Rating Transition Matrices
A transition matrix lists, for each starting credit rating, the probability of ending the year at every other rating — including default — turning a static letter grade into a forward-looking risk forecast.
Prerequisites: Credit Ratings and the Agencies
A rating tells you where a borrower stands today. It says nothing directly about where it's likely to be a year from now. Rating agencies address that by publishing transition matrices — historical tables showing, for every starting rating, what fraction of similarly-rated companies ended the following year upgraded, downgraded, unchanged, or in default. It's the closest thing credit markets have to a weather forecast for creditworthiness.
A transition matrix is a table of one-year migration probabilities built from decades of historical rating changes — read across a row to see, for a given starting rating, the odds of moving anywhere else including default.
Reading the table
Each row of a transition matrix represents a starting rating; each column represents an ending rating one year later; each cell is the historical probability of that specific move. Rows sum to 100%. High-grade ratings (AAA, AA) show heavy probability mass sitting right on the diagonal — they rarely move at all in a given year — while lower ratings show progressively more spread, including meaningful default probability in the bottom rows.
| From \ To | AAA | AA | A | BBB | BB | B | CCC | Default |
|---|---|---|---|---|---|---|---|---|
| AAA | 90.0% | 9.0% | 0.6% | 0.3% | 0.1% | 0.0% | 0.0% | 0.0% |
| BBB | 0.0% | 0.3% | 5.5% | 87.0% | 5.0% | 1.8% | 0.3% | 0.1% |
| B | 0.0% | 0.0% | 0.1% | 0.5% | 6.0% | 80.0% | 8.0% | 5.4% |
From one year to many
A small one-year default probability compounds into something much larger over a multi-year holding period, because the matrix effectively gets multiplied by itself for each additional year — a rating that has a small chance of slipping in any given year has a meaningfully larger chance of having slipped at least once after five or ten years in a row.
Worked example
A portfolio holds $100 million of BBB-rated bonds. Using the transition matrix above, the one-year expected value of the portfolio's rating outcome is: 87% stays BBB, 5.5% upgrades to A, 5% downgrades to BB, 1.8% to B, 0.3% to CCC, and 0.1% defaults. That 0.1% default probability alone represents an expected loss (ignoring recovery) of 100\text{m} \times 0.001 = \100{,}000$ from default risk in a single year — small in expectation, but the tail of that same row (the CCC and BB downgrade probabilities) drives the bulk of the portfolio's actual credit-spread volatility, since downgrades reprice a bond's spread long before default itself would.
What this means in practice
Banks and insurers use transition matrices directly in regulatory capital models to estimate expected credit losses over a horizon, and portfolio managers use them to stress-test what happens to a book's average rating under adverse migration. Multiplying a matrix by itself repeatedly projects multi-year, not just one-year, transition and default probabilities — the mechanism behind cumulative default curves published alongside these matrices.
Transition matrices are built from historical averages across an economic cycle, so they understate migration risk in a downturn and overstate it in a boom — using a through-the-cycle matrix to price risk at the peak of a recession will make defaults look far less likely than they're about to be.
Related concepts
Practice in interviews
Further reading
- Moody's, Annual Default Study: Corporate Default and Recovery Rates