Foreign Currency Debt, Risk Premia
and Macroeconomic Volatility
Anton Korinek
University of Maryland
Joint DG ECFIN / ULB / UBC Conference
Advances 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
I
2
has pro-cyclical pay-offs
often plays important role in financial instability
Many emerging markets made a push to develop
local currency debt markets over the past decade
Objective of this paper:
develop a simple portfolio model of foreign & local currency debt
examine role for exchange rate policy to improve attractiveness of
local currency debt markets
study macroeconomic implications
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
2 / 22
Benchmark Model
Defining feature: mutual endogeneity of
portfolio choice, i.e. currency demination of debt
macroeconomic volatility
risk premium on local currency debt
amount of dollar debt
macroeconomic
volatility
Anton Korinek (UMD)
risk premium
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
3 / 22
Benchmark Model
Small open economy with two types of agents:
I
I
representative domestic borrower
large international lenders
Two time periods: t = 0, 1,
productivity shock ω ∈ Ω in period 1
Two goods:
I
I
tradable good T with price pTω ≡ 1
non-tradable good N with price pNω
→ real exchange rate
Two assets in which to denominate initial debt D:
I
I
dollar debt F : return RF
local currency debt L: return RL pNω
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
4 / 22
Domestic Agents
Utility from tradable and non-tradable consumption:
I
o
n
U = E û(CTσ CN1−σ )
(or u(CT ) in simplified notation)
Period 0:
I
allocate existing debt D in foreign and local currency:
D =F +L
Period 1:
I
I
I
observe realization of endowment shock (YTω , ȲN )
repay creditors and consume
budget constraint:
CTω + pNω CN = YTω + pNω ȲN − RF F − RL LpNω
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
5 / 22
International Lenders
Large, risk-averse international lenders:
Exogenous pricing kernel Mtω
Return on dollar debt: RF = 1/E[Mtω ]
Risk premium on local currency debt s.t. (1 − ρ)RL = RF
pω
ω
→ solve for ρ = −Cov E[pN,1
,
R
M
ω ]
F 1
N,1
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
6 / 22
Period 1 Equilibrium
Equilibrium as a function of (F , L) determined by two equations:
1
FOC(CN ): pNω = MRS =
2
BC:
1−σ
σ
CTω
ȲN
= ψCTω
CTω = YTω − RF D − RL L pNω − (1 − ρ)E[pNω ]
ω
ω
ω
ψ CT = pN
CT
·
ω
ω
ω
ω
ψ CT = pN
CT
CH
CH
_
C
L=0
CL
YH
_
Y
YL
H
C
_
C
CL
_
C
L>0
YH
_
Y
ω
ω
ψ CT = pN
CT
L<0
YH
_
Y
YL
CL
L
Y
pωN
pωN
pωN
Figure: Equilibrium exchange rate and consumption for Y ∈ {Y L , Ȳ , Y H } and
(i) L = 0, (ii) L > 0, and (iii) L < 0
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
7 / 22
Period 1 Equilibrium
Equilibrium as a function of (F , L) determined by two equations:
1
FOC(CN ): pNω = MRS =
2
BC:
1−σ
σ
CTω
ȲN
= ψCTω
CTω = YTω − RF D − RL L pNω − (1 − ρ)E[pNω ]
Solution:
Note:
·
YTω − RF D + ψRL L · (1 − ρ)E[CTω ]
1 + ψRL L
1
=
1 + ψRL L
CTω =
dCTω
dYTω
.
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
7 / 22
Level of consumption Cω
T,1
Consumption as a Function of Output
_
CT,1
EYT,1
ω
Realization of output YT,1
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
8 / 22
Level of consumption Cω
T,1
Consumption as a Function of Output
more
L
1
_
CT,1
EYT,1
ω
Realization of output YT,1
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
8 / 22
Level of consumption Cω
T,1
Consumption as a Function of Output
more
L
1
_
CT,1
EYT,1
ω
Realization of output YT,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 consumption
2
the lower the volatility of consumption and the exchange rate
3
the lower the risk premium on local currency debt
4
the lower expected consumption
All four relationships are convex.
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
9 / 22
Description of Period 1 Equilibrium
Lemma (Natural Foreign Currency Debt Limit)
If RF F → ȲT , the economy reaches its natural foreign currency debt
limit at which volatility diverges.
Lemma (Current Account)
If L > 0 the current account covaries positively with output YTω ,
otherwise negatively.
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
10 / 22
Period 0 Equilibrium
Optimality condition for borrowers (‘demand’ locus DD):
FOC(L) : E u 0 (CTω )RL [pNω − (1 − ρ)E(pNω )] = 0
→ substitute pNω = ψCTω
→ use 2nd order Taylor approximation:
ρ
E[CTω ]u 0 (E[CTω ])
= Var(CTω )
u 00 (E[CTω ])
Optimality condition for lenders (‘supply’ locus SS):
ρE[CTω,1 ] = −R ∗ Cov CTω,1 , M1ω ' Std(CTω,1 )
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
11 / 22
Period 0 Equilibrium
ρ
ρ
D
D
S
E
D
Anton Korinek (UMD)
E
Var(CωT )
Foreign Currency Debt and Volatility
S
D
L
ECFIN/ULB/UBC Conference
12 / 22
Description of Period 0 Equilibrium
Proposition (Changes in Risk Aversion)
An increase in global risk aversion raises the risk premium, which
leads to a reduction in local currency debt and an amplified response
of the emerging economy to output shocks.
Proposition (Change in Domestic Risk)
An increase in domestic output risk will be offset by higher insurance
using local currency debt.
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
13 / 22
Increase in Global Risk Aversion
Risk premium ρ
S2
S1
D
Risk premium ρ
D
S2
S1
D
D
ω
Consumption volatility Var(CT )
Anton Korinek (UMD)
Amount of local currency debt L
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
14 / 22
Increase in Domestic Output Risk
ρ
D1 = D2
ρ
S1 = S2
E1 = E2
E1
E2
S2
S1
D2
D1
Var(CωT )
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
L
ECFIN/ULB/UBC Conference
15 / 22
Comparison with Constrained Planner
Assume planner is constrained to take the equilibrium conditions
ω } as given
that determine ρ and {pN,1
Comparison of first-order conditions:
∂CTω
0
ω
FOC(L)|CE : E u (CT ) ·
=0
∂L
dCTω
FOC(L)|SP : E u 0 (CTω ) ·
=0
dL
Proposition (Competitive Equilibrium and Social Optimum)
In our benchmark model, the decentralized equilibrium and the
constrained social optimum coincide.
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
16 / 22
Extended Model
Add an additional time period to benchmark model:
max U =u(CTω,1 ) + βu(CTω,2 )
s.t. CTω,1 = YTω − RF D − RL L {pNω − (1 − ρ)E[pNω ]} + F2ω
CTω,2 = YTω − RF F2ω
Euler equation DE:
u 0 (CTω,1 ) = u 0 (CTω,2 )
Euler equation SP:
u 0 (CTω,1 ) = u 0 (CTω,2 ) +
Anton Korinek (UMD)
ψRL L
0
ω
1+ψRL L E[u (CT ,1 )]
·
Foreign Currency Debt and Volatility
n
u 0 (CTω,1 )
E[u 0 (CTω,1 )]
−
M1ω
E[M1ω ]
o
ECFIN/ULB/UBC Conference
17 / 22
Extended Model
Interpretation of planner’s Euler equation: n
u 0 (CTω,1 )
ψRL L
0 (C ω )] ·
u 0 (CTω,1 ) = u 0 (CTω,2 ) + 1+ψR
E[u
T ,1
E[u 0 (C ω )] −
LL
T ,1
Planner can influence exchange rate through
→ exchange rate intervention
If risk markets complete, then
u 0 (CTω,1 )
E[u 0 (CTω,1 )]
=
ω
pN,1
M1ω
E[M1ω ]
o
= ψCTω,1
M1ω
E[M1ω ]
→ planner’s condition reduces to standard Euler equation
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
18 / 22
Optimal Exchange Rate Intervention
Interpretation of planner’s Euler equation: n
u 0 (CTω,1 )
ψRL L
0 (C ω )] ·
E[u
u 0 (CTω,1 ) = u 0 (CTω,2 ) + 1+ψR
0 (C ω )] −
T
,1
L
E[u
L
T ,1
M1ω
E[M1ω ]
o
For L > 0 planner uses “pro-cyclical” exchange rate intervention:
if
u 0 (CTω,1 )
E[u 0 (CTω,1 )]
<
M1ω
E[M1ω ]
in state ω, domestic agent is relatively better
off than international investor
. planner’s Euler equation implies u 0 (CTω,1 ) < u 0 (CTω,2 )
. planner increases period 1 consumption to appreciate the
exchange rate and increase repayments to international investors
if
u 0 (CTω,1 )
E[u 0 (CTω,1 )]
>
Anton Korinek (UMD)
M1ω
E[M1ω ]
opposite results
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
19 / 22
Optimal Exchange Rate Intervention
Proposition (Optimal Exchange Rate Intervention)
The planner chooses her intertemporal allocations so as to modify the
asset span of the economy to allow for better risk sharing.
For L > 0 (L < 0) this implies pro-cyclical (counter-cyclical) exchange
rate interventions.
In general equilibrium:
better insurance opportunities increases L
domestic economy obtains more insurance for cheaper price
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
20 / 22
Illustration of Exchange Rate Intervention
u’(Cω )
Mω
T,1
autarky
Yω
T
Yω
T
Figure: Relative marginal utilities under autarky
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
21 / 22
Illustration of Exchange Rate Intervention
u’(Cω )
Mω
T,1
autarky
DE
Yω
T
Yω
T
Figure: Relative marginal utilities in decentralized equilibrium
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
21 / 22
Illustration of Exchange Rate Intervention
u’(Cω )
Mω
T,1
autarky
DE
SP
Yω
T
Yω
T
Figure: Relative marginal utilities in constrained planner’s equilibrium
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
21 / 22
Illustration of Exchange Rate Intervention
u’(Cω )
Mω
T,1
Yω
T
Yω
T
Figure: Relative marginal utilities under Arrow-Debreu markets
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
21 / 22
Conclusions
1
Model of debt denomination in emerging economies
as 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 policy
to improve risk sharing with international investors
Anton Korinek (UMD)
Foreign Currency Debt and Volatility
ECFIN/ULB/UBC Conference
22 / 22