Expected Tail Loss vs Stressed VaR

[Angshuman]

Hi David,

1. What is the difference between 'Expected Tail Loss' and 'Stressed VaR'?

2. In case of private equities where we don't get quoted market values if we adopt an approach of simulating estimated cashflows and then finding out present value of the same for each simulated path then 99th percentile value of that series can we call it as 'Value at Risk' number?

3. Is the term 'Value at Risk' is inherently associated with trading portfolio?

 

[David Harper CFA FRM]

Hi Angshuman,

1. I sometimes think of VaR in two steps. First, the hard part is generating a distribution (where we have the 3 basic approaches and hybrids); Second, the easier part is selecting the quantile based on horizon and confidence. Stressed VaR concerns the first step; ETL the second.

Generically (I think) stressed VaR could refer to any VaR simulation where the underyling risk factors are "stressed" from normal to "downturn" or "worse case" (e.g., crisis). This is tanamount to shocking or reshaping the distribution. Specifically, in Basel II, BIS recently added the requirement to *add* a stressed VaR to the market risk capital requirement.

We typically consider ETL = Exp shortfall (ES) = conditional VaR (see Dowd for arcane differences; ETL is the family that includes ES, but ES is the metric we look at in FRM). ES = average loss in the tail (i.e., conditional on a loss in excess of the VaR)

so your question is very interesting to me because, for example, it's possible that:

ES = $100 because VaR @ 99%ile is (e.g) $80 because Avg Loss | $80 VaR = $100, and also
ETL = $100 because the stressed VaR @ 99% is $100

i.e., they are both $100, they get there very *different* ways, one goes beyond the VaR into the tail by using a tail metric, the other by stressing the distribution

2. In my opinion, yes. First, because VaR is merely a quantile; it is only a statistic. Second, VaR has been co-opted beyond the traditional (i.e., daily traded price) metric and used wherever a value distribution can be generated.; e.g., CFaR, Earnings at Risk, OpRisk, CreditVaR ... at the same time, criticisms against it may find even a better argument against your use (e.g., Taleb's critique that a specific number is false precision now finds even more strength against PV-model-estimated values ... he would have a field day!)

3. I would say, VaR is *traditionally* associated with trading portfolio because that's where it was first used (JP Morgan's CEO invented for its trading business; I recommend Gillian Tett's Fools Gold for some backstory)...but in modern risk study (e.g, FRM) it no longer denotes trading book/portfolio only ... it is still associated with market risk, but clearly (as evidenced by Basel) VaR is applied in market, credit and operational risk (VaR, CVaR, OpRisk VaR).

I hope that helps, thanks for an interesting question! David