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crash
10-29-2002, 03:49 PM
has anyone had trouble with question #469 from the actex study manuel? i can't find another question like it anywhere and i'm not sure that they've answered it correctly. i'm confused regardless. any comments? if anyone would like me to put the actual question up (ie. you don't have the actex) just let me know.

Michael
10-29-2002, 04:11 PM
Okay, let me take a look......Okay, there are several pieces to this that do seem familiar.....Calculating E[Z] where the benefit varies depending on when death occurs (within or after 20 years in this case) is best handled by "layering" deferred life insurances, which is what they did.....Where I got lost was on the number "3" in the E[z^2] calculation....Everything else seems routine....Is that where you're stumbling? I'm not sure about the source of the "3".......

Michael
10-29-2002, 04:30 PM
One more thought: I was less familiar with altering 20E40 according to the "double the force of interest" rule, and placing the (1.06)^20 in the denominator adjusts the 20E40 found in the SOA tables to the double force version.....That "3" though......Would like to know about that one!

crash
10-29-2002, 05:00 PM
thanks for looking at this. yah... i'm good with everything except the 3. i think what they might be doing is treating the second term 2A40 -v^20*20E40*2A60 like the second term of V(K), or with a 2k-1 multiple. i can't figure out how else they'd get the 3 but i don't know that it should be there either.

Agtuary
10-29-2002, 06:30 PM

LFC
10-30-2002, 02:58 AM

i agree..that would be helpful to all of us.

bg23516
10-30-2002, 10:30 AM
This is 469 from Actex 2002 edition. Hopefully, this is the question you are asking about.

Q:
An employer has 100 lives, age 40, and for each life a commitment to pay 100,000 at end of year of death if death is prior to 60, or 50,000 at end of year of death if death is after age 60. Given:
Mortality follows the ILT.
i=6%
100 lives are independent.

What fund is necessary st the employer is 90% certain of being able to meet his commitment? Use Normal Approx.

crash
10-30-2002, 04:04 PM
The answer actex gets is 1,309,922. I'm getting 1,223,777 which is not even one of their choices.

drctypea
10-30-2002, 04:21 PM
i get the same answer also if i set up E(Z^2) as

(50000^2)(2^A40) + (50000^2)(2^A40:20)... and then proceed doing
E(Z^2) - E(Z)^2....and then multiplying by 100 to get total variance. For some reason you cannot do it like this. The following shoudl be your expression for E(Z^2)

(100000^2)(2^A40:20) + (50000^2)(20P40)(v^40)(2^A60)...this will give you the right second moment and then you can proceed....

Been There Done That
10-30-2002, 04:32 PM
drctypea,

As it turns out, you can do it your first way, but you are missing a term.

Your formula gives the variance on a pair of 50,000 policies (one whole life, one 20 year term) on two independent lives.

To do the problem this way, you would need to include a covariance term.

drctypea
10-30-2002, 04:51 PM
i spoke with bg23516 on this one..and thats what we concluded that i needed a covariance term in there... if you die within the 20 year period it affects both of the insurance terms so they are correlated. doing it in the second method i stated alleviates the need for the covariance term. after getting an answer that wasnt there doing it this first way, i redid it the second way (without the covariance) and got the correct answer....thanks for pointing out the variance part though!

Bama Gambler
10-30-2002, 05:13 PM
Here is how I would approach the problem.

Let Z be the present value random variable. I think everyone agrees we need to find the E[Z] and the VAR[Z].

Let X be the present value of 20 year term insurance with appropriate face amount.

Let Y be the present value of 20 year deferred whole life insurance with appropriate face amount.

Z = X + Y
E[Z] = E[X] + E[Y]
VAR[Z] = VAR[X] + VAR[Y] + 2COV[X,Y]
COV[X,Y] = E[XY] - E[X]E[Y]

During the first 20 years X has some positive value but Y = 0 (b/c Y deferred)
After 20 years Y has some positive value buy X = 0 (b/c X term)

so E[XY] = 0
so COV[XY] = -2E[X]E[Y] (tangent - which probably has something to do with that mysterious 3 in Actex solution)

Hope this helps someone!!
Bama Gambler

Michael
10-31-2002, 01:00 PM
Is this a 5 versus 6 question, or a 9 versus 10 question?

Bama Gambler
10-31-2002, 01:23 PM
Is this a 5 versus 6 question, or a 9 versus 10 question?

9 versus 10, usually these normal approx. questions are MUCH easier.

Bama Gambler
10-31-2002, 01:23 PM
maybe 8 vs. 9

drctypea
10-31-2002, 01:39 PM
its interesting how we interpret these questions..i thought this was more like a 5 -6 question..whereas the one bg23516 asked (and i couldnt get either) was a 9 vs 10 question...weird how a question to one person may click and not to another

Bama Gambler
10-31-2002, 01:42 PM
its interesting how we interpret these questions..i thought this was more like a 5 -6 question..whereas the one bg23516 asked (and i couldnt get either) was a 9 vs 10 question...weird how a question to one person may click and not to another

Great point!! As long as there are enough "easy" questions (in your opinion) then you should be able to pass.

Michael
10-31-2002, 01:49 PM
.26 baby!

Michael
10-31-2002, 01:49 PM
Seriously, is it really 24? Or, have you added risk margin to that?

Bama Gambler
10-31-2002, 01:59 PM
Seriously, is it really 24? Or, have you added risk margin to that?

I figure 24 will be enough to pass, but I want to be sure I get 24 right (with almost 100% accuracy). Then surely I get a couple right on the 16 I "guess" on. I bet 24 right will get you a 7 (at least it did me for course 1).