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(1)

Modelling Corporate Bonds

Current Issues In Life Assurance

London 28 April 2004 / Edinburgh 20 May 2004

(2)

Presentation Outline

ƒ Why model corporate bonds?

ƒ Corporate bond investment characteristics

ƒ Monte Carlo models

ƒ Explaining bond spreads

ƒ Conclusions

(3)

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.

(4)

Corporate Bond Investment

Characteristics

(5)

Recent Good Corporate Performance

0 100 200 300 400 500 600 1990 1995 2000 E quities G ilts T bills Index linked C orporate

(6)

UK Corporate Bond Spreads: History

0% 1% 2% 3% 97 98 99 00 01 02 03 04 BBB A AA AAA swap year

10 year yield spread over gilts

(7)

Historic Cumulative Default Rates

0.00% 0.10% 0.20% 0.30% 0.40% 0.50% 0 1 2 3 4 5

Source: Standard and Poor’s EU 2003 Default Study

BBB

AA

A

AAA

Cumulative number of defaults by year

(8)
(9)

Individual Bond Models

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(10)

Structural Model (Merton)

Equity = Geared Equity + Debt

ƒ Credit spreads reflect an

option premium

ƒ Interest is expensed in accounting terms

ƒ but the option has cost and value

ƒ Prestige ratings reflect

lower option value

ƒ not “better” companies

Investor X

Investor X

equity finance

geared equity

debt

(11)

Credit Graded vs Structural Models

ƒ Model by grade is close

to how portfolios are

managed in practice

ƒ Grades are subjective,

out of date and

sometimes arbitrary

ƒ Historic data excludes

the main catastrophe

where modelling is

needed

ƒ Easily market

consistent, because

spread is a market price

ƒ Correlations: bond/bond

and bond/equity easily

calibrated

ƒ Structural model output

can be arranged into

bands and expressed as

transition matrix

(12)

Modelling Dilemma: Why we need to be

careful about small effects

ƒ 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.

ƒ 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.

ƒ Danger that asset selection outcome determined by asset model calibration and not (much) by business dynamics

(13)
(14)

Historic Default << Yield Spreads

0% 1% 2% 3% 1 2 3 4 5 AAA AA A BBB

annualised 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:

(15)

Yield Spread vs Default

ƒ Yield spread >> historic default rates

ƒ How do we explain the differences?

ƒ free lunch?

ƒ sampling error?

ƒ risk premium?

ƒ gilt collectors’ premium?

ƒ liquidity premium?

(16)

Default Risk Premiums are Explainable

ƒ Default involves extreme downside events

ƒ The existence of skews in

volatilities is well known in out-of-money options

ƒ default equates with extreme out-of-money puts

ƒ Yield spread vs default difference not an obvious anomaly

ƒ 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

(17)

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

(18)

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.

(19)

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.

(20)

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

(21)

Corporates – Subtle Considerations

ƒ Corporate bonds might behave like equity plus gilts, but

tax, statutory valuation and ECR treatment is different

ƒ Liquidity – needed to maintain credit exposure within

limits, so estimate transaction costs carefully

ƒ Investment management costs, including risk

management and audit

ƒ Possibility for income from repo market (especially on

most liquid gilts if there is a squeeze and they go

special on repo)

ƒ What matters is effect on a life office relative to what is

(22)
(23)

Conclusions

ƒ Many similarities: puzzles for corporate bonds and

puzzles for equities

ƒ why is the risk premium so high?

ƒ free lunch vs efficient markets vs arbitrage-free

ƒ Building a complicated simulation model can (maybe,

just maybe) give additional insights

ƒ 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

ƒ If an investment looks too good to be true - it probably is

ƒ actuaries’ equity free lunch claims discredited

(24)

Modelling Corporate Bonds

Current Issues In Life Assurance

London 28 April 2004 / Edinburgh 20 May 2004

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