Chapter 15 Stress testing, (dis)cordant pairs

[Bill SD]

Hi,
3 questions on Chapter 15: 'Introduction to risk modelling':

Page 20 of Acted notes says: Stress testing is similar to scenario or sensitivity analysis, but it focuses only on extreme scenarios or very large changes in input assumptions. There are two main categories of stress tests:

1. ‘top down’ stress-scenario tests
2. bottom up’ stress-variable tests, where, instead of looking at a particular scenario and varying all risk factors in a mutually-consistent fashion, the effect of a significant adverse change in a crucial factor (or a narrow range of crucial factors) is considered."

Q1: What are ‘top down’ stress-scenario tests - name sounds like 'scenario analysis' in previous section?

Q2: How does sensitivity testing differ from 'bottom up’ stress-variable tests'?

Q3: Acted Practice Question 15.1(iii) shows that it can be quite tedious counting the number of (dis)cordant pairs as part of calculating Kendall's tau. Has it ever come up in an exam to calculate Kendall's tau? If yes, is there a quick method to do this either by sight or with Excel? Many thanks

 

[Alvin Kissoon]

Hi Bill,

Thanks for the queries.

Q1 - 'top down' stress-scenario tests involves deciding ('top down') on an extreme scenario and then varying all of the risk factors in a mutually-consistent fashion. As mentioned in your quote, it differs from scenario analysis because it uses only extreme scenarios, as opposed to scenario analysis using more plausible scenarios.

Q2 - Similarly, 'bottom up' stress-variable tests talks about a significant change in a factor, whilst sensitivity testing considers less extreme movements.

Q3 - The last time it came up was in September 2014, Question 2(ii). The Course Notes provide an alternative formula for calculating pC-pD using ranks and an example of this approach, which may be easier in Excel.

Have a great festive period!

Alvin.

 

[Bill SD]

Thanks Alvin for your 3 answers.

Q1: You wrote above that "'top down' stress-scenario tests ... differs from scenario analysis because it uses only extreme scenarios, as opposed to scenario analysis using more plausible scenarios."

I'm confused as page 19 of Acted notes says: "To conduct scenario analysis ... by asking participants what the worst plausible event is that they can imagine happening to the organisation. Examples might be the collapse of a major financial institution, an earthquake, or a severe oil shortage." Guess there's no clear divide between extreme and plausible; ie. the 3 examples (the collapse of a major financial institution, an earthquake, or a severe oil shortage) could be plausible even if they sound to me very extreme.

Q2: You wrote above that "'bottom up' stress-variable tests talks about a significant change in a factor, whilst sensitivity testing considers less extreme movements."

Is this a strict rule in terminology? Again, the same page (19) in notes includes in the sensitivity testing section that "companies should investigate the effect of more significant changes in their assumptions to ensure that they have considered the full range of possibilities for future outcomes." I probably come across as pedantic and should just accept that different stakeholders use different terms to refer to the same thing

Q3: Thanks for this. The relevant paragraph in the Acted notes (page 16) explains: "The entry in the first row is 1-because two of Y ’s re-sequenced ranks (W') in subsequent rows are lower than 3, implying that they are not in the same sequence as X , thereby contributing 2-to the calculation, and one of Y ’s re-sequenced ranks in subsequent rows is higher than 3, contributing +1."
I just want to clarify the entries in final column for other rows: (i) the bottom row is always left blank in this method (and the V'4 & W'4 ranks are considered in the row above); (ii) the penultimate row scores -1 as W'4 =1 < V'4=4; and (iii) the 2nd row scores 0 as W'3 =4 >V'3 =3 which adds 1 to the score for the penultimate row (=-1).

 

[Bill SD]

Please ignore my revised Q3 (in message directly above) about calculating Kendall's Tau on page 16 of Acted notes. I now understand that always comparing Y ’s re-sequenced ranks (W't) to each other (and not to X's re-sequenced ranks (V't)). And I've been able to use the formula to correctly calculate Kendall's Tau in Practice Question 15.1 & Sept 2014 Q2. So thankfully no need to clarify.

 

[Alvin Kissoon]

Good points! As you mention the Core Reading itself provides the caveat that people use the same term to mean different things (and also as you say, or different terms to mean the same thing!). I think of a stress / extreme case as reflecting something which I consider to happen in '1-in-X' years (eg the Solvency II stress test is calibrated at 99.5% so would be extreme), rather than something reasonably likely to happen.

The key as mentioned in the Core Reading, is when responding to a question, to make clear what you intend the term to mean in your answer (and be aware of the definitions provided in the Principal Terms of the Core Reading).

 

[Bill SD]

Good points! As you mention the Core Reading itself provides the caveat that people use the same term to mean different things (and also as you say, or different terms to mean the same thing!). I think of a stress / extreme case as reflecting something which I consider to happen in '1-in-X' years (eg the Solvency II stress test is calibrated at 99.5% so would be extreme), rather than something reasonably likely to happen.

Just saw similar question appeared in the April 2020 exam Q2(ii) where the Examiners answer and definitions of scenario& stress testing and sensitivity analysis* are poor and duplicative - so hopefully won't come up again

*  Scenario analysis looks at outcomes under devised ‘what if’ scenarios, normally measuring loss under several related stressed variables without considering the probability of occurrence of that scenario.
 Stress testing measures loss under extreme values of the chosen variable without necessarily considering the probability of that extreme event.
 ‘Sensitivity analysis’ is often used to describe a stress test but under less extreme variation.