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Optimization in sovereign debt financing
Risk Management Optimization
for Sovereign Debt Financing
Stavros A. ZeniosUniversity of Cyprus
BruegelWharton Financial Institutions Center
Andrea Consiglio, University of Palermo
M. Athanasopoulou, A. Erce, A. Gavilan, E. MoshammerEuropean Stability Mechanism
ESM, Luxembourg, Dec. 2018.1 / 26
Optimization in sovereign debt financing
Some history
Consiglio and Zenios (January 2015)
The devil is in the tails, //Voxeu.org.
Consiglio and Zenios (2016)
Risk management optimization for sovereign debtrestructuring, Journal of Globalization and Development,6(2):181–213, J. Stiglitz et al. (editors).
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Optimization in sovereign debt financing
Research issues
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Optimization in sovereign debt financing
Contributions
Q1 Represent uncertainty
Q2 Risk measurement
Q3 Risk optimization of debt financing
1 Scenario trees
2 Introduce a risk measure
3 Simultaneously model debt stock and flow
4 Endogenous feedback of debt stock on flow
5 Optimize tradeoffs risk vs cost, and stock vs flow
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Optimization in sovereign debt financing
Q2. Risk management for debt financing
Risk management has not been part of analysis
Wright (2012), Harvard Business Law Review:
Need for development of criteria for “optimal”debt restructuring process.
Missing normative models capturing complex tradeoffs
Account for the reaction of the PDMO
Optimization normalizes the test of forecasting modules
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Optimization in sovereign debt financing
Q2. Risk management for debt financing
IMF Fiscal Monitor Report (2018)
The Wealth of Nations: Governments Can BetterManage What They Own and Owe
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Optimization in sovereign debt financing
The economic problem
Sovereign output Yt , primary balance PBt , debt stock Dt−1
Model the optimal choice of debt financing variables Xt
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Optimization in sovereign debt financing
The economic problem
Flow dynamics
GFNt = it−1Dt−1 + At − PBt
Debt financing equation
J∑j=1
Xt(j) = GFNt
Endogenous premia rt(j) = rft + ρ(dt , j)
Effective Interest Rate
it =it−1(Dt−1 − At) +
∑Jj=1 rt(j)Xt(j)
Dt
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Optimization in sovereign debt financing
The economic problem
Feedback loop
X → D → r → X
Uncertain correlated Yt ,PBt , rft
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Optimization in sovereign debt financing
Q1. Modeling uncertainty
First innovation: Scenario tree
Tt = τ(n)t− 1210
a(n)
P(n) n
NT
scenario
NtNt−1N2N1N0
Compact moment matching representationDiscrete state- and time-space
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Optimization in sovereign debt financing
Q1. Modeling uncertainty
First innovation: debt stock scenario dynamics
Dn = (1 + r a(n))Da(n) − PBn (+SFn)
Scenario dependent GDP
dn = Dn/Y n
gfnnt = GFNn
t /Ynt
pbn = PBn/Y n
Dn is term structure of debt
rn is term structure of sovereign rates
Scenario tree integrates economic and financial risk factors,using objective and risk neutral probabilities.(Consiglio, Carollo, Zenios, Quantitative Finance, 16:201-212, 2016.)
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Optimization in sovereign debt financing
Q1. Modeling uncertainty
19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
01
23
Yie
lds
(%)
Year
1%5%25%50%75%95%99%
(a) Risk-free rates
19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
02
46
GD
P G
row
th (
%)
Year
1%5%25%50%75%95%99%
(b) GDP growth
19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
0.4
0.6
0.8
1.0
1.2
1.4
PB
/Y (
%)
Year
1%5%25%50%75%95%99%
(c) Primary balance12 / 26
Optimization in sovereign debt financing
Q2. Risk measurement
Scenario dynamics of debt
1
3
4
6
14 15 16 17 18
GFN (% of GDP)
Tim
e
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Optimization in sovereign debt financing
Q2. Risk measurement
Second innovation: Conditional Flow at Risk (CFaR)
Ψ(gfn).
= E (gfn | gfn ≥ gfn�)
Gross financing needs (gfn)
Probability mass (1−α)[ ]
Rockafellar and Uryasev (2000,2002)
Ψ(gfn) = gfn� +1
1− α∑n∈N
pnzn
zn ≥ gfnnt − gfn�, zn ≥ 0 14 / 26
Optimization in sovereign debt financing
Q3. Risk optimization of debt financing
Sovereign issues debt X n(j) to finance its debt
NIPnt = Int +
∑m∈P(n)
∑Jj=1 X
mτ(m)(j)CFn
t (j ,m)
(NIP/D is the effective interest rate of debt)
Model (partial)
MinimizeX∑n∈N
pnNIPnt
s.t.
Ψ(gfn) ≤ ω
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Optimization in sovereign debt financing
Q3. Risk optimization of debt financing
What about debt stock dynamics?
Dnt = D
a(n)t−1 + GFNn
t −∑
m∈P(n)
J∑j=1
Xmτ(m)(j)1
n(j ,m)− Ant
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Optimization in sovereign debt financing
Q3. Risk optimization of debt financingg
Third innovation: Endogeneity of interest rates
rnt (j) = rnft + ρ(dnt , j)
ρ(dnt , j) = aj + (1 + bj)ρ̂(dn
t ).
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Optimization in sovereign debt financing
Q3. Risk optimization of debt financing
Model: Optimize policy design
–Cost and risk tradeoffs–Stock and flow tradeoffs
–Sustainability
Minimizex∑n∈N
pnNIPnt
s.t.
Ψ(gfn) ≤ ω
∂dn
∂t≤ δ
– Gross financing needs bounded by ω– Pace of debt decrease δ < 0 or debt increase δ > 0– Thresholds
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Optimization in sovereign debt financing
Q3. Risk optimization of debt financing
1 ConservativeConstrain the ratio for all states of the economy, i.e.,
gfnn ≤ ω, for all n ∈ Nt , t ∈ T
2 Risk neutralConstrain the expected value of the ratio, i.e.,
E[gfnn | n ∈ Nt ] ≤ ω, for all t ∈ T
3 Risk adjusted CFaR constrained
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Optimization in sovereign debt financing
Q3. Risk optimization of debt financing
To recap
1 Scenario dynamics for both debt stock and flow
2 Risk measure
3 Interest rate endogeneity
4 Dynamic debt financing decisions
Climb-down
Dynamic mix (time and state dependent)Adaptive fixed mix (time dependent, state invariant)Simple fixed mix rules (time and state invariant)
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Optimization in sovereign debt financing
Q3. Risk optimization of debt financing
The relevance of optimizing
Omega
Exp
ecte
d N
IP (
% o
f GD
P)
1.5
2.0
2.5
15 20 25 30
40−40−20
0−0−100
0−100−0
100−0−0
Dynamic Adaptive fixed mix Fixed Mix
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Optimization in sovereign debt financing
Q3. Risk optimization of debt financing
Tradeoff debt stock and debt flow
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510
1520
GF
N/Y
(%
)
Year
1%5%25%
50%
75%
95%
99%
ω = 24
ω = 15.54
19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 5940
6080
100
Deb
t/Y (
%)
Year
1%
5%
25%
50%
75%
95%
99%
ω = 24
ω = 15.54
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Optimization in sovereign debt financing
Q3. Risk optimization of debt financing
Additional fiscal effort and debt sustainability
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510
1520
GF
N/Y
(%
)
Year
1%
5%
25%
50%
75%
95%
99%
19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
6080
100
120
Deb
t/Y (
%)
Year
1%
5%
25%
50%
75%
95%
99%
J∑j=1
X nt (j) + utY
nt ≥ GFNn
t .
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Optimization in sovereign debt financing
Q3. Risk optimization of debt financing
Lesson 1. Risk management comes with a cost
Lesson 2. Trading off debt flow and stock dynamics
Lesson 3. Trade-offs are economically significant
Lesson 4. Cost savings from optimization increase as risktolerance declines
Lesson 5. Optimizing renders less volatile financing needsbut weighs on debt stock dynamics
Lesson 6. Optimizing helps more when the stock oflegacy debt is larger and its maturity shorter
Lesson 7. Feedback from debt stock into interest ratesaffects risk management
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Optimization in sovereign debt financing
Conclusions
Rich framework for studying sovereign debt sustainability
Stochastic debt stock and flow dynamicsCoherent risk measureEndogenous interest ratesOptimal fiscal stance
Capture and quantify complex tradeoffs
Replicate stylized model from economic literature:gambling for redemption (Conesa and Kehoe), cost ofdelays (Blanchard)
Extension of feedback loop
X → D → r → Y → PB→ X
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Optimization in sovereign debt financing
Publications
Athanasopoulou et al., Risk management for sovereignfinancing within a debt sustainability framework, EuropeanStability Mechanism, Working Paper Series 31, Luxembourg,July 2018.
Consiglio, A. and S.A. Zenios, Risk management optimizationfor sovereign debt restructuring, Journal of Globalization andDevelopment, 6(2):181–213, J. Stiglitz et al. (editors), 2016.
Consiglio, A., Carollo, A. and S.A. Zenios, A parsimoniousmodel for multi-factor arbitrage-free scenario trees,Quantitative Finance, 16:201-212, 2016.
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