Expected - / Unexpected Loss and Economic Capital

[RomanS]

Hi David,

I am a little confused about the three terms above though I know how to calculate them.

(1) What is Unexpected Loss (UL)?
Let L, EL and UL denote Loss, Expected Loss and Unexpected Loss respectively.
UL can be defined as the standard deviation of EL (according to Kaplan).
But looking at your (very nice) chart in the following post: http://forum.bionicturtle.com/viewthread/1734/
UL = EL + 1 x STDEV( L ).
How does that fit together?

(2) What is Econimc Capital (EC) ?
I find two contradicting statements in Kaplan:
a) EC = UL - EL ( only losses in excess of EL )
b) EC = UL

Can you help me out?
Kind regards,
Roman.

 

[David Harper CFA FRM]

Hi Roman,

Re (1), please see note (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."
This issue arises because the FRM employs Ong's credit UL (1 standard deviation) and also the more general UL.
So, there is one general form which might be best characterized by Crouhy:
UL(confidence) = WCL(confidence) - EL, or
UL(confidence) = absolute VaR (confidence) - EL
... see how this is the general case where there are many/infinite ULs depending on the confidence selected? Then the 1 Standard Deviation (which FRM-wise is really ONLY found in the Ong assigment) is just the special case of a low confidence corresponding to 1 SD.
... and that is why Ong does not give EC = his UL because it needs to be EC = multiple of [his UL]
... more on this here: http://forum.bionicturtle.com/viewthread/1791/

Re (2), this equation does NOT make sense to me: "EC = UL - EL ( only losses in excess of EL )"
because UL already implies net of EL, so UL - EL redundantly nets out EL

Now, there is indeed ambiguity in VaR that refers to the valid difference between absolute and relative VaR but this will not make EC = UL - EL, rather we can have:
* credit risk: EC = UL (typically assuming that credit does expect losses, so EL is already provisioned and capital covers UL only ) but could be UL + EL
* market risk: EC = UL (because assume EL = 0; and there is the absolute VaR that gives EC = UL - drift. So, only if we awkwardly characterized positive drift as EL, I think, could we awkwardly try EC (market) = -drift + UL = -EL + UL
* operational risk: EC = UL + EL (i.e., assuming expected operational losses are not provisioned for)
... i think i summarized these UL/EL relationships here http://forum.bionicturtle.com/viewthread/2390/

My tips (since it is confusing)
* As VaR is just a (distributional) quantile based on selected confidence, with infinite values, so too is UL: UL(confidence) = absolute VaR (confidence) - EL
* Ong's UL is merely the special case at low confidence; EC would be insufficient here b/c EC needs to be greater than 1 SD
* Following Basel II is good: CVaR (confidence) = EL + UL (confidence) ... but that's a credit VaR, can't blindly apply to market and operational risk

David

 

[RomanS]

Hi David,
thank's a lot for the answer / explanation. Gives me a much clearer picture.
Kind regards, Roman.

 

[Cipher2014]

Maybe it's confusing because of graphs like this:

Source: http://www.investopedia.com/articles/economics/08/economic-capital.asp

 

[NAndr5521]

This is a very usefull post however the links seem broken. Can the links be fixed or updated to the correct links if available?

 

[Clay Carter]

This is a very usefull post however the links seem broken. Can the links be fixed or updated to the correct links if available?

@NAndr5521 I'm working on fixing this. Because the post is so old its a little hard to find the links.