# ICAAP: Credit Risk: Stress Test: How to construct a Transition Matrix

One way of stress testing credit risk under the Internal Capital Adequacy and Assessment Process (ICAAP) is to stress test the rating grades transition matrix. In the post below we will first look at how a rating grades transition matrix is constructed.

# Transition matrix stress test

We will first consider some preliminary calculations before we discuss the transition matrix stress tests.

## How to construct a transition matrix

A transition matrix is a numerical representation of the changes in a population that can be described by a fixed countable number of attributes (e.g. rating grades). Each member of the population can only take on one of the attributes at any point in time. The transition matrix displays how the attributes assigned to a member of the population change over time between two distinct dates. The members of the population are the counterparties. Finally the movement can be quantified by absolute numbers or by some underlying monetary value. We use outstanding balances to quantify the movement.

Generating a transition matrix consists of the following steps:

• Determine frequency of transition, e.g. quarterly
• Determine credit ratings for start of period
• Determine credit ratings for end of period
• Determine outstanding exposure at the end of the period: The outstanding exposure at the end of the period is adjusted for any additional exposure taken after the start of period. This ensures that the transition amount is always a sub set of the original outstanding exposure.
• Finally, a transition matrix is calculated for each industry.

We have reviewed the step-by-step methodology for constructing a ratings grade transition matrix. In the next post we will look at the step-by-step procedure for deriving expected classification rates for the current loan portfolio.