Counparty Credit Exposure

[ydl33060]

Hi David,

Would appreciate if you could clarify the following:
3.2. Which counterparty credit exposure metric is typically used as a basis to determine the loan equivalent amount, i.e., even if multiplier might be applied to this basis?

a) Current exposure (CE)
b) Expected exposure (EE); aka, expected credit exposure (ECE)
c) Potential future exposure (PFE); aka, worst credit exposure (WCE)
d) Average expected credit exposure (AECE); aka, expected positive exposure (EPE)

3.3. The "loan equivalent exposure" for a certain portfolio is $480 million with an expected loss of 1.0% and a worst case expected loss of 3.0%. "Expected loss," per Crouhy’s usage refers to probability of default net of recoveries: EL = PD * LGD. "Worst case expected loss," then, refers to expected loss with 99% confidence. (For convenience, these are also exactly the numbers Crouhy uses in his example) Consider the following statements:
I. The credit risk capital (economic capital attributed to credit risk) is $9.6 million
II. To determine the loan equivalent exposure (the credit exposure) of $480 million, this approach uses potential future exposure (PFE or WCE) rather than average expected credit exposure (AECE or EPE), because it employs a confidence level
III. This approach is considered quite precise (rather than approximate) because it generates the full distribution of losses

The answer for both question indicate that average expected credit exposure shall be used.
(a) Why is that the case? I tot if one were to employ confidence level , we are looking at worst credit exposure instead of aaverage AECE.
(b) When shall "potential future exposure aka worst credit exposure" be used?

Thank you.

 

[David Harper CFA FRM]

Hi ydl33060,

I'd be tempted to flip it around: the issue is partly semantic, what is meant by "loan equivalent?" I think it has been used, both in practice and from a regulatory (Basel) standpoint, to return a value which is approximately similar to a funded (loan) position; e.g., if I pay (fund) $X as the price of a bond, X is my exposure.

In the instance of a derivative (bilateral), "loan equivalent,"despite a theoretical pricing basis, has no necessary (in my opinion) mathematical implication. Further, although EPE is a point estimate, there is nothing "precise" about it (e.g., it will vary with the simulation engine/inputs). Then, the usage of EPE is pricing or capital requirement; but please note EPE is not the capital requirement, per se, it is "merely" the input that multiplied by at a factor least 1.0 (e.g., 2.5 or more, for concentrated portfolio).

In this way, the very definition of loan-equivalent (i.e., as an input) implies something nearer to the "price" of a derivative position, than to a worst-expected (PFE or VaR-like) value. The PFE remains an utterly useful and viable analog to VaR, when risk (rather than pricing!) is the question.

The following is from Chapter 11 of Gregory, may be helpful:

"Practitioners have long used the concept of a “loan equivalent” in order to represent a random exposure in a simple way. Regulatory aspects are a key driver for this and will be discussed at length in Chapter 17. A loan equivalent represents the fixed exposure that would have to be used in order to mimic a random exposure. However, a loan equivalent must be defined with reference to a given characteristic of the loss distribution of the portfolio in question. It is important to emphasise that a loan equivalent will be an arbitrary correction or “fudge factor” that will depend on the nature of the underlying portfolio ...

Then EPE is the true (accurate) loan equivalent measure. Whilst this is only relevant as a theoretical result, it implies that EPE is a good starting point for a loan equivalent. One can then define a factor that will correct for the granularity of the portfolio in question. This factor has been named alpha ." -- Counterparty Credit Risk, Chapter 11