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1 The Exchange Rate Effect of Multi-Currency Risk Arbitrage CEPR Discussion Paper 3748 Harald Hau INSEAD
© 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, 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
© Harald Hau, INSEAD 6 Percentage Weight Change
© Harald Hau, INSEAD 7 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
© Harald Hau, INSEAD 8 Model Sequence of trading dates 1,2,3,...t,….T Price elastic currency (excess) supply function in each currency at each trading date (elasticity q i ) 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=w n -w o Speculators learn currency demand shock at date t
© Harald Hau, INSEAD 9 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:
© Harald Hau, INSEAD 10 Model Dynamics
© Harald Hau, INSEAD 11 How about forward rates? Assume all money market rates are constant and Covered Interest Parity holds. Forward rate impact at time t:
© Harald Hau, INSEAD 12 Exchange Rate Regression
© Harald Hau, INSEAD 13 Forward Rate Regression
© Harald Hau, INSEAD 14 Hedging Impact on Exchange Rate over 5 Day Window
© Harald Hau, INSEAD 15 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
© Harald Hau, INSEAD 18 Idea Currency 1) W+H ) W+H ) W-H ) W-H----- … Time line Arbitrage Trading Trading interval
© Harald Hau, INSEAD 19 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
© Harald Hau, INSEAD 20 Average Cospectrum Shift
© Harald Hau, INSEAD 21
© Harald Hau, INSEAD 22 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:
© Harald Hau, INSEAD 23 Spectral Band Regression
© Harald Hau, INSEAD 24
© Harald Hau, INSEAD 25 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
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