Carry Trades and Currency Crashes

Transcription

1 Carry Trades and Currency Crashes Markus K. Brunnermeier, Stefan Nagel, Lasse H. Pedersen Princeton, Stanford, NYU NBER Macro Annual, April 28

2 Motivation We study the drivers of crash risk (and return) in FX markets: Interest-rate differential an important driver of currency crash risk, i.e. conditional FX skewness Up by the stairs and down by the elevator Pricing of currency crashes: option prices Co-movements of currencies Examine the importance of Carry trades Global volatility and/or risk aversion Funding liquidity and unwinding of carry trades

3 Motivation: The Carry Trade 1. Example: Yen-Aussie carry trade (Nov. 8, 27) Borrow at.87% 3m JPY LIBOR ( funding currency ) Invest at 7.9% 3m AUD LIBOR ( investment currency ) Hope that JPY doesn t appreciate much Violation of UIP - Forward Premium Puzzle 2. Large exchange rate movements without news Example: October 7th/8th, 1998

4 Background: Literature Macro: near-random walk of FX (Messe & Rogoff 1983, Engel & West ) Funding liquidity constraints of speculators (Brunnermeier and Pedersen 27; Plantin and Shin 27) Unwinding of carry trades when funding liquidity dries up Endogenous negative skewness of carry trade returns Excess co-movement of funding currencies (investment currencies) Transaction costs (Burnside et al. 26, 27) Rare disasters (Farhi and Gabaix (28)) Consumption growth risk (Lustig and Verdelhan (27))

5 Our Main Results FX crash risk increases with interest rate differential (i.e. carry) past FX carry returns speculator carry futures positions and decrease with price of insurance (risk reversals) The price of FX crash insurance increases after crash An increase in VIX or TED (cf. global risk and risk aversion) associated with unwinding of carry trades Investment currencies move together, funding currencies ditto Carry trade exposed to and may lead to crash risk, this limits arbitrage, contributing to the forward premium puzzle

6 Data and Definitions FX rates ( ): s t (in logs) [Datastream] AUD, CAD, JPY, NZD, NOK, CHF, GBP, EUR per USD Interest rate differentials ( ): i i (in logs) [Datastream] 3m-LIBOR Foreign currency excess return: z t ( i t 1 i t 1) st Return from a carry trade where foreign currency is investment currency UIP: Et [z t+1 ] = Futures positions of non-commercial traders on the CME ( ): Futures t [CFTC] Risk Reversals ( ): RiskRev t [JP Morgan]

7 Summary Statistics Table 1: Summary Statistics AUD CAD JPY NZD NOK CHF GBP EUR Panel A: Means s t z t it 1 i t Futures pos Skewness Risk rev

8 Summary Statistics, Graphically

9 Summary Statistics, Graphically Speculator positions and interest-rate differentials.1.8 speculator position EUR CAD GBP.4.6 CHF.8.1 JPY i * i x 1 3

10 Predicting Crash Risk Use it i t to predict FX excess return z t+τ during quarter t + τ Positive coefficient: carry trade pays off (UIP violation) Futures positions at end of quarter t + τ Positive coefficient: consistent with carry trade activity Skewness of daily z t within quarter t + τ Negative coefficient: Carry trades are exposed to crash risk

11 Predicting Crash Risk Qtr z Futures Skewness t (.78) (5.6) (3.87) t (.7) (5.8) (3.71) t (.66) (4.68) (3.87) t (.63) (4.44) (4.65) t (.52) (3.47) (5.5) t (.48) (2.52) (5.) t (.49) (1.91) (4.9) t (.55) (2.12) (4.3) t (.63) (2.41) (3.45) t (.78) (3.26) (3.74) Notes: Panel regressions ( ) with country-fixed effects and quarterly data. Standard errors in parentheses are robust to within-time period correlation and are NW adjusted.

12 Predicting Crash Risk We confirm these findings in a VAR VAR(3) with it i t, z t, Skew t, Futures t , quarterly Impulse responses for shocks to i t i t with Choleski decomposition with ordering it i t, z t, Skew t, Futures t Bootstrap-after-bootstrap bias-adjusted confidence intervals for impulse response function (Kilian 1998) The usual caveats apply (sensitivity to specification etc.)

13 Predictable Return and Crash Risk of Carry Trades Impulse responses for shocks to i t i t 3 x 1 3 Interest rate differential.8 Cumulated excess return Implied by UIP Futures position.5 Skewness

14 Predicting Crash Risk 1 Quarterly Weekly Figure 1: Kernel density estimates of distribution of foreign exchange excess returns conditional on interest rate differential. Interest rate differential groups quarterly: < -.5 (red), -.5 to.5 (magenta), >.5 (blue);

15 Price of Crash Risk Table 3: Forecasting crashes and the price of crash risk Skewness t+1 Skewness t+1 Skewness t+1 RiskRev t RiskRev t it i t (11.59) (12.59) (11.52) (29.2) (25.91) z t (.6) (.69) (1.39) Futures t (.12) (.15) (.14) (.19) (.12) Skewness t (.5) (.5) (.5) (.9) (.1) RiskRev t -.16 (.4) R Notes: Panel regressions ( ) with country-fixed effects and quarterly data. Standard errors in parentheses are robust to within-time period correlation of residuals and are adjusted for serial correlation with a Newey-West covariance matrix with 1 lags.

16 Price of Crash Risk Positive interest rate differential predicts negatively skewed physical and risk-neutral distributions of FX returns Consistent with carry trades being exposed to crash risk After FX losses, the crash risk is lower, but the price of crash insurance is higher. Price of crash risk insurance is high when future skewness is low. The price of insurance goes up after an earthquake, although the risk of another earthquake is low Risk premium may be due to slow moving capital

17 Unwinding of Carry Trades Table 4: Sensitivity of weekly carry trade positions, price of skewness insurance, and carry trade returns to changes in VIX Fut t Fut t+1 RiskR t RiskR t+1 z t z t+1 VIX t sign(it 1 i t 1) (.77) (.57) (2.64) (3.39) (.11) (.11) Futures t (.1) (.1) RiskRev t (.2) (.2) R Notes: Panel regressions with country-fixed effects and weekly data. Standard errors in parentheses are robust to within-time period correlation of residuals and are adjusted for serial correlation with a Newey-West covariance matrix with 6 lags. The reported R 2 is an adjusted R 2 net of the fixed effects. CBOE VIX index and TED spread: Proxies for global volatility and funding liquidity: Prior evidence that funding liquidity dries up when VIX / TED spikes

18 Unwinding of Carry Trades Table 4: Sensitivity of weekly carry trade positions, price of skewness insurance, and carry trade returns to changes in the TED spread Fut t Fut t+1 RiskR t RiskR t+1 z t z t+1 TED t sign(it 1 i t 1) (2.27) (1.85) (1.2) (13.89) (.35) (.31) Futures t (.1) (.1) RiskRev t (.2) (.2) R

19 Funding Liquidity and Violations of UIP Table 6: Future excess FX return regressed on i t i t and its interaction Forecast with VIX Forecast with TED Qtr it i t VIX t sign(it 1 i t 1) it i t TED t sign(it 1 i t 1) t (1.36) (.26) (1.1) (.45) t (1.17) (.18) (.91) (.5) t (1.2) (.23) (.9) (.58) t (1.22) (.23) (.9) (.59) t (.82) (.16) (.58) (.29) t (.65) (.11) (.48) (.3) t (.9) (.16) (.57) (.28) t (.83) (.17) (.64) (.4) t (.79) (.18) (.68) (.34) t (.87) (.17) (.77) (.4)

20 Currency Co-movement If carry trades affect FX, it should also affect covariance matrix: Variables funding currencies move together, and so do investment currencies i.e., the lower the interest rate differential, the more their FX rates co-move Dependent variable: pairwise correlation of daily log FX changes within 13-week (non-overlapping) windows, mapped to real line by logistic transformation i1 i 2 = absolute pairwise interest rate differential at the start of the 13-week period. ρ(i1, i 2 ) = correlation of 5-day interest rate changes, estimated with overlapping windows, within each 13-week period. Average ρ( s 1, s 2 ) = the cross-sectional average of all pairwise correlations of daily FX rate changes within each non-overlapping 13-week periods.

21 Currency Co-movement Table 5: Correlation of FX rate changes and magnitude of interest rate differentials (1) (2) (3) (4) i1 i (3.81) (3.62) (4.5) (6.41) ρ(i1, i 2 ) (.16) (.8) (.17) (.8) Average ρ( s 1, s 2 ) (.8) (.8) Time Fixed Effects Yes Yes Country-Pair Fixed Effects Yes Note: The dependent variable is the pairwise correlation of daily FX rate changes, estimated within non-overlapping 13-week periods. The reported R 2 is an adjusted R 2 net of the fixed effects.

22 Conclusion Results consistent with idea that speculators trade carry partly correcting UIP, but only partly because they face crash risk due to their own funding liquidity constraints and other limits to arbitrage FX crash risk increases with interest rate differential (i.e. carry) past FX carry gains speculator carry futures positions and decrease with price of insurance, risk reversal The price of FX crash insurance increases with interest rate differential (i.e. carry) past FX carry losses An increase in VIX associated with carry losses, carry unwind (lower speculator positions) price of insurance increases Funding currencies move together, funding currencies ditto

23 Log interest rate differentials (blue, left axis) and log FX rate (green, right axis).3 Australia.8.2 Canada Japan New Zealand

24 Log interest rate differentials (blue, left axis) and log FX rate (green, right axis).4 Norway 3.2 Switzerland UK.2.2 Euro

25 Lagged log interest rate differentials (blue, left axis) and quarterly skewness of daily log FX rate changes (green, right axis).4 Australia 4.15 Canada Japan 2.5 New Zealand

26 Lagged log interest rate differentials (blue, left axis) and quarterly skewness of daily log FX rate changes (green, right axis).3 Norway 2.2 Switzerland x 1 3 UK 2.2 Euro

27 Log interest rate differentials (blue, left axis) and futures positions of non-commerical traders (green, right axis).2.1 Canada Switzerland Euro Japan UK