Yield curve risks in currency carry forwards

• Author: Kyong Joo Oh,Myoungji Lee,Jeong Wan Lee,Seungho Baek
• DOI: http://doi.org/10.1002/fut.22091
• Date: 01 April 2020
• Published date: 01 April 2020

J Futures Markets. 2020;40:651–670. wileyonlinelibrary.com/journal/fut © 2020 Wiley Periodicals, Inc.

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651

Received: 17 June 2019

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Accepted: 19 December 2019

DOI: 10.1002/fut.22091

RESEARCH ARTICLE

Yield curve risks in currency carry forwards

Seungho Baek

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Jeong Wan Lee

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Kyong Joo Oh

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Myoungji Lee

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1

Department of Finance, Koppelman

School of Business, Brooklyn College of

the City University of New York,

Brooklyn, New York

2

Department of Economics and Finance,

Nistler College of Business and Public

Administration, University of North

Dakota, Grand Forks, North Dakota

3

Department of Investment Information

Engineering, College of Engineering,

Yonsei University, Seoul, South Korea

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Financial Industry Regulatory Authority

(FINRA), New York, New York

Correspondence

Seungho Baek, Department of Finance,

Koppelman School of Business, Brooklyn

College of the City University of New

York, 2900 Bedford Avenue, Brooklyn, NY

11210.

Email: seungho.baek@brooklyn.cuny.edu

Abstract

We provide empirical evidence that cross‐country yield curve gaps (parallel gap,

twist gap, and butterfly gap) are predictive to the expected currency carry

premiums using currency forward contracts. We find that the expected currency

gains are more notable as these yield curve risk factors at time tindicate short‐

term bond prices of investment currencies to go up (positive parallel movement,

negative twist, and positive butterfly). We also find carry gains are more

sensitively affected by cross‐country monetary shocks than currency‐country

inflation pressures and business cycles. Our findings support that cross‐country

yield curve risk premiums still exist even after considering transaction costs.

KEYWORDS

currency forward contracts, forward premium anomaly, Nelson and Siegel model,

parallel–twist–butterfly factor model, term structure of yields

JEL CLASSIFICATION

G14; G15

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INTRODUCTION

A plethora of studies have shown the forward premium anomaly that currency exchange rates do not move on a one‐

for‐one basis with interest rate differentials across countries but tend to move in the opposite direction (e.g., see

Boudoukh, Richardson, & Whitelaw, 2016; Engel, 1996; Fama, 1984; Hodrick, 1987). The violation of the forward parity

introduces a currency carry trade where an investor borrows a currency that pays at a low interest rate on its bonds (i.e.,

funding currencies) and exchanges it to a currency that pays a higher interest rate on its bonds (i.e., investment

currencies). The interest rate differentials between funding currencies and investment currencies are associated with

carry gains over time on average (e.g., Brunnermeier, Nagel, & Pedersen, 2008; Burnside, Eichenbaum, Kleshchelski, &

Rebelo, 2011). But the interest rate differentials have less explanatory power and do not reflect economic fundamentals

in explaining the carry gains as discussed in Mark (1995) and Engel and West (2005).

Previously, Brunnermeier et al. (2008), Burnside et al. (2011), and Kim and Song (2015) view the currency gains as

the compensation for the systematic risk of currency investments from the interest differential for a currency pair. This

approach relates the nominal exchange rate to the discounted present value of its expected future fundamentals.

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But

measuring market expectations is not an easy task in that it needs additional assumptions of a linear process which are

imposed to link currency exchange rates with observable market fundamentals (e.g., see Engel & West, 2005; Mark,

1995). Over the last two decades plenty of research develop possible explanation of the anomaly with limited success

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The changes in interest rates and currency exchange rates are highly correlated with the changes in bond prices in capital markets. Because popular carry trades include investments in low‐grade

bonds (i.e., higher interest rate) financed by borrowings in high‐grade bonds (i.e., low interest rate), currency carry gains are associated with higher level of interest rate in an investment currency and

its market expectations. Thus, carry gains may be regarded as the risk reward for the volatility in the expected exchange rate fundamentals.

using the interest rate differentials. This is due to inappropriate proxies for market expectations of future fundamentals

rather than the failure of the models themselves.

To cope with the little explicability of the interest rate differentials and reflect economic fundamentals, several

studies have exploited the term structure of yields to investigate the forward premium anomaly in that the term

structure of yields is associated with future interest rates (Cochrane & Piazzesi, 2005; Estrella & Hardouvelis, 1991;

Piazzesi & Swanson, 2008). Furthermore, Berge, Jordà, and Taylor (2010), Chen and Tsang (2013), and Gräb, and

Kostka (2018) extend the basic carry trade strategies with relative Nelson and Siegel factors.

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Also, Dreher, Gräb, &

Kostka, (2018) investigate which of the three relative Nelson–Siegel factors provides the strongest signal for future

exchange rate dynamics while controlling for several pricing factors of carry returns, such as exchange rate volatility,

liquidity, and momentum. They find that the relative level, slope, and curvature factors are predictive to describe the

anomaly in reflecting market expectation of future fundamentals. However, although they examine the robustness of

their findings from the relative factor model, they do not validate the predictability of the model.

TherelativeNelson–Siegel factor model needs two strict requirements. First, the model requires the identical factor loading

for all the currency pairs. Second, in the relative factor model, the time decay parameter (λ), which controls the speed of

exponential time decay, should set to a fixed value of 0.0609 for all countries regardless of data sample periods. However, these

requirements can be questioned not only because each country has own economic fundamentals but also its fundamentals are

time varying over the period. Since the smaller the parameter the slower the time decay becomes in each factor loading of the

Nelson–Siegel model, determining the appropriate parameter does matter as in Diebold and Li (2006).

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In other words, the time

decay parameter plays an important role in determining factor loadings as to implement the Nelson–Siegel model in a sense

thatagoodness‐of‐fitforacountry‐specific Nelson–Siegel model heavily relies on the optimum time decay parameter. Thus, we

consider another method that reflects country‐specific factor loading for each of currency pairs while estimating the respective

optimal time decay parameters. To develop our model we first estimate individual time decay parameters for each country.

Next we compute the respective factor loadings for each country to develop our currency carry model.

Extending from the previous literature and our research motivation, we alternatively present a currency carry model

to link cross‐country yield curve differentials and currency carry gains. More specifically, we create cross‐country

parallel gap (PAG), cross‐country twist gap (TWG), and cross‐country butterfly gap (BFG) while emulating the

parallel–twist–butterfly factor approach as shown in Litterman and Scheinkman (1991) and Esseghaier, Lal, Cai, and

Hannay (2004).

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These parallel, twist, and butterfly examine the yield curve movement during the period between t−1

and t, whereas our approach contemporaneously compares the shapes of the yield curves between investing countries

and funding countries. Thus, we can further examine how cross‐country differentials in monetary policy, inflation

pressure, and business cycle are systematically associated with the forward anomaly.

The structure of key variables of the previous relative Nelson–Siegel model in Chen and Tsang (2013), Berge et al.

(2010), Dreher et al. (2018) and Gräb and Kostka (2018) is the difference in cross‐country factors between a funding

currency and an investment currency underlying the assumption of the identical factor loading over all countries.

However, based on this simple factor difference, it is hard to apply the relative model to currency portfolio investments

because the relative model regards that country‐specific factor loadings are not critical information in understanding

carry trades. But in fixed‐income investments, the changes in a product of a specific factor loading and its factor from

the Nelson–Siegel model are crucial determinants of a bond investment as documented by Litterman and Scheinkman

(1991) and Esseghaier et al. (2004). Following their approach, we include country‐specific factor loadings in developing

our carry model and analyze the applicability of our model in currency portfolio investments.

We look into currency carry gains considering a simple hedging strategy with a forward contract. In general,

currency risk can be reduced by locking in forward exchange rates. In this sense, investors can take investment

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Originally, the Nelson–Siegel level factors include meaningful market fundamentals. The Nelson–Siegel level factor is usually associated with long‐run level of inflation expectation. The

Nelson–Siegel slope factor represents the slope of a yield curve (the long‐term yield minus short‐term yield), which is related to the economic cycle. The Nelson–Siegel curve factor indicates the

monetary stance of a central bank. Using three yield curve components (i.e., level, slope, and curvature) of the Nelson and Siegel's term structure model (Nelson & Siegel, 1987) to proxy for future

market fundamentals, Chen and Tsang (2013) originally developed the relative Nelson–Siegel factors. Berge et al. (2010) and Dreher et al. (2018) and Gräb and Kostka (2018) have followed and

employed the relative Nelson and Siegel factors to examine their applicability in currency carry trades.

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The previous literature sets to 0.0609 following Diebold and Li (2006). However, the value is not an optimal value not only because Diebold and Li (2006) set the value for the purpose of simplicity and

convenience, but also because they estimate it using monthly yield data from January 1985 to December 2012. Thus, it should be appropriately estimated for different sample periods and for each

country in the sample. We estimate that the time decay parameters (λ) for Australia, Canada, Switzerland, Euro zone, the UK, Japan, and the US are 0.573, 0.510, 0.552, 0.403, 0.415, 0.259, and 0.487,

respectively.

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To measure the riskiness of fixed income securities, they develop parallel–twist–butterfly factors explaining the relation between the variation of a security prices and the change of the yield curve. In

fact, parallel shift (the level change in the yield curve), twist (the slope change in the yield curve), and butterfly (the curvature change in the yield curve) have been used to evaluate interest rate risk

and hedge bond securities.

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