In section 5 of this chapter on page 20; 1.) In the example given on that page, the surplus of £2800 is attributable only to a single contract issued 9 years ago to a 44-year-old male or to a group of similar policies issued to different people all of them being male who were issued the same policy 9 years ago when they were 44 years old? And if it is attributable to a single policy why don't we simply increase the sum assured £2800? 2.) In the 2nd point solution of question 6.10, it talks about smoothing of payout and smoother the bonus payments, the “safer” the policyholders feel. so my question is what does smoothing of payout mean? and why would policy holder feel safer if bonus payments are smoother?
(1) It's referring to a single policyholder. Your second point here is important. 2800 is the cash amount of the surplus available to pay to the policyholder. But if we increased the sum assured by this amount, the policyholder would only get his or her "cash" when they died, which is likely to be in many years' time. So the cash value of a reversionary bonus of 2800 would be much smaller than 2800, so the policyholder would be losing out on a lot of money! So instead we pay a bonus of B, and because the bonus is paid at the end of the year of future death (in this case) then the cash value of this bonus would be B.A53. As this has to be equal to 2800, then we get the equation shown. (2) If you imagine investing in equities, then the return you earn each year would be volatile, and so you would be quite uncertain about what you would get eg when you chose to sell your investment. A with-profits policy provides a much more stable return each year to the policyholder (ie it is more or less the same each year) so that the final payout is much more predictable and certain than investing in the equities directly. We describe this "levelling out" of returns as "smoothing", and the more "levelling" there is, the more similar the returns are each year and the more predictable they are. So policyholders are less worried that their investment won't perform.
