Currency Risk Factors in a Recursive Multi-Country Economy

Transcription

1 Currency Risk Factors in a Recursive Multi-Country Economy R. Colacito M.M. Croce F. Gavazzoni R. Ready NBER SI - International Asset Pricing Boston July 8, 2015

2 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)) 1 / 29

3 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 1 / 29

4 Overview 1. N Countries 2 / 29

5 Overview 1. N Countries 2. Complete markets and recursive preferences. News shocks are priced 2 / 29

6 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 2 / 29

7 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 3 / 29

8 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 3 / 29

9 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 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. 3 / 29

10 Empirical Motivation: Heterogeneous Exposure to Global News Shocks 4 / 29

11 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 }{{} xt 1 i Short-Run Shock xt i = ρ x xt 1 i + ϕ e σ ε i x,t }{{} Long-Run Shock 5 / 29

12 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 }{{} xt 1 i Short-Run Shock 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 (S.E.) ( ) ( ) ( ) ( ) NZ AUS UK GER CAN NOR JPN SUI US SWE β y i Estimation yields an empirical measure of the persistent NZ AUS UK GER CAN NOR JPN SUI US SWE β i 0.51 component 0.44 of 0.08 country 0.02 growth0.00 as in Colacito and Croce 0.26 (2013) and Bansal et al. (2010) 5 / 29

13 Global Risk Exposure 1. Exposure to Global Short-Run Risk: ( ) ( ) GDPt i = 1 + β y i 1 n GDPt i + ξt, i i {G10 countries}. n i=1 6 / 29

14 Global Risk Exposure 1. Exposure to Global Short-Run Risk: No Heterogeneity TABLE 1: Dynamics of Endowments ( and) Predictive Components ( ) GDPt i = 1 + β y i 1 n φ GDP ρ t i + ξt, i x i σ {G10 countries}. ϕ e n Parameters i=1 (S.E.) ( ) ( ) ( ) ( ) NZ AUS UK GER CAN NOR JPN SUI US SWE β y i NZ AUS UK GER CAN NOR JPN SUI US SWE β i / 29

15 Global Risk Exposure 1. Exposure to Global Short-Run Risk: No Heterogeneity TABLE 1: Dynamics of Endowments ( and) Predictive Components ( ) GDPt i = 1 + β y i 1 n φ GDP ρ t i + ξt, i x i σ {G10 countries}. ϕ e n Parameters i=1 (S.E.) ( ) ( ) ( ) ( ) NZ AUS UK GER CAN NOR JPN SUI US SWE β y i NZ AUS UK GER CAN NOR JPN SUI US SWE β i Exposure to Global Long-Run Risk: ( ) ( xt i = 1 + β i) 1 n xt i + ζt, i i {G-10 countries}. n i=1 6 / 29

16 Global Risk Exposure 1. Exposure to Global Short-Run Risk: No Heterogeneity TABLE 1: Dynamics of Endowments ( and) Predictive Components ( ) GDPt i = 1 + β y i 1 n φ GDP ρ t i + ξt, i x i σ {G10 countries}. ϕ e n Parameters i=1 (S.E.) ( ) ( ) ( ) ( ) NZ AUS UK GER CAN NOR JPN SUI US SWE β y i NZ AUS UK GER CAN NOR JPN SUI US SWE β i TABLE 1: Dynamics of Endowments and Predictive Components Exposure to Global Long-Run Risk: Substantial Heterogeneity ( ) ( xt i = 1 + β i) 1 n xt i + ζt, i i {G-10 countries}. n φ ρ x σ ϕ e Parameters (S.E.) ( ) ( ) ( ) ( ) NZ AUS UK GER CAN NOR JPN SUI US SWE i=1 β y i NZ AUS UK GER CAN NOR JPN SUI US SWE β i / 29

17 Model 7 / 29

18 Preferences N countries The utility of country i s agent is V i,t = (1 δ) C 1 1/ψ [ ] 1 i,t 1 1/ψ + δ E t V 1 θ 1 θ i,t+1, θ = γ 1/ψ 1 1/ψ 8 / 29

19 Preferences N countries The utility of country i s agent is V i,t = (1 δ) C 1 1/ψ [ ] 1 i,t 1 1/ψ + δ E t V 1 θ 1 θ i,t+1, θ = γ 1/ψ 1 1/ψ News are independently priced M i,t+1 = δ ( Ci,t+1 C i,t ) 1 ψ U1 γ i,t+1 E t [ U 1 γ i,t+1 ] 1/ψ γ 1 γ 8 / 29

20 Preferences N countries The utility of country i s agent is V i,t = (1 δ) C 1 1/ψ [ ] 1 i,t 1 1/ψ + δ E t V 1 θ 1 θ i,t+1, θ = γ 1/ψ 1 1/ψ News are independently priced M i,t+1 = δ ( Ci,t+1 C i,t ) 1 ψ U1 γ i,t+1 E t [ U 1 γ i,t+1 ] 1/ψ γ 1 γ Consumption bundle: Ct i = (xi,t) i α (xj,t) i 1 α N 1 j i 8 / 29

21 Endowments Endowment for country i is log X i t = µ x + log X i t 1 + z i,t 1 τ EC t + ε X i,t 9 / 29

22 Endowments Endowment for country i is log X i t = µ x + log X 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 + ɛ z i,t 9 / 29

23 Endowments Endowment for country i is log X i t = µ x + log X 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 + ɛ z i,t Long-run shocks can be decomposed into a global component and a local component ɛ z i,t = (1 + β z i,t 1)ɛ z global,t + ɛ z i,t β z i,t is modeled as a nearly permanent AR(1) 9 / 29

24 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. 10 / 29

25 Allocations Country i consumption of its own good is x i i,t = α α(n 1) j i S j,t S i,t 1 X i,t, Country i consumption of good j is i,t = 1 α 1 S j,t x i α N 1 S i,t x j i,t, 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 11 / 29

26 Results 12 / 29

27 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 13 / 29

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. 13 / 29

29 Heterogeneous Exposure: Endowments Simulate 5 countries to create heterogeneous exposure to long-run shocks ( ) ( ) xt i = 1 + β i 1 n xt i + ζt i n i=1 14 / 29

30 Heterogeneous Exposure: Endowments Simulate 5 countries to create heterogeneous exposure to long-run shocks ( ) ( ) xt i = 1 + β i 1 n xt i + ζt i n i=1 Endowment exposure to global short-run innovations ( ) ( ) GDPt i = 1 + β y i 1 n GDPt i + ξt i n i=1 14 / 29

31 Heterogeneous Exposure: Interest and Exchange Rates Construct portfolios w.r.t. to median base country 15 / 29

32 Heterogeneous Exposure: Interest and Exchange Rates Construct portfolios w.r.t. to median base country Cross section of Interest Rates 15 / 29

33 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 ɛ z global,t 15 / 29

34 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 ɛ z global,t 15 / 29

35 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 ɛ z global,t 15 / 29

36 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 ɛ z global,t 15 / 29

37 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 ɛ z global,t 15 / 29

38 Heterogeneous Exposure: Carry and Factor Structure Construct portfolios w.r.t. to median base country Carry trade returns in Model 16 / 29

39 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 16 / 29

40 CRRA case Interest Rate portfolio sorts with CRRA preferences 17 / 29

41 NFA, FX, and Interest Rates 18 / 29

42 Average Interest Rates and NFA Model: High β z i low r i f and positive NFA i 19 / 29

43 Average Interest Rates and NFA Model: High β z i low r i f and positive NFA i Precautionary savings at work 19 / 29

44 Volatilities Model: High β z i high σ( e i) and high σ(nfa i ) Risk sharing at work 20 / 29

45 Conditional Responses 21 / 29

46 Model: NFA and Exchange Rate Response to a positive global long-run shock High beta Low beta GDP 22 / 29

47 Model: NFA and Exchange Rate Response to a positive global long-run shock High beta Low beta GDP NFA 22 / 29

48 Model: NFA and Exchange Rate Response to a positive global long-run shock High beta Low beta GDP NFA e 22 / 29

49 Data: NFA NFA i,t = αi NFA + λ NFA i z global,t + ξ i,t GDP i,t 23 / 29

50 Data: NFA NFA i,t = αi NFA + λ NFA i z global,t + ξ i,t GDP i,t 300 AUS 100 NZ UK CAN US l NFA -100 GER JPN SWE -300 SUI -500 NOR b 23 / 29

51 Data: NFA NFA i,t = αi NFA + λ NFA i z global,t + ξ i,t GDP i,t 300 AUS NFA i,t = α GDP i 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 b 24 / 29

52 Data: Exchange Rate e i,t = α FX i + λ FX i z global,t + ξ i,t, 25 / 29

53 Data: Exchange Rate e i,t = α FX i + λ FX i z global,t + ξ i,t, 65 JPN 15 CAN l FX -35 NZ AUS UK GER NOR SUI -85 SWE b 25 / 29

54 Data: Exchange Rate e i,t = α FX i + λ FX i z global,t + ξ i,t, 65 e i,t = α i β z i z global,t (7.55) (11.97) JPN 15 CAN l FX -35 NZ AUS UK GER NOR SUI -85 SWE b 26 / 29

55 Robustness: Currency Portfolios Results are robust to the exclusion of specific countries and controlling for local shocks 27 / 29

56 Conclusion 28 / 29

57 Conclusion 1. Novel empirical evidence on heterogenous exposure to global news shocks 29 / 29

58 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. 29 / 29

59 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 29 / 29

60 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 29 / 29

61 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 29 / 29

62 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) 29 / 29

63 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 29 / 29