The Exchange Rate Effect of Multi-Currency Risk Arbitrage Harald Hau ∗ University of Geneva and Swiss Finance Institute February 15, 2014 Abstract Carry trade arbitrage strategies typically involve multiple currencies. Limits to arbitrageinsuchasettingnot onlyslowtheadjustmenttothefundamental equi- librium, butcanalsogeneratetransitoryover- or undershootingof eachexchange rate in accordance with the marginal risk contribution of each speculative posi- tiontotheoverallarbitragerisk. Thepaperusesanatural experimenttoidentify a particular global arbitrage opportunity and shows that arbitrage risk hedging modifies the exchange rate dynamics in the predicted manner. New spectral methods are applied to obtain a more precise inference on the cross-sectional trading pattern of the arbitrageurs. JEL classification: G11, G14, G15. Keywords: Speculation, Limited Arbitrage, Hedging, Exchange Rate Disconnect GFRI, University of Geneva, 40 Bd du Pont d’Arve, 1211 Genève 4, Switzerland. Tel.: (++41) 22 379 ∗ 9581. E-mail: [email protected]. Web: http://www.haraldhau.com. I would like to thank Bernard Dumas, Matthias Efing, Denis Gromb, Lucas Menkhoff, Michael Moore, Carol Osler, Hélène Rey, Astrid Schornik, Matti Suominen, Robert Whitelaw, and Charles Wyplosz for valuable comments on the paper. I amalsogratefulforvariouscommentsfollowingpresentationsattheEuropeanCentralbank,HEI(Geneva), Oxford University, the 5th Central Bank Conference on the Microstructure of Financial Markets in Zürich, 2009, and the EFA annual meeting, Frankfurt, 2010. 1 Introduction Notwithstanding the importance of carry trade strategies in international finance, little is known about the structure and exchange rate effects of speculative currency trading itself.1 Thispapercontributestoabetterunderstandinginfourdimensions; it(i)developsastylized model of speculative foreign exchange (FX) trading which highlights the hedging component of any arbitrage strategy involving multiple currencies, (ii) uses the natural experiment of the global MSCI index revision (with its clearly identified currency arbitrage opportunity) to predict the optimal arbitrage strategy of hedge funds, (iii) demonstrate the quantitative importance of risk hedging for the cross-section of short-run exchange rate returns, and (iv) proposes a new spectral inference method to strengthen the statistical evidence on the predicted short-run exchange rate dynamics. It is increasingly recognized that arbitrage occurs under frictions which may modify the validityofarbitragerelationships. Thereversaltopriceefficiencyafterexternalshocksmight be slow (Mitchell, Pedersen and Pulvino, 2007) and/or state contingent in its dependence on market funding (Brunnermeier and Pederson, 2009). Importantly, limited risk tolerance of arbitrageurs and constrained funding access may not only slow equilibrium adjustment, but give raise to new transitory asset pricing effects. In this paper we show how currencies can “overshoot” or “undershoot” because of transitory hedging demands if arbitrageurs pursue arbitrage strategies involving many currencies simultaneously. The degree of over- or undershooting is tied to the marginal risk contribution of each currency position to the overall arbitrage portfolio and can be predicted if the multi-currency arbitrage opportunity is properly identified. Hence, arbitrage frictions not only slow the equilibrium adjustment, but also imply a specific non-linear currency dynamics towards the new equilibrium. 1The terms ‘speculation’ and ‘risk arbitrage’ are used synonomously in line with the empirical literature on limits of arbitage and much of the investment profession. This terminology is different from the classic theoretical definition, which defines arbitrage as a riskless profit opportunity. 1 As a consequence exchange rate models with a direct and linear adjustment towards the fundamental exchange rate are likely to be misspecified. Such misspecification should be particularlypronouncedinaworldofcarrytradestrategieswhichtypicallyinvolveaportfolio of currencies so that risk hedging at the portfolio level becomes an important consideration. Yet, the empirical literature on international arbitrage relationships has largely ignored such a portfolio perspective and tested arbitrage theories based on individual currency pairs. An importantcontributionofourpaperistoshowthatsucharestrictiveapproachisproblematic both at the theoretical and empirical level. Recent empirical work has linked carry trade returns to various risk factors, for exam- ple foreign interest rate spreads over the dollar money market rate (Lustig, Roussanov and Verdelhan, 2010), innovations to global FX volatility (Menkhoff et al., 2011) or global liq- uidity factors (Brunnermeier, Nagel and Pedersen, 2009). Carry trade profits might (at least partially) be interpreted as compensation for risk. Yet the precise structure of currency speculation is not properly identified in such factor models and its effect on asset prices is difficult to disentangle from the underlying arbitrage opportunity, which is itself endogenous to monetary policy and other macroeconomic variables.2 In consideration of these identi- fication problems, this paper uses an event-based exogenous FX arbitrage opportunity and seeks to properly identify the structure and exchange rate effects of currency speculation relative to an (exogenous) arbitrage opportunity. The event approach gains methodological simplicity at the cost of empirical generality due to a focus on a particular data sample. The stylized theoretical part models a multi-currency setting where risk averse currency speculators (like hedge funds) faces a price elastic currency supply in each exchange rate. How does a hedge fund optimally trade if it acquires private information about a perma- nent future currency demand shock? In a multi-currency setting, the hedge fund’s trading 2For research relating uncovered interest parity violations to monetary policy see for example Grilli and Roubini(1992),McCallum(1994),SchlagenhaufandWrase(1995),andAlvarez,Atkeson,andKehoe(2006). 2 risk depends on the entire covariance structure of all currencies. A risk averse hedge fund manager should acquires positions characterized by two distinct components: The premium component isproportionaltotheexpectedexcessreturn; whereastherisk-hedging component is (negatively) proportional to the marginal arbitrage risk of each currency position and re- duces the overall risk. Importantly, such cross-sectional hedging can influence the short-run exchange rate dynamics in a complex manner. An expected premium change in one cur- rency can alter the hedging demand in many other currencies along with their prices; thus contributing to a temporary “disconnect” between exchange rate movements and exchange rate fundamentals.3 The empirical part tests the theoretical framework based on an exogenous market event which allows for a clear identification of the speculators’ optimal positions–including hedg- ingdemands. InDecember2000, themostimportantproviderofinternationalequityindices, Morgan Stanley Capital Inc. (MSCI), announced publicly that it would substantially alter the composition of its global equity indices. As a consequence, many countries experienced dramatic changes in their index representation, which resulted in a reallocation of indexed equity capital from down- to upweighted currencies. A massive exogenous capital realloca- tion of index capital should alter the fundamental value of the respective currency pairs, unless the marginal international investor is indifferent about the currency denomination of his assets. Based on a consultation process conducted by MSCI in November 2000, informed currency speculators were able to predict cross-sectional exchange rate changes in line with anticipated capital flows and to arbitrage their exchange rate effect prior to the official an- nouncement of the index modification. The MSCI global index revision therefore provides a unique occasion to identify an exogenous arbitrage opportunity and trace the price impact of speculative trading in the cross-sectional pattern of currency returns. 3See Obstfeld and Rogoff (2001), and Rogoff and Stavrakeva (2008) for a discussion of the “disconnect puzzle.” 3 Two independent statistical strategies are used to elucidate the structure of speculative trading. First, a classical event study methodology is applied to the MSCI index revision. The cross-section of 37 spot exchange rates exhibits both the positive premium and negative risk-hedging effects. The overall explanatory power of the cross-sectional regression is sub- stantial. Together, the premium and risk-hedging effects account for almost 55 percent of the exchange rate variation over a three-day window and more than 35 percent over a seven- day window. Excluding the risk-hedging effect from the regression reduces its explanatory power by more than half. A robustness check on a subsample of the most liquid curren- cies (using forward rates instead of spot rates) produces very similar results. The MSCI event returns therefore reveal that hedging arbitrage risk matters to currency speculators. Moreover, risk-hedging positions have an economically significant currency effect. The point estimates suggest that the exchange rate return difference between currencies with high and low hedging benefits (separated by two standard deviations in the hedging benefit) amounts to 3.6 percent over the five trading days of the event window. Assuming that such hedging operations by currency speculators are common practice, they could indeed contribute sub- stantially to the short-run dynamics of exchange rates. We know of no other event study which has highlighted the empirical relevance of such FX hedging effects. An obvious shortcoming of the conventional event study is limited statistical power if fewer than 40 cross-sectional observations are used (as is typical for exchange rate stud- ies) and the instances of speculative trading are spread over many event days. Therefore I propose a new statistical methodology based on high-frequency data and inference in the frequency domain to obtain stronger statistical results. The intuition is as follows: Con- sider a group of speculators implementing the optimal multi-currency strategy; they tend to trade sequentially, but synchronized across all currencies. Any non-synchronized position built-up would sacrifice important hedging benefits associated with the portfolio approach to speculative trading. Hence, their price impact across currencies should also be extremely 4 contemporaneous and be reflected in high-frequency comovements across different exchange rates.4 Such high-frequency comovements can be measured as the high-frequency compo- nents of the cospectrum of exchange rate returns. For example, exchange rate pairs for which the arbitrage position is long in both exchange rates should experience positive high- frequency comovements; whereas exchange rate pairs for which the arbitrage positions are long for one and short for the other should exhibit a more negative covariance at the high- est frequencies–corresponding to a negative shift of the high-frequency components of the cospectrum. An important methodological contribution of this paper is to show that the cospectrum at the highest frequencies can be a very powerful aggregator of speculative trading patterns if speculative interventions are very synchronized across currencies or markets as can be expected under portfolio risk considerations. The high liquidity of the exchange rate market allows the use of minute-by-minute price data. The cospectrum between a pair of exchange rate returns can be aggregated into a high-frequency band summing up all comovements withina15-minuteinterval, intoamedium-frequency band forcomovementsfrom15minutes to four hours, and a low-frequency band capturing all remaining comovements. The spectral analysis reveals that a large share of the change in the covariance of exchange rate pairs in the 7-day arbitrage period around MSCI’s pre-announcement of the index change is due to a change in the high-frequency band of the cospectrum. The event-related change in the exchange rate dynamics is characterized by strong cross-sectional return synchronicity. Moreover, the high-frequency cospectrum shift for each currency pair corresponds to the predicted arbitrage positions for the respective currency pair: The event period shift of the high-frequency cospectrum is positive if the speculative positions in both currencies have the same direction (both long or both short). The shift of the high-frequency cospectrum is 4Acommonprocedureistofilterout‘highfrequency’noise,asitisstronglydeterminedbytradingactivity. Thecurrentstudypursuestheoppositeobjectiveofidentifyingparticularpatternsofcross-currencytrading. 5 negative if optimal risk arbitrage requires speculative positions of opposite directions (one short and one long). In the final part of this paper, I showhowcospectral measures can be used to re-estimate thelimitedarbitragemodel. Usingspectralbandregressions,itispossibletorecoverthesame structural coefficients for both the premium and risk-hedging effects of arbitrage trading at much higher levels of statistical significance than in the conventional inference. The smaller standard errors allow me to make a quantitative assessment of the role of currency hedging demands on exchange rate returns. The spectral band regressions show that the (transitory) exchange rate effect of the hedging demand is at least as large as the premium effect. In the following section, I discuss the related literature. Section 3 presents the theory and develops testable hypotheses for both spot and forward exchange rates. Section 4 dis- cusses the MSCI index revision, its implications for the country weight changes, and the arbitrage risk related to an optimal speculative position. Cross-sectional evidence for daily spot rate returns and forward rate returns follows in section 5. Section 6 discusses the spectral methodology and corresponding evidence. Section 7 concludes. 2 Related Literature This paper contributes to the larger literature on exchange rate behavior by focusing on the particularroleofFXarbitragetrading. Abetterunderstandingofspeculativehedgingandits exchange rate effects may potentially reconcile two contrasting puzzles in the exchange rate literature. News,measuredbyabroadsetofmacroannouncementsinAndersenetal. (2003), generate an immediate impact on the exchange rate. But the infrequent occurrence of such public news events implies that the overall percentage of exchange rate variation explained remainsverysmall (EvansandLyons, 2008). Mostof thedailyexchangeratesvariationdoes notappeartorelatetoacontemporaneousmajornewsevents. Contrarytosuchfundamental 6 news proxies, financial market variables capturing (directional) currency trading, such as order flow, feature a high overall correlation with contemporaneous exchange rate changes. Evans and Lyons (2002a, 2002b) document that order flow accounts for between 44 and 78 percent of the daily variation in the spot exchange rate for major currency pairs. Speculative trading can anticipate future events and reduce the exchange rate effect aroundapublicannouncement–somethingwhichhaslongbeenrecognized. Yet,speculative hedging motives and their feedback effect on the exchange rate complicate the exchange rate dynamics further. Private information about future public news in one currency can trigger the build-up and later liquidation of hedging positions (and the corresponding order flow) in correlated currencies even if those currencies are not concerned by the news event itself. A currency may over- or undershoot its equilibrium price depending on its hedging value for correlated arbitrage positions and thus appear disconnected from it own fundamentals. The event study in this paper can elucidate this important aspect of speculative trading. Much of the literature on Uncovered Interest Parity (UIP) is concerned with providing explanations for persistent carry trade returns rather than causal inference on the effects of speculative trading on exchange rates. An exception here is Brunnermeier, Nagel, and Pedersen (2009); they provide evidence that so-called carry trades alter the distribution of exchange rate movements. The negative skewness of target currencies is interpreted as the result of a sudden unwinding of carry trades. Jylhä and Suominen (2011) explore the long- run profitability of carry trade strategies and show that the returns to carry trades have been decreasing over the last 32 years. Moreover, carry trade returns explain a significant part of hedge fund index returns. This paper belongs to a larger finance literature on speculative trading and limited ar- bitrage recently reviewed by Gromb and Vayanos (2011). Market index changes have been frequently used as a suitable exogenous event to analyze speculative trading. Closely related isHau, MassaandPeress(2011), whousethesameMSCIeventtodocument“currencyprice 7 pressure effects” of capital flows. But their analysis does not encompass a portfolio approach and abstracts from all currency hedging central to the analysis in this paper. The MSCI index event is also used in Hau (2011) to study the global integration of equity markets. Similar to this paper, hedging positions are shown to matter for the arbitrageurs, but take a different form, because the equity market speculators could anticipate changes in equity betas. By contrast, the arbitrage opportunity modelled here concerns the FX market and is assumed to be proportional to the capital flow of index investors. Moreover, the statistical inference method is adapted to the small cross-section of currency observations. An important feature of this paper is the multi-asset approach to speculation. Such a portfolio approach has previously been employed for speculative equity trading (Greenwood, 2005) and option pricing (Garleanu, Pedersen, and Poteshman, 2010). But in contrast to these papers, our framework assume that speculators face a price-elastic residual asset sup- ply. This distinguishing model feature implies that speculators can acquire optimal hedging positions instead of just absorbing an exogenous supply shock. Thus, currency risk arbitrage amounts to net position taking, which brings the model closer to a practitioner’s notion of speculation. The elastic asset supply assumption is similar to Vayanos and Vila (2007) and Greenwood and Vayanos (2010), where risk-averse speculators choose optimal arbitrage positions against a price-elastic net supply in bonds of different maturity. But unlike bond yields in their set-up, exchange rates in this paper are governed by asset-specific stochastic processes. This implies that the covariance structure of risk becomes an important element determining the optimal arbitrage position. The latter aspect is explained more formally in section 3 and distinguishes the analysis here. 8 3 Theory and Hypotheses 3.1 Model Assumptions This section develops a simple limit-to-arbitrage model, in which hedge funds (or other currency arbitrageurs) take optimal speculative positions in anticipation of an exogenous currencydemandshock. Intheempirical section, thisdemandshockconsistsofmajor global index revision. Changes in index weights of stocks imply that index funds, exchange traded funds and other investors closely tracking the index mechanically adjust their international stock weights and along with it their country weights with a predictable impact on exchange rates. The timing of their rebalancing is non-discretionary and has to coincide with the index change. Hedge funds can front-run such predictable rebalancing as soon as they learn about the index revision. The model spells out the optimal trading strategy for the hedge fund in a stochastic market environment summarized as follows: Assumption 1: Linear Stochastic Currency Supply A currency market allows simultaneous trading in currencies  = 123 Trading occurs through a uniform price auction at (equally spaced) time points  = 0∆2∆3∆ with ∆ =  The (residual) liquidity supply  of  currency  is characterized by a linear function of the exchange rate  (expressed  in dollars per local currency) given by  ( ) =  ( Φ + ) (1)       − where   0 is the liquidity supply elasticity of currency . The fundamental val-  ues Φ of currency  are combined in a stochastic vector Φ = (Φ Φ Φ )   1 2  0 given by ∆ Φ = 1+   (2) =∆  =∆ P intradinground Let 1denoteaunitvectorandinnovations  = (   )  1 2  0 have zero mean and a covariance (  ) = Σ∆ The term  denotes the  ∆  0  E− one-period money market interest rate in currency  minus the dollar money market rate. 9