Doubts from Chapter 1-5

[Kamal Sardana]

Chapter1:
Q:1 - Can you tell me the meaning or explanation with the help of an example of this line: "The slower the increase in reserves over the contract’s term, the faster any invested capital is released"?

Chapter3:

Q:2 - Page9 question where insurer sells immediate annuity having 5% initial expenses and int rate for pricing is 5.5%. Life annuity of 1$ per annum at this basis is 11.39
At valuation int rate i.e. 4%, Life annuity of 1$ per annum at this basis is 12.85. The insurance company is also required to hold solvency capital of 4% of reserves.
(a) Can you tell me how reserve calculation in solution is being done like that -: (100 - 5) *12.85/11.39 ?
I mean reserve is PV of Outflow minus PV of inflow. How did the solution calculate this thing. Can you please elaborate

Q:3 - Annuities

(A) Can you explain me this line with the help of an example:
"In the case of the endowment plus annuity combination, there may be a minimum guaranteed rate at which the lump sum will be converted into an annuity at the maturity date. Should this guaranteed rate exceed the rate the company is normally offering at the time of maturity, then the company will have to provide a higher benefit than it can comfortably afford, with a resulting loss of profit"

(B)Can you give me any example how with-profits immediate annuity will work ?

 

[Mark Willder]

Chapter1:
Q:1 - Can you tell me the meaning or explanation with the help of an example of this line: "The slower the increase in reserves over the contract’s term, the faster any invested capital is released"?

Chapter3:

Q:2 - Page9 question where insurer sells immediate annuity having 5% initial expenses and int rate for pricing is 5.5%. Life annuity of 1$ per annum at this basis is 11.39
At valuation int rate i.e. 4%, Life annuity of 1$ per annum at this basis is 12.85. The insurance company is also required to hold solvency capital of 4% of reserves.
(a) Can you tell me how reserve calculation in solution is being done like that -: (100 - 5) *12.85/11.39 ?
I mean reserve is PV of Outflow minus PV of inflow. How did the solution calculate this thing. Can you please elaborate

Q:3 - Annuities

(A) Can you explain me this line with the help of an example:
"In the case of the endowment plus annuity combination, there may be a minimum guaranteed rate at which the lump sum will be converted into an annuity at the maturity date. Should this guaranteed rate exceed the rate the company is normally offering at the time of maturity, then the company will have to provide a higher benefit than it can comfortably afford, with a resulting loss of profit"

(B)Can you give me any example how with-profits immediate annuity will work ?

Hi Kamal

Q1 Let's say the insurer needs capital of 10 at the start of the policy to set up reserves. Premiums are 5 each year and the reserve increases by 4 each year. So each year the premiums are more than enough to cover the increase in releases and the insurer gets back 1 of it's capital each year.

Now consider the same situation with reserves increasing more slowly by 3. The insurer now gets back capital of 2 each year.

I'll look at your other questions later.

Best wishes

Mark

 

[Mark Willder]

Chapter1:
Q:1 - Can you tell me the meaning or explanation with the help of an example of this line: "The slower the increase in reserves over the contract’s term, the faster any invested capital is released"?

Chapter3:

Q:2 - Page9 question where insurer sells immediate annuity having 5% initial expenses and int rate for pricing is 5.5%. Life annuity of 1$ per annum at this basis is 11.39
At valuation int rate i.e. 4%, Life annuity of 1$ per annum at this basis is 12.85. The insurance company is also required to hold solvency capital of 4% of reserves.
(a) Can you tell me how reserve calculation in solution is being done like that -: (100 - 5) *12.85/11.39 ?
I mean reserve is PV of Outflow minus PV of inflow. How did the solution calculate this thing. Can you please elaborate

Q:3 - Annuities

(A) Can you explain me this line with the help of an example:
"In the case of the endowment plus annuity combination, there may be a minimum guaranteed rate at which the lump sum will be converted into an annuity at the maturity date. Should this guaranteed rate exceed the rate the company is normally offering at the time of maturity, then the company will have to provide a higher benefit than it can comfortably afford, with a resulting loss of profit"

(B)Can you give me any example how with-profits immediate annuity will work ?

Hi Kamal

Q2 There is no future inflow as this is an annuity. So we just need the outflow. First we need to work out how much annuity the policyholders gets each year. The premium is 100 and the expenses are 5, so 95 is used to buy an annuity. The cost of an annuity of 1 per annum is 11.39, so the amount of annuity each year is 95/11.39. Using the reserving basis the cost of an annuity of 1 per annum is 12.85, so the reserve is the amount of the annuity multiplied by the annuity factor, ie (95/11.39)x12.85.

Q3(A) Sometimes endowments have a guaranteed annuity option as described here. They might guarantee that an annuity can be bought based on an interest rate of 3%. So if interest rates fall below 3%, say to 2%, then the annuity that the insurer has to pay will cost too much, ie they need an asset that earns 3% per annum, but they can only invest at 2%.

(B) I'm not sure whether you really want an example of a with-profits annuity as these are not really part of the course. A with-profits annuity would pay some guaranteed amount each year, but this could be increased with bonuses.

I think you may instead be referring to a with-profits endowment with a guaranteed annuity rate. As described in (A), this would give the policyholder a choice between receiving the lump sum at maturity or using the lump sum to buy an annuity at the guaranteed rate.

Best wishes

Mark

 

[Kamal Sardana]

Thanks for your responses mark. These are really helpful.

There is one question in Textbook on with profits immediate annuity and i am not sure how bonus structure would work in case of immediate annuity. Suppose PH paid insurer $100 and get basic annuity of $10p.a. and then Insurer announces reversionary bonus of 2%. Then annuity will be 10*1.02 for next year and then for the upcoming years minimum annuity will be 10*1.02 and increased by more rates each year as the co. announces bonus rates --> that is my understanding.
But I will come back to you on that later than because there is one question related to that and will ask that specific question

 

[Mark Willder]

Thanks for your responses mark. These are really helpful.

There is one question in Textbook on with profits immediate annuity and i am not sure how bonus structure would work in case of immediate annuity. Suppose PH paid insurer $100 and get basic annuity of $10p.a. and then Insurer announces reversionary bonus of 2%. Then annuity will be 10*1.02 for next year and then for the upcoming years minimum annuity will be 10*1.02 and increased by more rates each year as the co. announces bonus rates --> that is my understanding.
But I will come back to you on that later than because there is one question related to that and will ask that specific question

Hi Kamal

Yes, Question 11.6 does cover with-profits annuities. WP annuities can work in a number of different ways. As they are not covered in the Core Reading the question will have to tell you how they work (as it is testing application of skills rather than direct knowledge). In the case of question 11.6, the annuity amount actually decreases every year by 5% unless bonuses are added. So taking your example, if bonuses were 2%, 3% and 1% for the first three years, then the payments would be 10 x 1.02 / 1.05, 10 x 1.02 x 1.03 / 1.05^2 and 10 x 1.02 x 1.03 x 1.01 / 1.05^3.

Best wishes

Mark