Chapter 19

[kimiko]

Hi, can you kindly explain this is the solution to Practice Question 19.1(ii): "By working backwards from the last negative non-unit cashflow it is possible to ensure that, net of changes in reserves, the net cashflow is negative in no future time period."

 

[Mark Willder]

Hi, can you kindly explain this is the solution to Practice Question 19.1(ii): "By working backwards from the last negative non-unit cashflow it is possible to ensure that, net of changes in reserves, the net cashflow is negative in no future time period."

Hi Kimiko

A numerical example might help.

In some countries, negative non-unit reserves are not allowed. It is important to work backwards when calculating the reserves. Working forwards may give the wrong example.

For example we may have the following cashflows at the end of each year.

-1, -1, -1, -1, 2

Working forwards (ignoring discounting etc) we would calculate the initial reserve as:

V0 = 1 + 1 + 1 + 1 - 2 = 2

But working backwards from the last negative cashflow we see that reserves at time t, Vt should be:

V3 = 1

V2 = 2

V1 = 3

V0 = 4

So working out the reserves going forwards gives the wrong answer and would mean running out of money.

Best wishes

Mark

 

[kimiko]

Hi Mark,

(a) If we have this cashflow instead: -1, -1, 4, -1, 5, would the negative non-unit reserves be 1 and, if negative non-unit reserves were not allowed to be held by regulation, the reserves would be zero?

(b) Is this what "After taking account of the future non-unit reserves, there are no future negative cashflows for the policy ie there should be no future valuation strain." is referring to from the notes? What does the "After taking account of the future non-unit reserves" part mean?

(c) Also, this is under prudential valuation, right? If it was BE valuation, the reserves would be 2 for your example and negative non-unit reserves of 6 in my example?

I hope my understanding is correct for this.

 

[Mark Willder]

Hi Mark,

(a) If we have this cashflow instead: -1, -1, 4, -1, 5, would the negative non-unit reserves be 1 and, if negative non-unit reserves were not allowed to be held by regulation, the reserves would be zero?

(b) Is this what "After taking account of the future non-unit reserves, there are no future negative cashflows for the policy ie there should be no future valuation strain." is referring to from the notes? What does the "After taking account of the future non-unit reserves" part mean?

(c) Also, this is under prudential valuation, right? If it was BE valuation, the reserves would be 2 for your example and negative non-unit reserves of 6 in my example?

I hope my understanding is correct for this.

Hi Kimiko

No, I'm afraid this isn't right. I think you have it the wrong way round.

If we were holding prudent reserves we would hold 2. If we were holding best estimate reserves we would hold -6.

Let's say we held a reserve of 1 as you suggest. At time 1 there is a negative cashflow of -1. This is ok as we can use the reserve to cover the cashflow at time 1. But at time 2 there is another negative cashflow of -1. We have no reserves left and so we have valuation strain, ie we need to ask the shareholders for some money now to meet the negative cashflow. That's why the prudent reserve has to be 2 at time zero.

Best wishes

Mark