Credit Transition Matrix: Rating Migration Probabilities

Key Takeaways

• Each row sums to 100 percent; the final column shows the one-year probability of default for each rating class.
• CCC-rated issuers default in roughly 20–30 percent of years; AAA issuers have effectively zero one-year default probability.
• Multi-year default probabilities are computed by raising the one-year matrix to the nth power, assuming a Markov process.
• Migration risk, downgrades that widen spreads without default, accounts for a significant share of total credit loss.

What It Is

A transition matrix has rating classes along both rows (starting rating) and columns (ending rating). Each row sums to 100 percent and shows all possible outcomes for issuers that started the period in that rating. The final column is usually D, the default state.

S&P Global Ratings and Moody's publish annual global transition matrices covering 40+ years of history. A simplified 1-year matrix derived from the S&P 2024 study looks roughly like this:

From\To   AAA   AA    A     BBB   BB    B     CCC   D
AAA      88.0  10.0   0.9   0.1   0.0   0.0   0.0   0.0
AA        0.6  88.5   9.5   1.0   0.2   0.1   0.0   0.0
A         0.0   1.9  89.9   7.3   0.6   0.2   0.0   0.1
BBB       0.0   0.1   3.9  89.8   4.7   0.9   0.3   0.2
BB        0.0   0.0   0.1   5.0  82.0   8.4   1.0   0.7
B         0.0   0.0   0.1   0.2   5.9  78.5  10.0   3.6
CCC       0.0   0.0   0.0   0.3   0.5  13.7  47.0  26.5

Exact numbers vary slightly by vintage and agency. The pattern is always the same: diagonal dominance (most issuers keep their rating), falling default probability with higher ratings, and sharp default rates at CCC.

The Intuition

Default is rare for top-rated borrowers but not zero. The 1-year AAA-to-D probability across 40+ years of S&P data is effectively 0 percent, while BB is around 0.7 percent, B roughly 3 to 4 percent, and CCC typically 20 to 30 percent. Over longer horizons the probabilities compound, so 10-year cumulative default rates reach 1 to 2 percent for A, 20+ percent for B, and past 50 percent for CCC.

A transition matrix captures two kinds of credit risk. Default risk is the last column. Migration risk is the spread of the other off-diagonal entries: a bond downgraded from A to BBB loses value even if it never defaults, because spread widening repriced the position.

How It Works

For a portfolio of N bonds, the 1-year loss distribution is built by mapping each bond to its starting rating row and drawing from the 8-state outcome distribution. Losses combine default-triggered write-downs and migration-triggered spread changes.

Multi-year default probability compounds the 1-year matrix. If P is the 1-year transition matrix, the 2-year matrix is P squared (matrix multiplication), the n-year is P to the n, assuming the process is Markovian.

P(n years) = P^n

In practice credit is not Markovian. Rating "momentum" exists: a recently downgraded issuer is more likely to be downgraded again than a previously stable issuer at the same rating. Agencies report separate "recently downgraded" cohorts to account for this.

Worked Example

A portfolio holds 100 BBB-rated corporate bonds, 10 million each, total 1 billion. Using the 1-year matrix above, the expected distribution of outcomes is:

• About 89.8 bonds stay BBB, zero loss
• 3.9 upgrade to A, unrealized gain from tightening spread
• 4.7 downgrade to BB, spread widening (high-yield premium)
• 0.9 downgrade to B, sharper widening
• 0.3 fall to CCC, large spread hit
• 0.2 default, LGD-driven loss (say 60 percent)

Expected default loss: 0.2 x 10 million x 60 percent = 1.2 million. Expected migration loss (mark-to-market from downgrades, net of upgrades): often 2 to 4 million depending on spread curves. Total expected credit loss: roughly 4 to 5 million on a 1 billion BBB book.

Over 5 years the cumulative default probability rises to around 2 percent, so 2 bonds on average would default. The full transition matrix generates the distribution around that average, which is what VaR and CVaR calculations feed on.

Common Mistakes

• Treating transitions as Markovian. Rating history matters. Using a single pooled matrix without rating momentum underestimates near-term downgrade risk on recently downgraded names.
• Mixing through-the-cycle and point-in-time ratings. S&P and Moody's target through-the-cycle ratings that are slow to move. Internal bank ratings are usually point-in-time. Mixing them in one matrix produces inconsistent numbers.
• Using old matrices in new regimes. Default rates differ sharply between benign vintages (2013, 2017) and stress vintages (2001, 2009, 2020). Rolling historical averages smooth over regime shifts; stress tests need separate crisis matrices.
• Forgetting the "NR" (not rated) column. Issuers drop from agencies for reasons other than default. Ignoring the NR pocket biases the remaining probabilities.
• Assuming independence across issuers. The matrix is marginal. A portfolio analysis needs joint transitions, typically through a correlated factor model.

Frequently Asked Questions

What is the difference between a through-the-cycle and a point-in-time transition matrix? Through-the-cycle matrices, published by S&P and Moody's, are derived from ratings that agencies deliberately keep stable across business cycles, so transitions are slow and default probabilities are smoothed averages. Point-in-time matrices use ratings that reflect current economic conditions, so they shift more with the cycle and produce higher default probabilities in recessions. Mixing the two types in one model produces inconsistent loss estimates.

How do you compute a five-year cumulative default probability from a one-year matrix? If the one-year transition matrix is P, then the five-year matrix is P raised to the fifth power through matrix multiplication. Each entry in the resulting matrix gives the probability of moving from the starting rating to the ending rating over five years, assuming the process is Markovian. In practice, the Markov assumption underestimates cumulative defaults for recently downgraded names because rating momentum means prior downgrades increase future downgrade probability.

What does migration risk mean in the context of a credit portfolio? Migration risk is the mark-to-market loss caused by a downgrade that does not result in default. When a bond is downgraded from BBB to BB, its spread widens to reflect the higher-yield category, and the bond price falls even though the issuer continues to pay coupons. For a large portfolio, migration losses often exceed default losses in a given year because downgrades are far more frequent than defaults.

Why does the credit transition matrix have diagonal dominance? Most issuers retain their rating from one year to the next, so the on-diagonal probabilities are the largest entries in each row. Rating agencies aim for stability, and genuine creditworthiness rarely shifts dramatically in 12 months for most companies. The off-diagonal entries represent the minority of issuers whose fundamentals or market access changed enough to warrant a rating action.

How does a recession-vintage matrix differ from a full-cycle average matrix? In recession years such as 2001, 2009, and 2020, default and downgrade rates spike well above long-run averages, so recession-vintage matrices show much higher off-diagonal and default-column probabilities. A full-cycle average matrix blends benign and stress years, making it inappropriate for capital stress tests that are meant to capture severe scenarios. Risk managers typically maintain a separate stress matrix calibrated to recession cohorts for use in worst-case scenario planning.

Sources

1. S&P Global Ratings. 2024 Annual Global Corporate Default and Rating Transition Study. https://maalot.co.il/Publications/FTS20250331162126.pdf
2. S&P Global Ratings. 2023 Annual Global Corporate Default and Rating Transition Study. https://www.spglobal.com/ratings/en/regulatory/article/240328-default-transition-and-recovery-2023-annual-global-corporate-default-and-rating-transition-study-s13047827
3. Scope Ratings. Credit Rating Transition and Default Study 2024. https://scoperatings.com/dam/jcr:92660a21-858c-4d53-86de-d1a677985008/Scope%20Ratings%20Transition%20and%20Default%20Study%202024.pdf
4. Credit Benchmark. Managing Credit Portfolio Default Risk With Credit Rating Transition Matrices. https://www.creditbenchmark.com/managing-credit-portfolio-default-risk-with-credit-rating-transition-matrices/

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.