Modelling the Liquidity Premium on Corporate Bonds

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Griffin Colin Payne
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1 1 Modelling the Liquidity Premium on Corporate Bonds Paul van Loon (*), Andrew J.G. Cairns, Alex McNeil Heriot-Watt University & The Actuarial Research Centre (ARC) (**) Alex Veys Partnership Acknowledgements: (*) PhD funding from Partnership and the ARC. (**) The ARC is funded by the Institute & Faculty of Actuaries and by industry co-sponsors including Partnership.

Veys Partnership Acknowledgements: (*) PhD funding from Partnership and the ARC.

2 2 Plan The problem Stylised decomposition of bond prices and spreads Modelling the Bid-Ask Spread Modelling the Credit Spread Discussion

3 3 The problem How to decompose the credit spread on a corporate bond? Expected default and rerating losses Risk premium for default/rerating risk Illiquidity premium Other factors Hold to maturity versus sell before maturity Impact on liability valuation

default/rerating risk Illiquidity premium Other factors Hold to

4 4 Equivalent Bond Yields Corporate Bond Yields (Stylised!) Yield (%) BID Very illiquid ASK Medium illiquidity Corp.; Perfectly liquid; PLUS risk premium Corp.; Perfectly liquid; NO risk premium Risk Free Liquid Date (years) Maturity

illiquidity Corp.; Perfectly liquid; PLUS risk premium Corp.

5 5 Illiquidity Premium (LQP) Corporate Bond Yields (Stylised!) Yield (%) BID Very illiquid ASK Medium illiquidity Corp.; Perfectly liquid; NOT OBSERVED! Risk Free Liquid Illiquidity Premium Date (years)

) Yield (%) 0 1 2 3 4 5 6 7 BID Very illiquid ASK Medium

6 6 Data Markit: GBP investment grade corporate bonds Daily from 2003 to 2013 ( = 125million items) Contractual data: e.g. coupon rate, maturity, issuer, seniority etc. Unpredictable, time dependent data Bid and Ask prices (quotes not transactions!) Credit rating Credit spread etc.

coupon rate, maturity, issuer, seniority etc.

7 7 Modelling Summary Stage 1: Model the Bid-Ask spread as a function of various inputs Output: Relative Bid-Ask Spread for each bond (RBAS) Stage 2: Model the Credit-Spread as a function of various inputs Stage 3: Estimate the price of each bond as if it was perfectly liquid Difference in yield = illiquidity premium

Credit-Spread as a function of various inputs Stage 3: Estimate the price of

8 Bid-Ask Spreads (BAS): Time t, Bond i, Rating r r(i, t) 8 BAS(i, r, t) = (Ask Price Bid Price)/Bid Price I X (i, t) = characteristic X indicator: 0 or 1 log BAS(i, r, t) = c(r, t) +β 1,F (r, t) log duration(i, t) I F in (i) +β 1,NF (r, t) log duration(i, t) I NF (i) +β 2 (r, t) log notional(i, t) + β k (r, t) I k (i, t) k + log RBAS(i, t) (residual). Indicators: Financials; Sovereign; Senior; Collateralised; Bond age...

t) I F in (i) +β 1,NF (r, t) log duration(i, t) I NF (i) +β 2 (r, t) log notional(i, t) + β k (r, t) I k

9 9 Beta A rated Bonds: Beta Coefficient log Duration Non Financials Financials Non Financials Financials Beta A rated Bonds: Beta Coefficient log Notional Amount Larger issues: more liquid Larger issues: less liquid Date Date x-axis: e.g means 1 January 2008

10 10 Distribution of RBAS (A rated) on Distribution of RBAS (A rated) on Frequency R squared = 0.9 Frequency R squared = RBAS RBAS e.g. RBAS = 2 BAS is 2 the predicted BAS RBAS = 0 BAS = 0; perfectly liquid RBAS uncorrelated with inputs

9 Frequency 0 5 10 15 20 25 30 R squared = 0.

11 11 Credit Spreads log CS(i, r, t) = d(r, t) +γ 1 (r, t) log duration(i, t) +γ 2 (r, t) RBAS(i, t) +γ 3 (r, t) I (bond age(i, t) < 1) +γ 4 (r, t) coupon(i, t) + γ k (r, t) I k (i, t) k +ϵ(i, t) (residual). Indicators: Financials; Senior; Collateralised;...

12 12 A rated Bonds: Gamma Coefficient log Duration (Non Financials) A rated Bonds: Gamma Coefficient Relative Bid Ask Spread (RBAS) Gamma Rising CS Curve Falling CS Curve Gamma Positive Liquidity Premium Zero Liquidity Premium Date Date

4 Rising CS Curve Falling CS Curve Gamma 0.0 0.2 0.4 0.

13 13 A rated Bonds: Gamma Coefficient Non Financial Indicator A rated Bonds: Gamma Coefficient Seniority Indicator Gamma Zero difference Non Financials: lower credit spread Gamma Zero difference Senior bonds: lower credit spread Date Date

0 Zero difference Non Financials: lower credit spread Gamma 0.6 0.4 0.2 0.

14 14 Median Liquidity Premium in bps (A rated) Median Liquidity Premium in % (A rated) Liquidity Premium (bps) Liquidity Premium (%) Date Date

(bps) 0 50 100 150 200 Liquidity Premium (%) 10 0 10

15 15 Observations Method applies to all quoted bonds on individual basis Objectivity: Method requires no subjective inputs Parameter estimates are robust Parameter dynamics consistent with market events Illiquidity premium (LQP) as a percentage of credit spread Varies considerably: between bonds; over time; rating e.g. A-rated bonds during 2011: Median LQP 40%; 10% quantile 32%; 90% 55% More generally: LQP ranges from 20% to > 70% Exception: much lower just before Northern Rock collapse

of credit spread Varies considerably: between bonds; over time; rating

16 Discussion: Holding Time Decomposing the Credit Spread (Stylised) 16 Maturity Percentage of Credit Spread Credit Spread Volatility Risk Premium for Rerating and Default Losses Liquidity Premium Reward for Persistence??? `Unexplained` Risk Premium Expected Losses from re ratings Expected Losses from defaults Trader Holding Time Pension Fund

and Default Losses Liquidity Premium Reward for Persistence?

17 17 Discussion and Future Work Markit data: quotes, not actual transactions Ongoing work: Compare hold-to-maturity with sell-on-bb-downgrade: How much of the Illiquidity premium do we sacrifice?

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