Hi, I had a doubt regarding the retrospective method under Section 4.1 It is mentioned that "Except by chance the surrender value will not run into the maturity value" why would this happen for without-profits contracts where on the contrary in the prospective method , the surrender value will run into the maturity value?
Hi Sayantani The most commonly used retrospective method is the asset share. This is the accumulation of the past premiums less expenses and less claims using the actual experience of the insurer. As such, it represents the money that a particular policy has contributed to the insurer. The insurer will have priced the contract so that at maturity the asset share should be more than the maturity value so that the insurer has made a profit. So the asset share will only equal the maturity value if experience is worse than expected by exactly the right amount to cancel out all the expected profit precisely. The prospective method will calculate the present value of the future claims plus expenses less premiums (just like most reserving calculations). The maturity value is one of the possible claims that is being discounted here. So as time goes by and more of the claims / expenses / premiums before maturity have been paid, this method inevitably approaches the maturity value. Best wishes Mark
Hi Mark, Thanks for the reply above. It makes sense. I had doubts related to Section 5.2-Retention of Profit 1. It is mentioned here that "If these surrender value assumptions exactly represent future experience, then the total profit retained will be the same as the contract had not been surrendered." Could you please explain what is the meaning of these lines and also how does EAS - SV' represents the profit that has been made to date? 2. Next doubt is the meaning of these lines: " the difference between the asset share and the premium basis value gradually grows because of the margins in the premium basis, which is why the Core Reading mentions this as sensible measure of 'profit made to date'(Profit A in diagram). It is one such measure , although we have seen other measures such as change in embedded value"
Hi Sayantani 1. If the surrender value is equal to the present value of the cashflows that would have been paid if the contract was not surrendered, then it makes no difference to the insurer whether the contract is surrendered or not. So the insurer makes the same profit from the surrender as it would have made if the contract had continued. The reason why EAS - SV' is the accrued profit to date is explained by the graph on page 14. At the start of the contract EAS-SV' is equal to zero, and at the end of the contract EAS-SV' is equal to the final profit. This makes sense as the accrued profit should start at zero and gradually grow to equal the final profit. See you also the answer to 2. 2. The premium basis is calculated with margins, eg the investment return will be prudently low. So the asset share will hopefully grow at a faster rate as it is based on the actual experience, rather than the prudently low growth rate in the premium basis calculation. So the difference between the two lines is a measure of profit to date as it represent the better than expected (according to the premium basis) experience so far. This is just one way to measure profit, but it ignores factors such as the cost of capital in holding reserves, so perhaps other measures of profit such as embedded values would be better for some purposes. Best wishes Mark
Hi Mark, Thanks for the reply above. It is a bit clearer now. However I am still not very clear as to how EAS - SV' is the accrued profit to date and how it gives the final profit at the end of the contract. Is it possible to explain this in the form of the equations or perhaps a numerical example. Also in the second point is it possible to explain this how the SV' compares with the EAS in terms of margins with the help of an example?
Hi Sayantani We'll do a very simple calculation so we can focus on the principles. Consider a 2 year single premium without-profits endowment. We'll ignore expenses, mortality and withdrawals. So we'll just focus on the investment assumption. The single premium is 100. Let's assume that the best estimate of future returns is 10% and that reality turns out to be exactly the same as expected. Then the asset share AS_t at each future time t is: AS_0 = 100 AS_1 = 110 AS_2 = 121 Now let's assume that pricing is performed using margins in the investment assumption, let's say 8%, and that there is no explicit profit margin (this is the assumption used in the formulae and graph in the notes too). On this basis the sum assured is SA = 100 x 1.08^2 = 116.64. Calculating the reserve V_t using the same basis as the premium basis (which is the assumption used for SV') gives us V_0 = 100 V_1 = 108 V_2 = 116.64 If we were to use the above numbers as the surrender values we would get the following profits: AS_0 - V_0 =100 - 100 = 0 ie no profit - we haven't accrued any profit yet as the contract has just been sold AS_1 - V_1 = 110 - 108 = 2 ie the profit accrued so far because we earned an extra 2% interest on the investment AS_2 - V_2 = 121 - 116.4 = 4.6 ie the extra 2% of interest for the two years. This is the total profit. The insurer has assets of 121, but only needs to pay out 116.64. I hope that helps to make it clearer. Best wishes Mark
Hi Mark, Thanks a lot for the above example. Yes the above example clears the concept. I have another doubt from the Practice Questions-Question 21.3 1)In the solution to part i) it is mentioned that "The main reason for loss will be the heavy initial expenses compared with those implicit in the premium basis and perhaps also investment returns to date below the premium basis guarantee." When we are talking about loss from surrender value we are mentioning the premium basis, is it because ultimately the profit/loss is being broken up in terms of Profit A and Profit B where Profit A is the difference between EAS and prospective value of policy on premium basis? 2)the second doubt is in Solution iii) It is mentioned that "the realistic interest rates should be higher than assumed in the new premium rates thus avoiding the surrender and re-entry option" Do the above lines mean that if realistic interest rates are higher, then the prospective value of the policy on a realistic basis would be low which means the surrender value would be low as compared to the premium rates and hence it doesn't give the incentive to the policyholder to surrender at a high value and re-enter with a low value premium? 3) "If the company is mismatched due to being invested too long, and interest rates were to rise then the earned asset share would fall by more than the prospective value, even if the latter were calculated at the new proposed higher interest rate" Why would the EAS fall by more than the prospective value?
Yes looking at profit A we would make a loss if actual experience in the asset share was worse than predicted in the premium basis, assuming that the premium basis calculation is used to set the surrender value.
This isn't quite right. Note that the policyholder is not surrendering the policy. They are altering it and we are considering how to value the altered policy. Let's assume that the policy was originally priced at 4%, but the interest rates have now gone up to 6%. If we valued the altered policy at 4%, this would make the altered policy look expensive compared to a new policy valued at 6%. So the policyholder would lapse and re-enter. If instead we value the altered policy at 6%, then the policyholder will get a better deal and so will not want to lapse and re-enter.
If the assets are invested too long that means we have assets with term of 10 say, when the liabilities have term of only 5 say. Changing interest rates have a bigger impact on the cashflows with the longer term, as there is more discounting. Interest rates going up pull the value of the cashflows down. So the longer term assets will fall by more than the liabilities. The asset share behaves in the same way as the assets as it is calculated using the actual best estimate return. Best wishes Mark
I was wondering what the principle: "treat surrendering and continuing policyholders equitable" actually meant? For instance, does this mean that both types of policyholders contribute the same amount of profit to the company (hence surrenders will be very low at beginning) or is a balance struck where policyholders surrendering early contribute some profit to the company but not the same amount as a continuing policyholder (they contribute less than the continuing policyholder who may surrender later e.g. perhaps only profit released upto the point of surrender rather than profit released from future experience). Also i was wondering whether we should know the surrender principals for with profit contracts. The September 2000 paper (Question 1) discussed with profit surrenders and discussed items I hadnt considered before - "Where a policy surrenders close to the outset of the contract, it is likely that the asset share will be significantly less than the accrued premiums paid. It is important that the policyholder is not given an expectation that the value will be consistent with the premiums paid at early durations and that all reasonable steps have been taken at the point of sale to explain the expenses incurred in setting up the contract. This is usually best illustrated by supplying example surrender values for the first few years. Given the management of the policyholders’ expectations the company can then decide whether it will pay out more than the asset share in these early years so the policyholders do appear to get a fair value. At the other end of a policy’s lifetime it is important that the surrender value smoothes into the maturity value over the last few years of the contractual policy term. The smoothed asset share would apply at maturity as per the company’s philosophy and policy, and no termination charge should be applied." I thought we should aim to pay approximately the premiums paid at the beginning? Also what is the companies maturity value for a with profits contract? Expected payout amount?
Hi Different people will have different views on what constitutes fairness. It's not something we can give a definitive answer on. However, the suggestions you make are all common interpretations of fairness. In the exam, briefly discussing these could score marks. September 2000 is a very old question - I'm not sure what was in the syllabus back then. The current syllabus covers without-profits surrenders in detail and briefly covers unit-linked. The course does not give a list of principles for with-profits contracts. With-profits maturity payouts are usually set with reference to asset shares, subject to smoothing and any guarantees. Surrender values are also often based on asset shares, subject to smoothing and guarantees, although as the solution mentions, the surrender value might have to deviate from this in the very early years. Best wishes Mark
