Once again we can substitute the values from the table to get, using
the same value for the surprise above
Finally we simulate default or Poisson by a straight comparison of
the spread with a level which would constitute a default in this case
we took 20 per cent.
1.12 Risk management of xed income
We now start looking at approaches to managing the credit risk in a
portfolio context. A portfolio is a very complicated entity. Consequently,
we start at the very basic level and begin with an examination of the
credit risk for just one bond.
Even a humble bond presents a number of challenges to the provi-
sion of a comprehensive risk treatment. We are going to step back
from credit for a moment because there is a general framework for
managing risk; anticipating that credit risk can be addressed within
this architecture. So before continuing with credit we need to under-
stand this general edifice.
This general framework divides the labour necessary to produce a
risk report. The basis of this distinction is the separation between the
spread(10,0,2) 0.02 0.01 surprise
0.01 10
2 0.034.
54 Credit risk: from transaction to portfolio management
Share price
Figure 1.32 A Gaussian process.
general behaviour of the market and the characteristics of the asset.
This is a quite natural division because on the one hand we have the
market which we usually described by a set of rates. The description
must capture how much these rates are likely to move and also the
relationship between their co-movement. On the other hand we have a
financial asset within the portfolio which changes value mainly as a
result of the underlying market change. So quite a natural risk para-
digm is displayed in the bullet points below:
Identify a set of metrics which characterize the marketplace.
Find out how your instrument depends on these metrics.
Capture movement in the metrics and their interaction.
We apply this methodology for both the single bond and then a port-
folio bonds. First off, then we have to identify metrics, this is not
straightforward as there is a great deal of flexibility in this choice. They
can be completely abstract or they can actually be observable in the
market. For example if I had a 5- and 10-year government bond within
my portfolio then a natural set of risk factors will consist of the 5- and
10-year yields. But I could equivalently choose the principal com-
ponents of the curve. The main constraint when choosing a set of
risk factors is that they are mathematically independent variables.
Consequently it should be possible to isolate the change in the port-
folio value due to the change in one risk factor.
Since our portfolio consists of just one credit bond the risks inher-
ent in holding the bond will consist of the general market risk together
with the further risk due to the credit exposure. We will call these fac-
tors M and S respectively. These are the risk metrics. Aside from worry-
ing about how these factors actually move we can now examine the
second bullet point which is how the bond changes in value due to a
change in either of these factors. Well any graduate new to the trading
floor can price a bond dependent upon a credit spread (drawing upon
the concept of yield to maturity). We reproduce the graduates work in
the equation below for a 10 year bond:
We can now think of this value changing because of either a movement
in the general market conditions, or it could change due to a variation
in the credit worthiness of the issuer. The upshot is that we have an
expression which isolates a change in the holding due to either
Present value
(1 )
(1 )
time 10
time 1
Fixed income credit 55

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