Credit risk stress testing

There is, of course, no reason why stress testing should be constrained to market
risk factors. In fact, it makes sense to stress all risk factors to which the bank is
exposed and credit risk is, in many cases, the largest risk factor. It would seem
natural having identified a potentially damaging market risk scenario to want to
know what impact that same scenario would have on the bank’s credit exposure.
Table 8.5 shows a series of market scenarios applied to trading credit risk exposures.

In general, a bank’s loan portfolio is considered to be relatively immune to market
scenarios. This is not strictly true, as the value of a loan will change dependent on
the level of the relevant yield curve; also, many commercial loans contain optionality
(which is often ignored for valuation purposes). Recently there has been a lot of
discussion about the application of traded product valuation techniques to loan
books and the desirability of treating the loan and trading portfolio on the same
basis for credit risk. This makes eminent sense and will become standard practice
over the next few years. However, it is clear that the value of traded products, such
as swaps, are far more sensitive to changes in market prices than loans.

Table 8.5 shows a portfolio containing two counterparties (customers) the value of
their exposure is equal at the present time (£5 million). Four different market risk
scenarios have been applied to the portfolio to investigate the potential changes in
the value of the counterparty exposure. The four scenarios applied to the portfolio
can be taken to be a series of increasing parallel yield curve shifts. It is not really
important, however, it may be the case that the counterparty portfolios contain
mainly interest rate instruments, such as interest rate swaps, and that the counterparty
portfolios are the opposite way round from each other (one is receiving fixed
rates whilst the other is paying fixed rates).

The thought process behind this series of stress could be that the systematic stress
testing carried out on the market risk portfolio has enabled the managers to identify
market risk scenarios that concern them. Perhaps they result from stressing exposure
to a particular country. Risk managers then remember that there are two counterparties
in that country that they are also concerned about from a purely credit perspective,
i.e. they believe there is a reasonable probability of downgrade or default. They
decide to run the same market risk scenarios against the counterparties and to
investigate the resultant exposure and potential losses given default. Of course,
multiple credit risk stress tests could be run with different counterparties going into
default, either singly or in groups.

Table 8.5 shows that exposure to counterparty A becomes increasingly negative as
the scenarios progress. Taking scenario D as an example, the exposure to counterparty
A would be ñ£7.04 million. In the case of default, the profit and loss for the
total portfolio (unrealized plus realized profit and loss) would not change. Prior to
default, the negative exposure would be part of the unrealized profit and loss on the
portfolio. After default, the loss would become realized profit and loss.7 As the net
effect on the portfolio value is zero, counterparties with negative exposure are
normally treated as a zero credit risk.

More worrying is the rapid increase in the positive value of exposure to counterparty
B, this warrants further analysis. Table 8.5 gives further analysis of the credit risk
stress test for counterparty B in the grey shaded area. The line after the exposure
shows the value of collateral placed by counterparty B with the bank. At the current
time, the exposure to counterparty B is fully covered by the value of collateral placed
with the bank. It can be seen that this situation is very different, dependent on the size
of the market shock experienced. In the case of scenario D the value of the collateral
has dropped to £1.375 million – against an exposure of £11.04 million, i.e. the collateral
would only cover 12.5% of the exposure! This may seem unrealistic but is actually
based on market shocks that took place in the emerging markets in 1997 and 1998.

The next part of the analysis is to assume default and calculate the loss that would
be experienced. This is shown in the next two lines in Table 8.5. The first line assumes
the collateral agreement is enforceable. The worst-case loss scenario is that the collateral
agreement is found to be unenforceable. Again this may sound unrealistic but
more than one banker has been heard to remark after the Asian crises that ‘collateral
is a fair-weather friend’. The degree of legal certainty surrounding collateral agreements
– particularly in emerging markets is not all that would be wished for.

Note that the credit risk stress test does not involve the probability of default or
the expected recovery rate. Both of these statistics are common in credit risk models
but do not help in the quantification of loss in case of an actual default. The recovery
rate says what you may expect to get back on average (i.e. over a large number of
defaults with a similar creditor rating) and does not include the time delay. In case
of default, the total loss is written off, less any enforceable collateral held, no account
is taken of the expected recovery rate. After all, it may be some years before the
counterparty’s assets are liquidated and distributed to creditors.

The final piece of analysis to undertake is to examine the impact the default has
on the total portfolio value. For a real portfolio this would need to be done by stripping
out all the trades for the counterparties that are assumed to be in default and
recalculating the portfolio values under each of the market scenarios under investigation.
In the very simple portfolio described in Table 8.5, we can see what the impact
would be. It has already been noted that the impact of counterparty A defaulting
would be neutral for the portfolio value, as an unrealized loss would just be changed
into a realized loss.

In the case of counterparty B, it is not quite so obvious. Once a credit loss has
occurred, the portfolio value is reduced by the amount of the loss (becoming a
realised loss). The final line in Table 8.5 shows the total portfolio loss as a combination
of the market scenario and the default of counterparty B. This is actually the result
of a combined market and credit risk stress test.