Unexpected Loss(UL) & Usage Given Default(UGD)

[Sunil Natarajan]

Hi David,
Chapter 5 (Page 113) of Ong the formulae for UL=AE*(EDF*Std(LGD)^2+LGD*Std(EDF)^2)^0.5
but in page 115
UL=AE*(EDF*Std(LGD)^2+(LGD)^2*Std(EDF)^2)^0.5.
On page 100 Chapter 4 of Ong it is mentioned UGD follows some indeterministic process, but it is difficult to treat the UGD as a stochastic variable.
On page 132 Chapter 6 of Ong it is mentioned Usage given migration is a stochastic/random variable. But banks would have systems to actually calculate the draw down rate suppose the rating for the client declines by a couple of notches.
Micheal Ong in Chapter 4 mentions that the loan distribution is not symmetrical and it faces liquidity issues, hence recovery rates are lower . But on page 447 of Chapter 19 of Jorion it is mentioned that for a particular counterparty loan obligation is rated higher than bond obligation leading to higher recovery rates.

Regards,
Sunil

 

[David Harper CFA FRM]

Hi Sunil,

1. Good catch. Page 113 of Ong contains a typo (I cannot find an errata for Ong, the book is several years old, if anyone knows of an errata, I'd love to find it?). The LGD is squared per your second citation.

2. Re pages 100 & 132, please let me know if i missed your question, but i would offer this in regard to UGD & UGM. I think Ong has only two points here, really: (i) that UGD tends to correlated with ratings; lower rating implies lower UGD (but note the imperfect pattern in table 4.1 so i doubt this is a testable concept) and (ii) more importantly, UGD is something of a random (stochastic) variable ("hard to parameterize") despite best efforts.

3. Bond versus loan recovery. I see this sample question but IMO this would be an unfair (bad) question for 2008 FRM. Jorion says loan recoveries are higher than bond recoveries (and, yes, much research supports this) but I do not think this is a key point in the assigned de Servigny (LGD Chapter). For our purposes relating to recovery (LGD), I think the bond/loan distinction is irrelevant; where Ong and de Servigny agree, aside from paucity of loan data, is that bond/loan difference is less important than seniority and collateral. So the important factors (determinants) of recovery LGD are seniority and collateral; so, for example, we would assume a secured bond has better recovery (lower LGD) than an unsecured loan. I would advise a focus on the de Servigny recovery factors: seniority, industry, economy, collateral, etc

David

 

[Sunil Natarajan]

Hi David,
You have mentioned more importantly, UGD is something of a random (stochastic) variable ("hard
to parameterize") despite best efforts. I think it should be UGM as per Ong. What does he exactly mean when he says that tha UGD is a indeterministic variable and not stochastic in nature.

Regards,
Sunil

 

[David Harper CFA FRM]

Hi Sunil -

Well, I don't read him that way (i could be wrong). To me, indeterministic = stochastic, where stochastic = a series of random variables (i.e., characterized by a distribution) over time. So, I don't know what this means: "indeterministic variable and not stochastic in nature."

I see your point about UGD vs UGM - I missed this before, but I *think* he is saying the UGM is even more random than UGD; i.e., because UGM has a different PDF/CDF distribution for each rating class (to be honest, at this point, i start to think the terms are covering for "we have no idea!?")

But in regard to the original text on 100 "UGD follows some indeterministic process, but it is difficult to treat the UGD as a stochastic variable," my interpretation is simply: UGD is stochastic (i.e., random) but it is simply difficult to assign a distribution (PDF) to UGD. "Good random" is when the distribution is random, but known and predictable (e.g., an i.i.d. return series is random but can be characterized); "bad random" is so random that no PDF will fit. So, a distribution (over time) signifies stochastic but it's still *hard* to find/fit a distribution that is reliable to UGD/LGD.

David