Credit Migration and Rating Deterioration

Why Rating Migration Matters

A borrower’s credit quality can change before any default occurs. A rating upgrade or downgrade records a change in an agency’s assessment of creditworthiness, while a default is a distinct credit event. For a lender, insurer, or investor, these changes matter because a deteriorating rating can signal a worsening credit position even when contractual payments are still being made. Rating migrations can also affect risk monitoring and the value of a credit-sensitive asset.

A useful first step is to represent ratings as states and describe movement between them over a specified period. The period must be stated: a one-year transition probability, for example, is not interchangeable with a quarterly probability. This tutorial focuses on interpreting and summarizing those transitions, rather than estimating default probabilities or credit losses.

Definition: A rating migration is a change in an obligor’s credit-rating state between two specified times. An upgrade is a move to a higher credit-quality rating; a downgrade is a move to a lower credit-quality rating. Remaining in the same nondefault rating is an unchanged rating. A transition from a nondefault rating into a separate Default state is a default transition, not an unchanged rating.

Ratings are usually ordered by credit quality, such as AAA, AA, A, BBB, BB, B, and CCC, with Default shown separately. The exact labels and categories depend on the rating system. A notch is one step between adjacent rating categories within that system. The ordering lets us classify a move as an upgrade or downgrade, but it does not imply that the distance between all adjacent ratings represents an equal amount of credit risk.

One-Period Transition Probabilities

Let \(R_0\) be an obligor’s rating at the beginning of a period and \(R_1\) its rating at the end. For a specified period, define \(p_{ij}\) as the probability that an obligor starting in state \(i\) ends in state \(j\). The states should include Default when the analysis treats default as a possible outcome.

p_{ij}=P(R_1=j\mid R_0=i)

For each starting state \(i\), the probabilities across all possible ending states must sum to one. A transition matrix places starting states in rows and ending states in columns. This row convention matters: each row describes the possible outcomes for obligors that began in that row’s rating.

\sum_j p_{ij}=1 \qquad \text{for every starting state } i

If Default is included as a separate state, its probability belongs in the same row as the other possible outcomes. A migration analysis may also treat Default as an absorbing state over a multi-period model, meaning a defaulted obligor stays in Default in later periods. That is a modeling convention, not a requirement for every transition analysis. For a single specified period, the key point is simply that a transition from a nondefault rating to Default is a transition out of the starting state.

Worked Example: Classifying Outcomes for a BBB Cohort

A hypothetical portfolio has 200 obligors, all rated BBB at the start of a one-year period. At year-end, 16 are rated A, 144 remain BBB, 30 are rated BB, and 10 have entered Default. Classify the outcomes and calculate each proportion. Assume every obligor is assigned exactly one year-end state.

Method. Divide each ending-state count by the starting cohort of 200. Since A is higher than BBB and BB is lower, A is an upgrade and BB is a nondefault downgrade. Default is reported separately.

Upgrade proportion: \(16/200=0.0800\), or 8.00%.

Unchanged-rating proportion: \(144/200=0.7200\), or 72.00%.

Nondefault downgrade proportion: \(30/200=0.1500\), or 15.00%.

Default proportion: \(10/200=0.0500\), or 5.00%.

The proportions sum to \(0.0800+0.7200+0.1500+0.0500=1.0000\), as required. If “deterioration” is defined to include both nondefault downgrades and defaults, its proportion is \(0.1500+0.0500=0.2000\), or 20.00%. The common mistake is to combine that 20.00% figure with the separate 5.00% default proportion as if they described disjoint outcomes. They do not: the 20.00% already includes default under this definition.

From Individual Rows to a Portfolio Summary

A transition matrix gives probabilities conditional on the starting rating. To summarize a portfolio with multiple starting ratings, weight each row by the proportion of obligors in that starting state. This follows from the law of total probability: an obligor can end in state \(j\) after starting in any of the portfolio’s initial states.

P(R_1=j)=\sum_i P(R_0=i)\,P(R_1=j\mid R_0=i)

In a finite portfolio, the same calculation can be done with counts: apply each starting group’s transition proportions to its group size, then add the resulting ending-state counts. Do not take a simple average of transition rows unless the starting groups have equal weights.

Worked Example: Aggregating Two Starting Ratings

A hypothetical portfolio contains 40 obligors rated A and 60 rated BBB at the start of a one-year period. The one-year transition probabilities are shown below. Each row sums to one; all probabilities are conditional on the stated starting rating.

Starting rating	Ending AA	Ending A	Ending BBB	Ending BB	Ending Default
A	0.0500	0.8500	0.0800	0.0000	0.0200
BBB	0.0000	0.0200	0.8800	0.0800	0.0200

Method. Multiply each row by its starting proportion: 40/100 for A and 60/100 for BBB. Then add the contributions to each ending rating.

Ending AA: \((40/100)(0.0500)+(60/100)(0.0000)=0.0200\).

Ending A: \((40/100)(0.8500)+(60/100)(0.0200)=0.3400+0.0120=0.3520\).

Ending BBB: \((40/100)(0.0800)+(60/100)(0.8800)=0.0320+0.5280=0.5600\).

Ending BB: \((40/100)(0.0000)+(60/100)(0.0800)=0.0480\).

Ending Default: \((40/100)(0.0200)+(60/100)(0.0200)=0.0080+0.0120=0.0200\).

The resulting portfolio proportions sum to \(0.0200+0.3520+0.5600+0.0480+0.0200=1.0000\). Upgrades are A-to-AA and BBB-to-A, giving \(0.0200+0.0120=0.0320\), or 3.20%. Nondefault downgrades are A-to-BBB and BBB-to-BB, giving \(0.0320+0.0480=0.0800\), or 8.00%. Default is 2.00%, reported separately. Unchanged ratings are A-to-A and BBB-to-BBB, totaling \(0.3400+0.5280=0.8680\), or 86.80%. These four outcome categories sum to 100.00%.

The common mistake is to average the A and BBB rows equally. That would incorrectly treat the portfolio as if it contained the same number of obligors in each starting rating. Here, the BBB row receives a weight of 60%, not 50%.

Summarizing Rating Movement with Notches

For a compact descriptive measure, an analyst may assign an ordinal score to each rating and calculate the average change in score. This requires an explicitly chosen scoring convention. For example, relative to a starting rating of BBB, one could assign +1 to A, 0 to BBB, −1 to BB, and −2 to B. These scores count category steps; they are not probabilities and do not establish that risk changes by a constant amount per notch.

Default has no ordinary rating notch in this scoring scheme. One clear approach is to report the default probability separately and calculate an average notch movement conditional on ending in a nondefault rating. The denominator is then the probability of a nondefault outcome, not the entire starting cohort.

E[\text{notch change}\mid \text{nondefault}] = \frac{\sum_{j\ne D}p_{ij}s_j}{\sum_{j\ne D}p_{ij}}

Here \(s_j\) is the score assigned to ending rating \(j\), measured relative to the starting rating, and \(D\) denotes Default. This average can help summarize direction of movement, but it does not replace the full transition distribution. Two portfolios can have the same average notch change while having quite different probabilities of severe downgrades.

Worked Example: Average Nondefault Notch Change

A hypothetical BBB-rated obligor has the following one-year transition probabilities: 0.0200 to AA, 0.1200 to A, 0.7000 to BBB, 0.1200 to BB, 0.0300 to B, and 0.0100 to Default. Use scores of +2, +1, 0, −1, and −2 for AA, A, BBB, BB, and B, respectively. Calculate the nondefault downgrade probability, default probability, and expected notch change conditional on a nondefault outcome.

Method. Sum the probabilities of nondefault ratings below BBB for the nondefault downgrade probability. Keep Default as a separate outcome. For the conditional average, multiply each nondefault probability by its score and divide by the total nondefault probability.

The nondefault downgrade probability is \(0.1200+0.0300=0.1500\), or 15.00%. The default probability is 0.0100, or 1.00%. The nondefault probability is \(1-0.0100=0.9900\).

The probability-weighted score numerator is \(0.0200(2)+0.1200(1)+0.7000(0)+0.1200(-1)+0.0300(-2)\). Term by term, this is \(0.0400+0.1200+0.0000-0.1200-0.0600=-0.0200\).

Therefore, the conditional average notch change is \(-0.0200/0.9900=-0.0202\) notches, rounded to four decimal places. The small negative average indicates a slight average deterioration under this scoring convention among nondefault outcomes. It does not mean that the default outcome is negligible; the default probability remains 1.00% and must be reported separately.

A common error is to divide the score numerator by 1.0000 while calling the result conditional on nondefault. That uses the whole cohort, including Default, in the denominator, contrary to the stated conditioning. Another error is to assign Default a score of −3 without defining that extra convention; doing so would mix a default event into a measure intended to describe nondefault notch migration.

Migration Risk Is Not Default Risk

Migration risk is the possibility that an obligor’s credit rating changes. It includes favorable upgrades, unfavorable nondefault downgrades, and—when Default is modeled as a state—the transition into Default. In practice, analysts often report the nondefault migration outcomes separately from the default outcome because they convey different information.

Default risk concerns the possibility of a specified default event. A rating downgrade can occur without a default, and the rating can remain unchanged over a period without default if the obligor stays in its nondefault state. A transition from a nondefault state into Default is a separate transition and does not leave the rating state unchanged. The event definition and boundaries used to identify default should be consistent with the earlier material on default definitions and credit event boundaries.

This distinction is useful in portfolio monitoring. For example, a portfolio may have few defaults over a period but still experience a notable shift toward lower nondefault ratings. Conversely, an unchanged rating does not prove that an obligor’s underlying credit condition has not changed; ratings are assessments, and their timing may not match every change in financial condition. A matrix summarizes observed or modeled transitions under its definitions and time horizon; it is not a guarantee about an individual obligor.

Rating migration is also not itself a dollar loss calculation. A downgrade can be relevant to the value or risk management of a credit-sensitive position, but calculating credit loss requires additional information and a separate model. Keep the transition classification precise: identify the starting state, the ending state, the horizon, and whether the outcome is an upgrade, a nondefault downgrade, unchanged, or Default.

Key takeaway: Read each transition probability as conditional on a stated starting rating. Weight rows by the portfolio’s actual starting composition when aggregating outcomes. Report Default separately from unchanged ratings and nondefault downgrades, and state any scoring convention used to summarize notch movement.

Check Your Understanding

For each problem, use the stated one-year horizon and classify Default separately from nondefault rating migration.

A hypothetical cohort of 160 obligors starts at BBB. At year-end, 12 are A, 112 are BBB, 28 are BB, and 8 are in Default. Calculate the upgrade, unchanged, nondefault downgrade, and Default proportions. (Answer: 0.0750 upgrade, 0.7000 unchanged, 0.1750 nondefault downgrade, and 0.0500 Default.)
A portfolio is 25% A and 75% BBB. From A, transition probabilities to AA, A, BBB, and Default are 0.0400, 0.9000, 0.0500, and 0.0100. From BBB, probabilities to A, BBB, BB, and Default are 0.0300, 0.8500, 0.1000, and 0.0200. Calculate portfolio proportions of upgrades, unchanged ratings, nondefault downgrades, and Default. (Answer: 0.0325 upgrades, 0.8625 unchanged, 0.0875 nondefault downgrades, and 0.0175 Default.)
A BBB obligor has probabilities 0.1500 to A, 0.6500 to BBB, 0.1600 to BB, 0.0300 to B, and 0.0100 to Default. Using scores +1 for A, 0 for BBB, −1 for BB, and −2 for B, calculate the nondefault downgrade probability and the conditional expected notch change among nondefault outcomes. (Answer: 0.1900 nondefault downgrade probability; \(-0.0700/0.9900=-0.0707\) notches.)
A portfolio has 60 BBB obligors and 40 BB obligors. BBB transitions to A, BBB, BB, and Default with probabilities 0.1000, 0.7500, 0.1200, and 0.0300. BB transitions to BBB, BB, and Default with probabilities 0.0800, 0.8200, and 0.1000. Calculate the portfolio ending proportions in A, BBB, BB, and Default, then give the upgrade and nondefault downgrade proportions. (Answer: A 0.0600, BBB 0.4820, BB 0.4000, Default 0.0580; upgrades 0.0920 and nondefault downgrades 0.0720.)

What You'll Learn