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

Discussion in 'Today's Daily Questions' started by David Harper CFA FRM, Apr 10, 2012.

  1. David Harper CFA FRM

    David Harper CFA FRM David Harper CFA FRM (test) Staff Member

    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.


    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

  2. SamuelMartin

    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

  3. David Harper CFA FRM

    David Harper CFA FRM David Harper CFA FRM (test) Staff Member

    HI @SamuelMartin sure, I have:
  4. SamuelMartin

    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
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  5. hemmu23

    hemmu23 New Member

    is there any simpler way to find LGD variance the way we find Variance PD.
    It will of great help


  6. ShaktiRathore

    ShaktiRathore Well-Known Member

    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.
  7. nicolas2529

    nicolas2529 New Member


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

    Arnaudc Member

    Hi @nicolas2529 ,

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

    Kind regards,
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  9. nicolas2529

    nicolas2529 New Member

    Thanks a million !
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