Expected loss (EL) on credit asset if PD, LGD are correlated

Expected loss (EL) calculations typically assume no correlation (i.e., they assume independence) between probability of default (PD) and loss given default (LGD). Basel II internal ratings-based (IRB) approach to a capital charge assumes independence between PD & LGD. How can we compute expected loss (EL) if there is correlation between EDF/PD and LGD/recovery?

Category:

Howto & Style

Tags:

• credit
• default
• given
• loss
• recovery
• risk

[bionicturtledotcom]

@Nazdrovje I don't disagree with your scaling based on the number of defaults, but the entire exercise above is a single (n= 1) credit. The stddev(EDF) is the stddev of a Bernoulli as EDF is a percentage. So, 9.95% = SQRT(99%*1%)

So, i would stand by the expression Standard deviation of EDF, as EDF is (by definition, to my thinking) a Bernoulli (0 - 100%) and, the example, in any case never goes beyond n=1. But thank you for making the binomial point!

[Nazdrovje]

@bionicturtledotcom Thanks for your explanation. Silly, but I thought you were discussing a loan portfolio. Anyway, for the n=1 case both approaches yield the same result. I wonder how your approach would scale to a portfolio of size n. A first approach would be to say that the expected loss would be n times the EL you calculate in your presentation. My approach would lead to a sqrt(n) fold increase. Intuitively I'd say that's wrong but I can't see where the reasoning goes awry. Any clue?

[Nazdrovje]

[Continued] The SD of the PD simplifies to sqrt(rho(rho-1)/n). So, it scales inversely proportional to the square root of the number of counterparties.

[Nazdrovje]

[continued] ... and notice this is not the SD of the PD but the SD of the number of defaults. The SD of the PD as calculated from observed defaults (OD)/number of counterparties (NC) is given by sqr(expected_value((OD/NC)^2) - expected_value(OD/NC)^2) which is (rho-rho^2+n rho^2)/n-rho^2. With your PD=1% you get a SD of 3%, 0.99%, 0.3%, and 0.099% for n=10, 100, 1000, and 10,000 respectively. Your 9% is therefore way too high.

[Nazdrovje]

I feel you made an error in the calculation of the SD of the PD (EDF). The problem is confusing percentages with numbers. If the number of defaults is binomially distributed then the mean number of defaults is n*rho with n the number of counterparties and rho the PD. So, count the number of defaults, divide by the number of counterparties and you get the PD. The SD of the number of defaults is sqrt(n*rho(1-rho)). Notice the n in the equation...

[dajieda0]

so the correlation here is not the correlation between assets in a loan portfolio?

[dajieda0]

@bajoespacio there is a video clip talks about the factors affecting LGD (1-RR) in David's channel. basically there are non-systematic factors (e.g. collaterals) and systematic factors (e.g. the downturn of the economy) determining the LGD.

[gouxu]

@khanpreston1 volatility

[bajoespacio]

Hey David, thanks for the lessons. I'd like to know how to determine LGD. I wish you give at least a clue. It's the only component of the EL equation I haven't been able to understand. Thanks again.

[ngeorgiev]

@khanpreston1 variability