Quantifying Liquidity and Default Risks of Corporate ...

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Quantifying Liquidity and Default Risks of Corporate Bonds over the Business Cycle Hui Chen1

Rui Cui2 1

Zhiguo He3

MIT Sloan and NBER 2

3 4

Konstantin Milbradt4

Chicago Booth

Chicago Booth and NBER

Northwestern Kellogg and NBER

October 2015

Outline

Introduction Model Calibration Decomposition Conclusion

Motivation Default risk only accounts for part of corporate bond spreads œ œ

Longstaff, Mithal, Neis (2005): Aaa/Aa 50%; Baa 70% Structural models with macroeconomic risks mostly target default component of credit spreads: Chen, Collin-Dufresne, Goldstein (2009); Bhamra, Kuehn, Strebulaev (2010); Chen (2010)

This paper: structural model to explain total credit spread œ œ

Introducing time-varying search frictions and macro risks Disciplined by matching default probability, credit- & BA-spread moments cross-sectionally and over the business cycle

Previous literature usually posits additive decomposition of credit spreads into one liquidity and one default component This paper: Model-based decomposition of credit-spreads with interactions between default and liquidity components œ œ

framework for policy evaluation recognition of "credit loss" vs "trading loss"

Literature Overview Default-liquidity interactions: He and Milbradt (2014) Our paper: œ œ

Introduction of macroeconomic risks OTC search market with non-constant holding costs

Structural credit model with macroeconomic risks: œ

Chen et al. (2009); Bhamra et al. (2010); Chen (2010),...

Liquidity frictions in OTC search market: œ

Duffie, Garleanu, Pedersen (2005),...

Empirical liquidity & yield estimations: œ

Edwards, Harris, Piwowar (2007), Bao, Pan, Wang (2009),...

Model Setup

Structural credit model in Leland tradition with OTC bond market Aggregate shocks to parameters: 2-state Markov chain: normal state (G) and recession (B) œ œ

Shocks to price of risk & real production process Jumps in secondary market liquidity frictions

Liquidity constrained investors face holding costs: Holding costs related to uncollateralized borrowing & haircuts

Baseline Model: Leland ’94b

Reissue

Firm: dy!Μdt#ΣdZ

Default at yb : D!Αvb

D: c dt

Maturity m

Idiosyncratic Liquidity Shocks

Reissue

Firm: dy!Μdt#ΣdZ

DH : c dt

Maturity m

Ξ

Liq. Shock

Maturity

Default at yb

DL : !c%hc"dt

Secondary Market for Bond Trading

Reissue

Resale

DH : c dt

A!DH

Firm: dy!Μs dt#Σs dZ

Maturity m

Ξs

Liq. Shock

Interdealer Market

Maturity

Default at yb s : DH !ΑsH vb s DL !ΑsL vb s

DL : !c&hcs "dt

s

Λ Intermediation

B!DL #Β!DH &DL "

Haircuts & Holding Costs Liquidity shocks proxy for significant need for cash Uncollateralized financing at rate r + ¬

Collateralized financing via bond at rate r Bond haircut h (depends on riskiness of collateral) œ œ œ

° ¢ Marginal (flow) benefit of bond as collateral: ¬(1 ° h)P y Marginal (flow) benefit from immediate sale of bond: ¬B(y) Holding cost for illiquid bond: relative to cash

Haircuts & Holding Costs Liquidity shocks proxy for significant need for cash Uncollateralized financing at rate r + ¬

Collateralized financing via bond at rate r Bond haircut h (depends on riskiness of collateral) œ œ œ

° ¢ Marginal (flow) benefit of bond as collateral: ¬(1 ° h)P y Marginal (flow) benefit from immediate sale of bond: ¬B(y) Holding cost for illiquid bond: relative to cash

Where does the haircut come from? This paper: Assumed haircut function h (P) (decreasing in P) that delivers linear holding costs hc (P) = ¬ [N ° P] Chen-He-Milbradt 2016: Microfound h (P) via VaR constraint œ

Utilizing (endogenous) inverse relationship between bond volatility and price

Degrees of freedom

Reissue

Resale

DH : c dt

A!DH

Firm: dy!Μs dt#Σs dZ

Maturity m

Ξs

Liq. Shock

Interdealer Market

Maturity

Default at yb s : DH !ΑsH vb s DL !ΑsL vb s

DL : !c&hcs "dt

Λs Intermediation

B!DL #Β!DH &DL "

Note: Only one set of parameters to explain the ratings cross-section.

Calibration: Secondary Bond Market Bond Price Data: TRACE (2005-12) & FISD (1994-2004) Parameters for cash-flow process and SDF from literature When modeling search frictions, 3 "free" parameters (N, ¬G , ¬B ) Target "Investment Grade" BA spreads in both states and accross ratings (6 moments)

Calibration: Secondary Bond Market Bond Price Data: TRACE (2005-12) & FISD (1994-2004) Parameters for cash-flow process and SDF from literature When modeling search frictions, 3 "free" parameters (N, ¬G , ¬B ) Target "Investment Grade" BA spreads in both states and accross ratings (6 moments)

Model Parameters for Search Friction Symbol

Interpretation

G

ª Ø ∏ N ¬

Liquid shock int. Investor bargaining Intermediation int. Holding cost Holding cost

0.7

B

Justification

1.0

Bond Turnover Feldhutter 2012 Anecdotal

0.05 50

20 115 0.06 0.11

Default prob & credit spreads (10 year bonds) Maturity = 10 years Aaa/Aa

A

Baa

Ba

Panel A. Default probability (%) data model

2.1 1.6

3.4 3.9

7.0 7.9

19.0 15.9

Default prob & credit spreads (10 year bonds) Maturity = 10 years Aaa/Aa

A

Baa

Ba

Panel A. Default probability (%) data model

2.1 1.6

3.4 3.9

7.0 7.9

19.0 15.9

Panel B. Credit spreads (bps) State G data model

61.2 86.0

90.2 122

150 182

303 301

State B data model

106 136

159 185

262 261

454 404

Comparative Statics Credit Spread Maturity = 10 years Aaa/Aa

A

Baa

Ba

Credit spreads (bps) State G model hc = 0 hcs = csts

86.0 32.5 95.3

122 57.5 126

182 103 176

301 200 278

261 143 245

404 248 359

State B model hc = 0 hcs = csts

136 59.5 146

185 90.7 185

Default probability matching deteriorates only slightly

Bid-Ask Spread

State G data model hcs = csts

Superior 40 39 45

Investment 50 50 50

State B Junk 70 61 49

Superior 77 111 123

Investment 125 125 125

Model counterpart is a bond with time to maturity of 8 years (mean time-to-maturity of frequently traded bonds)

Junk 218 186 138

Structural Decomposition Standard View: CDS spread measures “Default component” Bond-CDS spread = Credit spread - CDS spread measures “Non-default component” Our view: Default component: 1. pure default from illiquidity free model (different default policy) 2. residual of liquidity-driven default

Liquidity component: 3. pure liquidity from risk-free bonds with same search frictions 4. residual default-driven liquidity

State G (Repo-Treasury spread ¢ =15 bps) ��

��

��

� �� /��

��-�� -��

State B (Repo-Treasury spread ¢ =40 bps) ��

�� /��

��

��-��

��-��

Changes in Spreads: G ! B ��

�� -��

��

��/�� -��

Structural decomposition in time series Panel A. Baa-rating

Panel B. Baa-rating 120

150

pure liquidity def-driven liquidity

basis points

100 80

100

60 pure default liq-driven default

50

40 20

0

95Q1

00Q1

05Q1

10Q1

0

95Q1

basis points

Panel C. B-rating 250

400

200

300

150 pure default liq-driven default

10Q1

pure liquidity def-driven liquidity

100

100 0

05Q1

Panel D. B-rating

500

200

00Q1

50

95Q1

00Q1

05Q1

10Q1

0

95Q1

00Q1

05Q1

10Q1

Comp. Statics: More frequent liquidity shocks Panel A. Baa-rating

Panel B. Baa-rating 120

150

pure liquidity def-driven liquidity

basis points

100 80

100

60 50

pure default liq-driven default

40 20

0

95Q1

00Q1

05Q1

10Q1

0

95Q1

basis points

Panel C. B-rating 250

400

200

300

150 pure default liq-driven default

10Q1

pure liquidity def-driven liquidity

100

100 0

05Q1

Panel D. B-rating

500

200

00Q1

50

95Q1

00Q1

05Q1

10Q1

0

95Q1

00Q1

05Q1

10Q1

Liquidity Provision

Debt holding values Injecting Liquidity cxv Liquidity Improves

Alleviating Rollover Losses

Equity holders delay default

Here: Injecting liquidity means improving dealer contact intensity ∏s and reducing the uncollaterialized borrowing premium, lowering holding costs hcs

Liquidity Provision Policy evaluation: What are the effects of “injecting liquidity” on lowering “borrowing cost” (setting state B liquidity parameters same as in G)? Pure liquidity channel is dominant for higher rated bonds; default-driven liquidity channel important for lower rated bonds.

Credit Spread Aaa/Aa G Aaa/Aa B Ba G Ba B

Contributions to Change (%)

w/o policy

w policy

pure LIQ

LIQ!DEF

DEF!LIQ

71.1 96.0 286 364

41.9 44.4 234 262

83 83 46 42

5 3 12 9

12 14 42 49

Conclusion Tractable structural model that embeds aggregate liquidity effects in a capital structure model Ability to explain total credit spread, i.e., credit risk premium and liquidity premium, cross-sectionally (across rating classes) and over the business cycle (across aggregate states) Holding costs motivated by cost of collateralized vs uncollateralized borrowing (haircuts) Counterfactual analysis reveals sizable benefits of injecting liquidity in bad times through default-liquidity interaction terms.

Jensen’s Inequality: Heterogeneity in the Data Rating class defined by the empirical distribution of market leverages as given by distribution dPrating for each quarter Normal A

Normal Baa

Normal Ba

Recession Aaa/Aa

Recession A

Recession Baa

Recession Ba

0 .1 .2 .3 .4 .5 .6 .7 .8 .9

0 .1 .2 .3 .4 .5 .6 .7 .8 .9

0 .1 .2 .3 .4 .5 .6 .7 .8 .9

0 .1 .2 .3 .4 .5 .6 .7 .8 .9

0 8 6 4 2 0

Density

2

4

6

8

Normal Aaa/Aa

Market Leverage

Jensen’s Inequality: Implementation David (2008), Bhamra et al. (2010): map each firm-quarter to its model counterpart, then aggregate within each rating class œ

Match empirical leverage distribution for each rating class

D Each market leverage (ML = D+E ) implies an initial cash-flow state y0 , which then gives model-implied credit-spread, liquidity measure and default probability

Average credit spread for each rating class: csrating =

Z1 0

° ¢ cs y (ML) dPrating

Given rating, we explain average credit spread across firms, not credit spread of an average firm because strong non-linearities

Calibration: Fundamental and Aggregate Shocks X ° ∑(s ,s ) ¢ d§t (s ,s ) = °r (st ) dt ° ¥ (st ) dZtm + e t° t ° 1 dMt t° t §t 0 st 6=st

Model Parameters Symbol

Interpretation

r ¢ ≥P e∑ µP ¥ æm æf m !

Risk-free rate T liq premium Transition Density Jump Risk Premium Cash Flow Growth Risk Price Systematic Vol Idiosyncratic Vol Maturity Intensity Primary issuance cost

G

B

0.05 15 bps 40 bps 0.10 0.50 2 0.50 0.045 0.015 0.17 0.22 0.10 0.11 0.25 0.2 0.01

Justification Data Repo-Treasury spread Chen 2010 Chen 2010 Chen 2010 Chen 2010 Equity vol Baa def. prob Data/ Chen et al 2012 Chen 2010

Calibration: Post-Default Bond Market For counterfactual analysis, we need bond recovery w/o post-default illiquidity. So need ultimate recovery Moody’s Default and Recovery Database covering 1987-2012 Risk adjust: discounting these return with a public market benchmark (SP500) over the same horizon, known as Public Market Equivalent (PME)

Table: Mean Annualized Net PME on Defaulted Bonds

Default Time Non-Recession Recession Full Sample

# Def. Bonds 512 130 642

Net PME 0.3126 0.5537 0.3613

Emergence (Yrs) 1.37 1.31 1.35

ˆ Æˆ G = 87.96%, Æˆ B = 64.68%. Ultimate recovery rate Æ:

Model-implied Bond-CDS Spread Assume CDS contracts perfectly liquid (doubtful empirically; Bongaerts et al 2011: CDS seller earns liquidity premium) CDS contract with maturity T requires flow payment f s.t. ∑Zmin{ø,T } ∏ £ § Q °rø Q °rt E 1{ø∑T } e LGD (s) = E e f · dt 0

œ œ

ø is the time the firm defaults loss-given-default LGD (s) 2 [0, 1]: face-value p (wlog p = 1) minus recovery value right at default at state s

Bond-CDS spread: Bond credit spread minus CDS spread 0 1 1°e°yT ° ¢ ° ¢ y A y ° r ° f = y ° c @1 ° 1°EQ [e°r(ø^T ) ] r

œ

In Leland ’94 world, for small r and y, (1) par-bonds have zero spread, (2) discount bonds have positive spread, (3) premium bonds have negative spread

Model-implied Bond-CDS Spread (10 year bonds) Sample: 2005-2012, firms with CDS, 5- and 10-year bonds Treasury spread 15bps G, 40 bps B (netted out) Bond-CDS spreads (bps) 10 years Aaa/Aa

A

Baa

Ba

State G Credit Spread Bond-CDS spread

71 48

107 53

167 61

286 61

State B Credit Spread Bond-CDS spread

96 69

145 79

221 92

364 107