Estimation of the liquidity premium in corporate bond yields

Transcription

1 May 2009 Estimation of the liquidity premium in corporate bond yields John Hibbert 0

2 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 1

3 What is the (il)liquidity premium & why does it matter? 2

4 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. 3

5 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. 4

6 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? 5

7 CFO views are modified + On December 19 th, the CFO Forum stated: the CFO Forum remains committed to MCEV and the Principles published in June 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. 6

8 CROs views + CRO Forum: Comments on the Financial Crisis, 24 October 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. 7

9 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. Remember - economic, market-consistent valuation breaks the link between liability value and backing assets. 8

10 Why might a liquidity premium be on offer? 9

11 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 10

12 What are do academic researchers & practitioners have to say? 11

13 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. 12

14 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. 13

15 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. * Some hedge fund strategies are designed to accumulate LP by supplying liquidity. *Survey of Recent Hedge Fund Articles, EDHEC, September 2005 Hedge fund alphas: do they reflect managerial skills or mere compensation for liquidity risk bearing?, Gibson & Wang, February

16 How might the liquidity premium be estimated? 15

17 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. 16

18 A reminder: Decomposition of market spreads + 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 defaultrelated credit risks. 17

19 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. If the marginal investor faces a half-spread of 5% and anticipates an average [riskneutral] holding period of 3 years, then the fair liquidity spread will be approx 60 bps for a typical 10-year bond. Liquidity Premium (bps) Is there market risk here since 50 dealer spreads are a function of vol? 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 18

20 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. Basis Points Itraxx EUR 5 Yr CDS Iboxx EUR Corporate 5 7yr Z Spread + A fundamental change in the basis followed the disclosure of AIG s problems in September Dec 04 Dec 05 Dec Dec 04 Dec 05 Dec 06 Dec 07 Dec 08 Dec 09 Dec 07 Dec 08 Dec 09 Basis Points 19

21 Approach #3: An estimate for the fair spread using the Merton model Corporate debt pay-off = Risk-free bond payout Put option payout Or Firm assets sold call 20

22 Merton s Model + The Black-Scholes valuation formulae for a European call option on a company s assets are E + Where d 1 0 = A0 d ln( A0e = rt N( d1) De N( 2 ) rt / D) + ( σ / 2) T σ A T 2 A d 2 = d 1 σ A T + The current value of the company s assets,(a 0 ) + The volatility of the company s assets,( σ A ) usually estimated from the company s equity + The outstanding debt( D) + The debt maturity (T) + The discount rate ( r ) 21

23 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 recovery rates 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. 22

24 Parameters and inputs

25 Inputs for fair value of spreads List 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 volatility 2 = (Index volatility 2 + Firm specific volatility 2 )*De-gearing factor 24

26 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: c b = c T b e ( r+ μ ) T N( d1) d 1 = ln( A 0 e ( r + μ ) T σ / D) + ( σ A T 2 A / 2) T + Since the option pricing formula always discounted back to time zero, we adjust this, T + ( 1 r + μ) * c = real world probability of default + f b + 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. 25

27 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. 26

28 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. 27

29 MC and RW equity index volatility term structure + The relation between real-world equity index volatility and market consistent equity index volatility term structure 40% 35% Equity Volatility (%) 30% 25% 20% 15% 10% 5% 0% Market Consistent Real World Term (Year)

30 B&H spread decomposition over time Average A Rated Credit Spread Decomposition (1970 onwards calibration) Liquidity Premium Credit Risk Premium Expected Defaults Credit Spread (bps) Dec 2005Mar 2006Jun 2006Sep 2006Dec 2006Mar 2007Jun 2007Sep 2007Dec 2007Mar 2008Jun 2008Sep 2008 Calibration Date 29

31 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. 30

32 Bank of England spread decomposition Sterling investment grade Sterling high-yield 31

33 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 32

34 Some comparisons At end-sep 2008 LPE Comparison 30/09/08 (bp) Exp. Def. CRP Liq. Prem. Index Yield BoE (IG) B&H (1970 ) B&H (1920 ) Increased ERP Alternative vol. method GARCH method (WIP)

35 Can we decompose the spread further? 34

36 Decomposition of the fair spread + Requires an additional assumption concerning the risk premium on the 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): Spread Dec '08 Expected default Risk Premium Liquidity premium Total GBP USD EUR Average % 51% 23% For the more conservative longterm default assumption, this falls to approximately 60 bps. 35

37 What are insurance firms doing? 36

38 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. 37

39 Conclusions 38

40 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 at year end

41 Some references Amihud, Y., and H. Mendelson, 1986, Asset pricing and the bid-ask spread, Journal of Financial Economics, 17, 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, Brooke, M., Cooper, N. and Scholtes, C. (2000) Inferring market interest rate expectations from money market rates, Bank of England Quarterly Bulletin: November 2000, Collin-Dufresne, P. and Goldstein, R. (2000) Do credit spreads reflect stationary leverage ratios?, AFA 2001 New Orleans (SSRN ). Cremers, M., Driessen, J., Meanhout, P. and Weinbaum, D. (2004) Individual stock-option prices and credit spreads, Yale ICF working paper no (SSRN ). Dignan, J.H. (2003) Nondefault components of investment-grade bond spreads, Financial Analysts Journal May/June 2003, Elton, E.J., Gruber, M.K., Agrawal, D. and Mann, C. (2001) Explaining the rate spread on corporate bonds, Journal of Finance, 56, Ericsson, J., Reneby, J. and Wang, H. (2005) Can structural models price default risk? Evidence from bond and credit derivative markets (SSRN ) Fleming, M.J., Are larger Treasury issues more liquid? Evidence from bill reopenings. Journal of Money, Credit, and Banking 3 (2), Houweling, P., Mentink, A. and Vorst, T. (2005) Comparing possible proxies of corporate bond liquidity, Journal of Banking and Finance, 29, 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, Merton, R.C. (1974) On the pricing of corporate debt: the risk structure of interest rates, Journal of Finance, 29, Perraudin, W.R.M. and Taylor, A.P. (2003) Liquidity and bond market spreads, EFA 2003 (SSRN ). 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. 40

42 Sensitivity of Input parameters

43 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%) Liquidity premium change in proportion ( ) Liquidity premium change in proportion ( ) 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% 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. 42

44 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 ( ) Liquidity premium change in proportion ( ) 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% 43

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