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# Stress Testing (Jorion's FRM Handbook Q26.14.3)

#### orit

##### Active Member
Hi David,
Can you please clarify a point regarding the calculation of Var:
Var is calculated as: Volatility*Deviate*Value
Where the deviate (sigma) is calculated as the distance from the mean.
but when calculating Var we ignore the mean(expected return) and we use the value of the portfolio.
Thanks,
Orit

#### orit

##### Active Member
Hi David,
Here is the question:
Philippe Noiroj, the manager of a \$150 million distressed bond portfolio, conducts stress tests on the portfolio. The portfolio’s annualized return is 12%, with a return volatility of 25%. In the past two years, the portfolio encountered several days when the daily value change of the portfolio was more than 3 standard deviations. If the portfolio would suffer a 4-sigma daily event, estimate the change in the value of this portfolio. Assume there are 252 trading days in a year.
Thanks,

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi orit,

Yes, that's an acceptable question, you will find this from last week helpful http://www.bionicturtle.com/forum/threads/standard-deviation-without-mean-in-ewma-garch.6803
i.e., it is not so much that mean is ignored but, when the VaR horizon is daily, we can assume the mean (drift) is zero.

Daily horizon is the special case where relative VaR = absolute VaR and renders the need to distinguish moot.
For longer horizons, it should be specified as to absolute vs relative, thanks,

append: I realized my link refers to the assumption that mean = 0 wrt variance calculation, rather than mean = 0 w.r.t VaR calculation. These are different concepts, but you can see are "similar" in the sense of "rounding down" the mean in a daily horizon/periodicity

#### ankitagarwal

##### New Member
How important topic is 'stress testing' with respect to FRM exam point of view.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @ankitagarwal I think it has moderate importance (is my guess). I (we) have a small batch of questions pending; do you want me to ask? I'm just not confident they will add anything to what we know, but i don't mind asking. I speculate that "stress testing" has moderate importance because:
1. Stress testing is fully the subject of three (3) readings in P1.T4
2. As I understand from the posted feedback, it has been asked about in recent exams; e.g., I think there is a mention here https://www.bionicturtle.com/forum/threads/may-2017-part-1-exam-feedback.10502 and there is this https://www.bionicturtle.com/forum/threads/stress-testing-principles-exam-relevance-high-low.9119/
3. It does appear among recent practice papers, although not frequently (maybe once or twice per P1 exam on average, i would roughly estimate)
4. On the other hand, IMO, it is inherently hard topic for which to write good questions, as evidenced by the fact that GARP 2017 example question arguably asks for common sense and doesn't really require careful study of the topic
If we are "going by the book," I think we've got to acknowledge that stress testing has a significant allocation (three readings) in the P1 syllabus. I hope that's helpful!

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