# 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

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?

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: $$\mathrm{ECap} = \inf\{x \in \mathbb{R} : F(x) > \alpha\}$$.
• Thanks, I actually had that done in Python. But how to examine the capital consumption with my given fields. Is it that if EL (expected loss) from previous period went up on the next period for a specific customer, then you could assume a higher capital consumption? Or how to quantify that? – maj3r Jun 21 '20 at 23:09
• So I believe I couldnt get hold of the economic capital with the fields I have. But what is important for the lender is that the expected loss is as low as possible I guess. Could I examine the EL between the periods by examining EL for all ID:s in period1 and compare them to what the EL for the same ID:s in period2? I mean is there a plot/barchart that would visualize this in an informative way? For example would it be meaningful to make a barchart over the EL:s for each credit rating in both periods? Or should I rather barchart the difference between the two periods? – maj3r Jun 22 '20 at 12:25
• I would do both. Visualization is a great way to understand your data better. Taking a closer look at the table with migrations is also helpful I think. My data is random and the counts are evenly spread over the table but I would expect that in the real data the diagonal is dominant. Are you seeing big moves? Is for some the rating quickly decreasing or increasing over the period? I wouldn't expect credit worthiness to increase too much in a short amount of time. – Bob Jansen Jun 22 '20 at 12:28
• LGD and EAD might also go up for low or non rated obligors depending on line of business and risk management practice. – Bob Jansen Jun 22 '20 at 13:37
• Thats true! Btw do you know what risk weight is saying? For example defining it as RWA/EAD, I am not too sure what it means. For example if it seems to increase, what does it really mean? – maj3r Jun 22 '20 at 13:47