Hi David
This was a tricky and unusual question, so I can understand it being tricky to get your head fully round. I'm assuming you've been using The Vault, or Revision Booklets for this, rather than the IFoA's solutions? (Not a problem either way, I'm just assuming you've already seen the explanation in the Vault, which talks about the "relatively large" DSAR - the IFoA solution doesn't use that wording).
I'm assuming you're comfortable with parts (i) and (ii), which are more mathematical in nature. so in part i) you show calculate the mortality profit of EDS - ADS. In this case, ADS is bigger than EDS, hence we have a mortality loss of £1,926.
Usually when you have a question like this, you have a group of identical policies - so all policyholders are the same age, same assumptions, same sum assured etc. So in such circumstance, ADS being bigger than EDS, for a whole life policy, can be intuitively understood as "more people have died than expected during the year, each death is a 'bad thing' for the insurer, as more money is paid out now rather than in later years, hence we have a mortality loss". But if you have non-identical policyholders, with eg different sums assured or similar, it may not quite be so simple.
Remember death strain isnt defined by "how much more money is paid out" but "how much more money is paid out compared to the reserve that would have been set up at the end of the year".
The individual death has definitely led to a death strain (as you would always expect for a death under a whole life). For that one life, the insurer has paid out £15,000, rather than setting up a reserve of 4,938.59. Hence the actual death strain is £10,016. But if a different individual person had died, the death strain would have been different. And what matters isnt the absolute amount of the payout, but the difference between the amount of payout and the reserve that would have been set up for them.
The expected death strain, across the entire group, was £8,090.62, but this isn't based on specific people dying. Essentially it assumes (conceptually!) that 2.222% of each person dies (!) Or, perhaps more realistically, 2.222% of the group dies, but keeping the relative proportions of the different policyholders the same.
So when, in part (ii) you calculate the expected death claims for the whole group of £16,447.24, this again assumes it's "on average" the average members who are dying.
So in part (iii) what's essentially happened is that the insurer has paid out death claims of £15,000, which is slightly less than the £16,447.24 expected. If all policyholders had identical ages, sums assured, characteristics, reserves etc, that would imply a lower ADS than the EDS. But in our case ADS is higher than EDS. So it must be that the person who actually died had a larger sum assured relative to the reserve that they would have had set up had they survived the year than the "average" member of the policyholder group. And hence a larger (relative) DSAR than average.
FWIW, the question doesnt suggest why that might be the case and I don't think we'd need to go into that...but it could be to do with how the reserve is calculated - for example expense loadings or similar. If you look at it from a slightly different perspective, you could say that the total benefits paid out over the year have been less than expected, but I would expect the total end of year reserve across all policyholders to be higher than expected. And it's that interaction which "matters", rather than just the total payout.
Hopefully that helps? It is a tricky one to get your head around though, I agree
