The question asks for the effect on EV of increasing interest rate on WOP statutory basis.
It also says the RDR is greater than any investment return assumption used.
It is stated that:
1. it reduces the Without-profits reserve and hence accelerates the release of profit.
Why does it accelerate the release of profit?
2. Because the RDR is higher than the return on assets, the free assets increase by more than the reduction in PV future transfers?
What does this mean?
I am really struggling to understand this. Please can someone use a simple example to explain this?
Yes, a simple example would be better to explain this.
Consider a simple one year contract with reserves of 100 (calculated as a prudent estimate of the claims of 102, discounted back at the valuation interest rate of 2%).
The expected claim at the end of the year on the EV projection basis is 80. The assets backing the reserve are expected to grow to 105 if the EV projection assumption is 5% interest. The profit at the end of the year is then 105 - 80 = 25. The VIF (value of in force business) is then 25 / 1.08 = 23.14815, assuming that the RDR is 8% (ie higher than the return on assets). If the insurer has assets of 120 then the EV is 120-100 + 23.14815=43.14815.
Now let's recalculate if the valuation interest rate goes up to 4%. The reserve is now 102/1.04=98.07692. The expected claim at the end of the year on the EV projection basis is still 80. The assets backing the reserve are expected to grow to 98.07692x1.05=102.98077 if the EV projection assumption is 5% interest as before. The profit at the end of the year is then 102.98077 - 80 = 22.98077. The VIF is then 22.98077 / 1.08 = 21.27849, assuming that the RDR is still 8%. The insurer has assets of 120 so the EV is 120-98.07692 + 21.27849=43.20157 (not much bigger than before, but the difference is significant if the fund is worth billions rather than 100 - the impact is also bigger for a longer term product).
In response to your two questions:
1. The reserves have reduced from 100 to 98.07692, so profit of (almost) 2 is released at time zero due to the change in basis. This is what we mean by accelerating the release of profit. The reserves are a lot bigger than the claim (due to prudence), so money is tied up in the reserves and is released as profit at a later date. By reducing the reserves we have released this profit a little faster.
2. The free asset were 20 and have increased (after the basis change) to 120-98.07692=21.92308. The VIF has fallen from 23.14815 to 21.27849. The EV increases because the free assets have increased more than the VIF has reduced. The reason why is that in the VIF equations above, we rolled up the assets backing the reserves at 5% and then discounted them back when they were released at 8%.
I hope this example helps.
Best wishes
Mark
