Modelling the Liquidity Risk Premium on Corporate Bonds · MotivationYield Decomposition Modelling...

Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix

Modelling the Liquidity Risk Premium onCorporate Bonds

Paul van Loon1,3, Andrew Cairns1, Alex McNeil1, Alex Veys2

1 Actuarial Research Centre (ARC) & Heriot Watt University2 Partnership Assurance

3 PhD funding from Partnership and the ARC (funded by IFoA)[email protected]

Monday 2nd June, 2014


Overview

1 Motivation

2 Yield Decomposition

3 Modelling ApproachDataModelling OverviewStage 1Stage 2Stage 3

4 Numerical ResultsLiquidity Premia

5 DiscussionModel ObservationsLiquidity Premia ObservationsOngoing work

6 Appendix


Motivation

Time of change in international insurance regulations

Market consistent valuation: assets and liabilities

What discount rate to value liabilities?

Risk free curveRisk free curve plus an illiquidity premiumRisk free plus other margin

Role of illiquidity premia in asset liability modelling


Corporate Bond Investors

Long Term: Hold to maturity

life insurerannuity provider/ pension

Medium Term: Sell before maturity

investment-grade-only mandateinvestment strategy / risk management

Short Term

e.g. convergence strategy, arbritage


Equivalent Bond Yields

0 5 10 15 20

01

23

45

67

Corporate Bond Yields (Stylised!)

MaturityDate (years)

Yiel

d (%

)

Risk Free Liquid

Corp.; Perfectly liquid; NO risk premium

Corp.; Perfectly liquid; PLUS risk premium

Medium illiquidity

Very illiquid

ASK

BID


Illiquidity Premium

0 5 10 15 20

01

23

45

67


Date (years)

Yiel

d (%

)

Corp.; Perfectly liquid; NOT OBSERVED!

Risk Free Liquid

Corp.; Perfectly liquid

Medium illiquidity

Very illiquid

ASK

BID

IlliquidityPremium


Data

Markit: GBP Investment Grade Corporate Bonds

Daily from 2003 - 2014(≈ 2500× 1000× 50 = 125M elements)

Contractual:

Coupon rateMaturity DateIssuerSeniorityetc.

Time Dependent:

Bid- and Ask pricesCredit RatingCredit Spreadetc.


Modelling Overview

Stage 1:

Modelling the Bid-Ask Spread→ Relative Bid-Ask Spread for each bond (RBAS)

Stage 2:

Modelling the Credit Spread

Stage 3:

Estimate Spread of perfectly liquid equivalent bonds→ Difference in yield = illiquidity premium


Bid-Ask Spreads

BAS = (Ask price - Bid price) / Bid price

log(BAS)(i , r , t) =c(r , t)

+β1,FIN(r , t)× log Duration(i , t)× IFIN(i)

+β1,NF (r , t)× log Duration(i , t)× INF (i)

+β2(r , t)× log Notional(i , t)

+∑k

βk(r , t)× Ik(i , t)

+log RBAS(i , t) (residual)

Indicators: Non-Financial, Sovereign, Seniority, CollateralisedTime t, Bond i , Rating r ≡ r(i , t)


Effect of Duration and Notional Amount

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

A−rated Bonds: Beta Coefficient log Duration

Date

Beta

2004 2006 2008 2010 2012 2014

Non−FinancialsFinancials

Non−Financials

Financials

−0.3

−0.2

−0.1

0.0

0.1

0.2

A−rated Bonds: Beta Coefficient log Notional Amount

Date

Beta

2004 2006 2008 2010 2012 2014

Larger issues: less liquid

Larger issues: more liquid

x-axis: e.g. ”2008” means 1 January 2008


Effect of Duration across Ratings

−0.5

0.0

0.5

1.0

Beta Coefficient: log Duration Non−Financials

Date

Beta

AAA bondsAAABBB

2004 2006 2008 2010 2012 2014

−0.5

0.0

0.5

1.0

Beta Coefficient: log Duration Financials

Date

Beta

AAA bondsAAABBB

2004 2006 2008 2010 2012 2014


Credit Spreads

log(CS)(i , r , t) =c(r , t)

+γ1,FIN(r , t)× log Duration(i , t)× IFIN(i)

+γ1,NF (r , t)× log Duration(i , t)× INF (i)

+γ2(r , t)× log Notional(i , t)

+γ3(r , t)× Coupon(i , t)

+γ4(r , t)× RBAS(i , t)

+∑k

γk(r , t)× Ik(i , t)

+ε(i , t) (residual)

Indicators: Non-Financial, Sovereign, Seniority, Collateralised, DebtTier


R2 as Goodness of Fit

0.0

0.2

0.4

0.6

0.8

1.0

Goodness−of−fit

Date

R2

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

AAA bondsAAABBB


Effect of Duration and RBAS

−0.

2−

0.1

0.0

0.1

0.2

0.3

0.4

A−rated Bonds: Gamma Coefficient log Duration (Non−Financials)

Date

Gam

ma

2004 2006 2008 2010 2012 2014

Rising CS Curve

Falling CS Curve

Northern Rock

0.0

0.2

0.4

0.6

A−rated Bonds: Gamma Coefficient Relative Bid−Ask Spread (RBAS)

Date

Gam

ma

2004 2006 2008 2010 2012 2014

Zero Liquidity Premium

Northern Rock


Effect of Financial Indicator and Seniority

−1.

0−

0.5

0.0

A−rated Bonds: Gamma Coefficient Non−Financial Indicator

Date

Gam

ma

2004 2006 2008 2010 2012 2014

Zero difference

Non−Financials: lower credit spread

Northern Rock

−0.

6−

0.4

−0.

20.

0

A−rated Bonds: Gamma Coefficient Seniority Indicator

Date

Gam

ma

2004 2006 2008 2010 2012 2014

Senior Bonds: lower credit spread


Perfectly Liquid Equivalent

0 5 10 15 20

01

23

45

67


Date (years)

Yiel

d (%

)

Corp.; Perfectly liquid; NOT OBSERVED!

Risk Free Liquid

Corp.; Perfectly liquid

Medium illiquidity

Very illiquid

ASK

BID

CS

CSliquid

~

~

IlliquidityPremium


Perfectly Liquid Equivalent II

Perfectly liquid equivalent

˜CSliq(i , r , t)← RBAS set to zero

Liquidity Premium

Liquidity Premiumbps(i , r , t) = C̃S(i , r , t)− ˜CSliq(i , r , t)

Liquidity Premium%(i , r , t) =C̃S(i , r , t)− ˜CSliq(i , r , t)

C̃S(i , r , t)

C̃S(i , r , t) is the estimated Credit Spread

˜CSliq(i , r , t) is the estimated Credit Spread of the perfectlyliquid equivalent


Observed Liquidity Premia

050

100

150

200

Median Liquidity Premium in bps (A−rated)

Date

Liqu

idity

Pre

miu

m (

bps)

2004 2007 2010 2013

−10

010

2030

4050

Median Liquidity Premium in % (A−rated)

Date

Liqu

idity

Pre

miu

m (

%)

2004 2007 2010 2013

Please refer to the Appendix for identical figures for other ratings


From Point-Estimate to Distribution

A−rated Liquidity Premium (bps) on 1 January 2006

Liquidity Premium (bps)

5 10 15 20 25 30 35 40

040

80

A−rated Liquidity Premium (%) on 1 January 2006

Liquidity Premium (%)

0 20 40 60 80 100

020

4060

A−rated Liquidity Premium (bps) on 1 January 2012

Liquidity Premium (bps)

0 100 200 300 400 500 600

040

8012

0

A−rated Liquidity Premium (%) on 1 January 2012

Liquidity Premium (%)

0 20 40 60 80 100

020

60


Ordering Liquidity Premia

AAA AA A BBB

Pre - Northern Rock 8.71% 19.47% 17.27% 22.28%Post - Northern Rock 20.30% 25.32% 39.19% 42.72%

Table: Dividing the sample period into two very loosely defined ’regimes’,with the Northen Rock event (14-09-2007) as cutoff, Table 1 shows anordering in premia.


Model Observations

Method addresses liquidity on individual bond level

Method requires no subjective parameterisation

Parameter estimates are robust

Parameter dynamics are economically intuitive


Liquidity Premia

Liquidity Premium varies:

over time

by rating

between bonds

Generally ranges from 20% to 65%

Exception: near 0% just before Northern Rock collapse


Quick Comparison: Bank of England

Structural model assesses fair default spread → residual is LP

Restrictions wrt bond sample, calibration & aggregated results

Taken from: Webber, L. (2007). Decomposing corporate bond spreads. Bank of England Quarterly Bulletin, 47(4)

BoE: all IG-bonds; approx. 45% - 50% LP during 2003-2007.Our estimates: IG (e.g. ’A’) are between 5% - 30%.


Quick Comparison: Barclays

Regression model, based on Barclays dealer data,

Proprietary measure LCS (Liquidty Cost Score) as proxy,similar to BAS

Taken from: Dastidar, S. G., & Phelps, B. D. (2010). Credit spread decomposition: decomposing bond-level credit

OAS into default and liquidity components. Barclays Capital: Cross Asset Strategy, 08 July 2010

Liquidity component accounts for approx. 20% - 45% of spread.


Quick Comparison: Dick Nielsen et al.

Use PCA of nine different liquidity proxies, TRACE (US)transaction data

Pooled regression (quarterly), controlling for credit risk (longterm debt:assets, operating income:sales, level/slope swapcurve, etc. )

Dick-Nielsen et al. (US) Our model (UK)

2005Q1:2007Q1 11% (5-18) 14% (5-25)

2007Q2:2009Q2 26% (14-39) 22% (15-30)

Liquidity premium in fraction of spread. Results are for A-rated bonds and approximate, figures taken from Table 5,

Dick-Nielsen, J., Feldhuetter, P., & Lando, D. (2012). Corporate bond liquidity before and after the onset of the

subprime crisis. Journal of Financial Economics, 103(3), 471-492.


Ongoing work

Liquidity term structure; interaction effectsCompare hold-to-maturity with sell-on-BBB-downgrade:How much of the illiquidity premium do we sacrifice?

Decomposing the Credit Spread

Trader Time Horizon Pension Fund

Maturity

Expected Losses from re−ratings

Expected Losses from defaults

Risk Premium

Reward for Persistence

Liquidity Premium


Appendix: Observed BAS dynamics0.

020.

040.

060.

080.

10

AAA−rated bonds: Bid.Ask.Spread

Bid

.Ask

.Spr

ead

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

AAA: FinancialsAAA: Non−Financials

0.02

0.04

0.06

0.08

0.10

AA−rated bonds: Bid.Ask.Spread

Bid

.Ask

.Spr

ead

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

AA: FinancialsAA: Non−Financials

0.02

0.04

0.06

0.08

0.10

AA−rated bonds: Bid.Ask.Spread

Bid

.Ask

.Spr

ead

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

A: FinancialsA: Non−Financials

0.02

0.04

0.06

0.08

0.10

BBB−rated bonds: Bid.Ask.Spread

Bid

.Ask

.Spr

ead

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

BBB: FinancialsBBB: Non−Financials


Appendix: Credit Spread: Two Components, A-rated

100

200

300

400

500

600

Median Credit Spread (two components) in bps (A−rated)

Date

Cre

dit S

prea

d (b

ps)

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

Full Credit Spread (incl. LP)Credit Spread (excl. LP)


Appendix: Distribution RBAS

Distribution of RBAS (A−rated) on2006−10−02

RBAS

Fre

quen

cy

0 1 2 3 4 5

010

2030

4050

R−squared = 0.9

Distribution of RBAS (A−rated) on2009−08−04

RBAS

Fre

quen

cy

0 1 2 3 4 5

05

1015

2025

30 R−squared = 0.74


Appendix: Liquidity Premia Estimates AAA

010

2030

40

Median Liquidity Premium in bps (AAA−rated)

Date

Liqu

idity

Pre

miu

m (

bps)

2004 2007 2010 2013

−10

010

2030

4050

Median Liquidity Premium in % (AAA−rated)

Date

Liqu

idity

Pre

miu

m (

%)

2004 2007 2010 2013


Appendix: Liquidity Premia Estimates AA

050

100

150

Median Liquidity Premium in bps (AA−rated)

Date

Liqu

idity

Pre

miu

m (

bps)

2004 2007 2010 2013

−10

010

2030

4050

Median Liquidity Premium in % (AA−rated)

Date

Liqu

idity

Pre

miu

m (

%)

2004 2007 2010 2013


Appendix: Liquidity Premia Estimates BBB

050

100

150

200

250

Median Liquidity Premium in bps (BBB−rated)

Date

Liqu

idity

Pre

miu

m (

bps)

2004 2007 2010 2013

010

2030

4050

Median Liquidity Premium in % (BBB−rated)

Date

Liqu

idity

Pre

miu

m (

%)

2004 2007 2010 2013

Modelling the Liquidity Risk Premium on Corporate Bonds · MotivationYield Decomposition Modelling...

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