Actuarial Outpost Risk Margin - Bootstrapping Method
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#1
12-31-2018, 01:08 AM
 beanie Join Date: Sep 2010 College: N/A Posts: 10
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.
#2
12-31-2018, 01:33 AM
 Transitive Tangerine Member COPA Join Date: Oct 2018 Studying for PA Posts: 494

Why do you expect it to be close to zero? What does the PDF of the lognormal look like?
#3
12-31-2018, 01:50 PM
 Harbinger Notes Contributor CAS Join Date: Feb 2005 Posts: 2,385

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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har·bin·ger (här'bin-jer): One that indicates or foreshadows what is to come; a forerunner.
#4
01-01-2019, 01:30 PM
 beanie Join Date: Sep 2010 College: N/A Posts: 10

Quote:
 Originally Posted by Harbinger 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.
You are right. Thank you!
#5
01-01-2019, 10:30 PM
 Harbinger Notes Contributor CAS Join Date: Feb 2005 Posts: 2,385

I meant 50.95th percentile, not 51.9th.
__________________
har·bin·ger (här'bin-jer): One that indicates or foreshadows what is to come; a forerunner.
#6
01-02-2019, 10:45 AM
 Transitive Tangerine Member COPA Join Date: Oct 2018 Studying for PA Posts: 494

Quote:
 Originally Posted by beanie You are right. Thank you!
np
#7
01-02-2019, 01:23 PM
 Westley Member Join Date: Nov 2001 Posts: 27,938

Quote:
 Originally Posted by Harbinger 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.

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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