the last question in chapter three says that the capital requirement of a policy can delay the emergence of profit thus reducing the value of the profits. I don't understand this because a higher capital requirement just means that more capital will need to be used and therefore whatever return earned will be less. This seems to have nothing to do with delaying emergence of profit which sounds like a "temporal" consideration. Please help me! Thank you
Sid, I don't have the reading in front of me, but I imagine the 'capital requirement' being referred to may be of two parts: 1) The amount needed to pay any day 1 expenses, commission and similar 2) The amount needed to set up a reserve for the policy. In this case, part 1) would act as you set out. However, for part 2), money which might otherwise be released immediately as profit must instead be held back to cover liabilities. This reserve would be released when the liabilities are paid off, leading to profit emerging, but later on in the process. In this way, the capital requirement delays the emergence of profit. Hope this helps.
I was thinking that a bigger capital requirement basically means that the reserving basis has been strengthened. In other words one of our assumptions has been made more prudent. So using q as the "real" morbidity rate and Q as the reserving basis parameter we should have in any year profit being released of (Q-q)*relevant figure. So if Q was bigger every year because of more prudence then it just means that more reserves will be released each year, but the underlying profit will be the same as determined by the pricing basis!!! So why is there a time-based implication? Thanks so much!
I think you're going off in a different direction entirely now! If the reserving basis is strengthened, more money must, regulatorily, be held, so less money is released as profit. The pricing basis, assuming it is up-to-date, should reflect any change to the regulatory basis, because reserves must be calculated as part of the pricing calculation too in order to work out what premium can be charged. There is no point calculating a premium based on premium, benefit and expense cashflows, only to find that the reserve assumption means money must be held back from the premium income and cannot be used to pay benefit outgo. So on the pricing basis too, a strengthened reserve assumption will delay the emergence of profit. Again, I haven't read the question, but your first post suggested that the capital requirement *can* delay the emergence of profit, whereas you now seem to be talking about an *increased* capital requirement. It might be worth considering these two scenarios separately? I don't know if that's any help or if I'm still talking round your issue, but thought I'd better try given your last post.
I'm with Pilate on this. When the policy is set up, capital is required to pay initial expenses and commission and to set up an initial reserve. However in this question, the "capital requirement" is referring to the reserve that must be held for each policy. (It tells us this much in the solution.) The profit declared year-by-year for a long-term care contract will be based on the reserves released each year (ie the decrease in reserves each year). The more realistic the capital (reserving) requirement, the smaller the reserves will be each year, ie more capital is released earlier on. The more prudent the reserves, the bigger they will be and so the later they will be released. So profit will be declared later if the capital requirement is higher. It doesn't affect the total amount of profit (not directly anyway), just when it is declared.
Whats bothering me is what I wrote in my last post - as far as I understand the reserve held will be increased by making any of the assumptions more prudent. Eg, by increasing morbidity in any year, say year j - maybe because of regulatory requirements - the reserve will increase. BUT after that year of increased morbidity,j, when the reserve is racalculated, it will not include that increased figure. So capital will be released. This capital is the sum of what was calculated by the old morbidity parameter and the increase. So all that was done by making the reserve more prudent was making a bigger capital release in that year. So, applying this effect to the whole basis, anytime we alter the assumptions used to calculate the reserve, all that will happen is that every year more capital will be released as supervisory profit. So there will be no delay in emergence of capital, only we will need to pay more for that capital. What am i missing? Thanks you
Delay of profits Your reasoning is correct, what is missing is the following: If you make the assumption less prudent in the following year, reserves will be released, and profits increased. If you now have to discount profits in order to calculate a npv of profits, then your npv will be less because there was a one year delay. 1 dollar today is not the same as 1 dollar next year. Profits have been delayed by one year, and therefore are worth less than if released immediately.
I still don't get it. You are not going to make the assumptions less prudent in the next year!!! The supervisory basis will remain the same in most cases unless for some reason there is a justifiable necessity to change it. So all that will happen is that larger amounts of supervisory profit will be released each year. And the actual profit made on the contract will remain the same. So where is the delay in profits? In other words, what I reffered to in my last post as the morbidity in year j - that didn't mean that only the assumption in year j was prudent.
Release of capital You are misunderstanding this issue. Let us assume that the supervisory basis states that morbidity rates are prudent in year j, like you said. Then the reserve calculated at the start of the contract will be higher than if the morbidity rates were not as prudent as this. As long as year j is in the future, this will affect the reserve now. When we get to the time after year j, the reserve will reduce, and the difference between what we are actually holding, and what we expect the claims experience to be, will be smaller. All the reserves that are no longer required to be held will be released as profit, but this has been delayed by j years, hence no longer as valuable as if released at outset. The basis is not altered every year, we are just keeping higher reserves because, according to the supervisory basis, we expect to pay high claims in year j, but after year j, we do not expect to pay high claims, so we release the unnecessary reserves. You must remember that profit in any given year is Premiums less claims less expenses less increase in reserves. The pricing basis helps you to calculate the premium that you will receive every year, if it is prudent, you will receive high premiums. The supervisory basis affects the increase in reserves (in our example, there will be a big increase in first year, and then minor changes in between, and then a huge decrease just after year j), the major increase will lead to losses in first year-depending on other items, and major decrease will lead to profits after year j.
