Currency Risk Factors in a Recursive Multicountry Economy

• Author: ROBERT READY,FEDERICO GAVAZZONI,RIC COLACITO,MARIANO M. CROCE
• Date: 01 December 2018
• DOI: http://doi.org/10.1111/jofi.12720
• Published date: 01 December 2018

THE JOURNAL OF FINANCE •VOL. LXXIII, NO. 6 •DECEMBER 2018

Currency Risk Factors in a Recursive

Multicountry Economy

RIC COLACITO, MARIANO M. CROCE, FEDERICO GAVAZZONI,

and ROBERT READY∗

ABSTRACT

Focusing on the 10 most traded currencies, we provide empirical evidence regarding

a significant heterogeneous exposure to global growth news shocks. We incorporate

this empirical fact in a frictionless risk-sharing model with recursive preferences,

multiple countries, and multiple consumption goods whose supply features both global

and local short- and long-run shocks. Since news shocks are priced, heterogeneous

exposure to long-lasting global growth shocks results in a relevant reallocation of

international resources and currency adjustments. Our unified framework replicates

the properties of the HML-FX and HML-NFAcarry-trade strategies studied by Lustig,

Roussanov, and Verdelhan and Della Corte, Riddiough, and Sarno.

AGROWING EMPIRICAL LITERATURE IN international finance examines the struc-

ture of risk in the cross section of currency returns (see, among others, Lustig

and Verdelhan (2007), Lustig, Roussanov, and Verdelhan (2014), Della Corte,

Riddiough, and Sarno (2016)). These studies sort currencies on various criteria

and highlight the empirical relevance of several economic and financial factors.

In this paper, we provide novel empirical evidence in support of a structural

dynamic equilibrium model that can account for these factor structures in the

context of a news shocks–based asset-pricing model. According to our find-

ings, heterogeneous exposure to global growth news shocks is a key driver of

∗Ric Colacito is at the Kenan-Flagler Business School, University of North Carolina–Chapel

Hill and the NBER. Mariano M. Croce is with Bocconi University, the CEPR, the NBER, and the

University of North Carolina–Chapel Hill. Federico Gavazzoni is with INSEAD. Robert Ready

is at the Lundquist College of Business, University of Oregon. None of the authors have rele-

vant or material financial interest that relates to the research described in this paper. We thank

Bernard Dumas, Xavier Gabaix, Tarek Hassan, Ken Singleton (Editor), Adrien Verdelhan, two

anonymous referees, and the Associate Editor at the Journal of Finance for their feedback. We also

thank our discussants, Philippe Bacchetta, Jie Cao, Emmanuel Farhi, Pierre-Olivier Gourinchas,

Christian Heyerdahl-Larsen, Matteo Maggiori, Thomas Maurer, and Pablo Ottonello, and seminar

participants at Cambridge University, INSEAD, the NBER SI (IAP group), the meetings of the

Econometric Society,the annual meeting of the European Finance Association, the Macro-Finance

Society Conference, University of Melbourne, Monash University, BI Norwegian Business School,

the annual meetings of the American Economic Association, the annual meeting of the American

Finance Association, the annual meeting of the Midwest Finance Association, Bocconi University,

the annual meeting of the Society for Financial Econometrics, the Fourth International Finance

Conference in Hong Kong, and the SITE Conference for useful comments and insights. All errors

remain our own.

DOI: 10.1111/jofi.12720

2719

2720 The Journal of Finance R

currency riskiness, interest rates, and international lending positions in the

cross section of countries.

Specifically,we analyze an economy populated by multiple countries engaged

in a frictionless recursive risk-sharing scheme, in the spirit of Colacito and

Croce (2013). This model features long-run growth news shocks, which are

directly priced by Epstein and Zin (1989) recursive preferences. This setting

is of particular interest given its documented ability to account for several

empirical regularities of the joint dynamics of international asset prices and

quantities in a two-country setting (see Colacito (2008), Colacito and Croce

(2011), Bansal and Shaliastovich (2013)). We expand and generalize this setting

in at least two relevant directions.

First, we show that the ability of the Colacito and Croce (2013) model to repli-

cate the failure of uncovered interest parity (UIP) is not sufficient to produce

a risk premium in the cross section of interest rate–sorted currencies. That

is, the mean of the Lustig, Roussanov, and Verdelhan (2011) Currency High

Minus Low (HML-FX) factor is close to zero in a model in which countries have

the same endowment exposure to global news shocks.

Second, we introduce heterogeneous exposure to growth news shocks in the

cross section of countries in a way that is consistent with our novel empirical

evidence on the 10 countries with the most traded currencies (henceforth, G-

10 countries). Specifically, we model persistent stochastic heterogeneity in the

exposure of country-level endowments to long-run global growth news. The

long-run wealth distribution in this economy is well defined, since we are still

adopting a symmetric calibration (see Colacito, Croce, and Liu (2018)). In finite

samples, however, our countries feature substantial heterogeneity, consistent

with the empirical investigation of Lustig, Roussanov, and Verdelhan (2011)

and Hassan and Mano (2014). These heterogeneous loadings are a reduced-

form way of capturing a mix of fundamental differences across countries, such

as size (Hassan (2013)), commodity intensity (Ready, Roussanov, and Ward

(2017)), monetary policy rules (Backus et al. (2010)), and financial development

(Maggiori (2017)).

Under our benchmark calibration, we are able to produce an average High

Minus Low (HML) annual spread of about 3%, which is as large as the uncon-

ditional HML-FX in the data. This currency risk premium originates from

a positive correlation between the returns to carry trade and global long-

run consumption news. When a negative long-run shock hits, the carry trade

yields a negative return due to the appreciation of the funding currencies (i.e.,

high-exposure countries). In good times, the carry trade earns a positive re-

turn due to the appreciation of the investment currencies (i.e., low-exposure

countries).

We also show that this setting can replicate the empirical distribution of

currency-portfolio betas on the HML factor. In addition, we document that, in

our model, sorting countries on interest rates is equivalent to sorting on net

foreign asset (NFA) positions and exposure to long-run global growth news.

This suggests that the factors proposed by Della Corte, Riddiough, and Sarno

(2016) and Lustig, Roussanov, and Verdelhan (2011) may be the risk-sharing

Currency Risk Factors in a Recursive Multicountry Economy 2721

outcome of a single fundamental source of heterogeneity,namely, their different

exposure to global long-run growth news.

To discipline our calibration, we use macroeconomic data from the 10

most traded currencies in the world. In our cross section of countries, the

price-dividend (p/d) ratio is a statistically significant predictor of future growth

rates of output. For this reason, in each country we use the projection of

the Gross Domestic Product (GDP) growth rate onto lagged values of the p/d

ratio as our measure of long-run growth. We denote the innovations to this

estimated component as long-run growth news shocks and show that they

have a sizeable impact on countries’ future growth prospects. We use the

residual of our predictive regressions as a measure of short-run growth shocks.

In a second step, we regress each country’s long-run risk on the cross-sectional

average long-run risk in our cross section of countries and take the estimated

coefficients to be a measure of each country’s exposure to global long-run risk.

We find a substantial degree of heterogeneity in the estimated exposures.1

In particular,countries like Australia and New Zealand, which are commonly

featured in the long leg of carry-trade strategies, have very low exposures

to global long-run risk, while countries like Switzerland, which represents a

typical funding currency in the carry trade, feature a substantially higher

degree of exposure to global long-run risk. Interestingly, we do not identify any

heterogeneity in terms of the exposure to global short-run risk, which implies

that abstracting from growth news shocks would prevent us from identifying a

key driver of the international heterogeneity.

Our theoretical explanation of the cross section of currency risk premia pro-

duces a rich set of novel testable predictions. We document that sorting the

average risk-free rates, the volatility of exchange rates, and the first two mo-

ments of NFA positions with respect to the exposure to global long-run risks

produces the same patterns in the model and in the data.

In addition, we explore the time series relation between the cross section of

exposures to global long-run risks and international capital flows. According to

our model, when a negative global shock materializes, the countries that are

less exposed to global shocks should provide insurance to the countries with a

large degree of exposure to global shocks. That is, countries with lower exposure

to global long-run news should experience a deterioration in their NFA posi-

tions, whereas highly exposed countries should retain a larger balance of NFA.

We provide empirical support for this prediction by showing that countries

like Australia and New Zealand experience a large decrease (increase) in their

NFA positions in times of negative (positive) long-run global growth prospects,

while countries on the other end of the spectrum, such as Switzerland, experi-

ence a large inflow (outflow) of assets from abroad when global long-run growth

prospects are weak (strong). Furthermore, the currencies of high-exposure

1We note that the estimation of these exposures is identical to regressing each country’s p/d

ratio onto the cross-sectional average p/d ratio. However, our first-step regressions are key to

documenting that p/d ratios have predictive power for macroeconomic fundamentals, and thus to

supporting the long-run risk model interpretation that we offer in this paper.