For ST2 Q&A Part 1 question 1.12 (ii), I don’t really get the solution for the mortality part, the first point, it says “the death benefit will be higher than asset share at early durations and so for this part of contract looked at isolation, higher than expected deaths would lead to a loss” I thought during the calcuation of asset share (for particular individual policy), we explicitly take off the cost of death benefit, say 0.01 * 100k where 0.01 is the expected death benefit and 100k is the death sum assured. If there is a higher than expected death, let's say actual is 0.018, then company would need to take off 0.018*100k, so is facing a loss of 0.008*100k? Am I corrrect here? If like the solution says, the death benefit is higher than asset share at early durations-my feeling is that this is true for all policies. So now let’s assume the reality turns out to be exactly the same as expected, for a particular policy (say which we’ve expected he would die), at the early duration, death benefit must be higher than asset share, so the policy is still making a loss even though our expectation turns out to be true. Am I corrrect here? If not, how should I interpretate the soluation here? Thank you very much in advance!
Hello I'd suggest interpreting the solution along the lines: A policy's asset share at any point in time is the amount that the company has accumulated in respect of that policy. If a policyholder dies, company has to pay out the death benefit. If this death benefit is greater than the asset share at that point, then the amount the company has to pay out is more than the amount the company has. So, the company makes a loss for each policyholder who dies. The company will have expected some policyholders to die (and so some losses to happen), but if more than expected die there will be bigger loss than expected. In terms of what then happens to the asset shares, you are right that asset shares do make a deduction for the cost of death benefits. Remember that asset shares are iterative, retrospective calculations reflecting actual experience. So an individual asset share might build up along the lines: AS(t+1) = [ AS (t) + P - E](1+i) - q x (DB - AS) where q is the actual mortality rate. It's the final term that's of interest to us here. q reflects the actual rate of deaths among a group of similar policies, and (DB - AS) is the loss made on each death. The more deaths there are, the smaller AS(t+1). Later on in the term of a with-profits policy, these smaller asset shares might result in lower terminal bonuses, ie less being paid out to policyholders. However, early on in a with-profits policy, the guaranteed benefits will be much bigger than the asset shares, so these losses are the company's problem. You're right that the company is still making a loss on deaths, even if they are as expected. But the company will have allowed for an expected level of deaths when setting the premiums/benefits. So, it is any higher-than-expected level of deaths that is the remaining risk. Hope this helps clarify things. Apologies - this reply ended up being more long-winded than I intended Lynn
