THE JOURNAL OF FINANCE•VOL.LXV,NO.1•FEBRUARY2010
Global Currency Hedging
JOHN Y.CAMPBELL,KARINE SERFATY-DE MEDEIROS,and LUIS M.VICEIRA∗
ABSTRACT
Over the period1975to2005,the U.S.dollar(particularly in relation to the Canadian
dollar),the euro,and the Swiss franc(particularly in the cond half of the period)
moved against world equity markets.Thus,the currencies should be attractive
to risk-minimizing global equity investors despite their low average returns.The
risk-minimizing currency strategy for a global bond investor is clo to a full currency
hedge,with a modest long position in the U.S.dollar.There is little evidence that risk-
minimizing investors should adjust their currency positions in respon to movements
in interest differentials.
W HAT ROLE SHOULD FOREIGN currency play in a diversified investment portfolio? In practice,many investors appear reluctant to hold foreign currency directly, perhaps becau they e currency as an investment with high volatility and low average return.At the same time,many investors hold indirect positions in foreign currency when they buy foreign equities or bonds without hedging the currency exposure implied by the foreign ast holding.Such investors receive the foreign currency excess return on their foreign asts,plus the return on foreign currency.hilook
陈展鹏电视剧In this paper,we consider an investor with an exogenous portfolio of equities or bonds and ask how the investor can u foreign currency to manage the risk of the portfolio.We assume that the investor’s domestic money market is riskless in real terms,and u mean-variance analysis tofind the foreign currency positions that minimize the risk of the total portfolio.We consider ven major developed market currencies,namely,the U.S.dollar,euro,Japane yen,Swiss franc,pound sterling,Canadian dollar,and Australian dollar,over the period 1975to2005.Any of the can be the investor’s domestic currency or can be available as a foreign currency.We assume a one-quarter investment horizon, but obtain similar results for horizons ranging from1month to1year. Although our framework is standard,and has been applied to U.S.holdings of foreign currencies by Glen and Jorio
n(1993),our implementation and empirical ∗Campbell is from the Department of Economics,Harvard University,and NBER.Serfaty-de Medeiros is from OC&C Strategy Consultants.Viceira is from Harvard Business School,NBER, and CEPR.Viceira acknowledges thefinancial support of the Division of Rearch of the Harvard Business School.We are grateful to Anna Milanez and Johnny Kang for rearch assistance,and to Cam Harvey(the editor),an anonymous referee,Roderick Molenaar,Sam Thompson,Tuomo Vuolteenaho,and minar participants at Brandeis University,Boston University,the University of Illinois at Urbana-Champaign,Harvard University,and the Stockholm School of Economics for comments and suggestions.
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results are novel in veral respects.Following Glen and Jorion,we start by considering an equity investor who choosfixed currency weights to minimize the unconditional variance of her portfolio.Such an investor wishes to hold currencies that are negatively correlated with equities.Ourfirst novel result is that our ven currencies lie along a spectrum.At one extreme,the Australian dollar and the Canadian dollar are positively correlated with local-currency returns on equi
ty markets around the world,including their own domestic markets.At the other extreme,the euro and the Swiss franc are negatively correlated with world stock returns and their own domestic stock returns.The Japane yen,the British pound,and the U.S.dollar fall in the middle,with the yen and the pound more similar to the Australian and Canadian dollars, and the U.S.dollar more similar to the euro and the Swiss franc.
When we consider currencies in pairs,wefind that risk-minimizing equity investors should short tho currencies that are more positively correlated with equity returns and should hold long positions in tho currencies that are more negatively correlated with returns.When we consider all ven currencies as a group,wefind that optimal currency positions tend to be long the U.S.dollar, the Swiss franc,and the euro,and short the other currencies.A long position in the U.S.–Canadian exchange rate is a particularly effective hedge against equity risk.
We obtain a cond novel result when we consider the risk-minimization problem of global bond investors rather than global equity investors.Wefind that most currency returns are almost uncorrelated with bond returns and thus risk-minimizing bond investors should avoid holding currencies;that is, they should fully currency-hedge their international bond positions.This is consistent with common practice of institutional investors,although global bond mutual funds are avai
lable with or without currency hedging.The U.S. dollar is an exception to the general pattern in that it tends to appreciate when bond prices fall,that is when interest rates ri,around the world.This generates a modest demand for U.S.dollars by risk-minimizing bond investors. In capital market equilibrium,one might expect that average currency re-turns would reflect the risk characteristics of currencies.Specifically,if rerve currencies are attractive to risk-minimizing global equity investors,the cur-rencies might offer lower returns in equilibrium.We analyze the historical av-erage returns on currency pairs and obtain a third novel result,that high-beta pairs have delivered higher average returns.However,the historical reward for taking equity beta risk in currencies has been quite modest,and much smaller than the historical average excess return on a global stock index.
Another way tofind a risk-return relation in foreign currencies is to condi-tion upon currency characteristics that are known to predict currency returns, and to ask whether the characteristics predict currency risks.Following an extensive literature on the predictive power of interest differentials for cur-rency returns,we u deviations of interest differentials from their time-ries averages as conditioning variables,imposing the constraint that they have the same effects on currency covariances regardless of the particular currency pair under consideration.Our fourth novel
result is that increas in interest rates have only modest effects on currency-equity covariances.Over the full
Global Currency Hedging89 sample period,and particularly thefirst half of the sample,increas in inter-est differentials are,if anything,associated with decreas in the covariances. This implies that risk-minimizing equity investors should tilt their portfolios towards currencies that have temporarily high interest rates,amplifying the speculative“carry trade”demands for such currencies rather than offtting them.
The organization of the paper is as follows.Section I ts the stage by briefly reviewing the related literature.Section II describes our data and conducts pre-liminary statistical analysis of stock,bond,and currency returns.Section III lays out the analytical framework we u for our empirical analysis and prents unconditionally optimal currency hedges for equity portfolios,and Section IV reports the analogous results for bond portfolios.Section V discuss the relation between unconditional risks of currencies and their unconditional average returns.Section VI introduces the possibility of conditional hedging, varying currency positions in respon to interest differentials.Section VII quantifies the risk reductions that are achievable with an unconditional or conditional currency hedging strategy,and discuss the effects of currency hedging on the Sharpe r
atios of equity and bond portfolios.Section VIII con-cludes.The Internet Appendix prents analytical details and additional em-pirical results.1
I.Literature Review
The academicfinance literature has explored a number of reasons investors might want to hold foreign currency.The can be divided into risk manage-ment demands,resulting from covariances of foreign currency with the state variables that determine investors’marginal utility,and speculative demands, resulting from positive expected excess returns on foreign currency over do-mestic safe asts.2
One type of risk management demand aris if there is no domestic ast that is riskless in real terms,for example,becau only nominal bills are available and there is uncertainty about the rate of inflation.In this ca,the minimum-variance portfolio may contain foreign currency(Adler and Dumas(1983)).This effect can be substantial in countries with extremely volatile inflation,such as some emerging markets,but is quite small in developed countries over short time intervals.Campbell,Viceira,and White(2003)show that it can be more important for investors with long time horizons becau nominal bills subject investors tofluctuations in real interest rates,whereas no
minal bonds subject them to inflation uncertainty,which is relatively more important at longer horizons.If domestic inflation-indexed bonds are available,however,they are 1An Internet Appendix for this article is online in the“Supplements and Datats”ction at /supplements.asp.
2Risk management demands are more commonly called hedging demands,but this can create confusion in the context of foreign currency becau hedging a foreign currency corresponds to taking a short position to cancel out an implicit long position in that currency.In this paper we u foreign currency terminology and avoid the u of the term hedging demand for asts.
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riskless in real terms if held to maturity and thus drive out foreign currency from the minimum-variance portfolio.
Another type of risk management demand for foreign currency aris if an investor holds other asts for speculative reasons,and foreign currency is correlated with tho asts.For example,an investor may wish to hold a globally diversified equity portfolio.If the foreign currency excess return on foreign equities is negatively correlated with the return on the foreign currency (as would be the c
a,for example,if stocks are real asts and the shocks to foreign currency are primarily related to foreign inflation),then an investor holding foreign equities can reduce portfolio risk by holding a long position in foreign currency.This type of risk management currency demand is the subject of this paper.
Many international investors think not about the foreign currency positions they would like to hold,but about the currency hedging strategy they should follow.3An unhedged position in international equity,for example,corresponds to a long position in foreign currency equal to the equity holding,whereas a fully hedged position corresponds to a net zero position in foreign currency.When currencies and equities are uncorrelated,risk management demands for foreign currencies are zero,implying that in the abnce of speculative demands,full hedging is optimal(Solnik(1974)).Empirically,Perold and Schulman(1988)find that U.S.investors can reduce volatility by fully hedging the currency exposure implicit in internationally diversified equity and bond portfolios. We derive optimal hedging strategies for global equity and bond investors. Like Glen and Jorion(1993),wefind that optimal currency hedging substan-tially reduces risk for equity investors.The benefits of optimal hedging are large even in countries like Canada where full hedging is actually riskier than no hedging at all.We report results for quarterly returns,but the results are r
过年送什么给长辈obust to variation in the investment horizon between1month and1year. Froot(1993)studies the dollar and the pound over a longer sample period and finds that risk-minimizing foreign currency positions increa with the invest-ment horizon,implying that long-horizon equity investors should not hedge their currency risk.We do notfind this horizon effect in our post-1975data t. Speculative currency demands require that investors perceive positive ex-pected excess returns on foreign currencies.A unique feature of currencies is that investors in every country can simultaneously perceive positive expected excess returns on foreign currencies over their own domestic currencies.That is,a U.S.investor can perceive a positive expected excess return on euros over dollars,whereas a European investor can at the same time perceive a posi-tive expected excess return on dollars over euros.This possibility aris from Jenn’s inequality and is known as the Siegel paradox(Siegel(1972)).It can explain symmetric speculative demand for foreign currency by investors bad in all countries.风中奇缘演员表
In practice,however,the speculative currency demand generated by this ef-fect is quite modest.If currency movements are log normally distributed and
3For a discussion of currency hedging from a practitioner’s perspective,e Jorion(1989)or the other papers collected in Thomas(1990).时光荏苒是什么意思
Global Currency Hedging91 the expected excess log return on foreign currency over domestic currency is zero(a condition that can be satisfied for all currency pairs simultaneously), then the expected excess simple return on foreign currency is one-half the variance of the foreign currency return.With a foreign currency standard de-viation of about10%per year,the expected excess foreign currency return is 50basis points and the corresponding Sharpe ratio is only0.05.A Sharpe ratio this small generates little demand from investors with typical levels of risk aversion.
A more important source of speculative currency demand aris from ex-pected excess returns on particular currencies,as oppod to all currencies simultaneously.Although unconditional average excess returns on currencies are clo to zero,there is evidence that conditional expected excess returns on currencies undergo short-termfluctuations that constitute the basis for active currency strategies.Most obviously,the literature on the forward premium puz-zle(Hann and Hodrick(1980),Fama(1984),Hodrick(1987),Engel(1996)) shows that currencies with high short-term interest rates deliver high returns on average.The currency carry trade,which exploits this phenomenon by hold-ing high-rate currencies and shorting low-rate currencies,was extremely prof-itable in and beyond our sample period until2008(Burnside et al.(2006), Brunnermeier,Nagel,and Pedern(2009)).
It is natural to ask whether the carry trade has risk characteristics that offt its profitability.Farhi and Gabaix(2008)argue that high-rate curren-cies are expod to the risk of rare economic disasters,whereas Lustig and Verdelhan(2007)find that high-rate currencies,in a sample that includes emerging market currencies,have higher nsitivity to sumption growth.We u nsitivity to world stock returns as a measure of risk,and find that developed market currencies with high unconditional average inter-est rates do have somewhat higher betas with the world stock market,but that there is no tendency for a currency who interest rate is temporarily high to have a temporarily higher beta.Over our full sample period and in thefirst half of the sample,currency betas even have a weak tendency to decline when interest rates increa.Thus,risk considerations might deter equity investors from implementing an unconditional form of the carry trade,but a conditional form of the trade that invests in currencies with temporarily high interest rates should be attractive even to risk-aver equity investors.
II.Data and Summary Statistics
Our empirical analysis us stock return data from Morgan Stanley Capi-tal International,and data on exchange rates,short-term interest rates,and long-term bond yields from the International Financial Statistics databa pub-lished by the International Monetary Fund.4We calculate log bond
returns from yields on long-term bonds using the approximation suggested in Campbell,Lo, 4In the ca of the Swiss short-term interest rate,our data source is the Organisation for Eco-nomic Co-operation and Development(OECD).We u euro-money rates up to1989,and London Interbank Offered Rate(LIBOR)rates afterwards,as published by the OECD.
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and MacKinlay(1997).5The data ries are available at a monthly frequency, and we report results for veral different investment horizons in the Internet Appendix,but our basic analysis assumes a one-quarter horizon and therefore runs monthly regressions of overlapping quarterly excess returns.We report results for ven developed economies:Australia,Canada,Euroland,Japan, Switzerland,the United Kingdom,and the United States.The sample period starts in July1975,the earliest date for which we have data available for all variables and for all ven markets,and ends in December2005.
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We define“Euroland”as a value-weighted stock basket that includes Ger-many,France,Italy,and the Netherlands.The are the countries in the euro zone for which we have the longest record of stock total returns,interest rates, and exchange rates.For simplicity,we refer to the Euroland stock portfolio
as a“country”stock portfolio when describing our empirical results,even though this is not literally correct.With regard to currencies,prior to1999we refer to a basket of currencies from tho countries,with weights given by their relative stock market capitalization,as the“euro.”
Of cour,our definition of Euroland implies some look-ahead bias,becau in1975it would not have been obvious whether a European monetary union would occur,or which countries from the region would have been part of that union.However,one can reasonably argue that the countries would have been candidates,and that from the perspective of today’s investors,it proba-bly makes n to consider the markets as a single market.We have also conducted our analysis including only Germany in Euroland and using the deutschemark to proxy for the euro before1999;this procedure gives very similar results.
Table I reports the full-sample annualized mean and standard deviation of short-term nominal interest rates,log stock,and bond returns in excess of their local short-term interest rates,changes in log exchange rates with respect to the U.S.dollar,and log currency excess returns with respect to the dollar. The means of log excess returns(geometric averages)are adjusted for Jenn’s Inequality by adding one-half their variance to convert them into mean simple excess returns(arithmetic averages).
Annualized average nominal short-term interest rates differ across coun-tries.They are lowest for Switzerland and Japan,and highest for Australia, 5This approximation to the log return on a coupon bond is
r c,n,t+1=D cn y cnt−(D cn−1)y c,n−1,t+1,
where r c,n,t+1denotes the log return on a coupon bond with coupon rate c and n periods to maturity, y cnt≡log(1+Y cnt)denotes the log yield on this bond at time t,and D cn is its duration,which we approximate as
D cn=1−(1+Y cnt)−n 1−(1+Y cnt)−1
.
In our computations we treat all bonds as having a maturity of10years,and assume that bonds are issued at par,so that the coupon rate equals the yield on the bond.We also assume that the yield spread between a9-year and11-month bond and a10-year bond is zero.
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