risk management optimization for sovereign debt financing · athanasopoulou et al., risk management...

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


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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//Voxeu.org.


Research issues

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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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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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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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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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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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Feedback loop

X → D → r → X

Uncertain correlated Yt ,PBt , rft

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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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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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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


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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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


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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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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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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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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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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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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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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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

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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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

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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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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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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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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risk management optimization for sovereign debt financing · athanasopoulou et al., risk management...

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