Crash-Neutral Currency Carry Trades

TLDR: In this paper, the authors compute returns to crash-hedged portfolios and demonstrate that the high returns to carry trades are not due to peso problems, but due to violations of uncovered interest rate parity in G10 currencies.

Abstract: Currency carry trades exploiting violations of uncovered interest rate parity in G10 currencies deliver significant excess returns with annualized Sharpe equal to or greater than those of equity market factors (1990-2012). Using data on out-of-the-money foreign exchange options, I compute returns to crash-hedged portfolios and demonstrate that the high returns to carry trades are not due to peso problems. A comparison of the returns to hedged and unhedged trades indicates crash risk premia account for at most one-third of the excess return to currency carry trades.

Figures

Table IV FX Variance and Skewness Risk Premia

Table VI Returns to the Crash-Neutral Currency Carry Trade Portfolios in G10 Currencies: Fixed moneyness hedging

Table III Returns to Crash-Neutral Currency Carry Trade Portfolios in G10 Currencies

Figure 3. Implied Volatility Functions for X/USD G10 Pairs. The figure illustrates the average implied volatility functions for foreign exchange options on nine G10 currencies versus the U.S. dollar. The implied volatilities have been scaled by the contemporaneous at-the-money implied volatilities to provide a scale-free representation of the skew. The implied volatilities at the five standardized value (10δ put, 25δ put, ATM, 25δ call, 10δ call) are actual observed quotes, and are marked with stars. All other volatilities were obtained by interpolating the data using the vanna-volga method. The dashed red (solid blue) lines correspond to time series means for periods in which the foreign one-month LIBOR rate was at least 1% above (below) the one-month U.S. dollar LIBOR rate. The underlying data are daily and cover the period from January 1999 to June 2012 (N = 3520 days).

Figure 4. Total Returns to Hedged G10 Currency Carry Trades. This figure plots the total accumulated wealth from investing in the spread-weighted, non-dollar neutral currency carry trade portfolio, under various FX option hedging schemes (top panel). Each of the option hedging schemes utilizes 10δ (out-of-the-money) FX options. Portfolios are rebalanced monthly, and returns are computed for the period from January 1999 to June 2012 (N = 162 months). The bottom panel plots the ratio of the hedged wealth to the unhedged wealth under the three hedging schemes over the same time period.

Table II Relation to Equity Market Factors

Full text

$61>-:;1<A7. -66;A4>)61)$61>-:;1<A7. -66;A4>)61)
"+074):4A75576;"+074):4A75576;
16)6+- )8-:; %0):<76)+=4<A!-;-):+0

:);0-=<:)4=::-6+A)::A#:),-;:);0-=<:)4=::-6+A)::A#:),-;
)3=*%=:-3
$61>-:;1<A7. -66;A4>)61)
7447?<01;)6,),,1<176)4?7:3;)<0<<8;:-87;1<7:A=8-66-,=.6+-(8)8-:;
 ):<7.<0-16)6+-75576;)6,<0-16)6+-)6,16)6+1)4)6)/-5-6<75576;
!-+755-6,-,1<)<176!-+755-6,-,1<)<176
=:-3%:);0-=<:)4=::-6+A)::A#:),-;
7=:6)47.16)6+1)4+76751+;



0<<8,@,717:/22E6-+7
<<0-<15-7.8=*41+)<176)=<07:&$#!'?);)F41)<-,?1<0&"##$#'=::-6<4A;0-1;)
.)+=4<A5-5*-:)<<0-&" #')<<0-$61>-:;1<A7. -66;A4>)61)
#01;8)8-:1;87;<-,)<"+074):4A75576;0<<8;:-87;1<7:A=8-66-,=.6+-(8)8-:;
7:57:-16.7:5)<17684-);-+76<)+<:-87;1<7:A87*7@=8-66-,=

:);0-=<:)4=::-6+A)::A#:),-;:);0-=<:)4=::-6+A)::A#:),-;
*;<:)+<*;<:)+<
=::-6+A+)::A<:),-;-@8471<16/>174)<176;7.=6+7>-:-,16<-:-;<:)<-8):1<A16+=::-6+1-;,-41>-:
;1/61E+)6<-@+-;;:-<=:6;?1<0)66=)41B-,"0):8-:)<17;-9=)4<77:/:-)<-:<0)6<07;-7.-9=1<A5):3-<
.)+<7:;D$;16/,)<)767=<7.<0-576-A.7:-1/6-@+0)6/-78<176;+758=<-:-<=:6;<7
+:);00-,/-,87:<.7417;)6,,-576;<:)<-<0)<<0-01/0:-<=:6;<7+)::A<:),-;):-67<,=-<78-;7
8:7*4-5;+758):1;767.<0-:-<=:6;<70-,/-,)6,=60-,/-,<:),-;16,1+)<-;+:);0:1;38:-51)
)++7=6<.7:)<57;<76-<01:,7.<0--@+-;;:-<=:6<7+=::-6+A+)::A<:),-;
1;+18416-;1;+18416-;
16)6+-C16)6+-)6,16)6+1)4)6)/-5-6<
755-6<;755-6<;
<<0-<15-7.8=*41+)<176)=<07:&$#!'?);)F41)<-,?1<0&"##$#'=::-6<4A
;0-1;).)+=4<A5-5*-:)<<0-&" #')<<0-$61>-:;1<A7. -66;A4>)61)
#01;27=:6)4):<1+4-1;)>)14)*4-)<"+074):4A75576;0<<8;:-87;1<7:A=8-66-,=.6+-(8)8-:;

Crash-Neutral Currency Carry Trades
Jakub W. Jurek
∗
Abstract
Currency carry trades exploiting violations of uncovered interest rate parity in G10 currencies deliver
significant excess returns with annualized Sharpe equal to or greater than those of equity market factors (1990-
2012). Using data on out-of-the-money foreign exchange options, I compute returns to crash-hedged portfolios
and demonstrate that the high returns to carry trades are not due to peso problems. A comparison of the returns
to hedged and unhedged trades indicates crash risk premia account for at most one-third of the excess return
to currency carry trades.
AUGUST 2013
∗
Jurek: Princeton University, Bendheim Center for Finance, e-mail: jjurek@princeton.edu; tel: (609) 258-4037, fax: (609) 258-0771.
I thank David Backus, David Bates, John Campbell, Mikhail Chernov (discussant), Joshua Coval, Itamar Drechsler, John Heaton (dis-
cussant), Stefan Nagel, Monika Piazzesi, Erik Stafford, Adrien Verdelhan (discussant), and seminar participants at Duke University, Yale
University, the Fall 2008 NBER Asset Pricing Meeting, the 2008 Princeton-Cambridge Conference, the 2008 Princeton Implied Volatility
Conference, the 2008 Conference on Financial Markets, International Capital Flows and Exchange Rates (European University Institute),
the 2009 Oxford-Princeton Workshop on Financial Mathematics and Stochastic Analysis, the 2009 American Finance Association Meet-
ings, the Society for Quantitative Analysts and the Harvard Finance Lunch (Fall 2007) for providing valuable comments. I am especially
grateful to Zhikai Xu for research assistance and J.P. Morgan for providing the FX option data.

Currency carry trades are simple strategies designed to exploit violations of uncovered interest rate parity
by investing in currencies with higher interest rates, while borrowing funds in currencies with lower interest
rates. Over the period from 1990 to 2012, such strategies delivered Sharpe ratios between 0.40-0.55, matching
or exceeding those of common equity market factors (Fama-French/Carhart). Simultaneously, carry trades have
exhibited negatively skewed returns and a positive exposure to equity market downside risks, as captured by
equity index put writing strategies. Taken together, these facts suggests that the excess returns to currency carry
trades may reflect compensation for exposure to the risk of rapid devaluations of currencies with relatively higher
interest rates. This paper investigates this hypothesis by constructing the returns to crash-hedged currency carry
trades using a unique dataset of foreign exchange options, which includes all G10 cross-rates (45 currency pairs).
A comparison of the returns to hedged and unhedged trades indicates that crash risk premia account for less than
one-third of the total excess return earned by currency carry trades over this period.
Returns to currency carry trades are comprised of the ex ante known interest rate differential (carry), and an
uncertain currency return component, capturing the change in the value of the long currency relative to the fund-
ing (short) currency. Uncovered interest parity (UIP) predicts that the currency return should exactly offset the
interest rate differential, such that investors would be indifferent between holding the two currencies. In practice,
this relationship is frequently violated, and currencies with relatively higher interest rates either appreciate, or
do not depreciate sufficiently to offset the carry.
1
As a consequence, a carry trade investor in G10 currencies
who went long (short) the currencies with the highest (lowest) one-month interest rates, weighting the positions
in proportion to the interest rate differential, would have earned 5.21% per annum (t-stat: 2.62) over the period
from 1990 to 2012 (Table I). However, these returns are punctated by infrequent, but severe episodes of rapid
depreciations, which induce a negative skewness exceeding that of the equity market excess return.
I investigate the excess returns to currency carry trades in G10 currencies from the perspective of the asso-
ciated FX option market, with the aim of addressing two questions.
2
First, do the high measured excess returns
reflect a “peso problem” owing to the exposure to currency crash risks, which have not materialized – or, are
insufficiently represented – in the sample? Second, to the extent that the high observed excess returns are not a
reflection of a statistical measurement problem, what fraction of the excess return can be attributed to currency
crash risk premia? To address these questions, I exploit a unique G10 exchange rate option panel dataset, which
1
Froot and Thaler (1990), Lewis (1995), and Engel (2013) survey the vast theoretical and empirical literature on exchange rates. The
leading explanations of UIP violations are generally subdivided into: exchange rate risk premiums, private information, near-rational
expectations, and peso problems.
2
Bates (1996) was the first to use currency option data to infer jump risks from dollar/yen and dollar/mark exchange rates. Bhansali
(2007) scales interest differentials using FX option implied volatilities to assess the attractiveness of carry trades. Burnside, et al. (2011)
and Farhi, et al. (2013) examine returns to currency carry trades hedged using X/USD options. Koijen, et al. (2012) study the dynamics
of carry trades across different asset classes.
1

includes daily price quotes for all 45 cross-rate pairs at five distinct strikes, to construct crash-neutral currency
carry trades in which the exposure to rapid depreciations in the relatively higher interest rate currency has been
hedged using a put option overlay.
3
I then compare the returns to the unhedged currency carry trades with those
of the corresponding FX option hedged portfolios.
First, I find that the excess returns to crash-hedged currency carry trades remain positive and statistically
significant, indicating that “peso problems” (Rietz (1988)) are unlikely to provide an explanation for the high
measured excess returns in G10 currencies. This finding contrasts with the results in Burnside, et al. (2011), and
reflects two major differences in the identification strategy. First, unlike them I do not rely on options, which are
at-the-money (50δ) to hedge crash risk, but rather focus attention on portfolios hedged using out-of-the-money
(10δ) options. This results in higher estimates of the mean returns to the crash-hedged portfolios. Second, I
hedge currency pairs (J/I) directly in their associated exchange rate option, rather than separately hedging the
long and short legs of the trade using J/USD and I/USD options. This is a much more efficient hedging scheme,
since it avoids paying for exposure to U.S. dollar risk in each option contract. I show that hedging using X/USD
options produces downward biased estimates of crash-hedged returns, consistent with evidence of a U.S. dollar
risk factor in the cross-section of currency returns (Lustig, et al. (2011, 2013)).
Second, I provide a simple, empirical decomposition of the excess returns to currency carry trade returns into
diffusive and jump (“crash”) risk premia. I show that the mean return to an appropriately constructed portfolio
of crash-neutral currency carry trades provides an estimate of the diffusive risk premium, while the difference
between the mean returns of the unhedged and hedged portfolios provides an estimates of the jump risk pre-
mium. The point estimates of the crash risk premium in G10 currencies range from 0.20% to 0.50% per annum,
depending on the portfolio weighting and option hedging schemes, and account for less than 10% of the excess
returns of the unhedged carry trade (Table III). These estimates are robust to the portfolio rebalancing frequency
(monthly vs. quarterly), and the imposition of constraints on the net dollar exposure of the portfolio (non-dollar-
neutral vs. dollar-neutral). The inclusion of a conservative estimate of option transaction costs – an ask-to-mid
spread equal to 10% of the prevailing implied volatility – raises estimates of the crash risk premium to 1.3% to
1.6% per annum, or 20-30% of the total portfolio currency risk premium (Table V). In a related exercise, I show
that in order to drive the point estimate of mean realized return of the hedged carry trade to zero, option-implied
volatilities would have had to have been roughly 40% higher than the values reported in the data. These results
3
The crash-hedged currency carry trades combine the position of the standard currency carry trade with a foreign exchange option
struck at a fixed delta. This implies the option roughly has a fixed probability of expiring in-the-money, or equivalently, will be struck
further away from at-the-money as option-implied volatilities increase. This construction reflects the view that a “crash” is a return
realization, which is viewed as large from the perspective of an investor’s ex ante assessment of volatility. In the robustness section, I also
examine returns to carry trades hedged at fixed moneyness (Table VI).
2

Frequently asked questions

Q1. What are the contributions in "Crash-neutral currency carry trades" ?

At the time of publication, author [ AUTHOR NAME ] was affiliated with [ INSTITUTION NAME ]. This journal article is available at ScholarlyCommons: https: //repository.