Retrospective vs Prospective view of PVFP

[Nicholas_B]

Hi there

I am referencing from Page 16-17 of Chapter 15 (Models (2)) from the 2021 Core Readings, on the question on why PVFP for existing business would be expected to be positive.

1) How are we able to 'see' the retrospective and prospective views in action here? For instance, the solution mentions on the role of supervisory solvency requirements in the prospective view, but makes no reference to it in the retrospective view. My lack of clarity comes from the my usual understanding on retro and prosp concepts of surrender values, which is a little difficult to be applied here.

2) In the prospective reasoning, it is also mentioned that:
'Alternatively, if reserves are calculated on a best estimate basis, the expected future experience in the EV basis should equal the reserving assumptions, so that positive profits emerge as the solvency capital is released'

However, earlier in the readings outlining the calculation of EV (Section 2.1), it mentions that profit emerging each year is expected to be zero if the supervisory reserve assumption were exactly the same as the assumptions used to calculate the cash flows in the EV calculation. So I was wondering how do I reconcile these 2 pieces of information together?


3) I see there are different forms of 'basis' being mentioned in the solution, namely:
-Embedded Value basis
-Best estimate basis
-Prudent reserving basis

a) Am I right to say that the embedded value basis is the basis we see in the calculation of the components found in the 'PV of future SH profits' part of the EV formula? (With the exception of the release of supervisory reserves component, as I believe this should be calculated under prudent reserving basis using more conservative assumptions)

b) Is there any difference between the embedded value basis and Best estimate basis in terms of the level of conservativeness used in the assumption setting?


Appreciate your help in the above clarifications, thank you.

Nicholas

 

[Mark Willder]

Hi there

I am referencing from Page 16-17 of Chapter 15 (Models (2)) from the 2021 Core Readings, on the question on why PVFP for existing business would be expected to be positive.

1) How are we able to 'see' the retrospective and prospective views in action here? For instance, the solution mentions on the role of supervisory solvency requirements in the prospective view, but makes no reference to it in the retrospective view. My lack of clarity comes from the my usual understanding on retro and prosp concepts of surrender values, which is a little difficult to be applied here.

2) In the prospective reasoning, it is also mentioned that:
'Alternatively, if reserves are calculated on a best estimate basis, the expected future experience in the EV basis should equal the reserving assumptions, so that positive profits emerge as the solvency capital is released'

However, earlier in the readings outlining the calculation of EV (Section 2.1), it mentions that profit emerging each year is expected to be zero if the supervisory reserve assumption were exactly the same as the assumptions used to calculate the cash flows in the EV calculation. So I was wondering how do I reconcile these 2 pieces of information together?


3) I see there are different forms of 'basis' being mentioned in the solution, namely:
-Embedded Value basis
-Best estimate basis
-Prudent reserving basis

a) Am I right to say that the embedded value basis is the basis we see in the calculation of the components found in the 'PV of future SH profits' part of the EV formula? (With the exception of the release of supervisory reserves component, as I believe this should be calculated under prudent reserving basis using more conservative assumptions)

b) Is there any difference between the embedded value basis and Best estimate basis in terms of the level of conservativeness used in the assumption setting?


Appreciate your help in the above clarifications, thank you.

Nicholas

Hi Nicholas

I have answered each of your questions below.

1) A numerical example might help.

Consider the retrospective approach first. Just before the first cashflows the PVFP must be positive (otherwise the contract isn't making a profit). Let's say the PVFP = 1. Then at the start of the contract the insurer receives a premium of 6, pays expenses of 4 and sets up a reserve of 3. These values were included in the PVFP of 1, so we must take them away to get the new PVFP. The PVFP is now 1 - 6 + 4 + 3 = 2, ie even more positive. At maturity the PVFP will be 0. So we can see that the PVFP starts positive and gradually falls to zero and does depend on the reserves.

Thinking prospectively the initial reserve is 3. But this has been calculated prudently, so maybe a best estimate would have been 1. So we expect the prudence in the reserves (3-1) to be released as profit in the future.

2) The difference between these two statements is the existence of solvency capital. The insurer will hold reserves plus any required solvency capital on top. PVFP is effectively the release of any prudence in the solvency calculation - this is the solvency capital plus the prudence in the reserves. If the reserves are best estimates and there is no solvency capital then there are no margins to release and the PVFP is zero - this is what Section 2.1 is saying. If the reserves are best estimates there are no margins here, but there may still be solvency capital to be released - this is what the question is saying (ie "so that positive profits emerge as the solvency capital is released").

3) Yes, your comment in (a) is exactly right. The solution says that the EV basis is usually best estimate, and so EV basis and best estimate basis is the same here.

Best wishes

Mark

 

[Nicholas_B]

Thanks Mark for the clarifications.