Foreign Currency Debt, Risk Premia and Macroeconomic Volatilityec.europa.eu/economy_finance/events/2010/20100723... · 2017. 1. 27. · Brussels, July 2010 Anton Korinek (UMD) Foreign

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

Anton Korinek (UMD) Foreign Currency Debt and Volatility ECFIN/ULB/UBC Conference 1 / 22

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


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


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


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


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

)


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


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



EYT,1

CT,1

_


Leve

l of c

onsu

mpt

ion

CT

,1ω moreL

1



EYT,1

CT,1

_


Leve

l of c

onsu

mpt

ion

CT

,1ω moreL

1


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.



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.



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)



ρ

Var(CTω)

D

D

S

E

D

DS

E

ρ

L



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.


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


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


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.


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 ]


Extended Model

Interpretation of planner’s Euler equation:u′(Cω

T ,1) = u′(CωT ,2) + ψRLL


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


Optimal Exchange Rate Intervention

Interpretation of planner’s Euler equation:u′(Cω

T ,1) = u′(CωT ,2) + ψRLL


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


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


Illustration of Exchange Rate Intervention

YTω

u’(CT,1ω )

YTω

Mω

autarky

Figure: Relative marginal utilities under autarky



YTω

u’(CT,1ω )

YTω

Mω

autarkyDE

Figure: Relative marginal utilities in decentralized equilibrium



YTω

u’(CT,1ω )

YTω

Mω

autarkyDESP

Figure: Relative marginal utilities in constrained planner’s equilibrium



YTω

u’(CT,1ω )

YTω

Mω

Figure: Relative marginal utilities under Arrow-Debreu markets


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


Documents

Foreign Currency Debt, Risk Premia and Macroeconomic Volatilityec.europa.eu/economy_finance/events/2010/20100723... · 2017. 1. 27. · Brussels, July 2010 Anton Korinek (UMD) Foreign