Netting concept

[singhr15]

Can someone explain me the answer:
Each of the following is true about a "netting set" EXCEPT for which is false"?
a) A “netting set” refers to a set of trades that can be legally netted together in the event of a default b) Within a netting set, expected exposure (EE) and credit value adjustment (CVA) are additive
c) Across netting sets, exposure will always be additive, whereas within a netting set MtM values can be added
d) A netting set may be a single trade and there may be more than one netting set for a given counterparty

Correct answer is b.
B. False. Within a netting set, quantities such as expected exposure and CVA are NON-additive. Gregory: "4.2.4. Netting sets and subadditivity: We will use the concept of a “netting set” which will correspond to a set of trades that can be legally netted together in the event of a default. A netting set may be a single trade and there may be more than one netting set for a given counterparty. Across netting sets, exposure will always be additive, whereas within a netting set MtM values can be added. A very important point is that within a netting set, quantities such as expected exposure and CVA are non-additive. Whilst this is beneficial, since the overall risk is likely to be substantially reduced, it does make the quantification of exposure (Chapter 9) and CVA (Chapter 12) more complex. This complexity arises from the fact that a transaction cannot be analyzed on its own but must be considered with respect to the entire netting set."

 

[singhr15]

David waiting for your reply???

 

[David Harper CFA FRM]

Hi @singhr15 Explaining this beyond the quoted answer spans several metrics and is therefore challenging in detail (I do like this question due to the challenging requirements!).

We first need to understand that a netting set (in simple math) is by definition a set of MtM values that can be summed. For example, assume a netting set has three positions with MtM values of {3, -5, 7}; if this is a netting setting, then the exposure = 3 - 5 + 7 = 5, rather then the exposure of 10 which would be implied without netting: 10 = max(0, 3) + max(0, -5) + max( 0, 7) as current exposure = Max(0, MtM). This reflects the true statements (a) and (c), which need to be understood first, I think. Values (either MtM or expected future value) are analogous to price and expected future value is the mean of a distribution. It is also analogous to expected loss (EL) which, as a mean, can be added across positions. So, a way to think about this is: these are distributional means (where MtM is a special case) and we can add means. Consider the E[A+B] = E[A] + E regardless of the correlation between variable (A) and (B); for example, if (A) and (B) are independent, it is still true that E[A+B] = E[A] + E.

I'm simplifying but we can think of most of the other credit exposure metrics as NOT distribution means; in which case, independence or correlations has a big impact. Much like we expect StdDev(A+B) < StdDev(A) + StdDev(B), we expect EE(A+B) < EE(A) + EE(B) and CVA(A+B) < CVA(A) + CVA(B). Expected exposure is a conditional mean, not an unconditional mean, so it's not additive. For example, if the exposure is represented by a random normal variable with zero mean, then sigma*0.4 is an estimate of EE. Take a random standard normal, sigma = 1, then EE = 1*0.4 = 0.4; i.e., the expected mean conditional on positive side of the distribution. Now if the netting set consists of two of these exposures which are independent (or anything less than perfectly correlated), because they can be netted it is much like portfolio theory, the EE of the set of two positions is less than 0.4*2. So my shorthand way of communicating this is to think of the mean (like expected loss in credit) as the distributional exception to the rule: it's the moment that can be added. The others (e.g., variance) cannot be simply added. This is the case with EE (which is a distributional metric but not the unconditional mean) and CVA. Gregory goes into depth in Chapters 9 and 12 but I hope that's a useful introductory frame, thanks!