EDF for UL

[Hend Abuenein]

Hi David,

A question in GARP 2010 practice exam asks to pick out true statements from 4.(Sorry I don't have no. of question)
One of the statements answered as true says that: " With increasing EDF, UL increases at a much faster rate than EL"

I was thinking mathematically, that EDF in UL equation is multiplied by variance of LGD which is much less than 1, and is under the square root. While in EL it has its full weight multiplied by LGD and AE.

So how is it possible for an equal increase of EDF to cause more change in UL than EL?

What do you think?

Thanks

 

[David Harper CFA FRM]

Hi Hend,

I agree with you and I think, strictly speaking, the statement is not true. That statement has been previously questioned (I can't seem to find the post); I wish I were skilled enough to take the derivative of UL with respect to EDF (to prove mathematically), but I get stuck on the calculus due to the variance(EDF) ... the GARP practice exam is merely referencing Ong's statements in Chapter 6 (page 121):

"Comparing the two charts, we observe the following obvious intuitive points:
* The higher the recovery rate (ie, the lower the LGD), the lower is the percentage loss for both EL and UL.
* EL increases linearly with decreasing credit quality (ie, with increasing EDF).
* UL increases much faster (and non-linearly) than EL with increasing EDF" -- Ong Chapter 6, page 121

Our 6.d.2 learning XLS replicates Ong's two charts and I added two columns, here @ https://www.dropbox.com/s/0x6n82fcggd40ny/ong_figure_6.1.xlsx

This shows two effects:

• Consistent with Ong's assertion, at low EDF, the rate of change of UL (and the absolute increase) does exceed changes in EL, given the same EDF. (Your point is true about the small variance [LGD], although it appears the square root dominates ... for example, square root of 0.01 is 0.1, which is a 10X increase). So, at low EDF, the statements appears to be true.
• However, at higher EDF, both the rate of change and the absolute change slow down for UL, such that the reverse is true and, past a certain point, EL increases faster than UL! For example, if LGD = 50% (Ong Fig 6.1), with respect to SLOPE (rate of change) and simple change, at EDF = 20%, EL overtakes the decelerating UL. If LGD = 25%, EL overtakes UL at about EDF = 29% or 30%.

I hope that's helpful, it's good to finally run the numbers on this! Thanks,

 

[Hend Abuenein]

Thank you