Rating Transition Matrices

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.

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 $100\text{m} \times 0.001 = \textdollar 100{,}000$ 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.