Modelling Corporate Bonds

Modelling Corporate Bonds Current Issues In Life Assurance London 28 April 2004 / Edinburgh 20 May 2004 Andrew Smith email AndrewDSmith8@deloitte.co.uk

Presentation Outline Why model corporate bonds? Corporate bond investment characteristics Monte Carlo models Explaining bond spreads Conclusions

Why Model Corporate Bonds? I hold them anyway and I need to model all my investments for realistic balance sheet / individual capital assessment. I want to investigate whether I should diversify into corporate bonds, and if so, how much is best to hold. I want to understand the impact of credit risk for product pricing and my own company share price.

Corporate Bond Investment Characteristics

Recent Good Corporate Performance 600 500 400 Equities Gilts T bills Index linked Corporate 300 200 100 0 1990 1995 2000 Source: Barclays capital

UK Corporate Bond Spreads: History 10 year yield spread over gilts 3% 2% 1% BBB A AA AAA swap 0% 97 98 99 00 01 02 03 04 year Source: Merrill Lynch / Datastream

Historic Cumulative Default Rates Cumulative number of defaults by year t 0.50% 0.40% 0.30% 0.20% 0.10% 0.00% BBB AA A AAA 0 1 2 3 4 5 Source: Standard and Poor s EU 2003 Default Study

Monte Carlo Models

correlation with stock market correlation with reinsurer bad debt Individual Bond Models new purchases / issues rebalancing rules recovery rates correlation between bonds spread by grade / term transition matrix default by credit grade Some complex individual bond models are now being used for capital modelling work. complicated model

Structural Model (Merton) Equity = Geared Equity + Debt Firm A equity finance Investor X Firm B geared equity debt Investor X Credit spreads reflect an option premium Interest is expensed in accounting terms but the option has cost and value Prestige ratings reflect lower option value not better companies

Credit Graded vs Structural Models Model by grade is close to how portfolios are managed in practice Grades are subjective, out of date and sometimes arbitrary Historic data excludes the main catastrophe where modelling is needed Easily market consistent, because spread is a market price Correlations: bond/bond and bond/equity easily calibrated Structural model output can be arranged into bands and expressed as transition matrix

Modelling Dilemma: Why we need to be careful about small effects Under arbitrage-free models, corporate bonds behave like a (dynamically rebalanced) mixture of gilts and equities. There is one equity risk, but two places in a model where that risk is priced the equity model and the corporate bond model. A strategy sell equities and buy corporate bonds is a close substitution whose attractiveness is very dependent on asset model parameters in particular the relative cost of equity risk implicit in the equity ad corporate bond models. Worse still, the decision can be dependent on flukes of a particular set of random simulations. Danger that asset selection outcome determined by asset model calibration and not (much) by business dynamics

Explaining Bond Spreads

3% Historic Default << Yield Spreads 3% 2% AAA AA A BBB 2% 1% 1% 0% 1 2 3 4 5 holding period (years) Source: S&P EU study annualised historic defaults 0% 97 98 99 00 01 02 03 04 Source: Merrill Lynch / Datastream yields vs gilts

Yield Spread vs Default Yield spread >> historic default rates How do we explain the differences? free lunch? sampling error? risk premium? gilt collectors premium? liquidity premium?

Default Risk Premiums are Explainable Skew effect: Default involves extreme downside events 40% The existence of skews in volatilities is well known in out-ofmoney options Implied Volatility 35% 30% 25% 20% 15% 10% 5% 0% 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 FTSE 100 implied vol Source: LIFFE K = 0.8*F K = 0.9*F K = F K = 1.1*F K = 1.2*F default equates with extreme out-of-money puts Yield spread vs default difference not an obvious anomaly If your asset model does not capture equity skew effect then its probably not worth trying to replicate historic bond defaults

Historic Default Rates = Small Samples So true default rates very uncertain anyway Number of EU bonds defaulting in year t 20 15 10 5 0 Investment grade Speculative grade 30% 20% 10% 0% -10% -20% -30% 91 92 93 94 95 96 97 98 99 00 01 02 03 Source: Standard and Poor s EU 2003 Default Study Equity return during year

The Peso Effect: Rare default events are over-represented if they occur in the data set and under-represented if they do not. 1 Value of 1 Argentine Peso (in US$ - left scale) 30% 0.5 Yield spread Argentine vs US 3 month rate (right scale) 20% 10% 0 0% 91 92 93 94 95 96 97 98 99 00 01 02 03 Source: DataStream

Annual equity capital return We can extrapolate equity returns but it is difficult to do the same for bond defaults 10 100 1000-10% Frequency (years) -20% -30% -40% -50% -60% 2001 1937 1929 1931 2002 1920 1973 1974 Barclays capital data extrapolated fit Historical defaults offer no convincing tool for estimating a 1 in 200 year credit event. Therefore avoid over-emphasis on historical transitions and concentrate on market prices (spreads) instead.

Swap / Gilt spread explained by: credit risk (repo vs libmid) and transaction costs (libor vs libmid) Spread between secured (GC repo) and unsecured (Libmid) interbank rates 0.5% 0.4% 0.3% 0.2% 0.1% 0.0% so gilt collectors item effect and corporate bond liquidity effect probably 5 bp at most 3 month 6 month 99 00 01 02 03 Source: Datastream Credit TC s Others = Swap-Gilt 3% 2% 1% BBB A AA AAA swap 15 10 0 25 bp 0% 97 98 99 00 01 02 03 04

Corporates Subtle Considerations Corporate bonds might behave like equity plus gilts, but tax, statutory valuation and ECR treatment is different Liquidity needed to maintain credit exposure within limits, so estimate transaction costs carefully Investment management costs, including risk management and audit Possibility for income from repo market (especially on most liquid gilts if there is a squeeze and they go special on repo) What matters is effect on a life office relative to what is priced into bonds in the first place

Conclusions

Conclusions Many similarities: puzzles for corporate bonds and puzzles for equities why is the risk premium so high? free lunch vs efficient markets vs arbitrage-free Building a complicated simulation model can (maybe, just maybe) give additional insights Risk that a decision to hold corporate bonds (or not) is effectively hard-coded in the guts of an asset model calibration rather than deliberate consequence of the business model If an investment looks too good to be true - it probably is actuaries equity free lunch claims discredited let us not repeat the mistake with corporate bonds

Modelling Corporate Bonds Current Issues In Life Assurance London 28 April 2004 / Edinburgh 20 May 2004 Andrew Smith email AndrewDSmith8@deloitte.co.uk