Sovereign Debt, Default Risk, and the Liquidity ofGovernment Bonds

Gaston Chaumont
University of Rochester
Fiscal Policy and Sovereign Debt
IMF-CARF-TCER-Waseda University Conference
June 7, 2024

Motivation: Greek GDP Cycle, Credit Spread, and Liquidity(A) GDP Cycle, Credit Spread, and Bid-Ask Spread
152500
2000
51500
01000

Basis Points% Dev. from Trend

10-5500-102006 2007 2008 2009 2010 2011 2012

0Quarter• Credit spreads and bid-ask spreads were very large in the crisis• Bid-ask spreads arise because bonds are traded in OTC markets• Liquidity is endogenous to macro conditions
1Dealers

MarketsStructure

Correlations

VolumesAuctionRates

Debt

This Paper
Liquidity:• Transaction cost perspective: resources and time to trade• Measured mainly through bid-ask spreads

2This Paper
Liquidity:• Transaction cost perspective: resources and time to trade• Measured mainly through bid-ask spreads
Research Questions:• How the state of the economy affects sovereign bonds liquidity?
• How does liquidity affect bond prices and gov’t incentives to default?

2This Paper
Liquidity:• Transaction cost perspective: resources and time to trade• Measured mainly through bid-ask spreads
Research Questions:• How the state of the economy affects sovereign bonds liquidity?
• How does liquidity affect bond prices and gov’t incentives to default?
Approach:• Incorporate trading frictions into a sovereign default model• Illiquidity due to search frictions in the secondary market• Liquidity and gross flows traded are endogenous and affects default risk
2
through bond prices

Outline

1. Overview of the default model with endogenous illiquidity
2. Some model Implications
3. Conclusions

3

ModelModelTime and markets• t = 1, 2, ...
• Centralized market: Walrasian, market clearing price for bonds is q
• Decentralized market: subject to search frictions
Three types of agents:• Government: Issues long-term bonds only in centralized market• Dealers: Access centralized market and decentralized market• Investors: Access only decentralized market• High type: Derive utility uh > 0 from bond holdings (”buyers”)• Low type: Derive utility u` < 0 from bond holdings (”sellers”)• Bond holdings are a ∈ {0, 1}• Investors distribution: {H0 , H1 , L1 }, I¯ = H0 + H1 + L1
Timing of Actions

4

Graphical Description of the Model

Environment

Dealers

MktClearing

Government

Default (Autarky)

Centralized Market
Dealers

Price = q

Dealers

Secondary Market
Submarket f1

Secondary Market
Submarket f2

Investors

Investors

5

Government’s Problem

more

Government’s option value of default is
V (y , B ) =max (1 − δ)V R (y , B ) + δV D (y ),δ∈{0,1}V D (y ) = U (h (y )) + βEy 0 |y V D (y 0 )V R (y , B ) = max
U (c ) + βE‘|y V (y 0 , B 0 )0Bwithc = y + q (y , B, B 0 ) B 0 − (1 − λ)B − λB
• B caputres potential demand and supply in secondary market:• Potential sellers are L1 = ζB and potential buyers are H0 = I¯ − B• Liquidity enters into Gov’t problem through V R (·)• In particular, through q (y , B, B 0 ), the price in centralized market
6

Centralized Market Clearing• Supply of bonds is upward slopping and given by+B 0 − (1 − λ) B + α f`1 (s; q ) (1 − λ) × [Mass of sellers(L1 )]
|{z}
{z}
|
Government’s supply

Dealers’ supply• Demand for bonds is downward slopping and given by−α fh0 (s; q ) × [Mass of buyers(H0 )]|{z}
Dealers’ demand7

Centralized Market Clearing• Supply of bonds is upward slopping and given by+B 0 − (1 − λ) B + α f`1 (s; q ) (1 − λ) × [Mass of sellers(L1 )]|{z}{z}|Government’s supply

Dealers’ supply• Demand for bonds is downward slopping and given by
−α fh0 (s; q ) × [Mass of buyers(H0 )]|{z}
Dealers’ demand• Trading probabilities derived from expected gains from trade:Buyers:0 , B 0 )] I 1 (s 0 ) − I 0 (s 0 )E1−δ(y[0y |y
max α(f ) −(f + q (s )) + uh +
1+r
f| {z }
ask priceSellers:

0 , B 0 )] I 1 (s 0 )E1−δ(y[0y |ymax α(f ) (q (s ) − f ) − u` −
1+rf| {z }bid price7

Quantitative Analysis

Model Calibration: New Parameters

Parameteruhu`
ζγI¯

Value
0.001
-0.1600.315
0.00025
5.000

Target/Source
Eu = 0.
mean S B −A
Quarterly turnover rate 0.78
Minimum S B −A ≈ 5 bpts
Large. Never binding

8

Quantitative importance of secondary market frictions
Key Parameters
Low type probability: ζ
Dealer’s entry cost: γ × 100
Moments
Mean bond spread (%)
Std. dev. bond spread (%)
Debt to output (%)
Mean bid-ask spread (bps.)
Bonds turnover rate (%)

Baseline
0.315
0.025
Baseline
3.42
2.18
124
76
78

Frictionless—
0.000
Frictionless
2.67
2.67
139
—
—

Longer holding
0.15750.025
Longer holding
3.03
2.81
134
74
42

Hold to maturity
0.000
0.025
Hold to maturity
2.00
1.83
137
71
6

1. Trading frictions significantly tighten the borrowing constraint of thegovernment
2. If investors hold bonds for longer horizon spreads are lower andgovernment borrows more
9Additional model implications

Implication 1: Trading frictions are important for spreads
1. Trading frictions and secondary market flows matter for bond prices(A) Spreads Decomposition

Basis Points

2500
2000
1500
1000
5000
2006

2007

2008

20092010

2011

Quarter
Total Spread

Liquidity Premium

Default Risk

10

Implication 2: Risk and liquidity interact in equilibrium

2 Changes in default risk affect size of flows and change the liquidity
component in bond prices

Buyers:

Ey 0 |ymax α(f ) −(f + q (s )) +f| {z } 1 000Ih (s ) − Ih (s ) 1+r[1 − δ(y 0 , B 0 )]ask priceSellers:

001 (s 0 )E1−δ(y,B)]I[y 0 |y`max α(f ) (q (s ) − f ) −
1+rf| {z }bid price11

Implication 3: The distribution of bond holders matters
3 Changes in the distribution of bond holders affect bond prices• Supply of bonds is upward slopping and given by
+B 0 − (1 − λ) B + α f`1 (s; q ) (1 − λ) × [Mass of sellers(L1 )]|{z} |{z}Government’s supply

Dealers’ supply• Demand for bonds is downward slopping and given by−
α fh0 (s; q ) × [Mass of buyers(H0 )]|{z}
Dealers’ demand12Implication 4: Policy can affect liquidity and bond prices
4 Secondary market purchases of bonds can increase bond prices byincreasing average holding horizon and reducing sell volumes
0

Secondary Market Policies and Spreads

Basis points-50-100-150-200-250-300
2009

10% less sellers (20% less sellers
50% less sellers
No sellersSMP)

2010

2011

Quarter13

ConclusionsConclusions
I proposed a model of sovereign default with endogenous liquidity in thesecondary market
Implications:
1. Bond prices depend on trading frictions and secondary market flows
2. Changes in default risk affect size of flows and change the liquidity
component in bond prices
3. Changes in the distribution of bond holders affect bond demand andsupply flows, liquidity and prices
4. QE policy can affect liquidity and bond prices by changing the average
holding horizon of bonds and reducing sell volumes

Argentina14

Sovereign Debt, Default Risk, and the Liquidity ofGovernment Bonds

Gaston Chaumont
University of Rochester
Fiscal Policy and Sovereign Debt
IMF-CARF-TCER-Waseda University Conference
June 7, 2024

Default “shock” and yields in Argentina
Yields Argentine outstanding sovereign bonds (p.p.)
80
70
60
50
40
30
20
10

9/
2/
19
10/2
/1
9

7/
2/
19
8/
2/
19

5/
2/
19
6/
2/
19

2/
2/
19
3/
2/
19
4/
2/
19

9/
2/
18
10/2
/1
8
11/2
/1
8
12/2
/1
8
1/
2/
19

7/
2/
18
8/
2/
18

0

• Updated belief of elections upcoming election outcomes lead to large
increase in bond yields

Default “shock” and Bid-Ask Spreads in Argentina
Bid-Ask spreads Argentine sovereign bonds (basis pts.)
2000
1800
1600
1400
1200
1000
800
600
400
200

8/
2/
19
9/
2/
19
10/2
/1
9

4/
2/
19
5/
2/
19
6/
2/
19
7/
2/
19

1/
2/
19
2/
2/
19
3/
2/
19

9/
2/
18
10/2
/1
8
11/2
/1
8
12/2
/1
8

7/
2/
18
8/
2/
18

0

• Updated belief of elections upcoming election outcomes lead to large
increase in bid-ask spreads

Default “shock” and Bid-Ask Spreads in Argentina
Bid-Ask spreads Argentine sovereign bonds (basis pts.)
800
700
600
500
400
300
200
100

9/2/
1910/2
/1
97/
2/
198/
2/
19

5/
2/
19
6/
2/
19

2/
2/
19
3/
2/
19
4/
2/
19

9/
2/
18
10/2
/1
8
11/2
/1
812/2
/1
8
1/
2/
19

7/
2/
18
8/
2/
180

• Updated belief of elections upcoming election outcomes lead to large
increase in bid-ask spreads

Greece: Interest Rates in the Market and at Issuance

BackInterest Rates Secondary Market and at Auction
765432102003 2003 2004 2004 2005 2005 2006 2006 2007 2007 2008 2008 2009 2009 2010
Q1 Q3 Q1 Q3 Q1 Q3 Q1 Q3 Q1 Q3 Q1 Q3 Q1 Q3 Q1
MarketAuction

Greece: Secondary Market Volumes

Back

Volumes: Monthly Turnover Rate HDAT
Zoom

90.00
80.00

1.00

70.00
0.50

60.00
50.00

0.00
2010M540.00
30.00

2013M520.00
10.00
0.00

Turnover =Transactions
× 100.
Outstanding Bonds

2016M5Greece: Debt and International Investment Position(-) NIIP (%GDP) and Public Debt (%GDP)

180(-) NIIP (%GDP)
Public Debt (%GDP)

160% GDP14012010080602006

2007

2008

2009

Quarter

2010

2011

2012

Back

Sovereign Bonds are Traded in Decentralized Markets• Only a few banks can directly purchase bonds from gov’t

BackDealers• All other investors trade bonds in the secondary market:• Participants: banks, institutional investors, private investors, etc.
• Volumes in secondary market 12 times larger than primary market• Secondary markets are OTC where transactions are• Decentralized• Bilateral• Costly• Time consuming• A standard liquidity measure is the bid-ask spreads
S B −A ≡qA − qB
× 10, 000
(q A + q B ) /2

7.

GreeceGreece: List of Primary Dealers

BackA. List of Primary Dealers1
FIRM

Greece (GR)Firm’s location

Alpha Bank

XAthens

Bank of America Merrill Lynch

X

LondonBanca IMI

Barclays

BNP Paribas

X

X

X

Citigroup

X

MilanLondon

LondonLondonCommerzbank

XFrankfurt

Deutsche BankX

Frankfurt

Goldman Sachs

X

LondonX

LondonCrédit SuisseX

EFG Eurobank-Ergasias

HSBC

X

X

J.P. Morgan

Morgan Stanley

National Bank of Greece
NatWest Markets

NomuraX

LondonXUBSXTOTAL
KEY:Athens

LondonX

Unicredit

AthensX

X

Piraeus Bank

Société Générale

LondonXX21

AthensLondonAthensParisLondon
MunichSource: AFME and Greek Central Bank

PL1098
765432
10Jan-1718

41701622

21

20

65

LV

0

1098
7654
32
10

Jan-15Jan-16

Jan-14Jan-15Jan-16

Jan-14Jan-17Jan-16

5
Jan-13

10

Jan-15Jan-14Jan-13Jan-1320

Jan-09

Jan-08Jan-07

Jan-06

Jan-16

Jan-15Jan-14Jan-13Jan-12

Jan-16

Jan-15Jan-14Jan-13Jan-12

Jan-11

GR

Jan-1021

Jan-1122Jan-10Jan-09

Jan-08Jan-16Jan-15Jan-14Jan-13Jan-12Jan-11Jan-10Jan-09

Jan-084035302520151050Jan-12Jan-12Jan-11Jan-10Jan-09

Jan-08Jan-12LTJan-11UK

Jan-11Jan-10SK

Jan-07

23Jan-09

24Jan-08

0Jan-07

NL

Jan-0715Jan-06

Jan-160Jan-06

Jan-16

Jan-155Jan-06

Jan-16

Jan-15Jan-1424Jan-10198Jan-15

Jan-14FR

Jan-0912Jan-14

Jan-13Jan-12Jan-11

20Jan-08

3Jan-1025Jan-07

4Jan-09

Jan-08DE

Jan-06CZ

Jan-170Jan-164Jan-15

16Jan-13

5Jan-1320Jan-1210Jan-14SI

Jan-1110Jan-1212Jan-10Jan-1645403530252015
1050Jan-1316
Jan-090Jan-08

ITJan-11

20Jan-10

20Jan-09

2525

Jan-0815Jan-1230

Jan-1112Jan-10FI

Jan-07

Source: AFME Primary Dealers Handbooks and national DMOs

Jan-0913Jan-07

14Jan-07

Jan-150Jan-06BE

Jan-06

Jan-14Jan-1315

Jan-06

Jan-16

Jan-1525

Jan-07Jan-16

Jan-15Jan-12

Jan-11

Jan-10

Jan-0920

Jan-08Jan-06

Jan-16

Jan-14Jan-13Jan-12Jan-08Jan-0730

Jan-07

Jan-06

Jan-16

Jan-15Jan-14Jan-13Jan-12

Jan-11

Jan-10

Jan-06

5Jan-14Jan-13Jan-12

Jan-11

Jan-10

Jan-09

Jan-08Jan-16

Jan-15Jan-14Jan-13Jan-1210Jan-16Jan-15ROJan-156Jan-148Jan-1410Jan-13BG

Jan-134Jan-128Jan-1212Jan-116Jan-111412Jan-105Jan-1114Jan-09

10Jan-107Jan-08

15Jan-10SE

Jan-09

9Jan-08

15Jan-09

IE

Jan-0816Jan-09

18Jan-07

19Jan-07

ES

Jan-07

20Jan-06

Jan-16

21Jan-06

Jan-16

Jan-15Jan-110Jan-06

Jan-16

Jan-15Jan-14AT

Jan-07

Jan-06

Jan-17Jan-15Jan-14Jan-1025Jan-08

1

Jan-16

Jan-14Jan-13Jan-09

Jan-0820Jan-07

20Jan-15

Jan-13Jan-12Jan-11Jan-07

Jan-0630

Jan-06

Jan-17Jan-16

Jan-15Jan-14Jan-13

Jan-122018
1614121086420

Jan-14Jan-12

Jan-11

Jan-10

Jan-09

Jan-08Jan-07

Jan-06

5Jan-13Jan-11

Jan-10

Jan-09

Jan-08Jan-07

Jan-06

10Jan-13

20
Jan-12

Jan-10

Jan-09

Jan-08Jan-07

Jan-0615

Jan-12

16
1412
1086
420
Jan-11

6

Jan-11

8

Jan-1010Jan-09

8Jan-0822

Jan-102Jan-0724

Jan-094Jan-0623

Jan-082.12

Jan-07

Jan-06

Europe: Number of Primary Dealers 2006-2017
Source: AFME Primary Dealers Handbooks and national DMOs. Average and mediansof AT, BE, DE, DK, ES, FI, FR, GR, IE, IT, NL, PT, SE, SI and UK

Back

Number of primary dealers in Europe by jurisdiction: 2006-17

DK25

20

150PT

Source: Association for Financial Markets in Europe
Source: AFME Primary Dealers Handbooks and national DMOs

Government Bond Data Report
Page 10

Appendix to the ModelInvestors Types and Transitions
Investors: I¯ = H0 + H1 + L1
High type with 0 assets( H0 )
α(fh0 )

Outside themarket

λHigh type with 1 asset( H1 )λζ
Low type with 1 asset(L1 )• α (·) is trade prob., λ mature prob., ζ prob. type switchesα(f`1 )Timing of Actions

Environment

Government
B 0 chosen(y , B )repaytdefault
period t stops here
(start t + 1 in default)

preference shock
to investors

λB mature(y 0 , B 0 )t +1
markets open
(centralized anddecentralized)

Government

Back• Maximizes representative household utility: ∑t βt U (ct )• Income y ∈ Y ≡ {y1 , y2 , ..., yN } with Markov transitions πi,j
• Issues debt in the centralized market• Each bond matures randomly with probability λ ∈ [0, 1]• Can default on their debt obligations• There is an output loss h (y ) ≤ y• Goverment is excluded from debt markets• Regains market access with prob. φ ∈ (0, 1), and B = 0• Takes as given a pricing schedule q (·) and policies of investors anddealers

Dealers• Risk-neutral and there is competitive entry at cost γ > 0• No Inventories: permanent access to centralized market• Dealers are static and profits are Π(f ) = −γ + ρ(f )f• By free entry:
ρ (f ) =γf• Matching function implies α(f ) increasing and concave

DiagramDealer’s Problem and Market Tightness

BackDealers choose which submarket f to visit to maximize profits given bymax Π (f ) = max {−γ + ρ (θ (f )) [f + q (s ) − q (s )]}ffThen, free entry implies that
Π (f ) ≤ 0 and θ (f ) ≥ 0,with complementary slackness.
Market tightness in each submarket is given by(ρ−1 γfif Π (f ) = 0,
θ (f ) =0otherwise.

How are Bonds Priced? An Example
Assume investors hold bonds until maturity and a Telephone-Line matching functionM (d, n) =d ×nd +nThen, market clearing price isq (s ) =#2"11Ey 0 |y {[Ih1 (s 0 ) − Ih0 (s 0 )][1 − δ(y 0 , B 0 )]} − γ1+r|{z}1 − ∆BH|{z}|{z 0 }
Default Risk
Value of holding bondLiquidity Component

Liquidity Components:• Intermediation frictions γ: more efficient matching reduce liquidity penalty
• Relative supply ∆B/H0 = [B 0 − (1 − λ) B ] / I − (1 − λ) B : the larger relative
supply the higher liquidity penalty• Bond maturity λ: longer maturity implies less liquidity penalty (I¯ > B 0 )Pricing and the Bid-Ask Spread

BackImplied interest rate, rg (s ):q (s ) =λ + (1 − λ ) z
λ + rg (s )Interest Rate Spread, S R (s ):S R (s )≡ (1 + rg (s ))4 − (1 + r )44
λ + (1 − λ ) z=1+− λ − (1 + r )4 .
q (s )

Bid-Ask Spread
S B −A (s ) ≡q A (s ) − q B (s )q (s )q B (s )≡ q (s ) − f B (s )q A (s )≡ q (s ) + f A (s )Functional Forms

Back

Government utility function
U (c ) =c 1− σ1−σOutput under default
h (y ) = y − max 0, d0 y + d1 y 2
Matching function

M (d, n) =d ×nd +nModel Calibration: Standard Parameters

Parameterσρyηyφ
βd0
d1
λzr
Non-Targeted Moments

Value
2.000
0.953
0.020
0.050
0.976
-0.522
0.650
0.039
0.011
0.010

Back

Target/Source
Literature
AR(1) for GDP Cycle
AR(1) for GDP Cycle
5 years average exclusion
Match Default Probability of 0.68%average r (s ) − r
standard deviation of r (s ) − r
6.5 year average time to maturity
So price in PM is at par-value
˜4% annualNon-Targeted Moments

Momentσc /σyρS R ,tb/y
ρS R ,cρS R ,yρy ,tb/y
Back

Model
1.07
0.58
-0.77
-0.75
-0.43

Data0.98
0.71
-0.45
-0.56
-0.59