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#1
02-25-2012, 06:26 PM
 cab691 CAS SOA Join Date: Feb 2011 Location: ./ Studying for my work visa. Favorite beer: rochefort 8 Posts: 18
parallelogram method

Hi, I have a pretty basic question about the parallelogram method.

Let's say there's a single rate change of 8% at 7/1, and we want to put the earned calendar year premium on level. Naively, I'd guess that if seven eighths of the premium comes from policies written before 7/1, we'd use an overall rate factor of

$\frac{7}{8}1.08 + \frac{1}{8},$

the weighted average. But that's not what the parallelogram method prescribes! Instead, we use the harmonic weighted average:

$\frac{1.08}{\frac{7}{8} + \frac{1}{8}1.08}.$

Why is the harmonic weighted average better than the ordinary weighted average here?
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Last edited by cab691; 02-26-2012 at 11:10 PM..
#2
02-25-2012, 07:46 PM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 5,032

What are you computing with the parallelogram method?

Spoiler:
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#3
02-25-2012, 08:44 PM
 Vorian Atreides Wiki/Note Contributor CAS Join Date: Apr 2005 Location: Garroting Deep Studying for CAS Exam 7 College: Hard Knocks Favorite beer: Sam Adams Cherry Wheat Posts: 28,510

Suppose that there's a subsequent +5% rate change in the following year at, say, 4/1.

What factor is needed to bring the year in question's earned premium to on-level?
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#4
02-25-2012, 10:55 PM
 cab691 CAS SOA Join Date: Feb 2011 Location: ./ Studying for my work visa. Favorite beer: rochefort 8 Posts: 18

Yep, figured it out. Thanks a bunch!
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