Credit Risk: From Transaction to Portfolio Management

1.11 Credit risk

A vanilla bond issued by a high-investment grade corporate will have

two distinct components of investment risk. The major risk borne by

the bondholder will be the price volatility caused by variations in the

time value of money. Additionally there will be a risk due to the possi-

bility of the issuer defaulting. For the example we neglect liquidity risk

and assume that the inflation premium is included as a component of

the risk free rate.

The remaining two sources of risk each have their own independent

behaviour. The extra spread over the risk free rate is simply the mar-

ket’s estimate of default probability.

We can give a graphic illustration of these two components at work

with reference to Figure 1.27.

This may on first appearances look rather like a picture that Nasa

would be proud of. But a closer inspection reveals all the risk charac-

teristics of a corporate bond. First we will explain what the axes rep-

resent. From the middle and sloping down to the right is the return on

the bond, running into the page is the time horizon, in units of years.

The vertical axis represents an effective probability.

Two separate humps broadly characterize the diagram. The larger

hump to the left represents the influence of market risk. To begin

with, the market return is distributed equally about zero. If we observe

very closely it can be seen to approximate a normal distribution. As

time progresses the mean component of return on the bond begins

to dominate, even though for any one year there is still a distribution

about this mean. We can also see that the actual thickness about the

mean tends to decrease as the maturity on a bond gets closer. If we

just had a government bond that would conclude the story.

The credit risk manifests itself within the small hump to the right.

The saying is that a picture is worth a thousand words; well consider

44 Credit risk: from transaction to portfolio management

Euro broad investment grade

Government bonds

MSCI Europe

Euro high yield

0.00

10.00

20.00

Return (%)

10.00

20.00

30.00

99–00 00–01 01–02

Year

Figure 1.26 High-yield comparative performances.

yourself lucky because you have both. The picture repays a careful

study; this is rather like a kaleidoscope which at first is confusing

because your eye and mind are not quite coordinated. Initially the pic-

ture is missed but then with a bit of patience the shape materializes.

The hump is quite narrow to begin with because the chance of the

borrower defaulting is quite small post-issuance. This is quite intuitive

because young companies tend to be fairly liquid to begin with and

coupon payments to the bond holders will have a very high priority. As

time advances the probability of default will grow. This is because even

if the marginal probability, which represents the chance of default in

any one particular year remains constant, the so-called cumulative

default probability, which is the measure most relevant to a long-term

bond holder increases with time.

We will come back to this diagram a little bit later to discuss how the

risks are represented mathematically. But this is asking a little bit too

much to begin with. The actual details are quite complicated; we need

to build up slowly.

The first thing we are going to look at is the pricing of a 1-year zero

coupon bond issued by a non-government. We study a good-quality

credit which does not have any liquidity risk. We choose a zero coupon

bond because it highlights rather well the actual finances at work as

opposed to tedious bond maths.

We can price the bond exactly in the same manner as we would a

government bond, but the rate at which we use to discount the cash

flow requires an additional spread implicitly containing the market

Fixed income credit 45

0

10

20

30

40

50

60

70

80

90

100

1

10

0

50

100

150

200

250

300

350

400

450

Number of events

Present value

Time (years)

Figure 1.27 An illustration of the default process for a 10 year corporate bond.