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The transition matrix model (TMM) determines the probability of default (PD) of loans by tracking the historical movement of loans between loan states over a defined period of time – for example, from one year to the next – and establishes a probably of transition for those loan types between different loan states. That is, it determines the likelihood or probability of those loans moving from one state to another. It then runs those time-bracketed transition probabilities through Markov chains to determine long-term default rates. You apply and reapply the probabilities to determine a lifetime default rate for a particular category of loans.
The TMM process requires you first to determine your allowance segments, then establish loan states within each pool segment, essentially the sub-segments within a segment, between which you will track movement. By far, the most common active state drivers are risk ratings. In addition to the active states – risk ratings, delinquency, FICO scores and other default drivers – you will track movement to terminal states, that is, the end of the life of the loan, when it defaults or is paid off. A common transition matrix might have a six-point risk-rating scale and two categories for loans that have exited the transition.
Once you have established your loan states, look at the historical performance of your loans between the defined periods. Essentially, you are trying to determine the average probability of loans moving from one state to another by analyzing their historical transition, then averaging those transition rates over time. For example, if you have five years of historical data and five years of transitions, you can average those probabilities to apply to your current portfolio and project what the portfolio will look like going forward. This is when you run the Markov chain to see what your long-term probability is going to be. You eventually wind up migrating into the default or paid-off loan state, which is how the Markov chain process gets you from annual transition rates to a lifetime probability of default.
Your loss given default (LGD) calculates the losses you experience in cases of default. It is the simpler of the PD/LGD calculations. It is important to calculate the LGD by capturing the balance of loans at the time of default or just prior to default, then capture what losses occur to those loans following the default event. Eventual losses divided by balance prior to default equals LGD.
Because you run the Markov chains by period, a transition matrix methodology allows you to insert forecast adjustments more easily than other methodologies. You can make year-by-year adjustments to the transition probabilities as you run them out to determine lifetime results. And it is easy to revert to the historical mean once you can no longer make adjustments to default rates or other transition probabilities.
A transition matrix also may require a shorter window of historical data than some other methodologies because you are using defined time periods. You can execute the methodology with shorter periods of historical data and still project forward.
The transition matrix is a more complex calculation than some other methodologies, which will be difficult to manage in a manual spreadsheet-based calculation. As well, you will have to have been relatively consistent in your risk ratings. If your parameters for a grade-four rating have changed, for example, you won’t be able to use the historical transitions to and from that rating to make a reliable projection of what will happen with those loans going forward.
If you would like to see a transition matrix model example in the Loan Loss Analyzer, please schedule a demo.
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