Risk management for sovereign financing within a debt sustainability framework

Optimization in sovereign debt ﬁnancing
Risk Management Optimization
for Sovereign Debt Financing
Stavros A. Zenios
University of Cyprus
Bruegel
Wharton Financial Institutions Center
Andrea Consiglio, University of Palermo
M. Athanasopoulou, A. Erce, A. Gavilan, E. Moshammer
European Stability Mechanism
ESM, Luxembourg, Dec. 2018.
1 / 26

Some history
Consiglio and Zenios (January 2015)
The devil is in the tails, //Voxeu.org.
Consiglio and Zenios (2016)
Risk management optimization for sovereign debt
restructuring, Journal of Globalization and Development,
6(2):181–213, J. Stiglitz et al. (editors).
2 / 26

Research issues
3 / 26

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
4 / 26

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
5 / 26

Q2. Risk management for debt ﬁnancing
IMF Fiscal Monitor Report (2018)
The Wealth of Nations: Governments Can Better
Manage What They Own and Owe
6 / 26

The economic problem
Sovereign output Yt, primary balance PBt, debt stock Dt−1
Model the optimal choice of debt ﬁnancing variables Xt
7 / 26

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) + J
j=1 rt(j)Xt(j)
Dt
8 / 26

Feedback loop
X → D → r → X
Uncertain correlated Yt, PBt, rft
9 / 26

Q1. Modeling uncertainty
First innovation: Scenario tree
Tt = τ(n)t − 1210
a(n)
P(n) n
NT
scenario
NtNt−1N2N1N0
Compact moment matching representation
Discrete state- and time-space
10 / 26

First innovation: debt stock scenario dynamics
Dn
= (1 + ra(n)
)Da(n)
− PBn
(+SFn
)
Scenario dependent GDP
dn
= Dn
/Y n
gfnn
t = GFNn
t /Y n
t
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.)
11 / 26

19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
0123
Yields(%)
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
0246
GDPGrowth(%)
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
0.40.60.81.01.21.4
PB/Y(%)
Year
1%5%25%50%75%95%99%
(c) Primary balance
12 / 26

Q2. Risk measurement
Scenario dynamics of debt
1
3
4
6
14 15 16 17 18
GFN (% of GDP)
Time
13 / 26

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
pn
zn
zn
≥ gfnn
t − gfn , zn
≥ 0 14 / 26

Q3. Risk optimization of debt financing
Sovereign issues debt Xn
(j) to finance its debt
NIPn
t = In
t + m∈P(n)
J
j=1 Xm
τ(m)(j)CFn
t (j, m)
(NIP/D is the effective interest rate of debt)
Model (partial)
MinimizeX
n∈N
pn
NIPn
t
s.t.
Ψ(gfn) ≤ ω
15 / 26

What about debt stock dynamics?
Dn
t = D
a(n)
t−1 + GFNn
t −
m∈P(n)
J
j=1
Xm
τ(m)(j)1n
(j, m) − An
t
16 / 26

Q3. Risk optimization of debt ﬁnancingg
Third innovation: Endogeneity of interest rates
rn
t (j) = rn
ft + ρ(dn
t , j)
ρ(dn
t , j) = aj + (1 + bj )ˆρ(dn
t ).
17 / 26

Model: Optimize policy design
–Cost and risk tradeoffs
–Stock and flow tradeoffs
–Sustainability
Minimizex
n∈N
pn
NIPn
t
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 18 / 26

1 Conservative
Constrain the ratio for all states of the economy, i.e.,
gfnn
≤ ω, for all n ∈ Nt, t ∈ T
2 Risk neutral
Constrain the expected value of the ratio, i.e.,
E[gfnn
| n ∈ Nt] ≤ ω, for all t ∈ T
3 Risk adjusted CFaR constrained
19 / 26

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)
20 / 26

The relevance of optimizing
Omega
ExpectedNIP(%ofGDP)
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
21 / 26

Tradeoﬀ debt stock and debt ﬂow
19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
5101520
GFN/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 59
406080100
Debt/Y(%)
Year
1%
5%
25%
50%
75%
95%
99%
ω = 24
ω = 15.54
22 / 26

Additional ﬁscal eﬀort and debt sustainability
19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
5101520
GFN/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
6080100120
Debt/Y(%)
Year
1%
5%
25%
50%
75%
95%
99%
J
j=1
Xn
t (j) + utY n
t ≥ GFNn
t .
23 / 26

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 risk
tolerance declines
Lesson 5. Optimizing renders less volatile financing needs
but weighs on debt stock dynamics
Lesson 6. Optimizing helps more when the stock of
legacy debt is larger and its maturity shorter
Lesson 7. Feedback from debt stock into interest rates
affects risk management
24 / 26

Conclusions
Rich framework for studying sovereign debt sustainability
Stochastic debt stock and flow dynamics
Coherent risk measure
Endogenous interest rates
Optimal fiscal stance
Capture and quantify complex tradeoffs
Replicate stylized model from economic literature:
gambling for redemption (Conesa and Kehoe), cost of
delays (Blanchard)
Extension of feedback loop
X → D → r → Y → PB → X
25 / 26

Publications
Athanasopoulou et al., Risk management for sovereign
ﬁnancing within a debt sustainability framework, European
Stability Mechanism, Working Paper Series 31, Luxembourg,
July 2018.
Consiglio, A. and S.A. Zenios, Risk management optimization
for sovereign debt restructuring, Journal of Globalization and
Development, 6(2):181–213, J. Stiglitz et al. (editors), 2016.
Consiglio, A., Carollo, A. and S.A. Zenios, A parsimonious
model for multi-factor arbitrage-free scenario trees,
Quantitative Finance, 16:201-212, 2016.
26 / 26

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Risk management for sovereign financing within a debt sustainability framework