estimation of the liquidity premium in corporate bond...
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Estimation of the liquidity premium in corporate bond yields
John Hibbert [email protected]
May 2009
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Agenda
+ What is the (il)liquidity premium & why does it matter?– Market-consistent valuation
+ Why might a liquidity premium be on offer?+ What do academic researchers & practitioners have to say?+ How might the liquidity premium be estimated?
– 3 approaches used by researchers
+ Can we decompose the spread further?+ What are insurance firms doing?+ Conclusions
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What is the (il)liquidity premium & why does it matter?
What is the liquidity premium?
+ Liquidity and marketability are important characteristics of many financial contracts.
+ Providers of financial services and financial products tailor them to meet the investment horizons and liquidity objectives of their customers.
+ If the liquidity characteristics of an asset or liability (i.e. the cost of trading) are valued by price-setting ‘marginal investors’, they will be reflected in an asset’s expected return (and price).
+ In the case of corporate bonds, the implication is that issues that are relatively expensive to trade will offer yield premium over relatively liquid issues.
+ Liquidity premia have implications for the fair valuation of illiquid liability cash flows.
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Why does the LP matter?Market consistency: An emerging global standard
+ Individual regulatory initiatives in the UK, Switzerland (SST), South Africa (PGN110)..
+ Solvency II Directive, Article 74: “..calculation of technical provisions shall make use of and be consistent with information provided by the financial markets..”
+ QIS4 technical guidance:– Wherever possible, a firm must use "mark to market" methods in order to measure
the economic value of assets and liabilities;
– Where this is not possible, mark to model procedures should be used (marking to model is any valuation which has to be benchmarked, extrapolated or otherwise calculated from a market input). When marking to model, undertakings will use as much as possible observable and market consistent inputs.
+ MCEV, Principle 3:– “MCEV represents the present value of shareholders’ …after sufficient allowance
for the aggregate risks ... The allowance for risk should be calibrated to match the market price for risk where reliably observable.”
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Why does the liquidity premium matter?Argument #1: If liquidity is priced in financial markets then a
market-consistent valuation should value liquidity in an asset or liability in an identical way.
+ CFO Forum’s MCEV principles (June 2008)Principle 7: All projected cash flows should be valued using economic
assumptions such that they are valued in line with the price of similar cash flows that are traded in the capital markets.
G14.4 No adjustments should be made to the swap yield curve to allow for liquidity premiums or credit risk premiums.
+ Would a willing third party take liquidity (of liabilities) into account in a transfer/valuation of those liabilities?
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CFO views are modified
+ On December 19th, the CFO Forum stated: “the CFO Forum remains committed to MCEV and the Principles published in June
2008. However, the MCEV Principles were designed during a period of relatively stable market conditions and their application could, in turbulent markets, lead to misleading results. The CFO Forum has therefore decided to conduct a review of the impact of turbulent market conditions on the MCEV Principles, the result of which may lead to changes to the published MCEV Principles or the issuance of guidance. The particular areas under review include …… the effect of liquidity premia.”
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CROs’ views
+ CRO Forum: Comments on the Financial Crisis, 24 October 2008“...due to the fact the insurance liabilities are not traded in liquid markets, the
valuation of those liabilities should reflect actual illiquidity spreads.”
+ CRO Forum: Market Value of Liabilities for Insurance Firms: Implementing elements for Solvency II, July 2008
“The CRO Forum emphasises that market-consistency refers to values that are consistent with those observed in deep and liquid financial markets and therefore draws a distinction between market-consistent valuation and observed pricing practices in the insurance markets.”
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What liabilities might be viewed as illiquid?+ Insurance & pensions liabilities are long-term in nature.+ But there are significant differences in liquidity offered to
policyholders/savers:– Unit-linked assets which are usually assumed to have comparable liquidity to the
underlying asset portfolio.
– With-profits style contracts offer limited liquidity but subject to policyholder contract.
– Annuity contracts are highly illiquid (although there is some second order mortality risk so cash flows are not exactly predictable)
+ Do policyholders expect rewards for giving up liquidity?+ Conclusion: It is appropriate to apply an additional LP to a limited
class of liabilities.
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Remember - economic, market-consistent valuation breaks the link between liability value and backing assets.
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Why might a liquidity premium be on offer?
Why could there be a liquidity premium?+ Consider different types of investors in corporate bonds:
– Hedgers (“Buy-and-hold” investors) with no need to sell bond before maturity
– Speculators (“Mark-to-market” investors) who care about returns over shorter holding periods than bond maturity
+ Hedgers requires compensation for:– Default risk
– Recovery rate risk
+ Speculators requires compensation for:– Default risk
– Recovery rate risk
– Liquidity risk (i.e. risk of not finding a ready buyer at ‘fair’ market price)
– Pricing risk (i.e. risk of a fall in the market price of bond due to interest rate or credit spread movements)
+ Bond price will be determined by the marginal investor
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What are do academic researchers & practitioners have to say?
Researchers’ views
+ There is a vast literature on liquidity premia in many asset markets (including bonds).
+ Explanations for the ‘credit spread puzzle’ include the level of default expectations, tax effects, non-diversifiable credit risk, insufficient diversification, liquidity premia.
+ Estimates of bond LP magnitudes vary – liquidity premium typically 10-50bps.
+ Mixed evidence, but clear consensus is that:– Liquidity premia do exist in corporate bond markets
– They can be substantial
– They vary significantly through time.
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Some examples
+ Corporate Yield Spreads and Bond Liquidity, Chen, Lesmond, Wei; April 2005– “The most telling finding is the consistent significance of the liquidity variable
regardless of the specification used to define liquidity, regardless of the specification used for the yield spread determinants, or regardless of investment grade or speculative grade categories.”
+ Comparing possible proxies of corporate bond liquidity; Houweling, Mentink, Vorst; 2005– “All papers mentioned above, except for [2] found evidence of significant liquidity
premiums for at least one liquidity proxy.”
+ Are larger Treasury issues more liquid? Fleming, 2002– ‘Off-the-run’ (illiquid) treasury issues offer higher yields than ‘on-the-run’ (liquid)
issues.
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Practitioners’ views
+A recent Watson Wyatt / B+H survey of Asian C-level (Actuaries & CROs)
+The hedge fund view:– “In real options theory, one
explicitly values the optionality associated with decision-making flexibility. In essence, with illiquidity, a portfolio is short real options, and the investor gives up the flexibility of being able to readily liquidate their investments.” *
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*Survey of Recent Hedge Fund Articles, EDHEC, September 2005Hedge fund alphas: do they reflect managerial skills or mere compensation for liquidity risk bearing?, Gibson & Wang, February 2009
Some hedge fund strategies are designed to accumulate LP by supplying liquidity.
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How might the liquidity premium be estimated?
How might the liquidity premium be estimated?+ Our focus today will be on corporate bond yields.
– LPs are probably significant for small cap equity, real estate, private equity..
+ A number of possible approaches have been suggested by researchers:
1.A ‘direct’ approach aimed at estimating the benefit of avoiding market transactions costs by following a buy-and-hold policy.
2.A market-based approach inferred from the cost of credit insurance.3.By making an estimate of the fair spread excluding liquidity costs
and deriving the LP as a residual (B+H, BoE).+ Predictably, none of these approaches offers a perfect answer.+ Let us take a brief look at each.
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A reminder:Decomposition of market spreads
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+ Default-related credit risks are defined as the expected default loss on bonds plus the risk premium that investors demand for the possibility that corporate defaults will be higher than expected. The LP is the additional part of the spread which is not explained by default-related credit risks.
Approach #1:Market microstructure thinking+ The required liquidity spread will be a function of the marginal
investor’s dealing frequency and the cost of trading.+ Consider a simple model where we estimate the break-even spread
as a function of the [risk-neutral] probability of a trade being forced (average holding period) and the effective half-spread.
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If the marginal investor faces a half-spread of 5% and anticipates an average [risk-neutral] holding period of 3 years, then the fair liquidity spread will be approx 60 bps for a typical 10-year bond.
Is there market risk here since dealer spreads are a function of vol? 0
50
100
150
200
250
0 5 10 15 20
Liqu
idity Prem
ium (b
ps)
Time to Maturity (Years)
h/spd=1%, h/period=5y
h/spd=2%, h/period=5y
h/spd=5%, h/period=3y
h/spd=10%, h/period=2y
Approach #2:A market-based approach+ ‘Negative basis’ trade involves
manufacturing a risk-free bond by buying a corporate bond and insuring against default by buying a credit default swap.
+ A fundamental change in the basis followed the disclosure of AIG’s problems in September 2008.
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‐50
0
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100
150
200
250
Dec‐04
Dec‐05
Dec‐06
Dec‐07
Dec‐08
Dec‐09
Basis Po
ints
0
50
100
150
200
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400
450
Dec‐04
Dec‐05
Dec‐06
Dec‐07
Dec‐08
Dec‐09
Basis Points
Itraxx EUR 5 Yr CDS
Iboxx EUR Corporate 5‐7yr Z Spread
Approach #3:An estimate for the fair spread using the Merton model
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Corporate debt pay-off =
Risk-free bond payout – Put option payout
Or
Firm assets – sold call
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Merton’s Model
+ The Black-Scholes valuation formulae for a European call option on a company’s assets are
+ Where
+ The current value of the company’s assets,(A0)
+ The volatility of the company’s assets,( σA ) usually estimated from the company’s equity
+ The outstanding debt( D)
+ The debt maturity (T)
+ The discount rate ( r )
)()( 2100 dNDedNAE rT−−=
TTDeA
dA
ArT
σσ )2/()/ln( 2
01
+=
Tdd Aσ−= 12
How does the calculation work?
Step:1. Estimate levels of debt consistent with bonds of various terms and
credit ratings to match expected (real-world) default probabilities to historical data.
2. Estimate market-consistent volatility assumptions using equity index options and single equity options.
3. Use a fixed bankruptcy cost estimated to match historic recoveryrates for a typical 10 year ‘A’-rated senior unsecured bonds.
4. Estimate the ‘fair spread’ on the bonds by viewing companies’equity as a call option on its total assets where the strike is the value of debt.
5. Estimate the liquidity premium as the difference between the market spread and the fair value spread.
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Parameters and inputs
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Inputs for fair value of spreadsList of inputs for Merton’s model:
+ Value of Debt : The implied debt ratio is computed based on historical default rates of bonds of different terms and credit ratings. We use Moody’s global empirical cumulative default rates back to 1920s and 1970s in the calculation. (Source: Moody’s report).
+ Discount rate: long term swap rate (50 year maturity)
+ Dividend yield : using annual dividend yield from main equity
+ Cost of bankruptcy :14% of asset value when default happens.
+ Asset Volatility : There are two components for asset volatility calculation: the index volatility and specific volatility.– Index volatility: B&H market implied equity volatility surface (Source: banks survey)
– Firm specific volatility: we take the average of one year specific volatility of stocks from the main equity index for each economy.
Asset volatility2 = (Index volatility2 + Firm specific volatility2 )*De-gearing factor
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Value of Debt Calculation+ Value of Debt (D) : The implied debt ratio is computed based on historical default rates
of bonds of different terms and credit ratings. We use Moody’s global empirical cumulative default rates back to 1920s and 1970s in the calculation.
+ Using Merton’s model, we inverse the implied debt ratio by matching the empirical cumulative default rates for each credit rating and maturity. The default rates are modelled as cash or nothing put:
+ Since the option pricing formula always discounted back to time zero, we adjust this,
+ real world probability of default
+ Then we solve the to achieve a proper D which gives the minimum errors between real world probability of default and empirical cumulative default rates.
)( 1)( dNecc TrT
bb −= +− μ
TTDeA
dA
ATr
σσμ )2/()/ln( 2)(
01
+=
+
=++ bT
f cr *)1( μ
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Inputs for expected default loss+ In the real world evaluation, investors would require a premium for bearing additional
risk. Here, the expected return is not only depend on a risk-free rate but also dependent on risk preferences represented by the equity risk premium.
+ By adjusting two input parameters and keep the rest the same, we calculate the expected default loss:
– Discount rate : long term swap rate (50 year maturity) and Firm risk premium: 3% and 4% respectively (Sorensen, 2008) (B&H assumption).
– Asset Volatility: There are two components for asset volatility calculation: the index volatility and specific volatility.
+ B&H real world equity volatility term structure is used this time. The whole surface is kept the same as market implied equity volatility surface.
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Inputs for expected default loss+ In the real world evaluation, investors would require a premium for bearing additional
risk. Here, the expected return is not only depend on a risk-free rate but also dependent on risk preferences represented by the equity risk premium.
+ By adjusting two input parameters and keep the rest the same, we calculate the expected default loss:
– Discount rate : long term swap rate (50 year maturity) and Firm risk premium: 3% and 4% respectively (Sorensen, 2008) (B&H assumption).
– Asset Volatility: There are two components for asset volatility calculation: the index volatility and specific volatility.
+ B&H real world equity volatility term structure is used this time. The whole surface is kept the same as market implied equity volatility surface.
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MC and RW equity index volatility term structure+ The relation between real-world equity index volatility and market consistent equity
index volatility term structure
0%
5%
10%
15%
20%
25%
30%
35%
40%
0 5 10 15 20 25
Equity Volatility (%)
Term (Year)
Market Consistent
Real World
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B&H spread decomposition over time
7 17 13 13 9 11 9 22 4267 68
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2339 32 23 19 20 18
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44
58 58
85
4925 43 56 59 56 64
78
88
132104
175
0
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400
450
Dec 2005Mar 2006Jun 2006Sep 2006Dec 2006Mar 2007Jun 2007Sep 2007Dec 2007Mar 2008Jun 2008Sep 2008
Cred
it Spread (bps)
Calibration Date
Average A Rated Credit Spread Decomposition (1970 onwards calibration)
Liquidity Premium
Credit Risk Premium
Expected Defaults
BoE model implementation
+ Use Leland and Toft extension of Merton model – allows for bond coupons and default prior to maturity.
+ Aggregate all investment grade bonds and assume 10 year term.+ Again choose fixed gearing due to impact of firms changing debt
levels, equal to long-run average leverage – roughly equal to BBB gearing in B&H model.
+ Again use fixed bankruptcy cost, based on academic research -significantly higher than B&H figure.
+ Use average of 1 year option-implied volatility and 10 year historical volatility – significantly lower than B&H figures.
+ Estimate firm risk premium dynamically based on equilibrium model.
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Bank of England spread decomposition
Sterling investment grade Sterling high-yield
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Possible refinements
Alternative model calibrations might make greater allowance for current conditions e.g.+Increase forward-looking equity risk premium due to increased risk aversion+Split different sectors, in particular Financials and Non-Financials+Try refining volatility model to allow for term structure of single stock option implied volatility+Or use GARCH model to estimate volatilities due to reduced liquidity in options markets
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Some comparisonsAt end-Sep 2008
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Exp. Def. CRP Liq. Prem. Index YieldBoE (IG) 103 109 155 368B&H (1970‐) 136 85 175 396B&H (1920‐) 167 97 132 396Increased ERP 117 104 175 396Alternative vol. method 80 62 254 396GARCH method (WIP) 65 57 274 396
LPE Comparison 30/09/08 (bp)
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Can we decompose the spread further?
Decomposition of the fair spread
+ Requires an additional assumption concerning the risk premium onthe firm’s assets.
+ Assumed in line with our standard assumptions on equity risk premia.
+ Example overall analysis at end-2008 for A- rated issuers (average of 5, 10 & 15 year maturities, 1970/2007 default data):
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Expected default
Risk Premium
Liquidity premium Total
GBP 140 274 115 529USD 108 247 147 502EUR 107 169 43 319Average 118 230 102 450
26% 51% 23%
Spread decomposition @ Dec '08For the more conservative long-term default assumption, this falls to approximately 60 bps.
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What are insurance firms doing?
What are insurance firms doing?
+ Among large insurance groups, approximately equally split between swaps and government bonds as the risk-free rate.
+ The majority (approx 75%) have opted to apply an LP to certain classes of business.
+ A wide range of assumptions from around 50 bps (over swaps) to 250 over (government bond yields).
+ Use of the negative basis appears to be the most common approach –often tailored to the firm’s own bond portfolio.
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Conclusions
Conclusions+ Unsurprisingly, given the extraordinary behaviour of market in 2008,
there has been re-appraisal by insurers of the importance of liquidity in asset pricing in bond markets.
+ There is a rich academic literature which supports the existence of liquidity premia.
+ Policymakers and accountants have been forced to re-think their positions but appear to have accepted the addition of LPs to reference rates for certain classes of business.
+ However, estimation of liquidity premia turns out to be challenging and different approaches and assumptions suggest there is genuine uncertainty about the ‘true’ level of LPs.
+ Given this uncertainty firms have adopted diverse assumptions atyear end 2008.
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Some referencesAmihud, Y., and H. Mendelson, 1986, “Asset pricing and the bid-ask spread,” Journal of Financial Economics, 17, 223-249.
Berndt, A., Douglas, R., Duffie, D., Ferguson, M. and Schranz, D. (2005) Measuring default risk premia from default swap rates and EDFs (2005) SSRN working paper.
Black, F. and Scholes, M. (1973) The pricing of options and corporate liabilities, Journal of Political Economy, 81, 637-54.
Brooke, M., Cooper, N. and Scholtes, C. (2000) Inferring market interest rate expectations from money market rates, Bank of England Quarterly Bulletin: November 2000, 392-402.
Collin-Dufresne, P. and Goldstein, R. (2000) Do credit spreads reflect stationary leverage ratios?, AFA 2001 New Orleans (SSRN 177408).
Cremers, M., Driessen, J., Meanhout, P. and Weinbaum, D. (2004) Individual stock-option prices and credit spreads, Yale ICF working paper no. 04-14 (SSRN 527502).
Dignan, J.H. (2003) Nondefault components of investment-grade bond spreads, Financial Analysts Journal May/June 2003, 93-102.
Elton, E.J., Gruber, M.K., Agrawal, D. and Mann, C. (2001) Explaining the rate spread on corporate bonds, Journal of Finance, 56, 247-77.
Ericsson, J., Reneby, J. and Wang, H. (2005) Can structural models price default risk? Evidence from bond and credit derivative markets (SSRN 637042)
Fleming, M.J., 2002. Are larger Treasury issues more liquid? Evidence from bill reopenings. Journal of Money, Credit, and Banking 3 (2), 707–735.
Houweling, P., Mentink, A. and Vorst, T. (2005) Comparing possible proxies of corporate bond liquidity, Journal of Banking and Finance, 29, 1331-58.
Longstaff, F.A., Mithal, S. and Neis, E. (2005) Corporate yield spreads: default risk or liquidity? New evidence from the credit default swap market, Journal of Finance, 60, 2213-53.
Merton, R.C. (1974) On the pricing of corporate debt: the risk structure of interest rates, Journal of Finance, 29, 449-70.
Perraudin, W.R.M. and Taylor, A.P. (2003) Liquidity and bond market spreads, EFA 2003 (SSRN 424060).
Webber & Rohan, Decomposing corporate bond spreads, Bank of England Quarterly Bulletin, 2007 Q4
Willemann, S. (2004) Calibration of structural credit risk models: implied sensitivities and liquidity discounts, University of Aarhus working paper.
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Sensitivity of Input parameters
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Discount rate
– We select 3 scenarios, 3%, 4% and 5% for the risk free rate. Taking End March 2009 , 4% as a base case, the change of risk free rate has relatively small effect on the
– Liquidity premium change in proportion giving different risk free rates (base: 4%)
– On average, there are around 5% changes in proportion in liquidity premium across all the rating in 3% and 5% risk free rate scenarios. However, the change in interest rate has much bigger effect to bonds with higher credit ratings than lower credit ratings.
Liquidity premium change in proportion (1920-2008 ) Liquidity premium change in proportion (1970-2008 )
Risk free rate AAA AA A BBB BB B Risk free rate AAA AA A BBB BB B
5% 8.8% 9.1% 4.9% 8.3% 0.6% 1.1% 5% 10.1% 6.0% 4.2% 6.8% 0.7% 1.2%
3% 10.2% 10.6% 5.7% 9.7% 0.7% 1.2% 3% 11.7% 7.0% 4.8% 8.0% 0.7% 1.3%
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Cost of bankruptcy
+ In our standard calculation, we use 14% of future value of assets as cost of bankruptcy. We stress this value by change the value to 12% and 16% respectively. Keeping the rest inputs constant, we present the liquidity premium change in proportion
+ Liquidity premium change in proportion giving different cost of bankruptcy (base: 14%)Liquidity premium change in proportion (1920-2008 ) Liquidity premium change in proportion (1970-2008 )
Bankrupcy cost AAA AA A BBB BB B Bankrupcy cost AAA AA A BBB BB B
12% 16.8% 19.5% 10.6% 20.1% 3.9% 8.2% 12% 18.9% 11.6% 8.6% 15.8% 3.9% 9.0%
16% 17.2% 19.9% 10.9% 20.5% 4.0% 8.4% 16% 19.3% 11.9% 8.8% 16.2% 4.0% 9.2%
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