Tracking Credit Rating Migration and Distinguishing Expected Loss from Capital
Summary
The document describes a basic way to compare credit portfolios across two observation periods. Match customer records by ID, calculate changes in economic capital for matched customers, and create a cross-tabulation of prior and current ratings to summarize rating transitions. Also identify customers present in only one period, since additions and removals affect the comparison. The same workflow can be implemented in common data tools.
It distinguishes expected loss, the mean of the loss distribution, from economic capital, a high percentile of that distribution. Both describe aspects of loss risk, but one cannot be converted directly into the other without more information about the distribution and chosen confidence level. The example is a simple data-processing illustration, not a complete migration-risk model; it does not specify timing, portfolio assumptions, or how to explain observed capital changes.
Key ideas
- Join period-specific customer records by ID before comparing their risk measures.
- Use a rating transition table to summarize migrations between the two periods.
- Check which customers entered or left the dataset, since they are not matched transitions.
- Expected loss is the mean of the loss distribution, while economic capital is a selected upper quantile.
- The two measures cannot be mapped directly without additional information about the loss distribution.
Tags
Full text
# Credit Migration Risk
# Credit Migration Risk
I have a problem in which I have been given data for two periods over a set of customers.
Each set consists of the fields: ID, rating, PD, LGD, Exposure (on- and off-balance sheet exposures), EAD, RWA, Required Capital, Expected Loss (EL= EADxPDxLGD).
PD = Probability of Default
LGD = Loss Given Default
EAD = Exposure at Default
RWA = Risk weighted assets
EL = Expected Loss
I am not really sure how to identify scope of risk migration between the two periods given some data. In fact I dont have information about if these periods are consecutive or which years they cover (maybe it doesnt matter too much).
How is capital consumption related to expected loss?
## Answer by Bob Jansen (score 2)
https://quant.stackexchange.com/a/55110
If you have the data in two different tables, doing this in base R is quite easy. For example:
```
set.seed(1L)
N <- 100L
current <- data.frame(
ID = 1:100,
Rating = sample(1:5, N, replace = TRUE),
ECap = runif(N, 0, 1e6)
)
previous <- data.frame(
ID = 25:124,
Rating = sample(1:5, N, replace = TRUE),
ECap = runif(N, 0, 1e6)
)
merged <- merge(previous, current, by = 'ID')
# Change in ECap
merged$ECap_delta <- merged$ECap.y - merged$ECap.x
# Rating migrations
table(merged$Rating.y, merged$Rating.x)
```
You'll also want to look at ID that are added or removed from the two sets.
The same steps can be done in SQL or Python as well.
You're right that Economic Capital (ECap) is related to Expected Loss, they both tell us something about the different the loss distribution. However, there is no function that takes you from one to the other directly.
- The Expected Loss is the expected value of the loss distribution $F$, i.e. $\mathrm{E}(L) = \mathrm{E}(\mathrm{Loss})$
- The ECap is an upper percentile $\alpha$ of the loss distribution, analogous to the Value at Risk, mathematically: $\mathrm{ECap} = \inf\{x \in \mathbb{R} : F(x) > \alpha\}$.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.