2000 #38

[Doc]

My question is regarding parts (d) and (e). The solution say to use the extension of exposure method, but couldn't we say that the parallelogram method would be viable since we do not have detailed individual policy information available to re-rate these policies at current rates and factors? Or we do not need to worry about this due to it being a uniform rate increase of 15%?

[Vorian Atreides]

First: What's the key assumption for the parallelogram method regarding how policies/exposures are written during the time period in question?
Exposures are written uniformly throughout the time period in question.

Second (and this is the clincher): Does the data presented satisfy this assumption?
NO!

Additional comments for those interested:

For the problem given, you have all of the necessary info to "rerate" all policies.

Don't confuse Exam problems for being "realistic" problems--especially with the older Exam problems.

You always want to use Extension of Exposures to bring premium levels to a common level since that's most accurate. Parallelogram method is available to approximate the impact of historical rate change(s) on prior premium levels.

And with the uniform rate change provided in the problem, all rating elements are affected the same way. So you could just use $500*1.15 = $575 as the rate to apply to the number of car years earned in 1998 to get the answer to part (e).

On top of all this, you could use the parallelogram method, but you'd need to do it on a quarterly basis and that would be a lot of extra work. Extension of Exposures answer: 575(900*1.00 + 1100*0.75 + 1300*0.50 + 1500*0.25) and you're done!

[Doc]

Thanks!