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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

© Harald Hau, INSEAD 5

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?

© Harald Hau, INSEAD 16

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

© Harald Hau, INSEAD 17

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