The Exchange Rate Effect of Multi-Currency Risk Arbitrage - CiteSeer

60 Pages·2010·0.51 MB·English

The Exchange Rate Effect of
Multi-Currency Risk Arbitrage
Harald Hau
∗
INSEAD and CEPR
April 27, 2010
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
five-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, Hélène Rey, Michael Moore, Carol Osler, Astrid
Schornik, Matti Suominen, Robert Whitelaw, and Charles Wyplosz for valuable comments on the paper. I
amalsogratefulforvariouscommentsfollowingpresentationsattheEuropeanCentralbank,HEI(Geneva),
Oxford University, and the 5th Central Bank Conference on the Microstructure of Financial Markets in
Zürich, 2009.
The Exchange Rate Effect of
Multi-Currency Risk Arbitrage
April 27, 2010
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
five-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: G15, G14, G11.
1 Introduction
Research into the limits and structure of speculative trading has developed into an impor-
tant topic in financial economics. A better understanding of risk arbitrage holds particular
promise for the currency market because of contrasting empirical evidence. Microeconomic
studies on exchange rates have explored how public news events affect exchange rates at
daily or intraday frequencies. News, measured by a broad set of macro announcements in
Andersen et al. (2003), generates an immediate impact on the exchange rate. But the infre-
quent occurrence of such public news events implies that the overall percentage of exchange
rate variation explained remains very small. Most of the daily exchange rates variation does
not appear to relate to major news events. Contrary to such fundamental news proxies,
financial market variables capturing (directional) currency trading, such as order flow, fea-
ture 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. The contrasting
microeconomic evidence begs the question how news events about exchange rates relate to
short-term currency trading. Do currency speculators anticipate public ‘news events’? Do
their short-term trading strategies obfuscate the link between public announcements and
their related exchange rate impact? Do risk arbitrage strategies feature important return
spill-overs into correlated currencies?1
In this paper, I provide evidence on these questions based on a unique natural exper-
iment. In December 2000, the most important provider of international equity indices,
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
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
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. The MSCI global index revision therefore
provides a unique occasion to derive the optimal risk arbitrage strategy and trace its price
impact in the cross-sectional pattern of currency returns.
To guide the empirical analysis, I propose 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
−
asettingcanbeinterpretedasareducedformrepresentationforamacroeconomicmodelfea-
turing imperfect international asset substitutability.2 Importantly, risk averse arbitrageurs
anticipatea(one-time)futurecapitalreallocationandtakeoptimalarbitragepositionsacross
all currencies to front-run these international capital flows.3 Their arbitrage positions af-
fect the exchange rate return pattern and generate cross-sectional returns with two distinct
components: The first fundamental component is proportional to the expected excess return
inducedbythecapitalflowsintoeachcurrency. Currencieswithinflows(outflows)experience
anappreciation(depreciation)duringthebuild-upof speculativepositions. Asecondpricing
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 future capital flows, but also try to minimize the overall risk of their arbitrage
positions. As a result, the optimal arbitrage strategy downweights (upweights) currencies
that contribute 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.4
2Thereisabandonedevidencethatinternationalequityflowscorrelatewithrelativelypersistentexchange
rate effects. Recent macroeconomic models endogenize portfolio choice to account for this evidence. Market
segmentation (by currency) implies that both informed and uninformed equity flows produce exchange rate
effects.
3For related evidence of front-running on mutual fund fire sales in equity markets, see Chen, Hanson,
Hong and Stein (2008) and Coval and Stafford (2007).
4At monthly or quarterly frequencies, the lack of explanatory power for standard marcroeconomic
variables is refered to as the exchange rate ‘disconnect puzzle’ (Obstfeld and Rogoff, 2001; Rogoff and
Stavrakeva,2008). The ‘disconnect’ considered in this paper concerns shorter horizons.
2
The empirical part of this paper uses two independent statistical strategies to elucidate
the structure of speculative trading. First, a classical event study methodology is applied to
examinethedailyreturnpatternoverdifferenteventwindows. Indeed,thecross-sectionof37
spotexchangeratesexhibitsboththepositivefundamentalandnegativerisk-hedgingeffects.
The overall explanatory power of the cross-sectional regression is substantial. Together, the
fundamental 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 currencies (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
(separatedbytwostandarddeviationsinthehedgingbenefit)amountsto3.6percentoverthe
five trading days of the event window. Assuming that such hedging operations by currency
speculatorsarecommonpractice, theycouldindeedcontributesubstantiallytotheshort-run
dynamics of exchange rates.
An obvious shortcoming of the conventional event study is limited statistical power, if
fewer than 40 observations are used (as is typically the case for exchange rate studies). A
new statistical methodology is therefore proposed, using high-frequency data and inference
in the frequency domain to obtain stronger statistical results. 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 high-frequency
co-movements across different exchange rates.5 Such high-frequency co-movements can be
measured as the high-frequency components of the cospectrumof exchange rate returns. For
example, exchange rate pairs for which the arbitrage position is long in both exchange rates
should experience positive high-frequency co-movements. Instead, exchange rate pairs for
5Acommonprocedureistofilterout‘highfrequency’noise,asitisstronglydeterminedbytradingactivity.
Thecurrentstudypursuestheoppositeobjectiveofidentifyingparticularpatternsofcross-currencytrading.
3
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 correspond 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 co-movements within a 15-minute interval, into
a ‘medium-frequency band’ for co-movements from 15 minutes to four hours, and a ‘low-
frequency band’ capturing all remaining co-movements. It is shown that a large share of the
changeinthecovarianceofexchangeratepairsinthesevendayarbitrageperioddirectlyprior
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).
In the final part of this paper, I show how cospectral measures can be used to re-estimate
the limited arbitrage 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 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 (if not
larger) than the fundamental 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
4
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
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 im-
perfect substitutes was originally formulated in the ‘portfolio balance theory’ (Kouri, 1983;
Branson and Henderson, 1985).6 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
empirical work on international portfolio choice has found support for the hypothesis of
market segmentation due to exchange rate risk (Hau and Rey, 2004, 2006, 2008). Market
segmentation by 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.
Financial market speculation by arbitrageurs is essential to the ‘overshooting’ outcome.7
Three important differences to my theory of cross-currency hedging should be highlighted.
First, this paper yields either over- or undershooting of the exchange rate depending on the
correlation structure of all exchange rates. Second, it relies neither on nominal rigidities
nor on a monetary model. The purely financial structure of my model mechanism can be
6For 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.
7Empirical work could never find supportive evidence for the Dornbusch framework (Rogoff, 2001).
5
combined with any model of long-run exchange rate determination. Third, over- and un-
dershooting effects due to risk-hedging demands work across currencies and may therefore
affect exchange rates that do not experience any change in their own fundamentals. Testing
the proposed theory becomes more difficult as speculative spillovers cannot be correctly cap-
tured 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). This 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 relates to
research on news events. Andersen et al. (2003) show that the surprise 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 foreign exchange (FX) microstructure literature is that ‘active
trading’ makespricesinformative, assuggestedbythestrongrelationshipbetweenorderflow
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 ag-
gregator. Evans 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 uncertain interpretation of most macroeconomic news whereby information aggrega-
tionreliesontrading. Theevidenceinthispaperalsoallowsforanalternativeinterpretation.
Therelativeimportanceoftheindirecttradingchannelforexchangeratechangesmaypartly
result from complex speculative trading strategies. The MSCI index revision illustrates that
6
FX order flow may be order flow in pursuit of the anticipated fundamental change or alter-
natively, order flow in pursuit of hedging motives. Risk-hedging flows should make any link
between order flow and news events less tight.
The finance literature contains many contributions on ‘limited risk arbitrage.’ This lit-
erature is mostly concerned with equity markets with a prominent role played by stock
index inclusions and exclusions.8 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, 2010). But in contrast
to these papers, in this paper speculators face a price-elastic residual asset supply. This
distinguishing model feature implies that speculators can acquire optimal hedging positions
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 notion
of speculation. The elastic asset supply assumption is similar to Greenwood and 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 section 3.
8See for example Garry and Goetzmann (1986), Harris and Gurel (1986), Shleifer (1986), Shleifer and
Vishny(1987),DillonandJohnson(1991),BeneishandWhaley(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
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
agents.9 Currency order flow moves currency prices along the liquidity supply schedule and
generatespersistentexchangerateeffectsdocumentedinthemicrostructureliterature. Inthe
long run, the elasticity parameter should be related to the willingness of financial investors
9A theoretical foundation based on other financial market participants would seek to determine the elas-
ticity parameter q in a rational expectation model with informed and uninformed currency traders. Alter-
i
natively, an elastic currency supply may simply be motivated by limited international asset substitutability
of international portfolio investors. Even uninformative flows resulting from the global index change then
generate permanent exchange rate effects.
8