Currency Risk Factors in a Recursive Multi-Country Economy

Currency Risk Factors in a Recursive Multi-Country Economy Ric Colacito Max Croce F. Gavazzoni Rob Ready 1 / 28

Motivation 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)) We propose a structural equilibrium model: 1. address simultaneously UIP failure and carry trade 2. unified framework for abovementioned empirical results 2 / 28

Overview 1 N Countries 3 / 28

Overview 1 N Countries 2 Complete markets and recursive preferences. News shocks are priced 3 / 28

Overview 1 N Countries 2 Complete markets and recursive preferences. News shocks are priced 3 Heterogeneous exposure to global long-run growth news Provide novel evidence from G-10 countries Captures cross-sectional variation in currency returns Endogenous cross-sectional variation in macro quantities 3 / 28

Literature 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 and Rey (2007), Della Corte, Riddiough, and Sarno (2013), Hoffmann and Suter (2013),... Here: Unified G-E framework 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 4 / 28

Empirical Motivation: Heterogeneous Exposure to Global News Shocks 5 / 28

Estimating Persistent Predictable Component in GDP Estimate the following system for i G-10 currency countries GDPt i = φ pdt 1 i +σ }{{} ε i t }{{} Short-Run Shock x i t 1 xt i = ρ x xt 1 i + ϕ e σ ε i x,t }{{} Long-Run Shock 6 / 28

Estimating Persistent Predictable Component in GDP Estimate the following system for i G-10 currency countries GDPt i = φ pdt 1 i +σ }{{} ε i t }{{} Short-Run Shock x i t 1 x i t = ρ x x i t 1 + ϕ e σ ε i x,t }{{} Long-Run Shock TABLE 1: Dynamics of Endowments and Predictive Components φ ρ x σ ϕ e Parameters 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 SWE β y i 0.28 0.18 0.05 0.12 0.14 0.61 0.15 0.11 0.11 0.16 Estimation yields an empirical measure of the persistent component NZ AUS UK GER CAN NOR JPN SUI US SWE β i 0.51 of country 0.44growth 0.08as in 0.02 Colacito0.00 and Croce 0.08 (2013) 0.12 and0.26 Bansal 0.27 et al. 0.33 (2010) 6 / 28

Global Risk Exposure 1. Exposure to Global Short-Run Risk: ( ) ( ) GDPt i = 1 + β i n 1 y GDPt i + ξ i n t, i {G10 countries}. i=1 7 / 28

Global Risk Exposure 1. Exposure to Global Short-Run Risk: No Heterogeneity TABLE 1: Dynamics of Endowments ( and ) Predictive Components ( ) GDPt i = 1 + β i n 1 y GDPt i + ξ i n t, i {G10 countries}. φ ρ x σ ϕ e Parameters 0.005 i=1 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 SWE β y i 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 SWE β i TABLE 1: Dynamics of Endowments and Predictive Components 0.51 0.44 0.08 0.02 0.00 0.08 0.12 0.26 0.27 0.33 2. Exposure to Global Long-Run Risk: Substantial Heterogeneity xt i = ( ( ) 1 + β i) n 1 xt i + ζ i n t, i {G-10 countries}. φ ρ x σ ϕ e Parameters 0.005 0.773 0.020 0.058 (S.E.) ( 0.000 ) ( 0.006 ) ( 0.000 ) ( 0.001 ) NZ AUS UK GER i=1 CAN NOR JPN SUI US SWE β y i 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 SWE β i 0.51 0.44 0.08 0.02 0.00 0.08 0.12 0.26 0.27 0.33 7 / 28

Model 8 / 28

Preferences N countries, N goods The utility of country i s agent is V i,t = (1 δ) C1 1/ψ [ i,t 1 1/ψ + δ E t V 1 θ i,t+1 ] 1 1 θ, θ = γ 1/ψ 1 1/ψ 9 / 28

Preferences N countries, N goods The utility of country i s agent is V i,t = (1 δ) C1 1/ψ [ i,t 1 1/ψ + δ E t Consumption bundle: V 1 θ i,t+1 ] 1 Ct i = (xi,t) i α (xj,t) i 1 α N 1 j i 1 θ, θ = γ 1/ψ 1 1/ψ 9 / 28

Preferences N countries, N goods The utility of country i s agent is V i,t = (1 δ) C1 1/ψ [ i,t 1 1/ψ + δ E t Consumption bundle: News are independently priced M i,t+1 = δ V 1 θ i,t+1 ] 1 Ct i = (xi,t) i α (xj,t) i 1 α N 1 j i ( Ci,t+1 C i,t ) 1 ψ 1 θ, θ = γ 1/ψ 1 1/ψ U1 γ i,t+1 E t [ U 1 γ i,t+1 ] 1/ψ γ 1 γ 9 / 28

Endowments Endowment for country i is logx i t = µ x + logx i t 1 + z i,t 1 τ EC t + ε X i,t 10 / 28

Endowments Endowment for country i is logx i t = µ x + logx i t 1 + z i,t 1 τ EC t + ε X i,t z i,t s are small predictable components z i,t = ρ i z i,t 1 + ε z i,t 10 / 28

Endowments Endowment for country i is logx i t = µ x + logx i t 1 + z i,t 1 τ EC t + ε X i,t z i,t s are small predictable components z i,t = ρ i z i,t 1 + ε z i,t Long-run shocks can be decomposed into a global" component and a local" component ε z i,t = (1 + β z i,t 1)ε z global,t + ε z i,t β z i,t is modeled as a nearly permanent" AR(1) 10 / 28

Complete Markets Financial Markets are complete The budget constraint for agent i can be written as N j=1 ( p j,t xj,t i + ) A i,t+1 ζ t+1 Q t+1 (ζ t+1 ) = A i,t + p i,t X i,t ζ t+1 p i,t is the price of good i (p 1 = 1) A i,t ( ζ t ) is country i s claims to time t consumption of good X 1 Q t+1 (ζ t+1 ) gives the price of one unit of time t + 1 consumption of good X 1 contingent on the realization of ζ t+1 at time t + 1. In equilibrium, i A i,t = 0 and i x j i,t = X j,t, t. 11 / 28

Allocations Country i consumption of its own good is x i i,t = ( 1 + 1 α α(n 1) j i S j,t S i,t ) 1 Xi,t, Country i consumption of good j is i,t = 1 α 1 S j,t x α N 1 S i,t, i i,t x j where S j,t = S j,t 1 SDF ( ) j,t Cj,t /C j,t 1 SDF 1,t C 1,t /C 1,t 1 12 / 28

Results 13 / 28

No Heterogeneous Exposure - Takeaways 1 UIP failure and carry trade are distinct phenomena 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 ). Bilateral measures are misleading when news shocks are priced. 14 / 28

Heterogeneous Exposure: Endowments Simulate 5 countries to create heterogeneous exposure to long-run shocks xt i = ( ( ) 1 + β i) n 1 xt i + ζ i t n i=1 15 / 28

Heterogeneous Exposure: Endowments Simulate 5 countries to create heterogeneous exposure to long-run shocks xt i = ( ( ) 1 + β i) n 1 xt i + ζ i t n i=1 Endowment exposure to global short-run innovations GDPt i = ( ( ) ) 1 + β i n 1 y GDPt i + ξ i t n i=1 15 / 28

Heterogeneous Exposure: Interest and Exchange Rates Construct portfolios w.r.t. to median base country 16 / 28

Heterogeneous Exposure: Interest and Exchange Rates Construct portfolios w.r.t. to median base country Cross section of Interest Rates 16 / 28

Heterogeneous Exposure: Interest and Exchange Rates Construct portfolios w.r.t. to median base country Cross section of Interest Rates Exposure of e j t = log M j,t log M 3,t to ε z global,t 16 / 28

Heterogeneous Exposure: Carry and Factor Structure Construct portfolios w.r.t. to median base country Carry trade returns in Model 17 / 28

Heterogeneous Exposure: Carry and Factor Structure Construct portfolios w.r.t. to median base country Carry trade returns in Model Lustig, Roussanov, and Verdelhan (2011) in Model 17 / 28

Motivation Empirical Motivation 0 Model Setup Model Results Conclusion t 2Beta w.r.t 3 Global 4 5Output Beta w.r.t Global LR Shock 2 3 4 5 Interest Rate portfolio sorts with CRRA preferences t 2Beta 3w.r.t Global 4 5LR Shock Return 1Beta w.r.t 2 Global 3 LR 4 Shock t Beta w.r.t Global Output 50 Return w.r.t Global Output terest Rates (Annual %) 1 Mean Interest Rates (Annual %) 2 3 4 5 2 3 4 5 n 2Beta 3w.r.t 4Global 5 Output t Beta w.r.t Global LR Shock ean NFA/Y (%) 2 3 4 5 2 3 4 5 Beta 2 w.r.t 3 Global 4 5LR Shock n Beta w.r.t Global Output -1 Return 1 2 3 4 CRRA Beta w.r.t case Global Output 1 Mean Portfolio Returns (Annual %) 0 2-1 0-2 1 2 3 4 250 200-50 10 15-1 5 1 2 3 4 1 2 3 4 Return 1 Beta 2 w.r.t 3HML Factor 4 1Return Beta w.r.t Global LR Shock 50 Mean Portfolio NFA/Y (%) 100 0 0-1 0-50 1 2 3 4-100 1 2 3 4 Mean Portfolio 1 2 Returns 3 (Annual 4 %) Return Beta w.r.t HML Factor 12 0-2 0 2 3 4 5-1 1 2 3 4 2 3 4 5 1 2 3 4 terest Rates (Annual %) Mean Interest Rates (Annual %) Beta w.r.t Global LR Shock 25Mean Portfolio Returns (Annual %) 20 152 18 / 28

NFA, FX, and Interest Rates 19 / 28

Average Interest Rates and NFA Model: High β z i low r i f and positive NFA i Precautionary savings at work 20 / 28

Volatilities Model: High β z i high σ( e i) and high σ(nfa i ) Risk sharing at work 21 / 28

Conditional Responses 22 / 28

4 6 8 10 0 2 4 6 8 10 Motivation Empirical Motivation Model Setup Model Results Conclusion 10-3 5 Model: 0 NFA and Exchange Rate -5 4 6 8 10 0 2 4 6 8 10 Short-Run Shock Global Long-Run Shock Response to a positive 0.1 10-3 global long-run shock 1 0 0.5 High beta Low beta -0.1 0 l Short-Run 44 66 Shock 88 10 10 00Global 2 Long-Run 4 6 GDP Shock 8 10 0.1 0.2 10-3 1 0.5 00-0.1-0.2 0 44 66 88 10 10 0 0 2 4 6 8 10 10 NFA 0.1 10-3 51 0-0.1-1 4 6 8 10-5 0 2 4 6 8 10 0 10 10 Periods -3 2 4 6 8 10 e 5 Periods 0.1 C1 0 C5 0-5 4 6 8 10-0.1 0 2 4 6 8 10 4 6 8 10 0 2 4 6 8 10 0.1 0.2 0 0 23 / 28

Data: NFA NFA i,t = α NFA i + λ NFA i z global,t + ξ i,t GDP i,t 300 AUS NFA i,t = α GDP i + 107.31 609.24 β z i z global,t i,t (7.42) (29.66) 100 NZ UK CAN US l NFA -100 GER JPN SWE -300 SUI -500 NOR -700-0.55-0.45-0.35-0.25-0.15-0.05 0.05 0.15 0.25 0.35 b 24 / 28

Data: Exchange Rate e i,t = α FX i + λ FX i z global,t + ξ i,t, 65 e i,t = α i + 26.11 33.02 β z i z global,t (7.55) (11.97) JPN 15 CAN l FX -35 NZ AUS UK GER NOR SUI -85 SWE -135-0.55-0.45-0.35-0.25-0.15-0.05 0.05 0.15 0.25 0.35 b 25 / 28

Robustness: Currency Portfolios Results are robust to the exclusion of specific countries and controlling for local shocks 26 / 28

Conclusion 27 / 28

28 / 28 Motivation Empirical Motivation Model Setup Model Results Conclusion Conclusion 1. Novel empirical evidence on heterogenous exposure to global news shocks 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