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
9900 0001 0102
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.

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