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# UL of a single credit

#### Liming

##### New Member
Dear David,

Can you please kindly explain the formula of UL for a single credit, which you used in the spreadsheet "2008 CREDIT: Portfolio EL & UL (Ong Ch 6)" on page http://www.bionicturtle.com/premium/spreadsheet/2008_credit_portfolio_el_ul_ong_ch_6/ ?

It seems that the formula you used is as follows:

UL of one single credit = {EDF * Standard deviation(LGD)^2 + LGD^2*Standard deviation(EDF)^2 }^1/2

What are the multiplication of EDF and standard deviation of LGD for?
And why you raised LGD and standard deviation of EDF to the power of 2, but not for the firm parameter EDF?

Thank You!

Cheers
Liming
27/09/2009

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi Liming,

I don't have an intuition for the formula of UL, sorry...The formula is from Chapter 5 of Ong's internal credit risk models (Chapter: UL). Ong actually shows the mathematical derivation in the appendix (page 116) which, IMO, is non-trivial (amazingly, GARP actually assigned the derivation of UL last year and of portfolio UL & RC , and I requested they delete it...I am sure I wasn't the only one!) and I don't really have a shortcut or a natural direct intuition on the formula

David