Loan Portfolios and expected losses

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hi David,
i was reading something about expected losses and unexpeted losses and would appreciate it if you clarify this for me. i read that expected losses are those anticipated reduction in value of loans advanced to borrowers by a bank over time for a given exposure while unepected losses also denotes the variability in potential loan loss around the expected loss.

if the unexpected loss is about variability then can i infer that unexpected loss is the standard deviation of expected loss?

thank you

 

[David Harper CFA FRM]

Hi baffour,

Yes, you have nicely summarized Ong's view (internal credit risk models). For years in the FRM, but frankly the theory of which has only weakly manifested into the exam compared to other authors like Jorion.

If we consider Basel II/III (IRB) credit risk, the Credit VaR = 99.9% one-year VaR = EL + UL
This UL is not equal to one standard deviation, it is rather some multiple of standard deviation.
So, contrary to Ong (your above), we typically say that unexpected loss (UL) is based on a distributional quantile; e.g., UL @ 99%? UL @ 99.9%?

but any of these correspond to some multiplier on 1-standard deviation
(in the same way that, there exists some low confidence level that corresponds to one standard deviation)

so, to reconcile Ong, we would prefer to say, if we are using a standard deviation : UL = k*Standard Deviation(EL)
... and then the useful (IMO) "meditation" is to see that we are simply talking about "which confidence level?"
e.g., shareholder perspective: maybe the low confidence level implied by 1 sigma; regulatory perspective, the high confidence level implied by k*1 sigma

If you are with me then, I would edit your final to the following:
Parametric unexpected loss is some number of standard deviation(s), including the special class of one sigma if we are settling for low confidence, of expected loss?

(why "parametric"? b/c we are using the standard deviation to get to a quantile. We don't need it if we simulate)

Hope that helps, David