2004 # 32

[abc123]

I will only show the part I don't understand

Calendar year 2004 is being reviewed for an indicated rate change with an effective date in 2004. Assume 50% of the business has an effective date of January 1, with the remaing business written evenly thoughout the year.
Describe the adjustments that should be made to historical premium if a rate increase was taken in April 2002.

My method
Since before April 2002, the permium factor is 1, with (0.5+ 3/12*0.5) = 0.625 of the business, after the premium factor is 1+x, and with 9/12*0.5 = 0.375 of the business, thus the average premium for 2002 is 0.625 + (1+x)*0.375 = 1+0.375 x, thus the current rate level factor = (1+x)/(1+0.375x)
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The solution by CAS is
CRLF = (1+x)/(1+(0.5+(3/12)(0.5))x) = (1+x)/(1+0.625x)
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What is wrong with mine? Thanks.

[J.T.]

Nothing. The CAS solution calculates the 2003 CRLF.

[Yanb]

This solution implies that we are finding a on-level factor for written premium.

However, if we are finding a on-level factor for earned premium the factor would be (1+x)/(0.5+((0.7187+(1+x)*0.2813)/2)).

Refering to the original question there is noting stating that we have to find a on-level factor for written or earned premium.

Does historical premium=written premium?

How have you determined which premium(written or earned) should we use?

Thanks!

[dumples]

Well after wasting a lot of time reading the CAS solution and your solution and trying to align them with what I would do, I checked what Howard Mahler said in his solution guide, and I matched Mahler.

Here is our solution.

on lever factor = (1+x)/(.5 * 1 + .5 * (23/32 * 1+ 9/32*(1+x)) = (1+x)/(1+9/64x)

this corresponds with Yan's solution.

while we're listing complaints. They were vague about when the rate change went into effect. April 1st or April 30th makes a difference

[dumples]

Nothing. The CAS solution calculates the 2003 CRLF.
I don't know what you mean by this, but I would say that if the April 1st rate change (x) was the only change to date. Then the 2003 earned premium levelling factor would be:

(1+x)/(.5*(1+x)+.5 * (1/32 * 1 + 31/32* (1+x))) = (1+x)/(1+63/64*x) <> CAS solution

if we're talking written premium, then all of the premium written in 03 is with the april 1st change. -> 1

I'm also assuming 1 year policy terms. The question doesn't specify that either. ( though less than 1 year doesn't make sense because the 1/1 customers would renew en mass at 7/1 if it were a 6 month policy)

[J.T.]

Yes, very true. I was trying to do this while juggling fifteen projects at the same time.

I at first couldn't figure out how in the world they were coming up with things that didn't correlate to EP. Once I made the jump about 2002 WP instead of EP, I automatically (incorrectly) made the assumption to the 2003 WP.

[bubs]

Glad to see this question here, as I had looked at it last night and couldn't follow the solution provided.
I think that in a case like this the best thing is just to state your assumptions e.g. written vs. earned etc.

[dumples]

Grabbing your butt, that's not very ladylike.

[Yanb]

I don't know what you mean by this, but I would say that if the April 1st rate change (x) was the only change to date. Then the 2003 earned premium levelling factor would be:

(1+x)/(.5*(1+x)+.5 * (1/32 * 1 + 31/32* (1+x))) = (1+x)/(1+31/32*x) <> CAS solution

if we're talking written premium, then all of the premium written in 03 is with the april 1st change. -> 1

I'm also assuming 1 year policy terms. The question doesn't specify that either. ( though less than 1 year doesn't make sense because the 1/1 customers would renew en mass at 7/1 if it were a 6 month policy)


Are you also assuming that 50% of exposures are written on January 1,2003 to get this solution? What would be on-level factor for calendar year 2003 if 2003 had uniform exposures (not 50 % on January 1)?

Thanks!

[dumples]

Are you also assuming that 50% of exposures are written on January 1,2003 to get this solution? What would be on-level factor for calendar year 2003 if 2003 had uniform exposures (not 50 % on January 1)?

Thanks!
I made a mistake before. What I wrote on the left side of the equation was correct, but I got sloppy when I simplified the expression.

yeeeeha for partial credit!