results from table 6 indicate that cross-sectionally, more (less) negative correlation results in lower (higher) return of the hedged portfolio relative to the implied underlying. This provides evidence against the argument that the differences in returns are simply being driven by the hedging fees. Moreover, this effect is more pronounced when currency return standard deviation is large. Explanatory power of the correlation and standard deviations of hedged return and currency return are quite large. R2 value in specification (2) where we only include these variables and a constant is 0.456 accounting for almost half of the variation in return differences. Number of weeks which represents the age of the funds is also marginally significant. This implies that the difference in geometric averages accumulates over time which makes sense. The magnitude of the coefficient on the correlation variable ranging from 0.5% to 0.7% per week is economically substantial. This implies that funds with correlation of -0.5 would incur incremental loss of at least 0.5% per week compared with funds with correlation of 0.5 simply because they are engaged in dynamic hedging schemes. Over one year, this difference could accumulate up to 30% when compounded. Even a small difference in correlation, for example 0.1, could generate an additional loss of 2.6% per year. These results provide a clear warning against adopting dynamic hedging scheme without careful consideration of the correlation structure between the underlying and currency. Above analysis is based on one observation per fund pair based on weekly returns which has limited power due to a small number of observations. Since dynamic hedging is typically conducted over daily intervals, an ideal test of (H.2) would be to use daily returns to create correlations and standard deviations at weekly or monthly intervals and use this weekly or monthly observations to test (H.2), which would enhance the power of the tests.
18
We obtain similar results when we replace the hedged return with the implied underlying for the purpose of calculating the correlations and standard deviations. - 23 -
Unfortunately, daily returns are not available in our sample. Nevertheless,to increase the power of the test based on weekly returns, we create a new set of observations as follows. For all weekly returns available in the sample, we group them by 5 week intervals, and calculate geometric average weekly return, standard deviation, and correlation between the underlying and currency return for each of the 5 week interval. Hence, the unit of observation here is each 5 week interval rather than the whole life of a fund. This creates multiple observations from one sample fund, and as a result, the total number of observations increases from 27 to 358. Using the newly created observations, we re-examine the effect of negative correlation on hedged fund return in a similar manner as in table 6. The results of the regression based on each 5 week intervals are presented in table 7. Instead of including fund characteristics which do not vary within a fund, we include various interaction terms between the correlation and standard deviations of underlying and currency return. As in table 6, we use hedged returns as a proxy for the underlying return for the purpose of calculating the correlation and standard deviation. 19 The results from specification (1) and (2) are consistent with those obtained in table 6 using fund level observations. That is, more negative correlation leads to lower return of the hedged portfolio relative to the implied underlying return. However, when we interact the correlations with the standard deviations in specification (3) and (4), we observe that correlation alone loses its explanatory power. Instead, negative correlation has impact on hedged fund’s return only when accompanied by large standard deviations in the underlying and currency return, which amplifies the fluctuations of the two series in the opposite direction consistent with the predictions in (H.2).
V. Conclusion
19
We obtain similar results when we replace hedged return with implied underlying return for the purpose of calculating correlations and standard deviations. - 24 -
Typical statement in favor of foreign currency hedging often provided by the popular press can be summarized as follows; “Suppose you made a large return on the underlying foreign currency asset. However, if the foreign currency depreciates, then your positive returns from the underlying are offset by the negative returns from the currency. To avoid this situation, you should hedge foreign currency risk so that you are not exposed to the changes in exchange rates.” But from a volatility minimizing investors’ perspective, this is exactly the situation when hedging foreign currency can go wrong, since the underlying return and currency return move in the opposite direction. That is, there is already a built-in hedge mechanism. Therefore, if an investor hedges against foreign currency risk, it could actually increase the volatility of the total fund return. In this paper, we analyze the effects of dynamic hedging on the performance of openended mutual funds that invests in overseas risky assets. In particular, we investigate how negative correlation between underlying foreign asset and corresponding foreign currency returns affects the hedging performance. We first develop a simple analytical framework in which negative correlation between underlying asset return and corresponding foreign currency not only increases return volatility, but also could reduce the value of the fund. Since dynamic hedging can increase the volatility of hedged assets, we refer to this case as a ‘friendly fire’ from volatility minimizing investor’s perspective. In addition, dynamic hedging can adversely affect the value of the hedged portfolio when the underlying return and currency return fluctuates in the opposite direction even when the expected return on currency is zero. We refer to this is the worse case of ‘friendly fire’. In order to test these hypotheses, we use a unique sample of ‘Siamese Twin’ international mutual funds in Korea. These two types of funds share the same underlying foreign currency denominated assets with the same portfolio weights, and management fees, but provides investors with the option to hedge or not hedge the currency risks. We use 27 pairs of hedged and nonhedged funds that have weekly returns available for the period between March 2007 and July - 25 -
2009, and provide evidence that supports the theoretical predictions. We also show that at the global level, the correlation structure between foreign assets and target currencies has been quite stable over time, and investors from a variety of regions, especially those from emerging markets investing in developed markets, are subject to a negative correlation between the two return series. Hence, we conclude that investors investing in overseas risky assets should examine the correlation structure before they choose to hedge the currency risks. The findings in this paper raise a few related questions that could be potentially answered in a future research. It seems odd that mutual funds would continue to hedge currency risks even after they acknowledge that dynamic hedging could be detrimental. Our conjecture is that there could be an organizational decentralization within the mutual fund where fund managers are only responsible for managing the underlying assets and not hedging activities. In other words, hedging activities could be mechanically implemented based on NAV and preset hedge ratio by someone else in another division. This inappropriate division of labor could make fund managers less sensitive to the loss incurred by dynamic hedging. More fundamentally, it would be interesting to explore the factors that affect the correlation between underlying asset and the currencies. One possibility is that in relatively smaller markets, demand (or lack of) for risky assets in up (down) markets by foreign investors could drive up the value of their respective currencies. Assuming equity markets are positively correlated around the world, this implies a negative correlation between relatively larger stock markets and their currency values.
- 26 -
References Campbell John Y., K. Serfaty-de Medeiros, and L. M. Viceira, 2010, Global Currency Hedging, Journal of Finance 65, 87-121. Cho,J., J. Choi, and T. Kim, 2010, International Diversification When Equity Returns and Exchange Rates Are Correlated, working paper. Eun, C. S., and B. G. Resnick, 1994, International Diversification of Investment Portfolios: U.S. and Japanese Perspectives, Management Science, 20, 140-161. Lee, S. H., 2010, Global Diversification through International Funds and Mean-Variance Spanning, Capital Market Perspective (published by Korea Capital Market Institute in Korean) Vol 2 No 2, 31-43. Park, H. J., 2009, Issues in Foreign Currency Hedging When Investing in Foreign Equities, Weekly Finance Brief (published by Korea Finance Institute in Korean) Vol 18 No 26, 3-9,
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Appendix: Derivation of Equation (1)
The following table shows the hedging positions and resulting cumulative profits and losses from the hedged position. We assume that the interest rates are the same for domestic and foreign countries. This implies that forward rates are equal to the spot rates. The fund intends to maintain the target hedge ratio of α. Value of Non-hedged Time Fund
Short Positions in F/X Forwards Taken at t
Cumulative Profits and Losses from Forward Contracts as of time i
0
NAV0 S0
α NAV0
n.a.
1
NAV1 S1
α (NAV1 –NAV0)
α NAV0 (S0 –S1)
2
NAV2 S2
α (NAV2 –NAV1)
α NAV0 (S0 –S2) + α (NAV1 –NAV0) (S1 –S2)
3
NAV3 S3
α (NAV3 –NAV2)
α NAV0 (S0 –S3) + α (NAV1 –NAV0) (S1 –S3) + α (NAV2 –NAV1) (S2 –S3)
…
…
…
…
t
NAVt St
α (NAVt –NAVt-1)
α NAV0 (S0 –St) + α (NAV1 –NAV0) (S1 –St) + α (NAV2 –NAV1) (S2 –St) + … + α (NAVt-1 –NAVt-2) (St-1 –St)
The cumulative profits and losses from forward contracts at time t, can be written as Value of Hedging t = − α NAV0 ( S t − S 0 ) − α
∑
t i =1
( NAVi − NAVi −1 ) ( S t − S i ) .
(A1)
The first term in (A1) represents the profits/losses from the initial position, while the second term, from the rebalanced positions from dynamic hedging. Since hedging is done by taking short positions in F/X forward, as the foreign currency appreciates against the home currency, dynamic hedging will incur losses. This is what happened mostly during the sample period of our empirical analysis. Now, by rearranging the terms in (A1), we can simplify the expression to yield the second term of Equation (1). This completes the proof.
- 28 -
Table 1 Correlation between Foreign Asset Returns and Currency Returns
This table presents the pair-wise correlation between the destination country’s weekly stock index returns and the weekly currency returns for selected countries around the world including BRICs countries between 1996 and 2009. Currency returns are based on home currency price of the destination currency. Panel A reports the results for the full period and panels B and C present the results for two sub-periods. Bold letters indicate statistical significance at 5% level. Panel A: 1996 - 2009 Brazil China Germany Brazil -0.22 -0.17 China 0.25 0.05 Germany 0.07 -0.10 Home HK 0.01 0.06 0.26 Countries India 0.19 -0.27 -0.01 Japan 0.02 0.23 0.13 Korea -0.01 -0.24 -0.11 Russia 0.03 0.07 -0.07 Taiwan 0.02 0.19 -0.31 UK 0.16 -0.14 -0.02 US 0.05 0.05 0.26
HK -0.29 -0.02 -0.12 -0.29 -0.02 -0.32 -0.10 -0.39 -0.19 0.07
Destination Countries India Japan Korea Russia Taiwan -0.10 -0.37 -0.07 -0.25 -0.14 0.41 -0.19 0.24 -0.11 0.31 -0.04 -0.13 0.06 0.15 -0.14 0.42 -0.20 0.25 -0.11 0.31 0.07 -0.28 0.18 -0.17 0.25 0.31 -0.07 0.12 -0.09 -0.33 -0.27 -0.08 0.05 -0.16 0.02 0.01 0.18 -0.26 0.22 -0.17 0.06 0.08 -0.18 0.20 -0.18 0.43 -0.19 0.25 -0.11 0.31
UK -0.15 0.15 0.09 0.14 0.03 0.21 -0.17 0.05 0.06
US -0.35 -0.02 0.05 0.00 -0.26 0.20 -0.25 -0.09 -0.13 -0.05
0.15
Panel B: 1996 - 2002 Brazil China Germany Brazil -0.08 -0.06 China 0.00 0.12 Germany -0.02 -0.03 Home HK 0.00 0.12 -0.01 Countries India 0.10 -0.06 0.00 Japan 0.10 -0.11 0.02 Korea -0.05 -0.10 -0.04 Russia -0.08 0.14 -0.16 Taiwan 0.08 -0.30 -0.01 UK 0.01 0.03 0.13 US 0.02 0.00 0.12
HK -0.15 0.01 -0.06 -0.09 -0.17 -0.20 -0.08 -0.40 0.00 0.03
Destination Countries India Japan Korea Russia Taiwan -0.03 -0.15 -0.03 -0.21 -0.03 0.13 -0.08 0.12 -0.22 0.24 0.08 -0.17 -0.12 -0.01 0.10 0.14 -0.08 0.12 -0.22 0.24 -0.09 0.11 -0.23 0.18 0.05 0.03 0.16 -0.23 -0.05 -0.14 0.06 -0.26 0.02 -0.10 -0.08 0.00 -0.01 -0.11 0.11 -0.25 0.08 0.07 0.18 -0.20 0.20 0.13 -0.08 0.12 -0.22 0.24
UK -0.04 -0.08 0.06 -0.08 -0.09 -0.08 -0.13 0.01 -0.12
US -0.18 0.05 0.10 -0.13 -0.02 0.09 -0.10 -0.09 -0.05 0.22
-0.08
Panel C: 2003 - 2009 Brazil China Germany Brazil -0.39 -0.44 China 0.42 0.24 Germany 0.23 -0.28 Home HK 0.01 0.43 0.24 Countries India 0.33 -0.43 -0.03 Japan 0.37 0.19 0.44 Korea 0.10 -0.50 -0.35 Russia 0.08 0.32 -0.15 Taiwan 0.34 -0.33 0.12 UK 0.19 -0.27 -0.17 US 0.06 0.43 0.23
HK -0.49 -0.02 -0.30 -0.48 0.21 -0.57 -0.23 -0.38 -0.37 0.11
Destination Countries India Japan Korea Russia Taiwan -0.17 -0.60 -0.17 -0.36 -0.32 0.58 -0.34 0.46 0.26 0.42 0.10 -0.37 0.35 -0.06 -0.05 0.58 -0.34 0.46 0.26 0.43 0.01 -0.08 -0.49 0.32 0.44 0.52 0.33 0.25 -0.17 -0.58 -0.30 -0.40 0.03 0.21 -0.39 0.35 0.10 0.35 -0.44 0.44 0.08 -0.42 0.25 -0.10 -0.11 0.59 -0.34 0.46 0.26 0.43
- 29 -
UK -0.28 0.30 0.17 0.30 0.12 0.47 -0.26 0.17 0.21 0.30
US -0.55 -0.03 -0.06 0.05 -0.42 0.32 -0.50 -0.15 -0.23 -0.22
Table 2 Sample Descriptive Statistics
This table presents the descriptive statistics of the mutual funds in our sample. The sample includes all foreign currency denominated mutual funds available in the Korean market that provide both hedging option and non-hedging options for retail investors. For each fund in the sample, the table shows the type, its masked ID, and the number of paired weekly returns available. The next two columns present the total asset under management separately for nonhedged assets and hedged assets. The next column presents the currency that the fund targets to hedge (for hedged assets). The last two columns report the correlation between weekly currency return and two proxies of underlying return, respectively. First proxy is the weekly return of the hedged portfolio and the second proxy is implied underlying return defined as the non-hedged return minus currency return divided by one plus the currency return. The sample period is from March 2007 to July 2009. Fund ID Number Asset under Mgmt (KRW bil) (masked) of Weeks Hedged Non-Hedged Regional China 1 23 1.1 0.3 2 22 28.2 92.5 3 19 67.9 4.7 4 54 0.5 0.2 5 91 22.8 1.0 6 90 0.7 0.0 Japan 7 123 18.4 9.7 8 119 0.0 0.8 Latin America 9 42 7.2 0.2 10 106 15.8 0.2 11 68 0.6 0.0 Emerging 12 55 5.1 0.4 13 82 20.5 0.5 14 42 2.1 3.4 BRICs 15 45 2.9 1.7 Europe 16 118 8.7 0.2 Middle East 17 66 11.4 0.7 Global 18 75 12.7 1.2 Sector Energy 19 62 1.7 0.1 Fund Type
Commodities Average
20
105
4.91
0.0
21 22
42 42
0.51 19.14
1.3 0.3
23
117
119.11
0.5
24
106
41.48
0.2
25 26 27
77 42 65 70.3
5.65 10.56 20.59 16.7
0.1 5.1 10.7 5.0
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Hedging Correlation between FX and Currency Hedged Implied Underlying HKD -0.520 -0.896 HKD -0.226 -0.406 HKD -0.086 -0.242 HKD -0.590 -0.757 HKD -0.541 -0.643 HKD -0.554 -0.730 JPY -0.700 -0.807 JPY -0.530 -0.787 USD -0.674 -0.693 USD -0.568 -0.639 USD -0.332 -0.752 USD -0.506 -0.609 USD -0.560 -0.619 Euro -0.603 -0.648 USD -0.668 -0.741 Euro -0.364 -0.520 USD -0.291 -0.341 USD -0.488 -0.570 USD -0.237 -0.440 Euro50% + USD45% + -0.411 -0.568 JPY5% USD -0.599 -0.616 USD -0.556 -0.602 SF + GBP + -0.409 -0.911 Euro; equally SF + GBP + -0.241 -0.809 Euro; equally USD -0.491 -0.572 USD -0.578 -0.617 USD -0.613 -0.704 -0.479 -0.639
Table 3 Distribution of Weekly Return Volatility: Hedged Assets vs. Non-Hedged Assets
This table presents return volatility comparison between foreign assets that hedge against the foreign currency risk and those that do not hedge. The first four columns present the type, its masked ID, and the number of paired weekly returns available. The next two columns present the standard deviation of the weekly returns for both hedged assets and non-hedged assets in each of our sample funds. The final column presents the difference in volatility between the hedged group and the non-hedged group. The last four rows show the means and medians as well as the corresponding test statistics. The sample period is from March 2007 to July 2009. Fund Type
Fund ID Numver of (masked) Weeks Regional China 1 23 2 22 3 19 4 54 5 91 6 90 Japan 7 123 8 119 Latin America 9 42 10 106 11 68 Emerging 12 55 13 82 14 42 BRICs 15 45 Europe 16 118 Middle East 17 66 Global 18 75 Sector Energy 19 62 20 105 21 42 22 42 23 117 24 106 25 77 Commodities 26 42 27 65 Mean t-stat Median p-value
Standard Deviation of Weekly Returns Hedged (A) Non-Hedged (B) Difference: (A)-(B) 2.30% 2.29% 0.01% 2.82% 3.30% -0.49% 2.04% 2.69% -0.64% 3.78% 3.11% 0.67% 5.18% 4.19% 1.00% 3.30% 2.96% 0.34% 3.90% 2.45% 1.45% 3.92% 2.43% 1.49% 9.29% 7.76% 1.53% 5.86% 5.07% 0.79% 5.19% 4.69% 0.50% 4.91% 4.35% 0.56% 4.06% 3.43% 0.63% 8.45% 7.52% 0.93% 7.09% 5.94% 1.14% 3.12% 3.05% 0.06% 5.16% 5.41% -0.25% 3.74% 3.34% 0.40% 3.31% 3.67% -0.36% 4.11% 3.67% 0.44% 11.69% 8.03% 3.66% 5.78% 5.02% 0.76% 3.85% 3.01% 0.84% 5.41% 5.01% 0.41% 5.97% 5.90% 0.07% 9.61% 8.37% 1.24% 6.55% 5.63% 0.93% 5.20% 4.53% 0.67% 4.16 4.91% -
- 31 -
4.19% -
0.63% 0.000
Table 4 Differences in Volatility between Hedged and Non-Hedged Assets: Cross-Sectional Analysis
This table presents OLS regression results where the dependent variable is the difference in volatility between hedged asset and non-hedged asset within each of the mutual fund pairs in our sample. The difference is measured as standard deviation of weekly returns of the hedged portfolio minus the corresponding number of the non-hedged portfolio. Correlation between the underlying and the currency return are calculated for each mutual fund using weekly return. Underlying return is proxied by the hedged portfolio’s return We take the natural log of assets under management (KRW million) to control for potential size related effect. Non-USD Currency is the dummy variable set to one of the currency being hedged is other than the US dollar and zero otherwise. t-statistics are presented in parentheses. ***, **, * correspond respectively to statistical significance at 1, 5, and 10%. The sample period is from March 2007 to July 2009. (1) Correlation between Underlying and Currency Return
(2)
-0.036*** (-4.592)
ln(Asset Under Mgmt, Hedged)
ln(Asset Under Mgmt, Unhedged)
-0.033*** (-4.051)
(3) -0.035*** (-4.324)
0.001 (0.865)
0.001 (1.208) -0.001 (-0.358)
-0.011** (-2.678)
-0.030*** (-3.395) -0.001 (-1.405)
Number of Weeks
2
-0.036*** (-4.473)
(5)
-0.001 (-1.214)
Non-USD Currency
Constant
(4)
-0.006 (-0.820)
-0.003 (-0.895) 0.000 (0.250)
0.000 (0.863)
-0.010** (-2.174)
-0.011** (-2.371)
-0.007 (-0.827)
R
0.458
0.496
0.460
0.459
0.521
N
27
27
27
27
27
- 32 -
Table 5 Distribution of Geometric Average Weekly Return: Hedged Assets vs. Non-Hedged Assets
This table presents geometric average return for each of the mutual fund pairs in the sample. The first column presents the masked ID as in tables I and II. The next four columns present the averages of weekly returns for the hedged asset, non-hedged asset, corresponding currency, and implied underlying asset. Implied underlying returns are measured as the non-hedged return minus currency return divided by one plus the currency return. The final two columns present the difference between hedged and non-hedged returns as well as those between hedged and implied underlying returns. The last four rows show the means and medians as well as the corresponding test statistics. The sample period is from March 2007 to July 2009. Fund ID (masked)
Hedged
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Mean t-stat
(A) 1.52% 1.33% 1.41% 0.08% -0.73% -0.26% -0.68% -0.68% -0.21% -0.28% -0.41% -0.63% -0.63% -0.65% -0.93% -0.56% -1.41% -0.99% -0.20% -0.51% -0.53% -0.42% -0.46% -0.58% -0.50% -0.06% -0.90% -0.33% -2.45
Median p-value
-0.51% 0.000
Geometric Averages of Weekly Returns Implied Non-Hedged Currency Underlying Difference (D) = [(B) - (C)] (B) (C) / [1+(C)] (A) - (B) (A) - (D) 1.52% -0.36% 1.88% 0.00% -0.36% 1.08% -0.26% 1.35% 0.25% -0.02% 0.60% -0.91% 1.52% 0.80% -0.12% 0.46% 0.40% 0.05% -0.38% 0.03% -0.26% 0.37% -0.63% -0.47% -0.10% 0.06% 0.38% -0.32% -0.32% 0.06% -0.18% 0.45% -0.62% -0.50% -0.06% -0.10% 0.47% -0.57% -0.58% -0.11% 0.20% 0.29% -0.09% -0.41% -0.12% 0.07% 0.31% -0.24% -0.36% -0.04% -0.42% 0.37% -0.78% 0.00% 0.37% -0.04% 0.41% -0.45% -0.59% -0.18% -0.15% 0.40% -0.55% -0.48% -0.09% -0.28% 0.20% -0.48% -0.37% -0.17% -0.30% 0.37% -0.67% -0.64% -0.27% -0.18% 0.31% -0.49% -0.38% -0.07% -0.95% 0.43% -1.37% -0.46% -0.04% -0.51% 0.42% -0.92% -0.48% -0.07% 0.18% 0.39% -0.22% -0.38% 0.02% -0.19% 0.35% -0.53% -0.33% 0.02% -0.52% 0.29% -0.81% -0.02% 0.27% -0.02% 0.29% -0.32% -0.39% -0.10% -0.09% 0.79% -0.87% -0.37% 0.41% -0.17% 0.88% -1.04% -0.41% 0.46% -0.05% 0.41% -0.46% -0.45% -0.04% 0.58% 0.29% 0.29% -0.64% -0.35% -0.37% 0.43% -0.80% -0.53% -0.10% 0.00% 0.30% -0.30% -0.33% -0.03% -0.01 4.66 -2.05 -5.56 -0.73 -0.10% 0.122
0.37% 0.000
-0.49% 0.002
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-0.39% 0.000
-0.07% 0.052
Table 6 Differences in Return between Hedged and Implied Underlying Assets: Cross-Sectional Analysis
This table presents OLS regression results where the dependent variable is the geometric average weekly return of hedged asset minus the geometric average weekly return of implied underlying asset within each of the mutual fund pairs in our sample. Implied underlying return is inferred as the non-hedged return minus currency return divided by one plus the currency return. Correlation between the underlying - proxied by hedged portfolio - and the currency return are calculated for each mutual fund using weekly return. We take the natural log of assets under management (KRW million) to control for potential size related effect. Non-USD Currency is the dummy variable set to one of the currency being hedged is other than the US dollar and zero otherwise. t-statistics are presented in parentheses. ***, **, * correspond respectively to statistical significance at 1, 5, and 10%. The sample period is from March 2007 to July 2009.
(1) Correlation between Underlying and Currency Return
0.005* (1.938)
(2) 0.005** (2.099)
(3)
(4)
0.005* (1.942)
0.007** (2.848)
Hedged Return STD
0.006 (0.355)
0.025 (1.397)
Currency Return STD
0.102*** (3.473)
0.079** (2.673)
ln(Asset Under Mgmt, Hedged)
0.000 (0.217)
-0.000 (-0.244)
ln(Asset Under Mgmt, Unhedged)
-0.000 (-0.847)
-0.000 (-1.192)
Non-USD Currency
-0.000 (-0.181)
0.000 (0.385)
0.000* (1.824)
0.000* (1.882)
Number of Weeks
Constant
0.002 (1.609)
-0.002 (-1.260)
0.001 (0.539)
-0.001 (-0.513)
R
0.131
0.456
0.336
0.622
N
27
27
27
27
2
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Table 7 Differences in Return between Hedged and Implied Underlying Assets: Cross-Sectional Analysis based on 5 Week Intervals
For all weekly returns available in the sample, we group them by 5 week, and calculate geometric average weekly returns, standard deviations, and correlations between the underlying –proxied by hedged portfolio - and currency return for each of the 5 week interval. Hence, the unit of observation here is each 5 week interval rather than the whole life of a fund. We run OLS regressions similar to those reported in table 6. Dependent variable is the difference in geometric average weekly return between hedged asset and implied underlying asset for each of the 5 week intervals as defined above. Implied underlying return is inferred as the non-hedged return minus currency return divided by one plus the currency return. t-statistics are presented in parentheses. ***, **, * correspond respectively to statistical significance at 1, 5, and 10%. The sample period is from March 2007 to July 2009.
(1) Correlation between Underlying and Currency Return
(2)
0.002** (2.528)
(3)
(4)
0.003*** (2.924)
-0.002 (-0.890)
0.003 (1.298)
Hedged Return STD
0.023 (1.495)
0.054* (1.677)
0.061* (1.932)
Currency Return STD
0.006 (0.282)
0.062** (1.996)
0.074** (2.378)
Correlation*Hedged Return STD
0.044 (0.909)
-0.070 (-1.165)
Correlation*Currency Return STD
0.130** (2.417)
-0.003 (-0.042)
Correlation*Hedged Return STD *Currency Return STD Constant
2.598*** (3.066) 0.001 (1.390)
-0.000 (-0.194)
R
0.017
N
370
2
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-0.002** (-1.998)
-0.003** (-2.552)
0.025
0.049
0.073
370
370
370
Figure 1. Overseas Stock Index Levels vs. Foreign Exchange Rates: Korean Case
This figure plots weekly overseas stock index levels and value of the corresponding foreign currency denominated in Korean Won for selected markets between 1996 and 2009. In panel A, overseas stock market is US and the foreign exchange rate is the value of US dollar denominated in Korean Won (i.e. KRW/US$). In panels B and C, the corresponding overseas markets are Hong Kong and Japan, respectively. Panel A: US Stock Index vs. KRW/US$
US Stock Index 1,800
KRW/US$ 2,000
KRW/US$
1,800
US Stock Index
1,600
1,600 1,400
1,400 1,200 1,200 1,000 1,000 800 800 600 600 400
400
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7/5/2009
1/5/2009
7/5/2008
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7/5/2007
1/5/2007
7/5/2006
1/5/2006
7/5/2005
1/5/2005
7/5/2004
1/5/2004
7/5/2003
1/5/2003
7/5/2002
1/5/2002
7/5/2001
1/5/2001
7/5/2000
1/5/2000
7/5/1999
1/5/1999
7/5/1998
1/5/1998
7/5/1997
1/5/1997
7/5/1996
200
1/5/1996
200
- 37 -
KRW/Yen 18
2
7/5/2009
1/5/2009
7/5/2008
1/5/2008
7/5/2007
1/5/2007
7/5/2006
1/5/2006
7/5/2005
1/5/2005
7/5/2004
1/5/2004
7/5/2003
1/5/2003
7/5/2002
1/5/2002
7/5/2001
1/5/2001
7/5/2000
1/5/2000
7/5/1999
1/5/1999
7/5/1998
1/5/1998
7/5/1997
1/5/1997
7/5/1996
1/5/1996
KRW/HK$ 250
1/5/2009
16
1/5/2008
1/5/2007
1/5/2006
1/5/2005
1/5/2004
1/5/2003
1/5/2002
1/5/2001
1/5/2000
1/5/1999
1/5/1998
1/5/1997
1/5/1996
Figure 1 - continued
Panel B: Hong Kong Stock Index vs. KRW/US$ HK Stock Index 5,000
KRW/HK$
HK Stock Index
200
150
100
50
-
Japanese Stock Index
4,500
4,000
3,500
3,000
2,500
2,000
1,500
1,000
500
-
Panel C: Japanese Stock Index vs. KRW/US$
Japanese Stock Index 3,500
KRW/Yen
3,000
14
12 2,500
10 2,000
8 1,500
6
4 1,000
500
-
Figure 2. Relationship between Differences in Volatility (Hedged vs. Non-Hedged) and Return Correlation (Underlying vs. Currency)
Y-axis represents differences in standard deviations between hedged and non-hedged assets using weekly returns for each of the funds in the sample. Ini panel A, X-axis represents the correlation between the underlying – proxied by hedged portfolio - and currency returns for each of the mutual funds in our sample. In panel B, underlying return is inferred as the non-hedged return minus currency return divided by one plus the currency return. Each dot in the figure represents one mutual fund. The sample period is from March 2007 to July 2009. Panel A: Underlying Proxied by Hedged Portfolio Hedged S.D Unhedged S.D 4.00% 3.50% 3.00% 2.50% 2.00% 1.50% 1.00% 0.50%
-80.00%
-70.00%
-60.00%
-50.00%
-40.00%
-30.00%
-20.00%
0.00% -10.00% 0.00% -0.50% -1.00%
Correlation between Hedged Portfolio and Currency Return - 38 -
Figure 2 - continued
Panel B: Implied Underlying Hedged S.D Unhedged S.D 4.00% 3.50% 3.00% 2.50% 2.00% 1.50% 1.00% 0.50% 0.00% -100.00 -90.00% -80.00% -70.00% -60.00% -50.00% -40.00% -30.00% -20.00% -10.00% 0.00% % -0.50% -1.00% Correlation between Underlying and Currency Return
- 39 -
