EOM 4 mortality

[Joseph_Z]

Hi, I've read through almost all the discussions on EOM 4, and I still couldn't figure out the errors in my calculation.

For EOM 4, I got the profit as premium to be around 28% which is definitely too high. But I think I carefully followed the instructions. I really appreciate any hints on where I messed up. Here is my calculation for band one.

Policies sold 20,000
Face amount in $000 is 1,000,000.
total premium collected 1,800,000.

Face amount BOY 1,000,000
reserve BOY 0
reserve EOY -3,276,146
Premium collected 1,800,000
underwriting expense 2,000,000
commission bonus 2,700,000
interest on BOY reserve 0
Interst on Cash flow -174,000
death claim 413,000 (in $)
Total cash flow -3,487,000
increase in reserve -3,276,146
profit -210,854

using the same calculation, 2nd year death claim is 545,075 and profit is 37,241
3rd year death claim is 611309, and profit is 79,572

total profit as % of premium for the 10 year period is 27.98%.

I've seen people mentioned the 1000 factor for mortality, my understanding is that the given mortality is for 1000 and the face amount is also in 1000, so to get the actual death claim amount in $. So I simply multiply the 70% adjusted mortality 0.413 for 1st year with the face amount 1,000,000. If I want to convert everything to 1$, then I can divide 0.413 by 1000 and at the same time use the real face amount of $1,000,000,000, then I will get exactly the same profit and death claim amount because the 1000s cancel out.

I know I must have missed something obvious because everyone seems to get around 5% profit.

Any hint is appreciated.
Thanks,
Joseph

[amyb2332]

Are you talking about tasks 3 and 4? I think the first problem is that you aren't using the correct policies sold, face amount, and premium collected. It says in the memo on page 5 (the last bullet point at toward the end) that you are supposed to assume the amount of new business is the same as for 2005. I think you are using the 2001 numbers. So for band 1 that would be 27,000 polices sold not 20,000 etc for the face amount and premium.

I went back and changed my numbers to match what you were doing and I got the rest my numbers to match yours but my profit still isn't higher than 5%. Is the profit you listed just for band 1? Maybe if you give those numbers I could help more.

[Joseph_Z]

Originally Posted by amyb2332

Are you talking about tasks 3 and 4? I think the first problem is that you aren't using the policies sold, face amount, and premium collected. It says in the memo on page 5 (the last bullet point at toward the end) that you are supposed to assume the amount of new business is the same as for 2005. So for band 1 that would be 27,000 polices sold not 20,000 etc for the face amount and premium.

Does that help?

Thanks for taking the time to respond. But no matter how many policies are sold, the percentage of profit to premium should be the same. I used 20,000 policies sold as an example to show some real numbers. Do you think I got the mortality right?

BTW, I used 2005 sales numbers (amount sold, premium, and # of policies sold), I got the same profit as % of premium.


Thanks,
Joseph

[amyb2332]

I think you are doing the mortality correctly. For the second year my mortality matches what you have. I didn't notice this the first time but I'm actually not matching your second year profit. I matched the first year profit but not the second. I got 156,278 for second year profit and 147,460 for 3rd year profit.

[Joseph_Z]

Originally Posted by amyb2332

I think you are doing the mortality correctly. For the second year my mortality matches what you have. I didn't notice this the first time but I'm actually not matching your second year profit. I matched the first year profit but not the second. I got 156,278 for second year profit and 147,460 for 3rd year profit.

so what is your overall profit as a % of premium? looks like your profit is even higher than mine.

Here are my 2nd year numbers (using 1,000,000 as original face amount)

Face amount BOY 949,608
reserve BOY -3,276,146
reserve EOY -2,243,179
Premium collected 1,709,294
underwriting expense 0
commission bonus 0
interest on BOY reserve (196,569)
Interest on Cash flow 102,558
death claim 545,075 (in $)
Total cash flow 1,070,208
increase in reserve 1,032,967
profit 37,241

3rd year
Face amount BOY 856,175
reserve BOY (2,243,179)
reserve EOY (1,348,380)
Premium collected 1,622,897
underwriting expense 0
commission bonus 0
interest on BOY reserve (134,591)
Interest on Cash flow 97,374
death claim 611,309 (in $)
Total cash flow 974,371
increase in reserve 894,799
profit 79,572

Thanks a lot!
Joseph

[amyb2332]

For band 1 my % of profit is 5.22%, band 2 is 5.41%, band 3 is 4.7% and the overall is 5.03%.

My end of year reserves in year 2 don't match yours and then that is throwing off some other stuff. I know that I played around the the lapse rate for one of the tasks though so that could be why we aren't matching. And it still shouldn't explain the high % of profit you are seeing.

I'm kind of at a loss! Sorry!

[IIRC]

The mortality is fine, don't forget to divide by 1000 somewhere along in your calculations, that's a common hiccup.

[Joseph_Z]

Originally Posted by IIRC

The mortality is fine, don't forget to divide by 1000 somewhere along in your calculations, that's a common hiccup.

Thanks, but specifically where should I divide it by 1000?. I think I got the death claim amount correctly by multiplying the mortality per 1000 with the face amount in 1000.

Thanks for taking the time to reply.
Joseph

[IIRC]

Sorry, I don't remember specifically, I just remember people not coming up with the right returns because they forgot to add 1/1000 somewhere in there calcs. What's your lapse rates? Been a while for me.

[Joseph_Z]

Originally Posted by IIRC

Sorry, I don't remember specifically, I just remember people not coming up with the right returns because they forgot to add 1/1000 somewhere in there calcs. What's your lapse rates? Been a while for me.

I've read the discussions about dividing 1000 in the calc, and I think I did it the right way and I still can't figure out my error.
My lapse rate was 5% for all years. But even a change from 5% to 10% in my calc won't reduce the profit % from ~28% to 5%.

What did you use for the recommended mortality in part 1 and 2. Is it still around 70% of CIA 86-92 table?


Thanks,
Joseph