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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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion 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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
Illiquidity Premium
0 5 10 15 20
01
23
45
67
Corporate Bond Yields (Stylised!)
Date (years)
Yiel
d (%
)
Corp.; Perfectly liquid; NOT OBSERVED!
Risk Free Liquid
Corp.; Perfectly liquid
Medium illiquidity
Very illiquid
ASK
BID
IlliquidityPremium
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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.
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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)
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
Perfectly Liquid Equivalent
0 5 10 15 20
01
23
45
67
Corporate Bond Yields (Stylised!)
Date (years)
Yiel
d (%
)
Corp.; Perfectly liquid; NOT OBSERVED!
Risk Free Liquid
Corp.; Perfectly liquid
Medium illiquidity
Very illiquid
ASK
BID
CS
CSliquid
~
~
IlliquidityPremium
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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.
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
Model Observations
Method addresses liquidity on individual bond level
Method requires no subjective parameterisation
Parameter estimates are robust
Parameter dynamics are economically intuitive
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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%.
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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.
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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.
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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)
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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
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Motivation Yield Decomposition Modelling Approach Numerical Results Discussion Appendix
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