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# P1.T4.26. Unexpected loss (UL), Ong

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
AIMs: Explain the objective for quantifying both expected and unexpected loss. Describe factors contributing to expected and unexpected loss. Define, calculate and interpret the unexpected loss of an asset. Explain the relationship between economic capital, expected loss and unexpected loss.

Questions:

26.1. Of a total original commitment (COM) of $10.0 million, 20.0% is outstanding (OS) such that$8.0 million is unused. The usage given default (UGD) assumption is 50.0% and the loss given default (LGD) assumption is 40.0% where the standard deviation of the LGD is 30.0%. If the probability of default (EDF) is 2.0%, what is the unexpected loss (UL) on the adjusted exposure (AE)?

a. $48,000 b.$421,540
c. $573,495 d.$933,381

26.2. An exposure has a default probability (PD) of 4.0% and loss given default of 50.0%. The standard deviation of the LGD is 25.0%. What is the ratio of the unexpected loss to the expected loss, UL/EL?

a. 1.33
b. 3.72
c. 5.50
d. 9.64

26.3. In the assigned reading on unexpected loss (Ong Chapter 5), unexpected loss (UL) is given as: UL = AE * SQRT[EDF*variance(LGD) + LGD^2*variance(EDF)]. Each of the following is TRUE about this definition of unexpected loss (UL) EXCEPT:

a. It assumes independence (zero default correlation) between the default probability and loss given default (LGD)
b. Economic capital will necessarily equal this value of this unexpected loss, as defined; i.e., EC = UL
c. This unexpected loss (UL) is the standard deviation (volatility) of the unconditional value of the asset at the horizon
d. Whereas expected loss (EL) increases as a linear function of EDF and LGD, unexpected loss (UL) increases as a non-linear function of EDF and LGD

#### SamuelMartin

##### New Member
Can I see how to calculate the Unexpected loss% for question 26.2?
I have UL = SQRT [EDF X variance (LGD) + LGD^2 X variance (EDF)] = SQRT [4% X 25% + 50% X 4%]
However, that formula does not come up with 11% which is the answer I had in the book

Thanks

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
HI @SamuelMartin sure, I have:
Unexpected loss (%) = SQRT[EDF * variance(LGD) + LGD^2 * variance(EDF)] = SQRT[4%*25%^2 + 50%^2*4%*96%] = 11.00%
Expected loss (%) = EDF*LGD = 4%*50% = 2.0%.
Ratio of UL/EL = 11.0%/2.0% = 5.50

#### SamuelMartin

##### New Member
Thank you so much. I don't know what I did but I didn't come up with the number. I see it now

#### hemmu23

##### New Member
hi,
is there any simpler way to find LGD variance the way we find Variance PD.
It will of great help

regards,
Himaanshu

#### ShaktiRathore

##### Well-Known Member
Subscriber
Hi
I dont think there is any particular simple method to calculate variance of LGD,i mean there is no simple formula from which u can get LGD variance as u get Variance of EDF. LGD estimation is a difficult exercise,i think its determined empirically,assuming some beta distribution there is no straight forward way of determining it.
Thanks

#### nicolas2529

##### New Member
Hi,

How are you calculating the variance of PD ? :/ I don't know the formula to get it ... thanks in advance !

#### Arnaudc

##### Member
Hi @nicolas2529 ,

The variance of PD is simply the variance of a Bernouilli variable: Variance (PD) = PD x (1-PD)

Kind regards,

#### nicolas2529

##### New Member
Hi @nicolas2529 ,

The variance of PD is simply the variance of a Bernouilli variable: Variance (PD) = PD x (1-PD)

Kind regards,

Thanks a million !