Sovereign Debt in the 21st Century, ADEMU at Toulouse School of Economics, 5/6 April 2018

1. Sovereign Default and Information Frictions
Christian Hellwig, Roberto Pancrazi, and Constance de Soyres
Toulouse School of Economics, University of Warwick, Toulouse School of Economics
August 22, 2017

2. The Sovereign Bond Spread Puzzle
• Sovereign bond spreads  historical default losses
→ high excess returns, esp. for low-rated bonds
• Spreads very volatile, only loosely connected to country fundamentals
• Longstaff et al.: Sovereign credit risk driven more by global than country-specific factors.
Global factor driving both default risk and default risk premia.
• Puzzle as large, if not larger than corporate credit spread puzzle
• Challenge for main models of sovereign debt dynamics in which default risk is fairly priced
and tightly linked to country fundamentals (Arellano 2008 etc.)

3. This paper
• Document some stylized facts supporting sovereign bond spreads puzzle
• Propose a resolution based on micro-structure frictions in bond markets (noisy information
aggregation)
• Explore impact of market frictions on country savings and default incentives.
• Key theoretical challenge: how to increase the level and volatility of spreads, and maintain or
increase borrowing incentives.

4. - EMPIRICS -

5. Empirical Motivation
Data:
• Dataset with CDS spreads on sovereign bonds of 69 countries, over
the period 2008-2014, at 4 maturities 2, 3, 5, and 10 years
(Datastream).
• History of sovereign credit ratings (Moody’s).
⇒ We construct a dataset of CDS spreads net of the US spread by
rating and by maturity.

6. Empirical Motivation
Stylized facts:
1 Sovereign bond CDS spreads are very high relative to historical
default losses.
2 The gap between CDS spreads and historical default losses is larger
for lower-rating bonds.
3 The gap present also for super safe (AAA, short maturity) bond:
something else than default risk per-se
⇒ Hard to explain in standard models, in which price reflects expected
losses and risk premium
⇒ The puzzle is as big, if not bigger, than for corporate bonds [Albagli,
Hellwig and Tsyvinski (2013)]

7. Empirical Motivation
Average CDS Spreads (bps) Annualized Loss Rates (bps)
2 yr 3 yr 5 yr 10 y 2 yr 3 yr 5 yr 10 yr
Aaa 12.52 14.45 27.71 26.05 0.00 0.00 0.00 0.00
Aa 47.52 55.54 73.38 79.11 0.00 2.55 7.20 4.36
A 112.23 120.99 137.85 139.05 1.55 7.04 9.77 22.99
Baa 174.47 189.63 212.26 222.43 9.95 10.91 10.26 7.56
Ba 244.48 258.92 278.30 281.07 32.41 40.98 45.83 51.31
B 977.91 959.56 907.97 892.71 120.43 107.03 94.25 69.34
Caa-C 1752.14 1583.39 1417.06 1235.32 939.29 724.24 434.55 217.27
Excess Return Sharpe Ratio CDS Spreads
2 yr 3 yr 5 yr 10 yr 2 yr 3 yr 5 yr 10 yr
Aaa 12.52 14.45 27.71 26.05 0.32 0.35 0.65 0.60
Aa 47.52 52.99 66.18 74.75 0.63 0.72 1.02 1.21
A 110.68 113.95 128.08 116.06 0.70 0.80 1.01 1.10
Baa 164.52 178.72 202.00 214.87 0.85 0.98 1.27 1.55
Ba 213.07 217.94 232.47 229.76 0.83 0.93 1.18 1.41
B 857.48 852.53 813.72 823.37 0.97 1.08 1.15 1.22
Caa-C 812.85 859.15 928.51 1018.05 0.44 0.49 0.55 0.61

8. Sovereign and Corporate Excess Returns

9. - THEORY -

10. A Super-Simple Model: Small Open Economy, 2 periods
• Preferences Uc0   EUc1 , where Uc  1
1−
c1−
• Date 0: Income y0  1, legacy debt b0
• Country decides whether to repay, borrows b1 at bond price q  qb1 .
• Date 1: Income y1  eu
, where u  N0,u
2
.
• Default at date 1 if y1 − b1 ≤ y1  u ≤ lnb1  − ln1 − 
• Value of default at date 0: D  default threshold for legacy debt B̄.

11. Country decision problem with no default at t  0:
max
b1
U1 − b0  b1qb1   EUmaxy1,y1 − b1 
• First-order condition for b1:
qb1   b1q′
b1 1 − b0  b1qb1 −
 Eeu
− b1 −
¦u ≥ lnb1  − ln1 − 
 Pru ≥ lnb1  − ln1 − 
• Evaluate date 0 default incentives through envelope condition on country objective.

12. Eaton-Gersovitz (1981)/Arellano (2008):
• Competitive bond-prices equal to repayment probabilities:
qb1   Pru ≥ lnb1  − ln1 −   1 − 
lnb1  − ln1 − 
u
• From FOC: qb1   b1q′
b1   qb1   Default option lowers marginal benefit of
borrowing
• Eeu
− b1 −
¦u ≥ lnb1  − ln1 −   Eeu
− b1 −
  Default option lowers marginal
cost of borrowing
• Ambiguous effect of borrowing option on debt level (negative if  is low, positive if  high)
• Idea: alter bond price formation to explore effect on savings incentives...

13. Eaton-Gersovitz with public signal of y1:
• Bond market has access to public signal z  Nu,z
2

qb1,z  Pru ≥ lnb1  − ln1 − ¦z  1 −  1 − 
lnb1  − ln1 −  − z
u
where   1/z
2
1/u
21/z
2 .
• Average bond price Eqb1,z  Pru ≥ lnb1  − ln1 −  doesn’t change (Martingale
property of information)
• Expected output, borrowing b1 and date 0 default threshold B̄ are all increasing in z.
• Information adds to volatility (but not level) of spreads, volatility is tightly linked to
informativeness of spreads about future default risk!

14. Noisy information aggregation:
• Unit measure of risk-neutral, informed foreign bond traders, decide whether to buy up to b1
units of bonds
• Private Information: signals xi  Nu,x
2
 iid across bond traders
• Demand by uninformed bond traders: b1s, where s  N,s
2
, stochastic, inelastic
• Noisy Rational expectations equilibrium: demand function dx,q ∈ 0,b1 , bond price
function qu,s, such that:
i bond traders’ demand is optimal, given information x,q, and
ii markets clear for all u,s.

15. Equilibrium Characterization:
• Equilibrium characterized by threshold rule: buy if xi ≥ x̂P
• Demand of bonds by informed traders: b1 1 −   x̂P − u
• Market-clearing:
b1  b1 1 −   x̂P − u  b1s
x̂P  z  u  xs
• Price

qb1,z determined from indifference condition for trader with signal x̂P  z:

qb1,z  Pru ≥ lnb1  − ln1 − ¦x  z,z  1 −  1 −


lnb1  − ln1 −  −

z
u
where

  1/x
21/z
2
1/u
21/x
21/z
2  .
• Market overweighs z: extra adjustment in marginal trader expectations to absorb shocks

16. Implications for Borrowing:
•

qb1,z  b1

q′
b1,z  qb1,z  b1q′
b1,z for most z: cheaper credit, higher b1 except if
initial b1 very high or z very low.
• Note: marginal costs (marginal disutility of repayment) is unchanged from before (since
based on undistorted expectations)
• Spreads loose disciplinary role (flatter in b1, less correlated with actual defaults)
• z only loosely connected to u  country credit conditions disconnected from fundamentals,
borrowing driven by noise trader shock
• Date 0 default incentives: lower for most realizations of z, but exposure to defaults driven by
noise trader shocks (low z realizations)

17. Implications for Default:
• higher default incidence at t  1: due to higher b1
• Ambiguous at date 0: higher for low initial b0 because of exposure to low z shocks...
• but lower for high initial b0 ("gambling for ressurrection")
• Conclusion: Noisy information aggregation model can jointly account for:
 higher, more volatile spreads
 higher debt levels
 higher default incidence

18. Theoretical model: Main Ingredients
• Sovereign debt model a la Arellano (2008)
• Simplifying assumptions: CRRA utility + random walk income
growth
• New ingredient: Information frictions between the traders who buy
the sovereign bonds

19. Theoretical model: Main Ingredients
• Sovereign debt model a la Arellano (2008)
• Simplifying assumptions: CRRA utility + random walk income
growth
• New ingredient: Information frictions between the traders who buy
the sovereign bonds
There are 2 types of traders:
• Informed traders: receive a private signal about future income growth
• Noise traders: buy a random fraction of the bonds
In an environment with dispersed information, the market-clearing
price is an endogenous public signal.

20. Model: Timing
• Sovereign: default decision, choose debt and consumption
• Traders: observe public/private signal and price the bond
t
(at, yt)
Default
Decision
yt+1 realizes (unobserved) Sovereign
forms expectations
on q(at+1, yt , ζt )
and chooses at+1
public signal ζt reveals
private signal xt realizes
traders submit bids
market clear bond price emerges
t + 1
(at+1, yt+1)
• If Default, permanent exclusion from financial market

21. Model environment: Sovereign
• Preferences:
Et
∞
s=0
ρs
U(ct+s)
where 0 < ρ < 1 is the discount factor, c is consumption, and U(·)
is increasing and strictly concave
• Income growth process:
ln (yt+1/yt) = ln t+1 ∼ N 0, σ2

22. Model environment: Assets and default
Sovereign
• has access to perpetuities paying {λ, λ (1 − λ) , λ (1 − λ)
2
, ...}
• can decide to default on its debt at any time
• after a default, all the sovereign’s debt is erased, it is excluded
permanently from financial markets, and it incurs direct output costs

23. Model environment: Sovereign’s value function
V (at, yt) = max V (yt), max
ct ,at+1
E {U (ct) + ρV (at+1, yt+1)}
under the budget constraint
ct + q (at+1, yt, yt+1, ζt) (at+1 − (1 − λ)at) = yt + λat
• V (at, yt): sovereign’s value function at time t
• V (yt): default value at time t

24. Model environment: Sovereign’s value function
V (at, yt) = max V (yt), max
ct ,at+1
E {U (ct) + ρV (at+1, yt+1)}
under the budget constraint
ct + q (at+1, yt, yt+1, ζt) (at+1 − (1 − λ)at) = yt + λat
• V (at, yt): sovereign’s value function at time t
• V (yt): default value at time t
The Sovereign’s Repayment set R(at+1):
R(at+1) = {yt+1 : V (yt+1) ≤ max
ct ,at+2
E {U (ct) + ρV (at+2, yt+2)}

25. Model environment: Assets and default
Traders
• Large number, competitive, risk neutral
• Have access to an international credit market where they can
borrow/lend at rate r
• Recover a fraction q ∈ (0, 1) of their initial investment if the country
defaults
• Face limits to their asset positions

26. Model environment: Assets and default
Traders
• Informed traders (unit measure) receive a noisy private signal
xt ∼ N ln
yt+1
yt
, β−1
• Noise traders buy a random fraction of the bonds Φ(ut) where
ut ∼ N 0, 1
δ2 .
• They all observe the endogenous public signal ζt coming from the
price as they submit their bids on the market.

27. Signal threshold condition
Informed trader submits an order of −a , whenever;
˜q (α + µ, ζ) ≤
1
1 + r
q +
∞
ln α+µ
α
λ + (1 − λ) ˜q ˜α α − q d ˜f ln | x, ζ
⇔ x ≥ x(α + µ, ˜q)
˜f (·)= cdf of the future income growth conditional on the public signal ζ
and the private signal x

28. Market Clearing and equilibrium bond price
The market clearing condition is:
a 1 − Φ β (x(α + µ, ˜q) − ln ) + a Φ(u) = a
Hence, the indifference condition for the signal threshold defines the
traders’ bond price:
˜q (α + µ, ζ) =
1
1 + r
q +
∞
ln
(α+µ)
α
λ + (1 − λ) ˜q ˜α α − q d˜h ln | ζ, x = ζ
where ˜h(· | ζ, x = ζ) is the conditional distribution of ln such that:
ln ( | ζ, x = ζ) ∼ N
β(1 + δ)
1
σ2 + β(1 + δ)
ζ,
1
1
σ2 + β(1 + δ)
= N γpζ, (1 − γp)σ2

29. Recursive equilibrium
A Recursive Bayesian Equilibrium consists of a bond price function ˜qt,
a value function ˜V (·), a policy rule ˜α(·), a repayment set R(at+1), a
schedule for the informed traders ai (at+1, yt, ˜qt, ζt, xt) ∈ [0, −at+1], and
informed traders’ beliefs H(· | at+1, yt, ˜qt, ζt, xt) such that:
(i) given the repayment set, ˜qt satisfies the bond price equation
(ii) the value function and the policy rule, combined with the repayment
set, solve the Bellman equation
(iii) the schedule for the traders is optimal given their beliefs
(iv) traders’ beliefs are consistent with Bayes’ rule
(v) the bond price function clears the market for all (at+1, yt, yt+1, ζt, ut).

30. Simplifying assumptions
Proposition Let us assume that U(c) = c1−ψ
/1 − ψ and V (y) = Dy1−ψ
where D is a constant, and ψ the CRRA parameter. With the income
growth process following a random walk, we can re-write the model using
a single state variable, the Asset/Debt-to-GDP ratio α = a/y. Then:
˜V (a, y) = y1−ψ
˜v(α)
˜q(a , y, ζ) = ˜q(a /y, ζ)
˜α(a, y) = ˜α(α)y
with:
• ˜α(α) = α + µ = a /y
• µ = (a − a)/y

31. Simplifying Assumption: Sovereign’s value function
˜v(α) = max D, max
c,µ
E U
c
y
+ ρ (α + µ)
1−ψ
(α )
ψ−1
˜v (α )
subject to:
c
y
= 1 + λα (1 − ˜q(α + µ, ζ)) − µ˜q(α + µ, ζ)
⇒ The sovereign decides to default whenever α ≤ α = ˜v−1
(D).

32. - NUMERICAL ANALYSIS -

33. Calibration
Parameter Value Explanation
ρ 0.82 Discount factor
ψ 2 Coefficient of relative risk aversion
σ 0.025 Standard deviation of output growth
λ 0.9 Maturity structure
r 0.02 Constant risk-free interest rate
κ 0.985 Share of output remaining after a default
q 0.6 Recovery value of lenders
Strategy:
• Vary the precisions of the signals (β, δ),
• (β, δ) → 0 = frictionless model; bond price reflects fundamental
default risk

34. Bond Price Schedule
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Debt-GDP ratio
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Traderbondprice
Low Public Signal
Average Public Signal
High Public Signal
Frictionless
(a) Higher Precision
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Debt-GDP ratio
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Traderbondprice
Low Public Signal
Average Public Signal
High Public Signal
Frictionless
(b) Lower Precision
Figure: Bond Price Schedule

35. Spreads and information frictions
Information frictions increase average spreads due to overreaction of
traders under bad signals
Info Precisions Frictionless Friction Model
δ = β std priv. std pub. ¯α Average ¯α Average Good Signal Bad Signal
0.75 2.6% 3.1% -0.43 0.24 -0.42 0.35 0.23 0.58
0.5 2.9% 4.2% -0.43 0.24 -0.37 0.43 0.24 0.74
0.25 3.5% 7.0% -0.43 0.24 -0.36 0.67 0.27 1.38
Table: Spreads

36. Info frictions and fundamental default risk
Information frictions are larger when default risk is higher
Info Precisions Frictionless Friction Model
ρ = 0.82
δ = β ¯α Average ¯α Average Good Signal Bad Signal
0.75 -0.43 0.24 -0.42 0.35 0.23 0.58
0.5 -0.43 0.24 -0.37 0.43 0.24 0.74
0.25 -0.43 0.24 -0.36 0.67 0.27 1.38
ρ = 0.875
δ = β ¯α Average ¯α Average Good Signal Bad Signal
0.75 -0.47 0.24 -0.45 0.35 0.23 0.58
0.5 -0.47 0.24 -0.44 0.40 0.23 0.64
0.25 -0.47 0.24 -0.40 0.53 0.23 0.99
Table: Information Frictions and Default Risk (i)

37. WHAT ARE INFORMATION
FRICTIONS?

38. Spreads, Rating, Transparency
Cross-section
0 1 2 3 4 5 6
Rating
-500
0
500
1000
1500
2000
2500
Spread Rating and Spread
ARG
AUSAUT
BHR
BEL BRA
BGR
CHLCHN
COL
CRI
HRV
CYP
CZE
DNK
DOM
EGY
EST
FINFRADEU
GRC
GTM
HUN
ISL
IDN
IRL
ISR
ITA
JAM
JPN
KAZ
KOR
LVA
LTU
MYS
MLT MAR
NLDNOR
PAK
PANPER PHLPOL
PRT
QAT
ROU
RUS
SLV
SAU
SRB
SGP
SVK
SVN
ESP
SWECHE
THA
TUR
UKR
GBR
URY
VEN

39. Spreads, Rating, Transparency
-500
1
0
500
0.8 6
1000
Spread
50.6
1500
BCI
4
2000
Rating
0.4 3
2500
20.2
1
0 0
(a) Rating, Transparency and Spreads

40. Spreads, Transparency, and Rating
Si = β0 + βf fundami + βj Xj + βT Transpi + βT,f fundami Transpi + εi .
(a) (b) (c) (d) (e) (f) (g) (h)
fundamental, βf 121.5*** 113.9*** 92.0* -98.1 -88.2 -58.7 -27.7 -3.8
(0.00) (0.00) (0.09) (0.24) (0.30) (0.50) (0.75) (0.54)
transparency, βT 155.9 -214.3 -458.1 -444.9 -553.4 -362.3
(0.63) (0.56) (0.24) (0.29) (0.20) (0.25)
Interaction, βT,f 301.2** 324.5** 286.4** 268.6** 24.24**
(0.01) (0.01) (0.02) (0.03) (0.01)
Constant, β0 -43.6 -719.7 -723.4 111.8 424.4 312.2 262.2 -12.6
(0.62) (0.49) (0.49) (0.39) (0.69) (0.78) (0.81) (0.98)
controls NO YES YES NO YES YES YES YES
dependent 2y 2y 2y 2y 2y 2y 2y 2y
transparency BCI BCI BCI BCI BCI CPI WGI BCI
fundamental rating rating rating rating rating rating rating FF
Table: Regressions - 2 year Spreads

41. Spreads, Transparency, and Rating
Main take-away:
Non-linear effect of Transparency on Sovereign Spreads
• Transparency does not affect spreads when default risk is low
• Transparency significantly affects spreads when default risk is high
• Robust to different maturity
• Robust to different measure of transparency

42. Conclusion
1 Sovereign bond Excess Return Puzzle:
• CDS spreads >> historical default losses.
2 Endogenous default model with information frictions:
• Bad signals on future income affects equilibrium spreads
• Effects larger when high fundamental default risk
3 Transparency, Ratings, and Spreads:
• Lack of Transparency contributes to increase spreads in higher
default risk country

43. Conclusion
1 Sovereign bond Excess Return Puzzle:
• CDS spreads >> historical default losses.
2 Endogenous default model with information frictions:
• Bad signals on future income affects equilibrium spreads
• Effects larger when high fundamental default risk
3 Transparency, Ratings, and Spreads:
• Lack of Transparency contributes to increase spreads in higher
default risk country
Next Steps:
• Work on refined calibration of the model
• Tighten the link between Transparency and Information frictions