Transition matrix (roll-rate matrix)
A transition matrix, also called a roll-rate matrix, shows the share of loans or balances that move from each delinquency status this month to each status next month. Each row represents this month’s status, and each column represents next month’s status.
Example
For illustration, take 100 loans that are 30 to 59 days past due this month. If 20 move to 60 to 89 days next month and 80 stay in the same status, the row shows a 20% roll forward rate and an 80% stay rate.
Building a matrix from monthly loan status
Use loan status for two adjacent months. For each status in the first month, tally where those loans appear in the second month. This shows how the starting group is distributed across next month’s statuses.
For a count-based matrix, calculate each destination’s share of the loans that started in that row. For a balance-based matrix, calculate each destination’s share of the starting balance. The percentages across a row sum to 100%.
Reading roll rates, cures and provision estimates
A move into a more delinquent bucket is a roll forward rate. A move back to current is a cure rate. The share that stays in the same bucket is the stay rate.
To estimate movement over several months, multiply the roll forward rates along the chain. This estimates how much of today’s current balance reaches charge-off. It is an estimate, not a guaranteed outcome.
For provision analysis, a matrix can show how balances move through delinquency statuses. It does not set a provision amount.
Questions we get asked
Why can a balance-based matrix differ from a loan-count matrix?
They weight the portfolio differently. A count matrix gives each loan equal weight, but a balance matrix gives more weight to larger loans, which can behave differently.
Does a transition matrix predict what will happen to one loan?
No. It summarizes shares across loans or balances in a group, so it does not say with certainty what will happen to one loan.
Does a roll-rate matrix give an exact charge-off forecast?
No. Chaining roll-forward rates estimates how much of today’s current balance reaches charge-off. It does not guarantee the balance that will charge off.
Decisimo’s free roll-rate calculator builds a transition matrix, roll chain and cure rates from a monthly loan status CSV, and the file stays in your browser.
