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April 2009 Q1 part 4

L

LastHurdles

Member
The examiners comments says: "A large number of candidates suggested a higher percentile (for the risk margin) should be used for classes with greater variability demonstrating the lack of understanding of percentiles"

What's wrong with doing this?
 
Classes with higher variability will have a more "spread out" distribution, so the 99.5th percentile will be "further away" from the best estimate than for more stable classes. So a higher margin is already built into the method, and a higher percentile is not required.
 
Thank you for the response Katherine. That now makes sense.
 
Katherine Young said:
Classes with higher variability will have a more "spread out" distribution, so the 99.5th percentile will be "further away" from the best estimate than for more stable classes. So a higher margin is already built into the method, and a higher percentile is not required.
Click to expand...
Hi Katherine,

Could you please explain this bit again?

In the answer it's also said that "Consider uncertainty in best estimate and distribution of uncertainty to decide on level of percentile, e.g. if there is a greater than usual level of uncertainty in the reserves, companies may wish to hold a higher margin in order to increase the likelihood that reserves will be adequate."
Does this not translate into holding a higher risk percentile?

Thanks,
Shradha
 
Could you please explain this bit again?
Click to expand...

If a distribution has a high variance, the 90th percentile (say) is a long way away from the mean. This means that companies who assume a distribution with a high variance will hold a higher capital.

Now, if you were to say that volatile classes should use a higher percentile (the 99.5th percentile say), that would be double-counting ... they're ALREADY holding more capital by virtue of using a distribution with a high variance.

Does this not translate into holding a higher risk percentile?
Click to expand...

Yes. They're saying that if parameter / model uncertainty is high, the percentile should be higher.
 
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