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#1




Risk Margin  Bootstrapping Method
Bootstrapping is a common method used in estimating the volatility and risk margins assumptions.
Refering to the example below from this paper: https://www2.math.su.se/matstat/repo...p13/report.pdf Page 36 (Table 5) Selected CoV = 20%, and assumed a lognormal distribution BE Reserves = 4,175,994 75th percentile = 4,678,623 (Margin = 12.0%) 25th percentile = 3,584,941 (Margin = 14.2%) I would like to find out the 60th percentile risk margin. Using the above example as illustration, I get a risk margin of 3.1%. I also computed the 50th percentile risk margin as a sense check, which is 1.9%. Now this is where I have a question. I am expecting the 50th percentile risk margin to be close to zero, but it is negative. Intuitively, it does not make sense, but is this acceptable? Or do I have to somehow shift the lognormal distribution such that the 50th percentile is exactly 0%? My concern is the 60th percentile risk margin is understated. 
#3




You’re confusing the 50th percentile with the mean. The lognormal distribution is often skewed right. It appears your mean is at the 51.9th percentile. You should not shift/adjust.
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#4




You are right. Thank you!

#7




Quote:
The fact that you (OP) were unclear on the need for adjustment means that it is likely that the reader/user is much MORE unclear, and calls for very careful communication/documentation. Too many actuaries (not necessarily OP) worry about getting the numbers correct, and aren't concerned enough that they are *used* correctly.
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