The Exchange Rate Effect of Multi-Currency Risk Arbitrage

59 Pages·2009·0.5 MB·English

The Exchange Rate Effect of
Multi-Currency Risk Arbitrage
Harald Hau
∗
INSEAD and CEPR
October 26, 2009
Abstract
This paper documents how currency speculators trade when international capital flows gen-
eratepredictableexchangeratemovements. TheredefinitionoftheMSCIworldequityindex
in December 2000 provides an ideal natural experiment identifying exogenous capital flows
of index tracking equity funds. Currency speculators are shown to front-run these capital
flows. Furthermore, they actively manage the portfolio risk of their speculative positions
through hedging positions in correlated currencies. The exchange rate effect of separate risk
hedging is economically significant and amounts to a return difference of 3.6 percent over
a 5 day event window between currencies with high and low risk hedging value. The large
price impact of hedging positions suggests that risk averse currency speculators contribute
to the ‘disconnect’ between the fundamental news about individual exchange rates and their
short-run returns.
JEL classification: G11, G14, G15.
Department of Finance, Boulevard de Constance, 77305 Fontainebleau Cedex, France. Telephone: (33)-1
∗
6072 4484. Fax: [phone]. E-mail: [email protected]. Web page: http://www.haraldhau.com.
I would like to thank Bernard Dumas, Denis Gromb, Helene Rey, Michael Moore, Carol Osler, Astrid
Schornik,MattiSuominen,andRobertWhitelawforvaluablecommentsonthepaper. Iamalsogratefulfor
various comments following presentations at the European Central bank, HEI (Geneva), Oxford University
and the 5th Central Bank Conference on the Microstructure of Financial Markets.
1 Introduction
Microeconomic research on exchange rates has explored how news events affect exchange
rates at daily or intraday frequencies. News measured by a broad set of macro announce-
ments in Anderson et al. (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 remains relative small. Most of the daily exchange rates
variation appears not relate to major news events. Contrary to such fundamental news
proxies, financial market variables capturing (directional) currency trading such as order
flow feature a high overall correlations 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. The contrasting
microeconomic evidence begs the question how news events about exchange rates relate to
short term trading? Do short term trading strategies by currency speculators obfuscate the
linkage between news about exchange rate fundamentals and its short-run exchange rate
impact?
Thispaperprovidesevidencethatcurrencyspeculationcangeneratesubstantialexchange
rate variations in advance of a public announcement. Moreover, currency speculators may
hedge their arbitrage risk exposure by simultaneous trading in correlated currencies. 1 Such
arbitrage risk hedging can create short term currency over- and undershooting which is
relatively difficult to capture unless the multi-currency framework is used. Intuitively, opti-
mal risk arbitrage strategies by risk averse speculators involve the build-up and consecutive
liquidation of short term hedging positions across multiple currencies. The exchange rate
impact of such hedging positions may substantially modify the exchange rate dynamics of
any particular currency. While the order flow retains its high explanatory power for the
exchange rate return, the latter may appear - at least temporarily - ‘disconnected’ from the
anticipated fundamental effect in the public announcement.2
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.
2At monthly or quarterly frequencies, the lack of explanatory power for standard marcroeconomic vari-
1
The emprical focus is on a unique natural experiment for which the direction and relative
magnitudeofglobalcurrencyflowscanbepreciselydetermined. InDecember2000, themost
important provider of international equity indices, Morgan Stanley Capital Inc. (MSCI), an-
nounced 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 curren-
cies. A massive exogenous capital reallocation 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. Currency speculators were able to predict
cross-sectional exchange rate changes in line with anticipated capital flows and arbitrage
their exchange rate effect prior to the official announcement of the index modification. For
the MSCI index announcement, it is possible to predict the optimal arbitrage strategy and
trace its price impact in the cross-sectional pattern of currency returns.
As guidance to the empirical strategy, this paper proposes a simple dynamic model of
limited arbitrage across multiple currencies. The currency market is represented by multiple
- stochastically evolving - price elastic net supply functions with a currency-specific supply
elasticity. Such a setting can be interpreted as a reduced form representation for a wide
range of exchange rate models. Importantly, risk averse arbitrageurs anticipate a (one-
time) future capital reallocation and take optimal arbitrage positions across all currencies
to front-run these international capital flows.3 Their arbitrage positions affect the exchange
rate return pattern and generate cross-sectional returns with two distinct components: The
fundamental component is proportional to the expected excess return induced by the capital
flows into each currency. Currencies with inflows (outflows) experience an appreciation
(depreciation) during the build-up of speculative positions. A second pricing factor, the
risk-hedging component, is (negatively) proportional to the ‘marginal arbitrage risk’ of each
currency position. Risk averse speculators do not only seek high returns by front-running
ablesisreferedtoastheexchangerate‘disconnectpuzzle’(ObstfeldandRogoff(2001),RogoffandStavrakeva
(2008)). The ‘disconnect’ considered in this paper concerns more daily or weekly horizons.
3For related evidence in equity markets of front-running on mutual fund fire sales, see Chen, Hanson,
Hong and Stein (2008) and Coval and Stafford (2007).
2
future capital flows, but also try to minimize the overall risk of their arbitrage positions. As
aresult, theoptimalarbitragestrategydownweights(upweights)currencieswhichcontribute
more (less) to the overall arbitrage risk. This second pricing factor - if large enough - creates
a temporary ‘disconnect’ between the country index weight change (as the fundamental
effect) and its exchange rate return.
The empirical part of the paper uses two independent statistical strategies to elucidate
the structure of speculative trading. First, a classical event study methodology is applied
which examines the daily return pattern over different event windows. The cross-section
of 37 spot exchange rates indeed exhibit the predicted positive fundamental effect and the
negative effect for marginal arbitrage risk. The overall explanatory power of the cross-
sectionalregressionisastonishing. Together, thefundamentalandthehedgingeffectaccount
for almost 55 percent of the exchange rate variation over a 3 day window and more than
35 percent over a 7 day window. Excluding the hedging effect from the regression reduces
its explanatory power by more than half. A robustness check on a subsample of the most
liquid currencies (using the forward rates instead of spot rates) produces verysimilar results.
The MSCI event returns therefore reveal that hedging arbitrage risk matters to currency
speculators. Moreover,thehedgingpositionshaveaneconomicallysignificantcurrencyeffect.
The point estimates suggest that the exchange rate return difference between currencies
with high and low hedging benefits (separated by 2 standard deviations in the hedging
benefit) amounts to 3.6 percent over the 5 trading days of the event window. Assuming that
such hedging operations by currency speculators are common practise, they could indeed
contribute substantically to the short-run dynamics of exchange rates.
An obvious shortcoming of the conventional event study consists in limited statistical
poweriflessthan40observationsareused(asistypicallythecaseforexchangeratestudies).
A new statistical methodology is therefore proposed which uses high frequency data and
inference in the frequency domain to obtain sharper statistical inference. The intuition is
as follows: Consider a sequence of speculators, each of whom implements an optimal multi-
currency strategy. They will each build their positions simultaneously across all currencies.
The price impact across currencies should also be simultaneous and be reflected in the high
3
frequency comovements across different exchange rates.4 Such high frequency comovements
can be measured as the high frequency components 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. Instead, 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 highest frequencies. The latter corresponds to a
negative shift of the high frequency components of the cospectrum.
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 within a 15 minute interval,
into a ‘medium frequency’ band for comovements from 15 minutes to 4 hours, and a ‘low
frequency’ band capturing all remaining comovements. It is shown that a large share of the
change in the covariance of exchange rate pairs in the 7 day arbitrage period directly prior
to MSCI’s announcement is due to a change in the high frequency band of the cospectrum.
The event-related change in the exchange rate dynamics is therefore characterized by strong
cross-sectional return simultaneity. 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 negative if optimal risk arbitrage requires speculative
positions of opposite directions (one short and one long).
The final part of the paper shows howthe cospectral measures can be used to re-estimate
the structural model. Using spectral band regressions, it is possible to recover the same
regression coefficients for both the fundamental and risk-hedging effects of arbitrage trading
at much higher levels of statistical significance than in the conventional inference. The
smallerstandarderrorsallowmetomakeaquantitativeassessmentabouttheroleofcurrency
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 (if not larger)
4Acommonprocedureistofilterout‘highfrequency’noiseasitisstronglydeterminedbytradingactivity.
Thecurrentstudypursuestheoppositeobjectiveofidentifyingparticularpatternsofcross-currencytrading.
4
than the fundamental effect.
The following section discusses the related literature. Section 3 presents the theory and
develops the testable hypotheses for both the spot and forward exchange rates. Section
4 discusses the MSCI index revision, its implications for the country weight changes, and
the arbitrage risk related to an optimal speculative position. The cross-sectional evidence
follows in section 5 for daily spot rate returns and forward rate returns. Section 6 discuses
the spectral methodology and the corresponding evidence. Section 7 concludes.
2 Related Literature
The evidence presented in this paper is predicated on limited international asset substi-
tutability. The idea that capital assets in different currencies should be regarded as imper-
fect substitutes was originally formulated in the ‘portfolio balance theory’ (Kouri (1983),
Branson and Henderson (1985)).5 Interest in this theory was revived by the growing impor-
tance of international financial flows over the last two decades. Some macroeconomic models
now feature endogenous portfolio choice in settings of asset heterogeneity (see Devereux and
Sutherland (2009) and Tille and Van-Wincoop (2007)). Evidence on market segmentation
by currency and exchange rate risk was originally scarce due to data limitations. Recent em-
pirical work on international portfolio choice has found support for the hypothesis of market
segmentationduetoexchangeraterisk(HauandRey(2006,2008)). Marketsegmentationby
currency can explain why currency speculators expected the MSCI index announcement and
the subsequent reallocation of index capital to move exchange rates in a predictable manner.
On a very basic level, the presented evidence is therefore evidence for limited international
asset substitutability (Hau, Peress, and Massa (2009)).
It is useful to contrast the speculation-based exchange rate dynamics in this paper with
Dornbusch’s seminal ‘overshooting model’ (1976). Dornbusch derived large exchange rate
volatility in a setting of perfect arbitrage of interest differentials under nominal rigidities.
5For a survey of the relevant literature, see Rogoff (1984). See also Edison (1993), Payne and Vitale
(2003), and Dominquez (2003) for the related issue of central bank intervention in the FX market and its
effectiveness.
5
Financial market speculation by arbitrageurs is essential to the ‘overshooting’ outcome.6
Three important difference to our theory of cross currency hedging should be highlighted.
First, the current paper yields either over- or undershooting of the exchange rate depending
on the correlation structure of all exchange rates. Secondly, it relies neither on nominal
rigidities nor on a monetary model. The purely financial structure of my model mechanism
can be combined with any model of long-run exchange rate determination. Thirdly, over-
and undershooting effects due to risk hedging demands work across currencies and may
therefore affect exchange rates which do not experience any change in their own fundamen-
tals. Testing the proposed theory becomes more difficult as speculative spillovers cannot be
correctly captured in a single currency framework. In a (misspecified) univariate framework,
predictable hedging effects may appear as a ‘disconnect’ from fundamentals.
Macroeconomic research has largely failed to identify fundamental variables with robust
explanatory power for exchange rates. This is often referred to as the exchange rate ‘discon-
nect puzzle’ (Obstfeld and Rogoff (2001), Rogoff and Stavrakeva (2008)). The current paper
provides insights as to why such an apparent ‘disconnect’ may exist at the short horizon of
currency speculators, which extend from a few days to a few weeks. My evidence also re-
lates to research on news events. Anderson et al. (2003) show that the surprises component
in news events indeed moves exchange rates in the right direction. But as pointed out by
Evans and Lyons (2008), the overall explanatory power of fundamental news events remains
extremely low. ‘Exchange rate disconnect’ at macroeconomic frequencies of a month or a
quarter is therefore matched by considerable unexplained exchange rate variation at daily or
weekly frequencies. This has been called the ‘news puzzle’. For a particular market episode,
this paper explains a surprisingly large share of the weekly exchange rate variation.
A central theme in the FX microstructure literature is that ‘active trading’ makes prices
informative as suggested by the strong relationship between order flow and spot exchange
rates (Evans and Lyons (2002a, 2002b), Sager and Taylor (2008)). While public information
could, in principle, be impounded directly in prices without trading, the existing evidence
highlights the importance of the trading mechanism as an information aggregator. Evans
6Empirical work could never find supportive evidence for the Dornbusch framework (Rogoff (2001)).
6
and Lyons (2008) find that roughly two-thirds of the effect of macro news is transmitted
indirectly via order flow. Their explanation emphasizes the heterogeneous and ex ante
uncertaininterpretationofmostmacroeconomicnewswherebyinformationaggregationrelies
on trading. The evidence in this paper also allows for an alternative interpretation. The
relative importance of the indirect trading channel for exchange rate changes may partly
result from complex speculative trading strategies. The MSCI index revision illustrates
that FX order flow may be order flow in pursuit of the anticipated fundamental change or
alternatively order flow in pursuit of hedging motives. Risk hedging flows should make any
linkage between order flow and news events less tight.
The finance literature comprises many contributions on ‘limited risk arbitrage’. This
literature is mostly concerned with equity markets with a prominent role played by stock
index inclusions and exclusions.7 Empirical work on limited arbitrage in the FX market is
less common. Most recently, Brunnermeier, Nagel and Pedersen (2008) 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, Suominen and Lyytinen (2008) 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. The microeconomics of currency speculation therefore deserves more attention.
An important feature of this paper is the multi-asset approach to speculation. Such a
portfolio approach has recently been employed for speculative equity trading (Greenwood,
2005) and option pricing (Garleanu, Pedersen, and Poteshman, 2008). But in contrast to
these papers, the speculators in the current paper face a price elastic residual asset supply.
This distinguishing model feature implies that speculators can acquire optimal hedging po-
sitions instead of just absorbing an exogenous supply shock. Currency risk arbitrage in this
paper amounts to ‘net position taking’, which brings the model closer to a practitioner’s no-
7See for example Garry and Goetzmann (1986), Harris and Gurel (1986), Shleifer (1986), Shleifer and
Vishny(1987),DillonandJohnson(1991),BenieshandWhaley(1996),LynchandMendenhall(1997). Kaul
et al. (2000) examine index reweighting for stocks in the Toronto Stock Exchange 300 index and find that
upweighted stocks experience a persistent positive price effect. See also Denis et al. (2003) and Hedge and
McDermott (2003).
7
tion of speculation. The model structure is similar to Greenwoodand Vayanos (2008), 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 the following section.
3 Theory and Hypotheses
3.1 Model Assumptions
This section develops a simple limit-to-arbitrage model, in which arbitrageurs take optimal
speculative positions in anticipation of an exogenous currency demand shock. The market
characteristics are summarized as follows:
Assumption 1: Linear Stochastic Currency Supply
A currency market allows simultaneous trading in currencies i = 1,2,3...,n.
Trading occurs through a uniform price auction at (equally spaced) time points
t = 0,∆t,2∆t,3∆t,...T, with ∆t = T/N. The (residual) liquidity supply S of
i
currency i is characterized by a linear function of the exchange rate e given by
it
S (e ) = q (e Φ r t), (1)
i it i it it i
− −
where q > 0 is the liquidity supply elasticity of currency i. The fundamental val-
i
ues Φ of currency i are combined in a stochastic vector Φ = (Φ ,Φ ,...,Φ )
it t 1t 2t nt 0
given by
k∆t
Φ = 1+ ε , (2)
t=k∆t t
t=∆t
P
intradinground k.Let 1denoteaunitvectorandinnovations ε = (ε ,ε ...,ε )
t 1t 2t nt 0
have zero mean and a covariance (ε ε ) = Σ∆t. The term r denotes the
t ∆t t 0t i
E−
one-period money market interest rate in currency i. The home money market
rate is set to zero.
Assumption 1 characterizes a general exchange rate model with a stochastic vector Φ
t
as the driving process. The net currency supply curve is upward sloping with individual
elasticities q . The net supply curve can be motivated empirically as a stylized representation
i
of an aggregate FX limit order book filled with orders from both financial and non-financial
8
agents.8 Currency order flow moves the currency prices along the liquidity supply schedule
and generates persistent exchange rate effects documented in the microstructure literature.
In the long-run, the elasticity parameter should be related to the willingness of financial
investors and non-financial firms to substitute home assets for foreign assets if the exchange
rate becomes more favorable.9 The linearity of the supply function is chosen for analytical
convenience. For the same reason, the supply in each currency depends only on its own price
and not on other exchange rates. It is also assumed that all quantities and corresponding
elasticities are expressed in the same reference currency. A multi-currency demand shock
denominated in the reference currency and represented by u = (u ,u ,...u ) changes each
1 2 n
exchange rate by 1u . Since all currencies are initially normalized to 1, it is convenient to
qi i
refer to the exchange rate change e e as the (approximate) exchange rate return.10
t+∆t t
−
In the absence of any demand shock, market clearing requires S (e ) = 0 for each time
i it
t and each currency i. The equilibrium exchange rate vector e = (e ,e ...,e ) follows as
t 1t 2t nt 0
e = 1 for t = 0 and for trading rounds numbered k = 1,2,...N as
0
k∆t
e = 1+ ε +rk∆t, (3)
k∆t t
t=∆t
X
where r = (r ,r ,...,r ) denotes the one-period foreign money market interest rate. By
1 2 n 0
construction, the uncovered interest rate parity condition is fulfilled for all periods, that is11
(e e r∆t) = 0. (4)
t t+∆t t
E − −
8A theoretical foundation based on other financial market participants would seek to determine the
elasticity parameter q in a rational expectation model with informed and uninformed currency traders.
i
Alternatively, an elastic currency supply may simply be motivated by the presence of a non-financial or
trade sector generating this function.
9We note that representative agent models appear generally inconsistent with existing evidence for steep
asset demand curves as argued by Petajisto (2008). Limited market participation and short-term liquidity
supply by financial intermediaries (market makers) may therefore be important market features.
10This amounts to a simple scale transformation of the net supply elasticity parameter.
11This paper does not focus on uncovered interest rate parity or carry trades motivated by violations of
uncovered interest parity. Unlike in the Dornbusch model, the validity of uncovered interest parity is not
important in the model mechanism, but assumed for expositional simplicity.
9