1 the exchange rate effect of multi-currency risk arbitrage cepr discussion paper 3748 harald hau...
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1
The Exchange Rate Effect of
Multi-Currency Risk Arbitrage
CEPR Discussion Paper 3748
Harald HauINSEAD
http://www.haraldhau.com
© Harald Hau, INSEAD 2
Motivation
Micro Disconnect Puzzle: Fundamental news events explain a very small proportion of total exchange rate volatility: 1%-5% of variation(Anderson, Bollersleve, Diebold, Vega, 2003)
Order Flow Puzzle: High contemporaneous correlation with daily exchange rates: 44%-78% correlation(Evans and Lyons, 2002)
How does fundamental news relate to trading?How to reconcile these two findings?
© Harald Hau, INSEAD 3
Explaining the FX Disconnect
This paper: Limited arbitrage by risk averse speculators creates disconnect between fundamental news and short term FX return
Risk aversion of speculators implies multi-currency hedging Hedging demands can have high price impact on correlated
currencies Can have over- or undershooting across rates
Dornbusch (1976): Perfect arbitrage in financial markets can create overshooting and explain short-term disconnect and high volatility
Monetary model with nominal rigidities and uncovered interest parity
Uncovered interest parity does not hold empirically Model not supported by the data
© Harald Hau, INSEAD 4
Outline
Model of multi-currency speculation Empirical strategy:
Use and exogenous event which represents a currency arbitrage opportunity (MSCI event study)
Show that hedging demand is highly price significant Methodology:
Classical panel inference Spectral inference on trading
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MSCI Index Redefinition
Dec. 1, 2000: Pre-Announcement that MSCI would announce their decision on the adoption of new free-float based index weights on Dec 10, 2000.
Industry consultation in Nov 2000 implies that some speculators could have anticipated the Dec 1 announcement.
MSCI global index important: $3 trillion of benchmarking and $350 billion of indexing
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Percentage Weight Change
on
on
ww
ww
21
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Further Events
Dec 10, 2000: MSCI announced move to free float weights
Implementation of new weights: First adjustment of 50% on Nov 30, 2001 Second adjustment of 50% on May 31, 2002
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Model
Sequence of trading dates 1,2,3,...t,….T Price elastic currency (excess) supply function in each
currency at each trading date (elasticity qi) Supply functions shift stochastically at increments
with
CARA speculators arbitrage between consecutive trading
periods starting at time s Exogenous currency demand shock at time T given by u=wn-wo
Speculators learn currency demand shock at date t<T
t
)( 'ttE
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What is the optimal arbitrage strategy?
Naïve Strategy (equal elasticities):
What is the problem?
Risk involved in this over a period:
Risk optimal risk return trade-off (for risk aversion rho):
Exchange rate impact at time t:
on wwux
uuxx ' '
)( tTuuxopt
)(1 tTuuqe
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Model Dynamics
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How about forward rates?
Assume all money market rates are constant and Covered Interest Parity holds.
Forward rate impact at time t:
uuqf 1
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Exchange Rate Regression
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Forward Rate Regression
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Hedging Impact on Exchange Rate over 5 Day Window
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How can we improve inference?
Small sample problem n=37 Event study does not use time properties of exchange
rate data
How can we construct a stronger tests? Available: Minute by minute high frequency data on each
exchange rate from Olsen Associates
Implementation of arbitrage strategies? Assume: A sequence of speculators implements the arbitrage
strategy simultaneously across all currencies What is the statistical footprint?
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Spectral Footprint of Risk Arbitrage
Sort currencies: W+H+: Weight increase, Hedging value high
= long position and rate increase W-H-: Weight decrease, Hedging value low
= short position and rate decrease
What high frequency comovement is expected? Currency pairs within groups W+H+ and W-H- should show
positive comovement= positive high frequency cospectral shift
Currency pairs across groups W+H+ and W-H- should show negative comovement
= negative high frequency cospectral shift
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Event Returns for Group Portfolio
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Idea
Currency
1) W+H+ + + + +
2) W+H+ + + + +
3) W-H- - - - -
4) W-H- - - - -
…
Time lineArbitrage Trading
Trading interval
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High Frequency Data
FX spot midprices at 1 minute intervals for all currencies over 7 day = 10,800 obs 7 day event window 7 day control window
Frequency band definition High frequency: 15 minutes = 15 highest freq. Medium frequency: Up to 4 hours Low frequency: Above 4 hours
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Average Cospectrum Shift
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Implications
Spectral analysis is a powerful tool to detect simultaneous execution of multi-asset trading strategies in high frequency data by a sequence of traders trading at arbitrary moments
Can also link back the cospectrum shift to model parameters:
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Spectral Band Regression
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Spectral Analysis for better Arbitrage Timing
Arbitrageurs know if other speculators are already engaging in front-running
Timing is crucial: Late front-running: Speculators face deteriorated
prices Early front-running: Speculators face carry risk
© Harald Hau, INSEAD 26
Summary
Speculators front-run capital flows in the FX market They rely on hedging strategies to reduce speculative
risk Hedging is evidence of the risk aversion of the
speculators The (transitory) price impact of hedging is as large as
the exchange rate impact of the predicted capital flow Price impact of hedging can help to explain the (micro)
disconnect puzzle, but is also consistent with order flow price impact