From carry trades to curvy trades

• Author: Thomas Kostka,Johannes Gräb,Ferdinand Dreher
• DOI: http://doi.org/10.1111/twec.12877
• Date: 01 March 2020
• Published date: 01 March 2020

758

|

wileyonlinelibrary.com/journal/twec World Econ. 2020;43:758–780.

© 2019 John Wiley & Sons Ltd

Received: 13 August 2019

|

Accepted: 11 September 2019

DOI: 10.1111/twec.12877

SPECIAL ISSUE ARTICLE

From carry trades to curvy trades

FerdinandDreher

|

JohannesGräb

|

ThomasKostka

European Central Bank, Frankfurt am Main, Germany

KEYWORDS

currency carry trades, Nelson‐Siegel factors, yield curve

1

|

INTRODUCTION

The forward premium puzzle has given rise to several studies that measure the economic return of

portfolios including long positions in high interest rate currencies and short positions in low interest

rate currencies, the so‐called carry trade. According to the principle of uncovered interest rate parity

(UIP), the differential of short‐term risk‐free bond yields between two currencies, also known as the

forward discount, equals the expected rate of depreciation of the higher yielding currency over the

maturity of the interest rate. That said, high interest rate currencies are found to appreciate rather than

depreciate over the short‐term (see, for instance Bilson, 1981; Fama, 1984). Carry trades exploit the

empirical failure of UIP by borrowing at low interest rates in one currency and investing the proceeds

into a higher yielding currency.

By trading on the relative forward discount, traditional carry trade strategies do not account for any

information embedded in the respective yield curves beyond short‐term interest rates. While this is,

by construction, an inherent feature of carry trades, it stands somewhat in contrast to a growing body

of evidence which suggests that the yield curve contains some signalling power for future interest

rates (Cochrane & Piazzesi, 2005; Piazzesi & Swanson, 2008), the macro‐economy (Ang, Piazzesi,

& Wei, 2006; Bekaert, Cho, & Moreno, 2010; Estrella & Hardouvelis, 1991; Moench, 2012), and in

particular the exchange rate (Chen & Tsang, 2013; Gräb & Kostka, 2018). Significant predictability

of excess currency returns across a number of currencies may indeed have substantial implications for

the optimal design of currency investments. Rather than exploiting the forward premium puzzle by

sorting currencies into portfolios based on the relative forward discount, an alternative currency strat-

egy could build upon trading signals derived from yield curve measures that contain some signalling

power for future currency returns.

In this paper, we show that an investment strategy based on the relative curvature factor, the curvy

trade, yields higher Sharpe ratios and lower negative return skewness than traditional carry trade strat-

egies. By testing the predictive content of Nelson‐Siegel factors for excess currency returns, we first

show that the relative curvature factor has some signalling power for unexpected currency movements

one to six months ahead. The lower the domestic curvature relative to the US curvature, the higher the

|

759

DREHER Et al.

average depreciation against the US dollar beyond UIP‐implied expectations. Building upon this find-

ing, we sort currencies into portfolios based on the relative curvature factor, short‐selling currencies

with a relatively low curvature and investing into currencies with a relatively high curvature. In line

with the respective trading strategies, higher economic returns of curvy trade portfolios relative to tra-

ditional carry trade strategies can be ascribed to higher returns from movements in the exchange rate

that tend to offset lower interest rate returns. The lower negative return skewness in turn reflects the

different set of funding and investment currencies. For instance, curvature trades build less upon the

typical carry trade funding currencies, like the Japanese yen and the Swiss franc, and are hence less

susceptible to crash risk. In line with that, standard pricing factors of traditional carry trade returns,

such as exchange rate volatility, fail to explain curvy trade returns in a linear asset pricing framework.

Our findings complement the literature on currency investment strategies and term structure

components in several ways. First, the significant predictability of exchange rates based on relative

Nelson‐Siegel yield curve factors when controlling for other global and country‐specific predictors of

exchange rates widely used in the carry trade literature (such as FX volatility, FX liquidity, commodity

prices) complements the existing evidence on the predictive content of yield curve factors for a num-

ber of currencies against the US dollar (Chen & Tsang, 2013; Gräb & Kostka, 2018). In this context,

we add to findings of exchange rate predictability using the term structure of forward rates (Clarida,

Sarno, Taylor, & Valente, 2003; Sarno & Valente, 2005). In contrast to the existing literature, we use

the term structure of interest rates for bonds with maturities up to ten years to measure the yield curve

curvature factor and also test for the economic significance of the term structure by forming portfolios.

Our approach is also considerably simpler than the affine term structure models linking currency and

bond risk premia (see, for instance, Sarno, Schneider, & Wagner, 2012). In this vein, our findings

also supplement the scant literature that benchmarks carry trade strategies that rely on signals from

long‐term interest rates and the slope of the yield curve against traditional carry trade strategies (Ang

& Chen, 2010). Second, we show that the negative skewness of the return distribution of currency

investments, widely documented in the carry trade literature (Brunnermeier, Nagel, & Pedersen, 2009;

Lustig & Verdelhan, 2007), is an inherent feature of the typical carry currencies. Building currency

portfolios based on prospective exchange rate movements yields return distributions which are less

skewed and thus less subject to tail risks. In this way, we also add to the related literature that ra-

tionalises the salient feature of negative return skewness with the stronger sensitivity of high interest

rate currencies to FX volatility, and, to a lesser extent, liquidity constraints and commodity prices

(Bakshi & Panayotov, 2013; Della Corte, Riddiough, & Sarno, 2016; Lustig, Roussanov, & Verdelhan,

2011; Lustig, Stathopoulos, & Verdelhan, 2013; Menkhoff, Sarno, Schmeling, & Schrimpf, 2012).

With the return distribution being broadly symmetric, excess returns of curvy trade portfolios cannot

be explained by observable risk factors—an assessment that is confirmed in a linear asset pricing

framework.

Finally and importantly, we offer an intuitive economic interpretation of the outperformance of

curvy trade returns that is line with recent interpretations of the curvature factor. While the yield

curve's level and slope may have ambiguous interpretations of underlying economic developments, let

alone exchange rates, the yield curve's curvature bears an unambiguous and forward‐looking interpre-

tation (Ang & Piazzesi, 2003; Ang et al., 2006).1 Abstracting from term premia, the curvature factor

proxies the speed at which the short‐rate converges to the long‐rate (at a given level and slope) and can

1 More generally, given the evidence for the term structure containing information about macroeconomic factors, yield curve

components of market rates provide an alternative and indirect link between macroeconomic factors and the exchange rate,

unconstrained by measurement and frequency shortcomings of macroeconomic data.