Currency Risk Factors in a Recursive Multi-Country Economy

Currency Risk Factors in a RecursiveMulti-Country Economy

R. Colacito M.M. Croce F. Gavazzoni R. Ready

NBER SI - International Asset Pricing

BostonJuly 8, 2015

Motivation Empirical Motivation Model Setup Model Results Conclusion

Motivation

I The literature has identified factor structures in currency returns

• Interest Rates (Lustig, Roussanov, and Verdelhan (2011))• Macroeconomic quantities (e.g NFA, Della Corte, Riddiough,

and Sarno (2013))• Persistent Heterogeneity Across Countries (LRV (2011),

Hassan and Mano (2014))

I We propose a structural equilibrium model:

1. address simultaneously UIP failure and carry trade2. unified framework for abovementioned empirical results

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Motivation

I The literature has identified factor structures in currency returns

• Interest Rates (Lustig, Roussanov, and Verdelhan (2011))• Macroeconomic quantities (e.g NFA, Della Corte, Riddiough,

and Sarno (2013))• Persistent Heterogeneity Across Countries (LRV (2011),

Hassan and Mano (2014))

I We propose a structural equilibrium model:

1. address simultaneously UIP failure and carry trade2. unified framework for abovementioned empirical results

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Overview

1. N Countries

2. Complete markets and recursive preferences.

I News shocks are priced

3. Heterogeneous exposure to global long-run growth news

I Provide novel evidence from G-10 countriesI Captures cross-sectional variation in currency returnsI Endogenous cross-sectional variation in macro quantities

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Overview

1. N Countries





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Overview

1. N Countries





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Literature

I Macro and Financial Currency Factors: among others Lustig,Roussanov, and Verdelhan (2011), Della Corte, Sarno, and Tsiakas(2011), Della Corte, Ramadorai, and Sarno (2014) , Gourinchas andRey (2007), Della Corte, Riddiough, and Sarno (2013), Hoffmannand Suter (2013), ...

Here: Unified G-E framework

I Growth news in int‘l finance: among others Colacito and Croce(2011, 2013), Bansal and Shaliastovich (2011), Lewis and Liu(2014), ...

Here: Introduce heterogeneous exposure to global growth shocks

I Asymmetries/Frictions: among others Backus, Gavazzoni,Telmer, and Zin (2010), Ready, Roussanov, and Ward (2012),Hassan (2013), Gabaix and Maggiori (2013), ...

Here: Frictionless recursive risk sharing.

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Literature







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Literature







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Empirical Motivation:Heterogeneous Exposure to Global News Shocks

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Estimating Persistent Predictable Component in GDP

I Estimate the following system for i ∈ G-10 currency countries

∆GDP it = φ · pd i

t−1︸︷︷︸x it−1

+σ · εit︸︷︷︸Short-Run Shock

x it = ρx · x it−1 + ϕe · σ · εix,t︸︷︷︸Long-Run Shock

I Estimation yields an empirical measure of the persistentcomponent of country growth as in Colacito and Croce (2013)and Bansal et al. (2010)

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Estimating Persistent Predictable Component in GDP

I Estimate the following system for i ∈ G-10 currency countries

∆GDP it = φ · pd i

t−1︸︷︷︸x it−1

+σ · εit︸︷︷︸Short-Run Shock

x it = ρx · x it−1 + ϕe · σ · εix,t︸︷︷︸Long-Run ShockTABLE 1: Dynamics of Endowments and Predictive Components

φ ρx σ ϕeParameters 0.005 0.773 0.020 0.058(S.E.) ( 0.000 ) ( 0.006 ) ( 0.000 ) ( 0.001 )

NZ AUS UK GER CAN NOR JPN SUI US SWEβi∆y −0.28 −0.18 0.05 −0.12 0.14∗ 0.61∗∗ 0.15 −0.11 −0.11 −0.16

NZ AUS UK GER CAN NOR JPN SUI US SWEβi −0.51∗∗∗ −0.44∗∗∗ −0.08 −0.02 0.00 0.08 0.12 0.26∗∗ 0.27∗ 0.33∗∗

1

I Estimation yields an empirical measure of the persistentcomponent of country growth as in Colacito and Croce (2013)and Bansal et al. (2010)

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Global Risk Exposure

1. Exposure to Global Short-Run Risk:

∆GDP it =

(1 + β i

∆y

)·

(1

n

n∑i=1

∆GDP it

)+ ξit , ∀i ∈ {G10 countries}.

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1. Exposure to Global Short-Run Risk: No Heterogeneity

∆GDP it =

(1 + β i

∆y

)·

(1

n

n∑i=1

∆GDP it


TABLE 1: Dynamics of Endowments and Predictive Components




1

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∆GDP it =

(1 + β i

∆y

)·

(1

n

n∑i=1

∆GDP it






1

2. Exposure to Global Long-Run Risk:

x it =

(1 + β i

)·

(1

n

n∑i=1

x it

)+ ζ it , ∀i ∈ {G-10 countries}.

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∆GDP it =

(1 + β i

∆y

)·

(1

n

n∑i=1

∆GDP it






1

2. Exposure to Global Long-Run Risk: Substantial Heterogeneity

x it =

(1 + β i

)·

(1

n

n∑i=1

x it

)+ ζ it , ∀i ∈ {G-10 countries}.





1

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Model

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Preferences

I N countries

I The utility of country i ’s agent is

Vi,t = (1− δ) ·C

1−1/ψi,t

1− 1/ψ+ δ · Et

[V 1−θi,t+1

] 11−θ

, θ =γ − 1/ψ

1− 1/ψ

I News are independently priced

Mi,t+1 = δ

(Ci,t+1

Ci,t

)− 1ψ

U1−γi,t+1

Et

[U1−γi,t+1

]

1/ψ−γ1−γ

I Consumption bundle:

C it = (x ii,t)

α∏j 6=i

(x ij,t)1−αN−1

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Preferences

I N countries


Vi,t = (1− δ) ·C

1−1/ψi,t

1− 1/ψ+ δ · Et

[V 1−θi,t+1

] 11−θ

, θ =γ − 1/ψ

1− 1/ψ


Mi,t+1 = δ

(Ci,t+1

Ci,t

)− 1ψ

U1−γi,t+1

Et

[U1−γi,t+1

]

1/ψ−γ1−γ


C it = (x ii,t)

α∏j 6=i

(x ij,t)1−αN−1

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Preferences

I N countries


Vi,t = (1− δ) ·C

1−1/ψi,t

1− 1/ψ+ δ · Et

[V 1−θi,t+1

] 11−θ

, θ =γ − 1/ψ

1− 1/ψ


Mi,t+1 = δ

(Ci,t+1

Ci,t

)− 1ψ

U1−γi,t+1

Et

[U1−γi,t+1

]

1/ψ−γ1−γ


C it = (x ii,t)

α∏j 6=i

(x ij,t)1−αN−1

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Endowments

I Endowment for country i is

logX it = µx + logX i

t−1 + zi,t−1 − τ ECt + εXi,t

I zi,t ’s are small predictable components

zi,t = ρizi,t−1 + εzi,t

I Long-run shocks can be decomposed into a “global” componentand a “local” component

εzi,t = (1 + βzi,t−1)εzglobal,t + ˜εzi,t

I βzi,t is modeled as a “nearly permanent” AR(1)

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Endowments









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Endowments









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Complete Markets

I Financial Markets are complete

I The budget constraint for agent i can be written as

N∑j=1

pj,txij,t +

∫ζt+1

Ai,t+1

(ζt+1

)Qt+1(ζt+1) = Ai,t + pi,tXi,t

I pi,t is the price of good i (p1 = 1)

I Ai,t (ζt) is country i ’s claims to time t consumption of good X1

I Qt+1(ζt+1) gives the price of one unit of time t + 1 consumption ofgood X1 contingent on the realization of ζt+1 at time t + 1.

I In equilibrium,∑

i Ai,t = 0 and∑

i xji,t = Xj,t ,∀t.

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Allocations

I Country i consumption of its own good is

x ii,t =

1 +1− α

α(N − 1)

∑j 6=i

Sj,tSi,t

−1

Xi,t ,

I Country i consumption of good j is

x ji,t =1− αα

1

N − 1

Sj,tSi,t

x ii,t ,

where

Sj,t = Sj,t−1 ·SDFj,t

SDF1,t·(Cj,t/Cj,t−1

C1,t/C1,t−1

)

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Results

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No Heterogeneous Exposure - Takeaways

1. UIP failure and carry trade are distinct phenomena

I Symmetric setup delivers UIP failure but no carry trade

↪→ UIP failure: heterogenous local shocks↪→ HML: heterogenous exposure to global news shocks

2. Risk-sharing measures: V (FX ) and Corr(C ,C∗).

I Bilateral measures are misleading when news shocks are priced.

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No Heterogeneous Exposure - Takeaways

1. UIP failure and carry trade are distinct phenomena

I Symmetric setup delivers UIP failure but no carry trade

↪→ UIP failure: heterogenous local shocks↪→ HML: heterogenous exposure to global news shocks

2. Risk-sharing measures: V (FX ) and Corr(C ,C∗).

I Bilateral measures are misleading when news shocks are priced.

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Heterogeneous Exposure: EndowmentsI Simulate 5 countries to create heterogeneous exposure to long-run shocks

x it =(

1 + βi)·(

1

n

n∑i=1

x it

)+ ζ it

I Endowment exposure to global short-run innovations

∆GDP it =

(1 + βi

∆y

)·(

1

n

n∑i=1

∆GDP it

)+ ξit

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Heterogeneous Exposure: EndowmentsI Simulate 5 countries to create heterogeneous exposure to long-run shocks

x it =(

1 + βi)·(

1

n

n∑i=1

x it

)+ ζ it

I Endowment exposure to global short-run innovations

∆GDP it =

(1 + βi

∆y

)·(

1

n

n∑i=1

∆GDP it

)+ ξit

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Heterogeneous Exposure: Interest and Exchange Rates

I Construct “portfolios” w.r.t. to median base country

I Cross section of Interest Rates

I Exposure of ∆e jt↑ = log Mj,t↓ − log M3,t� to εzglobal,t

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I Exposure of ∆e jt↑ = log Mj,t↓ − log M3,t� to εzglobal,t ↑

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Heterogeneous Exposure: Carry and Factor Structure


I Carry trade returns in Model

I Lustig, Roussanov, and Verdelhan (2011) in Model

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Heterogeneous Exposure: Carry and Factor Structure


I Carry trade returns in Model

I Lustig, Roussanov, and Verdelhan (2011) in Model

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CRRA case

I Interest Rate portfolio sorts with CRRA preferences

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NFA, FX, and Interest Rates

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Average Interest Rates and NFA

I Model: High βzi → low r if and positive NFAi

I Precautionary savings at work

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Average Interest Rates and NFA

I Model: High βzi → low r if and positive NFAi

I Precautionary savings at work

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Volatilities

I Model: High |βzi | → high σ(∆ei ) and high σ(NFAi )

I Risk sharing at work

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Conditional Responses

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Model: NFA and Exchange Rate

I Response to a positive global long-run shock

High beta Low beta

∆GDP

NFA

∆e

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High beta Low beta

∆GDP

NFA

∆e

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High beta Low beta

∆GDP

NFA

∆e

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Data: NFA

NFAi,t

GDPi,t= αNFA

i + λNFAi · zglobal,t + ξi,t

NZ

AUS

UK

GER

CAN

NOR

JPN

SUI

US

SWE

-700

-500

-300

-100

100

300

-0.55 -0.45 -0.35 -0.25 -0.15 -0.05 0.05 0.15 0.25 0.35

lNFA

b

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Data: NFA

NFAi,t

GDPi,t= αNFA


NZ

AUS

UK

GER

CAN

NOR

JPN

SUI

US

SWE

-700

-500

-300

-100

100

300

-0.55 -0.45 -0.35 -0.25 -0.15 -0.05 0.05 0.15 0.25 0.35

lNFA

b

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Data: NFA

NFAi,t

GDPi,t= αNFA


NZ

AUS

UK

GER

CAN

NOR

JPN

SUI

US

SWE

-700

-500

-300

-100

100

300

-0.55 -0.45 -0.35 -0.25 -0.15 -0.05 0.05 0.15 0.25 0.35

lNFA

b

𝑁𝐹𝐴𝑖,𝑡𝐺𝐷𝑃𝑖,𝑡

= 𝛼𝑖 + −107.31 − 609.24 ∙ 𝛽𝑖𝑧 ∙ 𝑧𝑔𝑙𝑜𝑏𝑎𝑙,𝑡

(7.42) (29.66)

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Data: Exchange Rate

∆ei,t = αFXi + λFX

i ·∆zglobal,t + ξi,t ,

NZAUS

UK GER

CAN

NOR

JPN

SUI

SWE

-135

-85

-35

15

65

-0.55 -0.45 -0.35 -0.25 -0.15 -0.05 0.05 0.15 0.25 0.35

lFX

b

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Data: Exchange Rate



NZAUS

UK GER

CAN

NOR

JPN

SUI

SWE

-135

-85

-35

15

65

-0.55 -0.45 -0.35 -0.25 -0.15 -0.05 0.05 0.15 0.25 0.35

lFX

b

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Data: Exchange Rate



NZAUS

UK GER

CAN

NOR

JPN

SUI

SWE

-135

-85

-35

15

65

-0.55 -0.45 -0.35 -0.25 -0.15 -0.05 0.05 0.15 0.25 0.35

lFX

b

∆𝑒𝑖,𝑡 = 𝛼𝑖 + −26.11 − 33.02 ∙ 𝛽𝑖𝑧 ∙ ∆𝑧𝑔𝑙𝑜𝑏𝑎𝑙,𝑡

(7.55) (11.97)

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Robustness: Currency Portfolios

I Results are robust to the exclusion of specific countries andcontrolling for local shocks

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Conclusion

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Conclusion

1. Novel empirical evidence on heterogenous exposure to global newsshocks

2. GE model with (i) recursive preferences, (ii) multiple countries, and(iii) heterogenous exposure to global news shocks

↪→ Unified framework for several phenomena.

Consistent with data, High news exposure countries have:

- Low interest rates- Safe currencies- Positive NFA positions- More volatile NFA and FX

(same for low risk exposure countries)

3. Future research: investment flows, interplay with frictions

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Conclusion








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Conclusion





- Low interest rates

- Safe currencies- Positive NFA positions- More volatile NFA and FX



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Conclusion





- Low interest rates- Safe currencies

- Positive NFA positions- More volatile NFA and FX



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Conclusion





- Low interest rates- Safe currencies- Positive NFA positions

- More volatile NFA and FX(same for low risk exposure countries)


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Conclusion








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Conclusion








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Currency Risk Factors in a Recursive Multi-Country Economy

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