## ICAAP: Credit Risk: Stress Test: Transition Matrix Stress Test

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In this post we discuss one way of stress testing a rating grades transition matrix. The stressed transition matrix will then be used in the other credit risk quantification calculations. The revised results will be compared to the original credit risk quantification calculations to determine the impact of the stress test.

# How to stress the transition matrix

The transition matrix stress test is based on a sector wide or industry wide down turn scenario. The level of stress test will depend on how many grades are used. The basic scenario will be based on a one notch downgrade. Considering that the stress test will focus on all names belonging to a particular the industry/ industries, a one notch downgrade is considered a fairly stressed scenario since it will have a portfolio wide impact.

The test aims to penalize portfolios that have classified customers belonging to the same sector. Since a rating downgrade does not take into account the amount of time elapsed, a customer rated 9 will always move to 10, a customer rated 10 will always move to 11 and a customer rated 11 will always move to 12.

On the other hand, portfolios consisting of only the highest ranked names in the industry will experience little or no impact from the one notch downgrade.

The rating grade stress tests does not factor in the amount of time required for the transition to take place. Transition matrix stress tests measure the impact of a shift in the underlying distribution based on industry outlook. For more conservative stress tests based on industry outlook, two notch and three notch downgrades will also be used.

In addition to distribution wide downgrades, specific areas of the distribution will be stressed. The rating scale will be distributed into three bands. Each band will be applied one of three levels of shocks, namely high, moderate and low.

By default, the highest rated band will be applied a high shock (this is because the greatest impact to profitability will be if the higher rated bands downgrade), following by the second band which will be applied a moderate shock and finally the lowest ranked customer band will be applied a low level of shock considering that this band is primarily in the non performing category and movement from one rating grade to the next is dependant to days past due.

The definition of the shock levels will be set as per the following specification by default with the ability to make modifications for more customized tests.

High Stress | 3 notch downgrade |

Moderate Stress | 2 notch downgrade |

Low Stress | 1 notch downgrade |

The stressed distribution using the above analysis will be then be translated into a capital charge. The capital associated with this stressed scenario will be calculated using the one year probability of default estimate based on historical transitions (i.e. using the stressed transition what is the probability of default for the given loan in the following year, where probabilities of default have been modelled using historical data and the chosen PD model).

The transition matrix stress test will be applied to sectors identified using early warning indicators based on methodologies such as HHI and DPD.

Once the stress test is applied, the next step is to quantify the impact of this shock. Based on tools such as expected classification, NPL stress test and profitability analysis, the change in risk profile will be quantified based on expected provisioning and profitability analysis. The stressed distribution will be used to calculate expected provisioning, which will in turn be used to calculate worst case loss. The difference between the revised and original worst case loss will be used as a proxy for the monetary impact of the stress test.

We have discussed how the original rating grades transition matrix can be stress tested. In the next post we will be reviewing the profitability analysis stress test.

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