Illiquidity in Sovereign Debt Markets by Global Interdependence Center

Illiquidity in Sovereign Debt Markets Juan Passadore

Yu Xu

Global Interdependence Center

February 27, 2020

Introduction

Outline

Introduction

Model: What we do?

Quantitative Analysis: What we Find?

Conclusions

Introduction

Sovereign debt: debt capacity, spreads, welfare...main friction: lack of commitment to issuanceâ&#x20AC;&#x2122;s and repayment credit risk premium However...Sov. bonds are traded in OTC, infrequent trading So, sovereign countries compensate credit+liquidity

Motivation

How much of total spreads is explained by each one? Welfare implications of frictions? How it varies over the cycle? Main Contribution: Quantify sovereign default and liquidity risk. Credit Risk Puzzle. Normative Implications. Why care? Long run policies. Debt management. Policies crisis.

Introduction

Motivation

Introduction

Motivation

Introduction

Motivation

Introduction

Motivation

Introduction

Motivation

Introduction

Motivation

Introduction

Motivation

Introduction

Motivation

Introduction

Motivation

Introduction

Motivation

Introduction

Motivation

Introduction

Today... What we do and What we Find

What we do? Present a framework for the sovereign setting: Default ⇐⇒ Liquidity

sov debt: endowment economy, incomplete markets, limited commitment, benevolent government, debt issued in prim. market, long term debt, recovery OTC: non-diversifiable liquidity shocks, search friction sec market ... with probability (ζ) liq shock , cost of carry (hC ) and find a match (λ)

What we find? Quantitative exercises calibrated to Argentina: Sizable component of total spreads...23 pct Match high spreads and low default frequency...credit risk puzzle Substantial welfare gains, business cycle frequencies

In the end, suggest some applications/extensions

Introduction

Today... What we do and What we Find

What we do? Present a framework for the sovereign setting: Default ⇐⇒ Liquidity

In the end, suggest some applications/extensions

Introduction

Today... What we do and What we Find

What we do? Present a framework for the sovereign setting: Default ⇐⇒ Liquidity

In the end, suggest some applications/extensions

Introduction

Today... What we do and What we Find

What we do? Present a framework for the sovereign setting: Default ⇐⇒ Liquidity

In the end, suggest some applications/extensions

Introduction

Today... What we do and What we Find

What we do? Present a framework for the sovereign setting: Default ⇐⇒ Liquidity

In the end, suggest some applications/extensions

Introduction

Today... What we do and What we Find

What we do? Present a framework for the sovereign setting: Default ⇐⇒ Liquidity

In the end, suggest some applications/extensions

Introduction

Today... What we do and What we Find

What we do? Present a framework for the sovereign setting: Default ⇐⇒ Liquidity

In the end, suggest some applications/extensions

Introduction

Related Literature Sovereign Debt and Default: Chattarjee and Eiyungor (2012), Eaton Gersovitz (1981), Aguiar Gopinath (2006), Arellano (2008), Arellano and Ramanayanan (2012), Yue (2010), Hatchondo Martinez (2009), Borri Verdelhan (2009), Yue (2009), Hathcondo et al (2016), Hatchondo et al (2017), Boccola Dovis (2017), Chaumont (2018), Morelli Ottonello Perez (2012), Aguiar et al (2019).

Search in OTC Markets: Duffie Garleanu Pedersen (2005), Duffie Garleanu Pedersen (2007), Afonso Lagos (2012), Atkeson (2013).

Liquidity and default in Corporate Finance: He and Milbrandt (2014), Leland Toft (1996), Chen Cui He Milbrandt (2016). Empirics sovereign bonds: Pelizzon Subrahmanyam Tomio Uno (2013), Bai Yulliard Yuan (2012), Pelizzon et al (2016).

Empirics corporate bonds: Longstaff Mithal Neis (2005) Edward Harris Piwowar (2007), Friewald et al (2012).

Introduction

Search in OTC Markets: Duffie Garleanu Pedersen (2005), Duffie Garleanu Pedersen (2007), Afonso Lagos (2012), Atkeson (2013).

Empirics corporate bonds: Longstaff Mithal Neis (2005) Edward Harris Piwowar (2007), Friewald et al (2012).

Introduction

Search in OTC Markets: Duffie Garleanu Pedersen (2005), Duffie Garleanu Pedersen (2007), Afonso Lagos (2012), Atkeson (2013).

Empirics corporate bonds: Longstaff Mithal Neis (2005) Edward Harris Piwowar (2007), Friewald et al (2012).

Introduction

Search in OTC Markets: Duffie Garleanu Pedersen (2005), Duffie Garleanu Pedersen (2007), Afonso Lagos (2012), Atkeson (2013).

Empirics corporate bonds: Longstaff Mithal Neis (2005) Edward Harris Piwowar (2007), Friewald et al (2012).

Introduction

Search in OTC Markets: Duffie Garleanu Pedersen (2005), Duffie Garleanu Pedersen (2007), Afonso Lagos (2012), Atkeson (2013).

Empirics corporate bonds: Longstaff Mithal Neis (2005) Edward Harris Piwowar (2007), Friewald et al (2012).

Model: What we do?

Outline

Introduction

Model: What we do?

Quantitative Analysis: What we Find?

Conclusions

Model: What we do?

Setting A Small Open Economy

Income y , P (yt+1 = y 0 | yt = y ) Representative household E

"∞ X

β t u(ct )

t=0

Benevolent government Issue debt prim mkt Resource constraint c = y − [m + (1 − m)z]b + q(y , b 0 ) b 0 − (1 − m)b

Model: What we do?

Setting A Small Open Economy

Income y , P (yt+1 = y 0 | yt = y ) Representative household E

"∞ X

β t u(ct )

t=0

Benevolent government Issue debt prim mkt Resource constraint c = y − [m + (1 − m)z]b + q(y , b 0 ) b 0 − (1 − m)b

Model: What we do?

Setting A Small Open Economy

Income y , P (yt+1 = y 0 | yt = y ) Representative household E

"∞ X

β t u(ct )

t=0

Benevolent government Issue debt prim mkt Resource constraint c = y − [m + (1 − m)z]b + q(y , b 0 ) b 0 − (1 − m)b

Model: What we do?

Setting A Small Open Economy

Income y , P (yt+1 = y 0 | yt = y ) Representative household E

"∞ X

β t u(ct )

t=0

Benevolent government Issue debt prim mkt Resource constraint c = y − [m + (1 − m)z]b + q(y , b 0 ) b 0 − (1 − m)b

Model: What we do?

Setting A Small Open Economy

Income y , P (yt+1 = y 0 | yt = y ) Representative household E

"∞ X

β t u(ct )

t=0

Benevolent government Issue debt prim mkt Resource constraint c = y − [m + (1 − m)z]b + q(y , b 0 ) b 0 − (1 − m)b

Model: What we do?

Setting Debt Market Before Default

Model: What we do?

Setting Debt Market Before Default

Model: What we do?

Setting Debt Market After Default

Model: What we do?

Setting Timing

Model: What we do?

Setting Intermediaries

Assumptions on Market Structure (AMS): L types sell and exit the market “Many” H types ready to jump in Dealers in perfect Bertrand competition holding no stock Buy form L and resell immediately

Proposition: Under AMS, A = M = qiH , B = αi qiH + (1 − αi )qiL , A − B = (1 − αi )(qiH − qiL )

Model: What we do?

Setting Intermediaries

Assumptions on Market Structure (AMS): L types sell and exit the market “Many” H types ready to jump in Dealers in perfect Bertrand competition holding no stock Buy form L and resell immediately

Proposition: Under AMS, A = M = qiH , B = αi qiH + (1 − αi )qiL , A − B = (1 − αi )(qiH − qiL )

Model: What we do?

Setting Intermediaries

Assumptions on Market Structure (AMS): L types sell and exit the market “Many” H types ready to jump in Dealers in perfect Bertrand competition holding no stock Buy form L and resell immediately

Proposition: Under AMS, A = M = qiH , B = αi qiH + (1 − αi )qiL , A − B = (1 − αi )(qiH − qiL )

Model: What we do?

A Markov Equilibrium (b,y) Government Decision

Value of the option V O (b, y ) = max

V D (b, y ), V R (b, y )

{D,ND}

Value of default V D (b, y ) = u(y − φ(y )) + βEy 0 θV O (R(b), y 0 ) + (1 − θ)V D (b, y 0 )

Value of a government that does not default h

V R (b, y ) = max u(c) + βEy 0 V O (b 0 , y 0 ) 0 b

H c = y − [m + (1 − m)z]b + qND (y , b 0 ) b 0 − (1 − m)b

Ey 0 |y (1 − d(b 0 , y 0 )) ≤ δ̄

Model: What we do?

A Markov Equilibrium (b,y) Government Decision

Value of the option V O (b, y ) = max

V D (b, y ), V R (b, y )

{D,ND}

Value of default V D (b, y ) = u(y − φ(y )) + βEy 0 θV O (R(b), y 0 ) + (1 − θ)V D (b, y 0 )

Value of a government that does not default h

V R (b, y ) = max u(c) + βEy 0 V O (b 0 , y 0 ) 0 b

H c = y − [m + (1 − m)z]b + qND (y , b 0 ) b 0 − (1 − m)b

Ey 0 |y (1 − d(b 0 , y 0 )) ≤ δ̄

Model: What we do?

A Markov Equilibrium (b,y) Government Decision

Value of the option V O (b, y ) = max

V D (b, y ), V R (b, y )

{D,ND}

Value of default V D (b, y ) = u(y − φ(y )) + βEy 0 θV O (R(b), y 0 ) + (1 − θ)V D (b, y 0 )

Value of a government that does not default h

V R (b, y ) = max u(c) + βEy 0 V O (b 0 , y 0 ) 0 b

H c = y − [m + (1 − m)z]b + qND (y , b 0 ) b 0 − (1 − m)b

Ey 0 |y (1 − d(b 0 , y 0 )) ≤ δ̄

Model: What we do?

A Markov Equilibrium (b,y) Government Decision

Value of the option V O (b, y ) = max

V D (b, y ), V R (b, y )

{D,ND}

Value of default V D (b, y ) = u(y − φ(y )) + βEy 0 θV O (R(b), y 0 ) + (1 − θ)V D (b, y 0 )

Value of a government that does not default h

V R (b, y ) = max u(c) + βEy 0 V O (b 0 , y 0 ) 0 b

H c = y − [m + (1 − m)z]b + qND (y , b 0 ) b 0 − (1 − m)b

Ey 0 |y (1 − d(b 0 , y 0 )) ≤ δ̄

Model: What we do?

A Markov Equilibrium (b,y) Government Decision

Value of the option V O (b, y ) = max

V D (b, y ), V R (b, y )

{D,ND}

Value of default V D (b, y ) = u(y − φ(y )) + βEy 0 θV O (R(b), y 0 ) + (1 − θ)V D (b, y 0 )

Value of a government that does not default h

V R (b, y ) = max u(c) + βEy 0 V O (b 0 , y 0 ) 0 b

H c = y − [m + (1 − m)z]b + qND (y , b 0 ) b 0 − (1 − m)b

Ey 0 |y (1 − d(b 0 , y 0 )) ≤ δ̄

Model: What we do?

A Markov Equilibrium (b,y) Valuations before Default

( H qND (y , b 0 )

(1 â&#x2C6;&#x2019; d(b , y ))

= Ey 0 |y

L H m + (1 â&#x2C6;&#x2019; m) z + Î¶qND (y 0 , b 00 ) + (1 â&#x2C6;&#x2019; Î¶)qND (y 0 , b 00 )

1+r

Î¶q L (y 0 , b 0 ) + (1 â&#x2C6;&#x2019; Î¶)qDH (y 0 , b 0 ) +d(b , y ) D 1+r 0

( L qND (y , b 0 )

= Ey 0 |y

(1 â&#x2C6;&#x2019; d(b , y ))

+d(b 0 , y 0 )

S (y 0 , b 00 ) + (1 â&#x2C6;&#x2019; Î»)q L (y 0 , b 00 ) â&#x2C6;&#x2019;hc + m + (1 â&#x2C6;&#x2019; m) z + Î»qND ND

1+r

S (y 0 , b 0 ) + (1 â&#x2C6;&#x2019; Î»)q L (y 0 , b 0 ) Î»qD D

1+r

S L H qND (y , b 0 ) = (1 â&#x2C6;&#x2019; Î±ND )qND (y , b 0 ) + Î±ND qND (y , b 0 )

Model: What we do?

A Markov Equilibrium (b,y) Valuations before Default

( H qND (y , b 0 )

(1 â&#x2C6;&#x2019; d(b , y ))

= Ey 0 |y

L H m + (1 â&#x2C6;&#x2019; m) z + Î¶qND (y 0 , b 00 ) + (1 â&#x2C6;&#x2019; Î¶)qND (y 0 , b 00 )

1+r

Î¶q L (y 0 , b 0 ) + (1 â&#x2C6;&#x2019; Î¶)qDH (y 0 , b 0 ) +d(b , y ) D 1+r 0

( L qND (y , b 0 )

= Ey 0 |y

(1 â&#x2C6;&#x2019; d(b , y ))

+d(b 0 , y 0 )

S (y 0 , b 00 ) + (1 â&#x2C6;&#x2019; Î»)q L (y 0 , b 00 ) â&#x2C6;&#x2019;hc + m + (1 â&#x2C6;&#x2019; m) z + Î»qND ND

1+r

S (y 0 , b 0 ) + (1 â&#x2C6;&#x2019; Î»)q L (y 0 , b 0 ) Î»qD D

1+r

S L H qND (y , b 0 ) = (1 â&#x2C6;&#x2019; Î±ND )qND (y , b 0 ) + Î±ND qND (y , b 0 )

Model: What we do?

A Markov Equilibrium (b,y) Valuations before Default

( H qND (y , b 0 )

(1 â&#x2C6;&#x2019; d(b , y ))

= Ey 0 |y

L H m + (1 â&#x2C6;&#x2019; m) z + Î¶qND (y 0 , b 00 ) + (1 â&#x2C6;&#x2019; Î¶)qND (y 0 , b 00 )

1+r

Î¶q L (y 0 , b 0 ) + (1 â&#x2C6;&#x2019; Î¶)qDH (y 0 , b 0 ) +d(b , y ) D 1+r 0

( L qND (y , b 0 )

= Ey 0 |y

(1 â&#x2C6;&#x2019; d(b , y ))

+d(b 0 , y 0 )

S (y 0 , b 00 ) + (1 â&#x2C6;&#x2019; Î»)q L (y 0 , b 00 ) â&#x2C6;&#x2019;hc + m + (1 â&#x2C6;&#x2019; m) z + Î»qND ND

1+r

S (y 0 , b 0 ) + (1 â&#x2C6;&#x2019; Î»)q L (y 0 , b 0 ) Î»qD D

1+r

S L H qND (y , b 0 ) = (1 â&#x2C6;&#x2019; Î±ND )qND (y , b 0 ) + Î±ND qND (y , b 0 )

Model: What we do?

A Markov Equilibrium (b,y) Valuations before Default

( H qND (y , b 0 )

(1 â&#x2C6;&#x2019; d(b , y ))

= Ey 0 |y

L H m + (1 â&#x2C6;&#x2019; m) z + Î¶qND (y 0 , b 00 ) + (1 â&#x2C6;&#x2019; Î¶)qND (y 0 , b 00 )

1+r

Î¶q L (y 0 , b 0 ) + (1 â&#x2C6;&#x2019; Î¶)qDH (y 0 , b 0 ) +d(b , y ) D 1+r 0

( L qND (y , b 0 )

= Ey 0 |y

(1 â&#x2C6;&#x2019; d(b , y ))

+d(b 0 , y 0 )

S (y 0 , b 00 ) + (1 â&#x2C6;&#x2019; Î»)q L (y 0 , b 00 ) â&#x2C6;&#x2019;hc + m + (1 â&#x2C6;&#x2019; m) z + Î»qND ND

1+r

S (y 0 , b 0 ) + (1 â&#x2C6;&#x2019; Î»)q L (y 0 , b 0 ) Î»qD D

1+r

S L H qND (y , b 0 ) = (1 â&#x2C6;&#x2019; Î±ND )qND (y , b 0 ) + Î±ND qND (y , b 0 )

Model: What we do?

A Markov Equilibrium (b,y) Valuations before Default

( H qND (y , b 0 )

(1 â&#x2C6;&#x2019; d(b , y ))

= Ey 0 |y

L H m + (1 â&#x2C6;&#x2019; m) z + Î¶qND (y 0 , b 00 ) + (1 â&#x2C6;&#x2019; Î¶)qND (y 0 , b 00 )

1+r

Î¶q L (y 0 , b 0 ) + (1 â&#x2C6;&#x2019; Î¶)qDH (y 0 , b 0 ) +d(b , y ) D 1+r 0

( L qND (y , b 0 )

= Ey 0 |y

(1 â&#x2C6;&#x2019; d(b , y ))

+d(b 0 , y 0 )

S (y 0 , b 00 ) + (1 â&#x2C6;&#x2019; Î»)q L (y 0 , b 00 ) â&#x2C6;&#x2019;hc + m + (1 â&#x2C6;&#x2019; m) z + Î»qND ND

1+r

S (y 0 , b 0 ) + (1 â&#x2C6;&#x2019; Î»)q L (y 0 , b 0 ) Î»qD D

1+r

S L H qND (y , b 0 ) = (1 â&#x2C6;&#x2019; Î±ND )qND (y , b 0 ) + Î±ND qND (y , b 0 )

Model: What we do?

A Markov Equilibrium (b,y) Valuations before Default

( H qND (y , b 0 )

(1 â&#x2C6;&#x2019; d(b , y ))

= Ey 0 |y

L H m + (1 â&#x2C6;&#x2019; m) z + Î¶qND (y 0 , b 00 ) + (1 â&#x2C6;&#x2019; Î¶)qND (y 0 , b 00 )

1+r

Î¶q L (y 0 , b 0 ) + (1 â&#x2C6;&#x2019; Î¶)qDH (y 0 , b 0 ) +d(b , y ) D 1+r 0

( L qND (y , b 0 )

= Ey 0 |y

(1 â&#x2C6;&#x2019; d(b , y ))

+d(b 0 , y 0 )

S (y 0 , b 00 ) + (1 â&#x2C6;&#x2019; Î»)q L (y 0 , b 00 ) â&#x2C6;&#x2019;hc + m + (1 â&#x2C6;&#x2019; m) z + Î»qND ND

1+r

S (y 0 , b 0 ) + (1 â&#x2C6;&#x2019; Î»)q L (y 0 , b 0 ) Î»qD D

1+r

S L H qND (y , b 0 ) = (1 â&#x2C6;&#x2019; Î±ND )qND (y , b 0 ) + Î±ND qND (y , b 0 )

Model: What we do?

A Markov Equilibrium (b,y) Valuations after Default

qDH (y , b) =

L qD (y , b) =

R(b) H 1−θ Ey 0 |y ζqDH (y 0 , b) + (1 − ζ)qDL (y 0 , b) + θ qND (y , R(b)) 1+r b

1−θ R(b) L S L Ey 0 |y −hc + λqD qND (y , R(b)) (y 0 , b) + (1 − λ)qD (y 0 , b) + θ 1+r b qDSale (y , b) = (1 − αD )qDL (y , b) + αD qDH (y , b)

Model: What we do?

A Markov Equilibrium (b,y) Valuations after Default

qDH (y , b) =

L qD (y , b) =

R(b) H 1−θ Ey 0 |y ζqDH (y 0 , b) + (1 − ζ)qDL (y 0 , b) + θ qND (y , R(b)) 1+r b

1−θ R(b) L S L Ey 0 |y −hc + λqD qND (y , R(b)) (y 0 , b) + (1 − λ)qD (y 0 , b) + θ 1+r b qDSale (y , b) = (1 − αD )qDL (y , b) + αD qDH (y , b)

Model: What we do?

A Markov Equilibrium (b,y) Valuations after Default

qDH (y , b) =

L qD (y , b) =

R(b) H 1−θ Ey 0 |y ζqDH (y 0 , b) + (1 − ζ)qDL (y 0 , b) + θ qND (y , R(b)) 1+r b

1−θ R(b) L S L Ey 0 |y −hc + λqD qND (y , R(b)) (y 0 , b) + (1 − λ)qD (y 0 , b) + θ 1+r b qDSale (y , b) = (1 − αD )qDL (y , b) + αD qDH (y , b)

Model: What we do?

A Markov Equilibrium (b,y) Valuations after Default

qDH (y , b) =

L qD (y , b) =

R(b) H 1−θ Ey 0 |y ζqDH (y 0 , b) + (1 − ζ)qDL (y 0 , b) + θ qND (y , R(b)) 1+r b

1−θ R(b) L S L Ey 0 |y −hc + λqD qND (y , R(b)) (y 0 , b) + (1 − λ)qD (y 0 , b) + θ 1+r b qDSale (y , b) = (1 − αD )qDL (y , b) + αD qDH (y , b)

Model: What we do?

A Markov Equilibrium (b,y)

A Recursive Equilibrium (with state b, y ) is a: set of policy functions (c(b, y ), d(b, y ), b 0 (b, y )), H L bond price functions qND (y , b 0 ), qND (y , b 0 ), qDH (y , b), qDL (y , b)

....such that c(b, y ) satisfies the resource constraint H Given qND (y , b 0 ), government optimizes d(b, y ), b 0 (b, y ) H L Bond prices qND (y , b 0 ), qND (y , b 0 ), qDH (y , b), qDL (y , b) are consistent

Model: What we do?

A Markov Equilibrium (b,y)

A Recursive Equilibrium (with state b, y ) is a: set of policy functions (c(b, y ), d(b, y ), b 0 (b, y )), H L bond price functions qND (y , b 0 ), qND (y , b 0 ), qDH (y , b), qDL (y , b)

Quantitative Analysis: What we Find?

Outline

Introduction

Model: What we do?

Quantitative Analysis: What we Find?

Conclusions

Quantitative Analysis: What we Find?

Preview

So...how much of spreads are due liquidity? Welfare? Focus on the case of Argentina period 1993:I and 2001:IV case studied in the literature (A 2008, HM 2009, CE 2012). fixed exchange rate defaulted debt traded in secondary market.

Quantitative Analysis: What we Find?

Preview

Quantitative Analysis: What we Find?

Preview

Quantitative Analysis: What we Find?

Preview

Quantitative Analysis: What we Find?

Preview

Quantitative Analysis: What we Find?

Results Model Moments and Credit Spread Puzzle

Moment Mean Debt to GDP Expected Recovery Mean Sovereign Spread Vol. Sovereign Spread Mean Bid-Ask Spread, ND Mean Bid-Ask Spread, D Mean Turnover Default frequency (annual)

Target 1.0 0.30 0.0815 0.0443 0.0050 0.0500 0.12 -

Baseline 1.0 0.297 0.0815 0.0437 0.0049 0.0503 0.12 0.028

Table: Model moments. Parameters

Targets

CE (2012) 0.7 0 0.0815 0.0443 0.068

Quantitative Analysis: What we Find?

Results Sovereign Spreads Decomposition

Total spreads: cs = csDEF + csLIQ A decomposition. Define: csDEF = cs(B, D, Îś = 0) Co-movement. Good times 30 pct. Bad times 25 pct.

Prices

Quantitative Analysis: What we Find?

Results Sovereign Spreads Decomposition

Total spreads: cs = csDEF + csLIQ A decomposition. Define: csDEF = cs(B, D, Îś = 0) Co-movement. Good times 30 pct. Bad times 25 pct.

Prices

Quantitative Analysis: What we Find?

Results Sovereign Spreads Decomposition

Total spreads: cs = csDEF + csLIQ A decomposition. Define: csDEF = cs(B, D, Îś = 0) Co-movement. Good times 30 pct. Bad times 25 pct.

Prices

Quantitative Analysis: What we Find?

Results Sovereign Spreads Decomposition

Total spreads: cs = csDEF + csLIQ A decomposition. Define: csDEF = cs(B, D, Îś = 0) Co-movement. Good times 30 pct. Bad times 25 pct.

Prices

Quantitative Analysis: What we Find?

Results Sovereign Spreads Decomposition

Total spreads: cs = csDEF + csLIQ A decomposition. Define: csDEF = cs(B, D, Îś = 0) Co-movement. Good times 30 pct. Bad times 25 pct.

Prices

Quantitative Analysis: What we Find?

Results Sovereign Spreads Decomposition

Total spreads: cs = csDEF + csLIQ A decomposition. Define: csDEF = cs(B, D, Îś = 0) Co-movement. Good times 30 pct. Bad times 25 pct.

Prices

Quantitative Analysis: What we Find?

Results Sovereign Spreads Decomposition...?

H qND

`ND

H (1 − pd ) m + (1 − m) z + qND = 1 + rU + `ND

+ pd qDH

How Bad z }| How Likely { H L z}|{ qND − qND qDH − qDL ζ × (1 − pd ) (1 − m) = + pd H H qND qND

Quantitative Analysis: What we Find?

Results Sovereign Spreads Decomposition...?

H qND

`ND

H (1 − pd ) m + (1 − m) z + qND = 1 + rU + `ND

+ pd qDH

How Bad z }| How Likely { H L z}|{ qND − qND qDH − qDL ζ × (1 − pd ) (1 − m) = + pd H H qND qND

Quantitative Analysis: What we Find?

Results Sovereign Spreads Decomposition...?

H qND

`ND

H (1 − pd ) m + (1 − m) z + qND = 1 + rU + `ND

+ pd qDH

How Bad z }| How Likely { H L z}|{ qND − qND qDH − qDL ζ × (1 − pd ) (1 − m) = + pd H H qND qND

Quantitative Analysis: What we Find?

Results Case Study: Argentinaâ&#x20AC;&#x2122;s 2001 Default

Replicate qualitative features. Decomposition: Liquidity premia sizable.

Quantitative Analysis: What we Find?

Results Case Study: Argentinaâ&#x20AC;&#x2122;s 2001 Default

Replicate qualitative features. Decomposition: Liquidity premia sizable.

Quantitative Analysis: What we Find?

Results Comparative Statistics and Welfare

X c 1−σ = V o (0, y ; hc )Π(y 0 ) (1 − β)(1 − σ) y 0 ∈Y

Moment Mean Debt to GDP Mean Spread Vol. of Spread Mean Bid-Ask Spread Welfare

Data 1.00 0.0815 0.0443 0.0050 -

hc = 0 1.017 0.0767 0.0474 0 1.0164

hc = 0.0005 1.012 0.0785 0.0466 0.0017 1.0158

hc = 0.001 1.007 0.0802 0.0450 0.0034 1.0152

hc = 0.00145 1.002 0.0815 0.0436 0.0049 1.0147

Table: Comparative Statistics.

frictions to baseline: -0.17 pct. Rep agent -0.40 pct.Sizable fraction of cost of fluctuations.

Quantitative Analysis: What we Find?

Results Comparative Statistics and Welfare

X c 1−σ = V o (0, y ; hc )Π(y 0 ) (1 − β)(1 − σ) y 0 ∈Y

Moment Mean Debt to GDP Mean Spread Vol. of Spread Mean Bid-Ask Spread Welfare

Data 1.00 0.0815 0.0443 0.0050 -

hc = 0 1.017 0.0767 0.0474 0 1.0164

hc = 0.0005 1.012 0.0785 0.0466 0.0017 1.0158

hc = 0.001 1.007 0.0802 0.0450 0.0034 1.0152

hc = 0.00145 1.002 0.0815 0.0436 0.0049 1.0147

Table: Comparative Statistics.

frictions to baseline: -0.17 pct. Rep agent -0.40 pct.Sizable fraction of cost of fluctuations.

Quantitative Analysis: What we Find?

Results Comparative Statistics and Welfare

X c 1−σ = V o (0, y ; hc )Π(y 0 ) (1 − β)(1 − σ) y 0 ∈Y

Moment Mean Debt to GDP Mean Spread Vol. of Spread Mean Bid-Ask Spread Welfare

Data 1.00 0.0815 0.0443 0.0050 -

hc = 0 1.017 0.0767 0.0474 0 1.0164

hc = 0.0005 1.012 0.0785 0.0466 0.0017 1.0158

hc = 0.001 1.007 0.0802 0.0450 0.0034 1.0152

hc = 0.00145 1.002 0.0815 0.0436 0.0049 1.0147

Table: Comparative Statistics.

frictions to baseline: -0.17 pct. Rep agent -0.40 pct.Sizable fraction of cost of fluctuations.

Quantitative Analysis: What we Find?

Results Comparative Statistics and Welfare

X c 1−σ = V o (0, y ; hc )Π(y 0 ) (1 − β)(1 − σ) y 0 ∈Y

Moment Mean Debt to GDP Mean Spread Vol. of Spread Mean Bid-Ask Spread Welfare

Data 1.00 0.0815 0.0443 0.0050 -

hc = 0 1.017 0.0767 0.0474 0 1.0164

hc = 0.0005 1.012 0.0785 0.0466 0.0017 1.0158

hc = 0.001 1.007 0.0802 0.0450 0.0034 1.0152

hc = 0.00145 1.002 0.0815 0.0436 0.0049 1.0147

Table: Comparative Statistics.

frictions to baseline: -0.17 pct. Rep agent -0.40 pct.Sizable fraction of cost of fluctuations.

Conclusions

Outline

Introduction

Model: What we do?

Quantitative Analysis: What we Find?

Conclusions

Summing up... Presented a framework Default â&#x2021;?â&#x2021;&#x2019; Liquidity

Exercises with this framework calibrated to Argentina Matches key moments, joint determination of credit and liquidity Sizable component of total spreads Welfare gains, business cycle frequencies

Applications and extensions that can build in this setting Maturity management Time varying liquidity conditions Risk premium Liquidity interventions during crises Links to the real economy

Conclusions

Summing up... Presented a framework Default â&#x2021;?â&#x2021;&#x2019; Liquidity

Exercises with this framework calibrated to Argentina Matches key moments, joint determination of credit and liquidity Sizable component of total spreads Welfare gains, business cycle frequencies

Applications and extensions that can build in this setting Maturity management Time varying liquidity conditions Risk premium Liquidity interventions during crises Links to the real economy

Conclusions

Summing up... Presented a framework Default â&#x2021;?â&#x2021;&#x2019; Liquidity

Exercises with this framework calibrated to Argentina Matches key moments, joint determination of credit and liquidity Sizable component of total spreads Welfare gains, business cycle frequencies

Applications and extensions that can build in this setting Maturity management Time varying liquidity conditions Risk premium Liquidity interventions during crises Links to the real economy

Conclusions

Summing up... Presented a framework Default â&#x2021;?â&#x2021;&#x2019; Liquidity

Exercises with this framework calibrated to Argentina Matches key moments, joint determination of credit and liquidity Sizable component of total spreads Welfare gains, business cycle frequencies

Applications and extensions that can build in this setting Maturity management Time varying liquidity conditions Risk premium Liquidity interventions during crises Links to the real economy

Conclusions

Summing up... Presented a framework Default â&#x2021;?â&#x2021;&#x2019; Liquidity

Exercises with this framework calibrated to Argentina Matches key moments, joint determination of credit and liquidity Sizable component of total spreads Welfare gains, business cycle frequencies

Applications and extensions that can build in this setting Maturity management Time varying liquidity conditions Risk premium Liquidity interventions during crises Links to the real economy

Conclusions

Summing up... Presented a framework Default â&#x2021;?â&#x2021;&#x2019; Liquidity

Exercises with this framework calibrated to Argentina Matches key moments, joint determination of credit and liquidity Sizable component of total spreads Welfare gains, business cycle frequencies

Applications and extensions that can build in this setting Maturity management Time varying liquidity conditions Risk premium Liquidity interventions during crises Links to the real economy

Conclusions

Summing up... Presented a framework Default â&#x2021;?â&#x2021;&#x2019; Liquidity

Exercises with this framework calibrated to Argentina Matches key moments, joint determination of credit and liquidity Sizable component of total spreads Welfare gains, business cycle frequencies

Applications and extensions that can build in this setting Maturity management Time varying liquidity conditions Risk premium Liquidity interventions during crises Links to the real economy

Conclusions

Summing up... Presented a framework Default â&#x2021;?â&#x2021;&#x2019; Liquidity

Exercises with this framework calibrated to Argentina Matches key moments, joint determination of credit and liquidity Sizable component of total spreads Welfare gains, business cycle frequencies

Applications and extensions that can build in this setting Maturity management Time varying liquidity conditions Risk premium Liquidity interventions during crises Links to the real economy

Conclusions

Summing up... Presented a framework Default â&#x2021;?â&#x2021;&#x2019; Liquidity

Exercises with this framework calibrated to Argentina Matches key moments, joint determination of credit and liquidity Sizable component of total spreads Welfare gains, business cycle frequencies

Applications and extensions that can build in this setting Maturity management Time varying liquidity conditions Risk premium Liquidity interventions during crises Links to the real economy

Conclusions

Summing up... Presented a framework Default â&#x2021;?â&#x2021;&#x2019; Liquidity

Exercises with this framework calibrated to Argentina Matches key moments, joint determination of credit and liquidity Sizable component of total spreads Welfare gains, business cycle frequencies

Applications and extensions that can build in this setting Maturity management Time varying liquidity conditions Risk premium Liquidity interventions during crises Links to the real economy

Conclusions

Summing up... Presented a framework Default â&#x2021;?â&#x2021;&#x2019; Liquidity

Exercises with this framework calibrated to Argentina Matches key moments, joint determination of credit and liquidity Sizable component of total spreads Welfare gains, business cycle frequencies

Applications and extensions that can build in this setting Maturity management Time varying liquidity conditions Risk premium Liquidity interventions during crises Links to the real economy

Conclusions

Summing up... Presented a framework Default â&#x2021;?â&#x2021;&#x2019; Liquidity

Exercises with this framework calibrated to Argentina Matches key moments, joint determination of credit and liquidity Sizable component of total spreads Welfare gains, business cycle frequencies

Applications and extensions that can build in this setting Maturity management Time varying liquidity conditions Risk premium Liquidity interventions during crises Links to the real economy

Conclusions

Preliminaries Bid Ask Spreads Emerging Bonds

Mexico (1/15/2014 maturity) 2000

1500

1000 500 0

bps

2000

bps

Argentina (6/2/2017 maturity) Brazil (7/14/2014 maturity) 2000

1000 500

2006

2008

2010

µ = 177bps, σ = 217bps

1000 500

2006

2008

2010

µ = 56bps, σ = 63bps

Bid Ask Spread =

Ask − Bid Mid

[Source: Bloomberg]

2006

2008

2010

µ = 57bps, σ = 54bps

Conclusions

Preliminaries Evidence and findings from the Corporate Bond Market

Magnitudes. Bid Ask Spreads on: Investment Grade, 40 (normal) basis points (EHP 2007) Speculative Grade, 50 (normal) basis points (EHP 2007)

Generate. Liquidity Premia: Reduced-form: 30 percent Baa Bonds (Longstaff et al 2005) Structurally: 40 percent Baa Bonds (He Milbradt 2014)

Liquidity premia increases on crises (Friewald et al 2012)

Conclusions

Preliminaries Evidence and findings from the Corporate Bond Market

Magnitudes. Bid Ask Spreads on: Investment Grade, 40 (normal) basis points (EHP 2007) Speculative Grade, 50 (normal) basis points (EHP 2007)

Generate. Liquidity Premia: Reduced-form: 30 percent Baa Bonds (Longstaff et al 2005) Structurally: 40 percent Baa Bonds (He Milbradt 2014)

Liquidity premia increases on crises (Friewald et al 2012)

Conclusions

Preliminaries Evidence and findings from the Corporate Bond Market

Magnitudes. Bid Ask Spreads on: Investment Grade, 40 (normal) basis points (EHP 2007) Speculative Grade, 50 (normal) basis points (EHP 2007)

Generate. Liquidity Premia: Reduced-form: 30 percent Baa Bonds (Longstaff et al 2005) Structurally: 40 percent Baa Bonds (He Milbradt 2014)

Liquidity premia increases on crises (Friewald et al 2012)

Conclusions

Preliminaries Evidence and findings from the Corporate Bond Market

Magnitudes. Bid Ask Spreads on: Investment Grade, 40 (normal) basis points (EHP 2007) Speculative Grade, 50 (normal) basis points (EHP 2007)

Generate. Liquidity Premia: Reduced-form: 30 percent Baa Bonds (Longstaff et al 2005) Structurally: 40 percent Baa Bonds (He Milbradt 2014)

Liquidity premia increases on crises (Friewald et al 2012)

Conclusions

Preliminaries Evidence and findings from the Corporate Bond Market

Magnitudes. Bid Ask Spreads on: Investment Grade, 40 (normal) basis points (EHP 2007) Speculative Grade, 50 (normal) basis points (EHP 2007)

Generate. Liquidity Premia: Reduced-form: 30 percent Baa Bonds (Longstaff et al 2005) Structurally: 40 percent Baa Bonds (He Milbradt 2014)

Liquidity premia increases on crises (Friewald et al 2012)

Conclusions

Preliminaries Evidence and findings from the Corporate Bond Market

Magnitudes. Bid Ask Spreads on: Investment Grade, 40 (normal) basis points (EHP 2007) Speculative Grade, 50 (normal) basis points (EHP 2007)

Generate. Liquidity Premia: Reduced-form: 30 percent Baa Bonds (Longstaff et al 2005) Structurally: 40 percent Baa Bonds (He Milbradt 2014)

Liquidity premia increases on crises (Friewald et al 2012)

Conclusions

Preliminaries Evidence and findings from the Corporate Bond Market

Magnitudes. Bid Ask Spreads on: Investment Grade, 40 (normal) basis points (EHP 2007) Speculative Grade, 50 (normal) basis points (EHP 2007)

Generate. Liquidity Premia: Reduced-form: 30 percent Baa Bonds (Longstaff et al 2005) Structurally: 40 percent Baa Bonds (He Milbradt 2014)

Liquidity premia increases on crises (Friewald et al 2012)

Conclusions

Preliminaries European Debt Crises

"U.S. investors have already expressed reluctance to take part in a Greek sale of U.S. dollar denominated bonds, citing in part lack of liquidity in the market."

"A foreign bank that wants to offload a remaining part of its Greek government bond portfolio would find it very hard to attract sufficient demand or appropriate prices... That isnâ&#x20AC;&#x2122;t good news for a country hoping to complete a U.S. [dollar] bond sale in coming weeks."

â&#x20AC;&#x153;the market has become a virtual ghost townâ&#x20AC;?

Conclusions

Preliminaries European Debt Crises

"U.S. investors have already expressed reluctance to take part in a Greek sale of U.S. dollar denominated bonds, citing in part lack of liquidity in the market."

â&#x20AC;&#x153;the market has become a virtual ghost townâ&#x20AC;?

Conclusions

Preliminaries European Debt Crises

"U.S. investors have already expressed reluctance to take part in a Greek sale of U.S. dollar denominated bonds, citing in part lack of liquidity in the market."

â&#x20AC;&#x153;the market has become a virtual ghost townâ&#x20AC;?

Conclusions

Preliminaries Two Ideas

Trading frictions are not a second order determinant of spreads in a developed bond market. .....and, Bid ask spreads observed in the â&#x20AC;&#x153;dataâ&#x20AC;? already hint that liquidity risk could be substantial for Sovereign Countries. Surprisingly, not studied......not obvious how to approach the problem...setting becomes non-tractable easily. Back

Conclusions

Preliminaries Two Ideas

Conclusions

Preliminaries Two Ideas

Conclusions

Preliminaries Two Ideas

Conclusions

Calibration Functional Forms

yt = e zt + t zt = Ď z ztâ&#x2C6;&#x2019;1 + Ď&#x192;z ut n

Ď&#x2020;(y ) = max 0, dy y + dyy y 2

R(b) = {0, bĚ&#x201E; â&#x2C6;&#x2019; b} Parameters: 8 standard parameters: Î˛, Îł Ď z , Ď&#x192;z , m, z,dy , dyy 3 additional in our setting bĚ&#x201E;,Î´Ě&#x201E;, Ď&#x192; 6 OTC parameters: r , hc ,Îś,Îť,ÎąND , ÎąD Back

Conclusions

Calibration Functional Forms

yt = e zt + t zt = Ď z ztâ&#x2C6;&#x2019;1 + Ď&#x192;z ut n

Ď&#x2020;(y ) = max 0, dy y + dyy y 2

Conclusions

Calibration Functional Forms

yt = e zt + t zt = Ď z ztâ&#x2C6;&#x2019;1 + Ď&#x192;z ut n

Ď&#x2020;(y ) = max 0, dy y + dyy y 2

Conclusions

Calibration Functional Forms

yt = e zt + t zt = Ď z ztâ&#x2C6;&#x2019;1 + Ď&#x192;z ut n

Ď&#x2020;(y ) = max 0, dy y + dyy y 2

Conclusions

Calibration Functional Forms

yt = e zt + t zt = Ď z ztâ&#x2C6;&#x2019;1 + Ď&#x192;z ut n

Ď&#x2020;(y ) = max 0, dy y + dyy y 2

Conclusions

Calibration Externally Calibrated

Îł standard value of 2. Ď z , Ď&#x192;z , Ď&#x192; use data from Neumeyer Perri 2005. r = 0.003 montly return on the 1 month T Bill. 1 m = 60 , z = 0.01, maturity of 60 months, coupon rate of 12 percent, CE 2012.

Î´ = 0.75. That is, the one month ahead probability of default cannot exceed 75 percent. Îť = 0.8647 from He Milbradt.

Back

Conclusions

Calibration Externally Calibrated

Î´ = 0.75. That is, the one month ahead probability of default cannot exceed 75 percent. Îť = 0.8647 from He Milbradt.

Back

Conclusions

Calibration Externally Calibrated

Î´ = 0.75. That is, the one month ahead probability of default cannot exceed 75 percent. Îť = 0.8647 from He Milbradt.

Back

Conclusions

Calibration Externally Calibrated

Î´ = 0.75. That is, the one month ahead probability of default cannot exceed 75 percent. Îť = 0.8647 from He Milbradt.

Back

Conclusions

Calibration Externally Calibrated

Î´ = 0.75. That is, the one month ahead probability of default cannot exceed 75 percent. Îť = 0.8647 from He Milbradt.

Back

Conclusions

Calibration Externally Calibrated

Î´ = 0.75. That is, the one month ahead probability of default cannot exceed 75 percent. Îť = 0.8647 from He Milbradt.

Back

Conclusions

Calibration GMM

Θ = [β, dy , dyy , hc , αD , αND , ζ] . "

bt E yt

Back

S,ND

, E [sprdt ] , σ (sprdt ) , E BAt

S,D

, E BAt

, E[Turnover ], E

min b, bdef bdef

## .

Conclusions

Calibration Targets

E bytt = 1: mean total debt as fraction of GDP Argentina 1993:I and 2001:IV . E [sprdt ] , Ď&#x192; (sprdt ): Argentinaâ&#x20AC;&#x2122;s EMBI Neumeyer Perri 2005, EMBI, 1993:I and i2001:IV. h E BAS,ND : 50 basis points for Argentina. Similar to Schumacher t et al, using MTS data for Greek bonds. Similar He Milbradt (2014) and Edwards et al (2007). h

E BAS,D : Edwards et al (2007) 200 bps during good times, Chen t et al (2017) 620 during recessions. 500 Basis points. E[Turnover ] 12 percent / month taken from Bao Pan Wang (2011) min{b,bdef } E : 0.3 percent following Yue, recovery realized for bdef Argentina. Back

Conclusions

Calibration Targets

E bytt = 1: mean total debt as fraction of GDP Argentina 1993:I and 2001:IV . E [sprdt ] , Ď&#x192; (sprdt ): Argentinaâ&#x20AC;&#x2122;s EMBI Neumeyer Perri 2005, EMBI, 1993:I and i2001:IV. h

E BAS,ND : 50 basis points for Argentina. Similar to Schumacher t et al, using MTS data for Greek bonds. Similar He Milbradt (2014) and Edwards et al (2007). h

Conclusions

Calibration Targets

E bytt = 1: mean total debt as fraction of GDP Argentina 1993:I and 2001:IV . E [sprdt ] , Ď&#x192; (sprdt ): Argentinaâ&#x20AC;&#x2122;s EMBI Neumeyer Perri 2005, EMBI, 1993:I and i2001:IV. h

E BAS,ND : 50 basis points for Argentina. Similar to Schumacher t et al, using MTS data for Greek bonds. Similar He Milbradt (2014) and Edwards et al (2007). h