Following on from the above, I tried to do this question starting with return on opening surplus calculated using expected investment return - i.e. the valuation rate of interest at the start of the year (the question calculates the actual return on opening surplus). I've also stuck to working from expected to actual for the experience variance items. Expected return on opening surplus = (409,210)(1.06) = 24,552 To calculated the experience variance items, I have the following starting point: My projected liabilities are the same as in the question = 5,107,422 My projected assets use the total assets at the start of the year (4.5m) - i.e. including surplus assets = 5,541,510 For each experience variance item, I've changed the relevant item from expected to actual (so my workings look the same except that assets use the 4.5m rather than those sufficient to meet the liabilities at the start (i.e. 4,090,790) Expense surplus = 5,300 Mortality surplus = 7,153 Investment return surplus = 238,430 Surplus from change in valuation basis = -543,863 My 5 items of surplus = 24,552 + 5,300 + 7,153 + 238,430 - 543,863 = -268,428. This results in a difference of 396 relative to the surplus arising calculated at the start of the question. Can this be attributable to "rounding errors" (it seems too large) or have I done something wrong? Any assistance would be appreciated.
Your description of the method here is perfect. I think you made a small calculator error in the mortality surplus. This should be 7,478, ie the same as the solution that uses actual return on surplus. The remaining difference is then sufficiently small to be ignored. In your approach the only thing you have changed is the assets allocated to the analysis. This will make the assets bigger by the same amount in both the old and new calculations in each step except for the investment surplus. So the difference in the assets cancels and you will get the same contribution to surplus for expenses, mortality and change in basis. Best wishes Mark
Thanks so much for looking at this, Mark. I can't seem to find my error though. For the mortality surplus, my calculation looks like this: Assets (using actual mortality): same as in the solution except for using assets of 4.5m = 5,561,500 Liabilities (using actual mortality): exactly the same as in the solution = 5,114,959 Mortality surplus = (5,561,500 - 5,114,959) - (A1 - V1) = 7,153 where: A1 = assets calculated in the previous step (using actual expenses) = 5,546,810 V1 = initial projected liabilities (since they aren't impacted by actual expenses) = 5,107,422 I'm also a bit confused about the process now. Am I right in saying that, if we're calculating actual return on opening surplus, then the rest of our analysis needs to use assets excluding surplus assets (otherwise we'd be double-counting the actual over expected return on opening surplus in our investment surplus component)? And conversely, if we were calculating expected return on opening surplus then the rest of our analysis, we should use assets including surplus assets? Thanks for your help!!
Thanks for showing me these steps. Your answer is actually correct - there are two valid approaches to doing this. For V1 you have used the value calculated in the solution of 5,107,422. This should also be the same as the asset allocated to the liabilities at the end of the year, which the solution calculates as 5,107,747. These two numbers should really be the same, so we can use them interchangeably. However the solution explains the difference in italics: "This is 325 less than the assets figure, but is due to a lack of decimal places in the commutation functions and amounts to less than 0.01%, so can be ignored." I'm sorry for the confusion. Mark
