Unexpected Loss

[notjusttp]

Hi David,

This is regarding the Unexpected loss discussion in video 4e. where you have drawn the diagram depicting Normal distribution of Loss. Kindly clarify on the following Doubts

1) What is been potted on X axis and what is been plotted on Y axis?

2) If the % of loss is been shown on Y axis how come WCL is such a small percent on the extreme right?

3) If economic capital covers the Unexpected loss how is the loss beyond this (depicted as WCL) been covered by a firm?

4) I am not very clear as to why should economic capital cover the region between Unexpected loss and VAR as it strictly covers only the unexpected portion of loss?

5) Practically if I as a risk manager calculate a VAR, logically "I EXPECT" that this much loss would occur to me with a certain probability within a certain time frame. Then why is there a divorce between Expected loss and loss due to VAR as explained in your diagram which is been covered by Economic capital?To my mind VAR is itself my expected loss.

My sincere apologies if i am bothering you a lot but i like the kind of discussions unfolded by your amazing grey cells....

Thanks & Warm Rgds
Amit

:roll:

 

[David Harper CFA FRM]

Hi Amit,

http://learn.bionicturtle.com/images/forum/aug_29_ul.png

1) The x axis represents losses; ie., to the right represents greater losses in dollars or returns(%). As this is a continous distribution, the y-axis is a PDF and is not especially important, it's just f(x), such that a probabilility is f(x)dx; i.e., an interval of a slice of area under the curve

2) The extreme tail here is the loss in excess of a credit VaR, so it is meant to occur with very low probability; e.g., if Basel II IRB, then this area should be 1-99.9% = 0.1% (with one-year horizon)

3). They probably are not covered, as these are unexpected losses for which it is too expensive to cover. That's a point Stulz makes in regard to ERM: regulators require a cushion (regulatory capital) and shareholder's want buffer but shareholders do not want the firm to be either riskless or to incur the opportunity cost of buffer with 100% confidence.

4) I hope the diagram/tutorial does not imply this? Please note: EC (confidence) = Credit VaR (confidence) - Expected Loss (EL).
EC refers to the region between EL and Credit VaR.
So I agree with EC "strictly covers only the unexpected portion of loss" and not the expected loss (assuming EL is already covered by provisions).
I think this is helpful @ http://www.bionicturtle.com/learn/article/economic_capital_practice_ops/

4b) My diagram does show Ong's UL as 1 SD but that is a special case of UL, where UL = VaR - EL but the confidence is low.

5) If the distribution is accurate, then our expected loss is a mean or a median (the 50th percentile). The VaR would converge with the mean/median only when the confidence was low at 50% (or higher but nearby, as skew implies mean > median), but that would not be a "potential loss" perspective. In practice, our VaR will be 99% (e.g.)...so typically we don't calibrate the VaR for expected losses, we calibrate it to rare, potential but short of absolute worst case, losses...

No apology needed, I like forum discussions!

Thanks, David

 

[notjusttp]

Thanks for an amazing detailed explanation David. You are absolutely non miserly in terms of your words when it comes to explaining things and the enthusiasm with which you explain is quite adorable.

Ever since i have been able to delve into your analytical thinking even i have started enjoying the forum discussions and the need to physical class is not felt by me. Keep up the Good work Dear.

Thanks & Best Regards
Amit