Foreign Currency Debt, Risk Premia and Macroeconomic...
Transcript of Foreign Currency Debt, Risk Premia and Macroeconomic...
Foreign Currency Debt, Risk Premiaand Macroeconomic Volatility
Anton Korinek
University of Maryland
Joint DG ECFIN / ULB / UBC ConferenceAdvances in International Macroeconomics:
Lessons from the Crisis
Brussels, July 2010
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Motivation
1 Foreign currency debt in emerging economies:I has pro-cyclical pay-offsI often plays important role in financial instability
2 Many emerging markets made a push to developlocal currency debt markets over the past decade
Objective of this paper:develop a simple portfolio model of foreign & local currency debtexamine role for exchange rate policy to improve attractiveness oflocal currency debt marketsstudy macroeconomic implications
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Benchmark ModelDefining feature: mutual endogeneity of
portfolio choice, i.e. currency demination of debtmacroeconomic volatilityrisk premium on local currency debt
amount of dollar debt
risk premiummacroeconomic
volatility
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Benchmark Model
Small open economy with two types of agents:I representative domestic borrowerI large international lenders
Two time periods: t = 0,1,productivity shock ω ∈ Ω in period 1
Two goods:I tradable good T with price pωT ≡ 1I non-tradable good N with price pωN→ real exchange rate
Two assets in which to denominate initial debt D:I dollar debt F : return RFI local currency debt L: return RLpωN
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Domestic Agents
Utility from tradable and non-tradable consumption:I U = E
u(Cσ
T C1−σN )
(or u(CT ) in simplified notation)
Period 0:I allocate existing debt D in foreign and local currency:
D = F + L
Period 1:I observe realization of endowment shock (Yω
T , YN)I repay creditors and consumeI budget constraint:
CωT + pωNCN = Yω
T + pωN YN − RF F − RLLpωN
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International Lenders
Large, risk-averse international lenders:Exogenous pricing kernel Mω
t
Return on dollar debt: RF = 1/E [Mωt ]
Risk premium on local currency debt s.t. (1− ρ)RL = RF
→ solve for ρ = −Cov( pω
N,1E [pω
N,1] ,RF Mω1
)
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Period 1 EquilibriumEquilibrium as a function of (F ,L) determined by two equations:
1 FOC(CN): pωN = MRS = 1−σσ ·
CωT
YN= ψCω
T
2 BC: CωT = Yω
T − RF D − RLL
pωN − (1− ρ)E [pωN ]
CTω
pNω
ψ CTω = p
Nω
YLCL
YC_
L=0_YHCH
CTω
pNω
ψ CTω = p
Nω
YL
CL
Y
C_
L>0_YH
CH
CTω
pNω
ψ CTω = p
Nω
YL
CL
Y
C_
L<0 _YH
CH
Figure: Equilibrium exchange rate and consumption for Y ∈ Y L, Y ,Y H and(i) L = 0, (ii) L > 0, and (iii) L < 0
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Period 1 Equilibrium
Equilibrium as a function of (F ,L) determined by two equations:
1 FOC(CN): pωN = MRS = 1−σσ ·
CωT
YN= ψCω
T
2 BC: CωT = Yω
T − RF D − RLL
pωN − (1− ρ)E [pωN ]
Solution: CωT =
YωT − RF D + ψRLL · (1− ρ)E [Cω
T ]
1 + ψRLL
Note:dCω
TdYω
T=
11 + ψRLL
.Anton Korinek (UMD) Foreign Currency Debt and Volatility ECFIN/ULB/UBC Conference 7 / 22
Consumption as a Function of Output
EYT,1
CT,1
_
Realization of output YT,1ω
Leve
l of c
onsu
mpt
ion
CT
,1ω
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Consumption as a Function of Output
EYT,1
CT,1
_
Realization of output YT,1ω
Leve
l of c
onsu
mpt
ion
CT
,1ω moreL
1
Anton Korinek (UMD) Foreign Currency Debt and Volatility ECFIN/ULB/UBC Conference 8 / 22
Consumption as a Function of Output
EYT,1
CT,1
_
Realization of output YT,1ω
Leve
l of c
onsu
mpt
ion
CT
,1ω moreL
1
Anton Korinek (UMD) Foreign Currency Debt and Volatility ECFIN/ULB/UBC Conference 8 / 22
Description of Period 1 Equilibrium
Lemma (Amplification/Mitigation of Shocks)The higher local currency debt L,
1 the lower the impact of a given shock on consumption2 the lower the volatility of consumption and the exchange rate3 the lower the risk premium on local currency debt4 the lower expected consumption
All four relationships are convex.
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Description of Period 1 Equilibrium
Lemma (Natural Foreign Currency Debt Limit)
If RF F → YT , the economy reaches its natural foreign currency debtlimit at which volatility diverges.
Lemma (Current Account)If L > 0 the current account covaries positively with output Yω
T ,otherwise negatively.
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Period 0 Equilibrium
Optimality condition for borrowers (‘demand’ locus DD):
FOC(L) : E
u′(CωT )RL [pωN − (1− ρ)E(pωN)]
= 0
→ substitute pωN = ψCωT
→ use 2nd order Taylor approximation:
ρE [Cω
T ]u′(E [CωT ])
u′′(E [CωT ])
= Var(CωT )
Optimality condition for lenders (‘supply’ locus SS):
ρE [CωT ,1] = −R∗Cov
(Cω
T ,1,Mω1)' Std(Cω
T ,1)
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Period 0 Equilibrium
ρ
Var(CTω)
D
D
S
E
D
DS
E
ρ
L
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Description of Period 0 Equilibrium
Proposition (Changes in Risk Aversion)An increase in global risk aversion raises the risk premium, whichleads to a reduction in local currency debt and an amplified responseof the emerging economy to output shocks.
Proposition (Change in Domestic Risk)An increase in domestic output risk will be offset by higher insuranceusing local currency debt.
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Increase in Global Risk Aversion
Consumption volatility Var(CTω)
Ris
k pr
emiu
m ρ
D
D
S2
S1
Amount of local currency debt LR
isk
prem
ium
ρ
D
D
S1
S2
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Increase in Domestic Output Risk
ρ
Var(CTω)
D1 = D
2
S1 = S
2
E1 = E
2
D1
D2
S1
S2
E1
E2
ρ
L
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Comparison with Constrained Planner
Assume planner is constrained to take the equilibrium conditionsthat determine ρ and pωN,1 as given
Comparison of first-order conditions:
FOC(L)|CE : E
u′(CωT ) ·
∂CωT
∂L
= 0
FOC(L)|SP : E
u′(CωT ) ·
dCωT
dL
= 0
Proposition (Competitive Equilibrium and Social Optimum)In our benchmark model, the decentralized equilibrium and theconstrained social optimum coincide.
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Extended Model
Add an additional time period to benchmark model:
max U =u(CωT ,1) + βu(Cω
T ,2)
s.t. CωT ,1 = Yω
T − RF D − RLL pωN − (1− ρ)E [pωN ]+ Fω2
CωT ,2 = Yω
T − RF Fω2
Euler equation DE:u′(Cω
T ,1) = u′(CωT ,2)
Euler equation SP:u′(Cω
T ,1) = u′(CωT ,2) + ψRLL
1+ψRLLE [u′(CωT ,1)] ·
u′(CωT ,1)
E [u′(CωT ,1)] −
Mω1
E [Mω1 ]
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Extended Model
Interpretation of planner’s Euler equation:u′(Cω
T ,1) = u′(CωT ,2) + ψRLL
1+ψRLLE [u′(CωT ,1)] ·
u′(CωT ,1)
E [u′(CωT ,1)] −
Mω1
E [Mω1 ]
Planner can influence exchange rate through pωN,1 = ψCω
T ,1→ exchange rate intervention
If risk markets complete, thenu′(Cω
T ,1)
E [u′(CωT ,1)] =
Mω1
E [Mω1 ]
→ planner’s condition reduces to standard Euler equation
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Optimal Exchange Rate Intervention
Interpretation of planner’s Euler equation:u′(Cω
T ,1) = u′(CωT ,2) + ψRLL
1+ψRLLE [u′(CωT ,1)] ·
u′(CωT ,1)
E [u′(CωT ,1)] −
Mω1
E [Mω1 ]
For L > 0 planner uses “pro-cyclical” exchange rate intervention:
ifu′(Cω
T ,1)
E [u′(CωT ,1)] <
Mω1
E [Mω1 ] in state ω, domestic agent is relatively better
off than international investor. planner’s Euler equation implies u′(Cω
T ,1) < u′(CωT ,2)
. planner increases period 1 consumption to appreciate theexchange rate and increase repayments to international investors
ifu′(Cω
T ,1)
E [u′(CωT ,1)] >
Mω1
E [Mω1 ] opposite results
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Optimal Exchange Rate Intervention
Proposition (Optimal Exchange Rate Intervention)The planner chooses her intertemporal allocations so as to modify theasset span of the economy to allow for better risk sharing.
For L > 0 (L < 0) this implies pro-cyclical (counter-cyclical) exchangerate interventions.
In general equilibrium:better insurance opportunities increases Ldomestic economy obtains more insurance for cheaper price
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Illustration of Exchange Rate Intervention
YTω
u’(CT,1ω )
YTω
Mω
autarky
Figure: Relative marginal utilities under autarky
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Illustration of Exchange Rate Intervention
YTω
u’(CT,1ω )
YTω
Mω
autarkyDE
Figure: Relative marginal utilities in decentralized equilibrium
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Illustration of Exchange Rate Intervention
YTω
u’(CT,1ω )
YTω
Mω
autarkyDESP
Figure: Relative marginal utilities in constrained planner’s equilibrium
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Illustration of Exchange Rate Intervention
YTω
u’(CT,1ω )
YTω
Mω
Figure: Relative marginal utilities under Arrow-Debreu markets
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Conclusions
1 Model of debt denomination in emerging economiesas outcome of optimal portfolio choice problem
2 Local currency L debt mitigates volatility
3 Economy responds differently to shocks when L endogenized
4 Planner may engage in exchange rate policyto improve risk sharing with international investors
Anton Korinek (UMD) Foreign Currency Debt and Volatility ECFIN/ULB/UBC Conference 22 / 22