Hi, I had doubts related to Chapter 17:Setting Assumptions, Section 1.4(Dealing with per-policy expenses) 1.It is mentioned in the reading that: "this means that, whilst we might have thought of the expense loading as being per policy, it will vary in practice in proportion to the size of the policy actually taken out" How is it that per policy expense is affected by size of the policy , is it related to benefit size. If yes then how? 2. Why is it a risk when expenses do not vary by size of contract? In fact shouldn't it be a risk when they vary by size of contract? 3. "the following are among the ways of coping with this risk: Individual calculation of premium rates or charges Here it is mentioned that "this would probably be done for large cases: very small policies priced on this basis would end up paying a large percentage of their premiums as expense loading." Why would it be a percentage of premium when these are fixed expenses even for small policy sizes?
To make sense of your quotation in (1.) we need to quote the ActEd text in full: "In the solution to the previous question, we included per-policy expenses (those that do not vary by policy size) explicitly as such in the basis. Part of the basis is also the average benefit size assumed for the particular policy. The pricing process will usually lead to a premium rate, expressed per unit of benefit, such that for the average sum assured the correct per-policy expense loading will be made. This means that, whilst we might have thought of the expense loading as being per policy, it will vary in practice in proportion to the size of the policy actually taken out." A numerical example might help to explain the text above. We perform the expense analysis and conclude that each policy has fixed expenses of 3 each year. The average benefit size is 300. We could price each policy by adding an expense of 3 to the regular premium. In this case, pricing and reality match up nicely. However, insurer's have often not priced in this way. They have often followed a simpler route by quoting premiums as a rate per 1000 sum assured. This is handy for salespeople as they can quote a price to a prospective policyholder by just multiplying the premium rate by the required sum assured and dividing by 1000. So they convert the per policy expense of 3 to an average rate of 1% = 3 / 300 and quote a premium rate of 10 per 1000 sum assured for the expenses (let's say the probability of death is 5%, so the overall rate that would be quoted is 60 per 1000). Now we can see that by using a premium rate per 1000 sum assured we have an expense loading that is effectively in proportion to policy size. If the benefit is 300, then the expense loading is 3 = 1% of 300 as desired. But if the benefit is 1000, then the expense loading is 10 = 1% of 1000, ie too much. Similarly if the benefit is 100, then the expense loading is 1 = 1% of 100, ie too little. This answers your question (2.), we now have a risk that we sell lots of small policies and only receive expense loading of 1 when the expenses are a fixed amount of 3. Finally to answer your question (3.) we could solve the problem by pricing each policy individually with a loading per policy of 3. But if the policy only has a benefit of 100, then this means that they have to pay 5 for the mortality risk and 3 for the expenses giving a relatively high premium of 8 compared to the premium of 6 that would have been paid using the premium rate per 1000 method, ie expenses have had a disproportionately large impact on the price. I hope the numerical example helps to explain what is happening. Best wishes Mark
