September 2004 Question 11 Query - COST OF RESERVES

[spjgriw]

Can somebody tell me why when calculating the increase to the cost of reserves in this question, the probability of a policy still being in force is not taken into account. I don't understand why this is the case for this question and not other questions similar to this.

Many thanks in advance,

Richard

 

[Hamilton]

which question

im looking at 105 paper September 2004 and it doesnt really seem to be what your talking about , is this correct?

 

[spjgriw]

The question is this:


A special 3-year endowment assurance policy provides that the death benefit payable
at the end of year of death is £10,000 plus the endowment assurance net premium
reserve for that year that would have been held had death not occurred. £10,000 is
payable on survival to the end of the 3 years.
On the basis set out below, use a discounted cash flow method to calculate the level
annual premium payable in advance for a life aged 57 exact. The requirement is that
at the discount rate defined below the value of the annual emerging surpluses should
sum to zero.
Basis: Mortality: AM92 Select for experience and reserves
Expenses: 20% of the first annual premium
5% of subsequent premiums
Reserves: Value as a normal endowment assurance for a 3-year term
on a net premium basis using a valuation rate of interest of
4% per annum. Ignore the effect on reserving of the extra
death benefit defined above.
Interest earnings: 7% per annum on cash flow
Discount rate: 10% per annum
Ignore tax and any other items.


In order to answer this question, a profit testing approach needs to be taken by setting up a table of cashflows including a cost of reserving entry. In the answer to this question the cost of reserving accounts for all policies and not just those where the policy is still in force. I don't understand why this is the case.

 

[Hamilton]

actually

we probably are looking at the same question . Em we are using "the formula" for calculating reserves and the answer that it spits out for our reserves at the end of year 1,2,3 are already , per in force contract .(love someone else to confirm this as doubt is setting in )

These other questions you refer to that do multiply by the survival probabilities , name some ? so we can have a look at the differences.

wrote this before i saw your response , does it answer your question?

 

[spjgriw]

I'm comparing it with for example question 14 from CT5 April 2007 where the increase in reserves is calculated by first of all calculating the reserve per policy at year end and then calculating the reserve at year end by multiplying the reserve per policy at year end by the proportion of policies surviving the year.

I don't understand why we don't do that for the September 2004 question.

 

[Hamilton]

hum

Right well i think I understand the answer to both questions but I doubt im gonna give ya the explanation your after , but i shall try .

Q11 2004)

we are told to hold net premium reserves for an endo ass , so we use "the formula" it spits out our end year reserves on an inforce basis , grand.equally could be viewed as the opening reserves required for year 2,3 ,(4 not really obviously only 3 year contract) onto the table hope you comfortable with the first 6 rows the 2nd last row are our in force probabilities and last row is where we multiply emerging surplus by probability of occurring , all thats left to do is discount at the 10% RDR.

wheras

Q14 2007)

we use "the formula" to tell us the opening reserve required at start year 2,3,4 , then our profit vector follows from just adding and subtracting along the rows.we dont multiply by in force probabilities till we start to calculate the profit margin .

sorry if this doesn't answer your question , probably wont .
I cant see what the differences between these questions you are refering too , to me they are exactly the same baring the point of each question is slightly different.
Perhaps its the fact that q11) is talking bout end year values and q14 is the more standard table with the emphasis on start year values.

 

[spjgriw]

But in question 14 we do multiply by survival probabilities to get the cost of increasing reserves. We then also multiply by survival probs to calculate NPV. This doesn't appear to be what's happening int the other question.

 

[Hamilton]

oh right sorry

Discard my previous statement/s.I blame my visit to the dentist today for my incompetence it appears you understand the answers to both these questions better than me .
I have to plead ignorance here .I think question 11 is just a question/method which isn't really on the course anymore or if it was would be defined a lot clearer , have you seen any reference to this "annual emerging surplus" in any other questions .The answer seems to start positively enough with
if St is the surplus in year t per policy in force

so have ya done it? q11) with the adjusted surpluses ?
wouldn't mind seeing it .God I need way more practice at these questions for October.

 

[Mark Mitchell]

The difference between these two questions (S04 Q11 and A07 Q14) is in the specification of the sum assured under the policies.

A07 Q14 gives a fixed amount on death, payable at the end of the year of death. This is the "usual" situation that forms the basis of most questions.

S04 Q11 gives a death benefit of a fixed amount, PLUS the net reserve that would otherwise be held. This is an "unusual" situation, but still, as far as I can see, on the syllabus. The fact that the reserve is also paid out on death is what changes the approach (effectively, the reserve is required at the end of each year whether the policyholder dies or not - if they die it's paid out along with the sum assured, and if they survive the reserve is required as usual).

Start off by understanding A07 Q14, then go back to S04 Q11, which is harder.