Modelling Corporate Bonds
Current Issues In Life Assurance
London 28 April 2004 / Edinburgh 20 May 2004
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
0 100 200 300 400 500 600 1990 1995 2000 E quities G ilts T bills Index linked C orporateUK Corporate Bond Spreads: History
0% 1% 2% 3% 97 98 99 00 01 02 03 04 BBB A AA AAA swap year10 year yield spread over gilts
Historic Cumulative Default Rates
0.00% 0.10% 0.20% 0.30% 0.40% 0.50% 0 1 2 3 4 5Source: Standard and Poor’s EU 2003 Default Study
BBB
AA
A
AAA
Cumulative number of defaults by year
Individual Bond Models
complicated model
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modelling
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Structural Model (Merton)
Equity = Geared Equity + Debt
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
Investor X
Investor X
equity finance
geared equity
debt
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out of date and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
Historic Default << Yield Spreads
0% 1% 2% 3% 1 2 3 4 5 AAA AA A BBBannualised historic defaults yields vs gilts
0% 1% 2% 3%
97 98 99 00 01 02 03 04
holding period (years) Source: S&P EU study
Source:
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
Default involves extreme downside events
The existence of skews in
volatilities is well known in out-of-money options
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
1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 K = 0.8*F K = 0.9*F K = F K = 1.1*F K = 1.2*F 0% 5% 10% 15% 20% 25% 30% 35% 40% Imp li e d Vo lat ilit y
FTSE 100 implied vol Source: LIFFE
Historic Default Rates = Small Samples
So true default rates very uncertain anyway
Number of EU bonds defaulting in year
t
Source: Standard and Poor’s EU 2003 Default Study
0 5 10 15 20 91 92 93 94 95 96 97 98 99 00 01 02 03 -30% -20% -10% 0% 10% 20% 30%
Equity return during year
Investment grade Speculative grade
0 0.5 1 91 92 93 94 95 96 97 98 99 00 01 02 03 0% 10% 20% 30% Value of 1 Argentine Peso
(in US$ - left scale)
Yield spread – Argentine vs US 3 month rate (right scale)
The Peso Effect: Rare default events are
over-represented if they occur in the data
set and under-represented if they do not.
We can extrapolate equity returns but it is
difficult to do the same for bond defaults
2001 1937 1929 1931 2002 1920 1973 1974 -60% -50% -40% -30% -20% -10% 10 100 1000
Barclays capital data extrapolated fit
Frequency (years)
Annual equity capital return
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)
0.0% 0.1% 0.2% 0.3% 0.4% 0.5% 99 00 01 02 03 3 month 6 month Source: Datastream
Spread between secured (GC repo) and unsecured (Libmid) interbank
rates
… so gilt collectors’ item effect and corporate bond liquidity effect probably 5 bp at most
0% 1% 2% 3% 97 98 99 00 01 02 03 04 BBB A AA AAA swap Credit TC’s Others = Swap-Gilt 15 10 0 25 bp
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
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
Modelling Corporate Bonds
Current Issues In Life Assurance
London 28 April 2004 / Edinburgh 20 May 2004