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Analysis of Surplus

A

actuaryinmaking

Member
Hi,

Can someone please explain what the difference is when going from actual to expected vs expected to actual.

I believe the question in Chapter 16 part iv went from expected to actual. What would the method be if we went from actual to expected for say the Expenses section?
 
Hi

Yes, the solution to part (iv) is working from expected to actual.

If we wanted to work from actual to expected, we would want to start with all items being calculated using actual experience during the year, in particular the assets at the end of the year being calculated as :
(4090790+1000*(800-25))*1.10521-3*10000 = 5,347,720

If expenses was going to be the first source of surplus we analysed, then we'd change from actual expenses (of 25) to expected expenses (of 30) in this calculation and identify how much impact that had on surplus arising.

We'd then keep that expense figure changed to expected, and change the next item from actual to expected, and so on...

Hope this helps
Lynn
 
Thank you Lynn! That makes a lot of sense.

Just to confirm, would we also work out the liabilities at the end of the year as the below?
997 x (10,000 x 0.85595 + 25 x 3.745 – 800 x 3.745) = 5,640,154
 
Hi, just one tweak to that I think - there's no mention of the expense basis changing, so still want to use 30 (rather than 25) as the expenses. (This is because the liabilties calc is prospective, ie forward-looking at the end of the year, and the 25 relates to the year just gone.)
 
Ah because for the end of the year liabilities, we are technically calculating how much we need to hold for the next year taking into account the number of policies in force at the end?

So the actual expenses is 25 for the year we are looking at, but in the valuation basis it still mentioned expenses at 30 so we assume 30 for the following year?
 
Thank you Lynn!

Sorry one more question on Analysis of Surplus. In assignment X4.1 part iii) it asked to describe other components that might have been included in the full analysis of surplus.

"Changes in economic assumptions, eg risk-free rates, inflation, exchange rates. If the economic assumptions change, the effects may be shown separately from the economic experience variance items. Changes in non-economic (insurance) assumptions: eg mortality, withdrawals, expenses. If the non-economic assumptions change, the effects may be shown separately from the non-economic experience variance items."

What's the difference between the change in economic/non-economic assumptions vs the experience variance items? Is this saying if the company changed its mortality basis part-way through the year for example?
 
"Run the adjusted model with the new non-economic assumptions to obtain the impact on the surplus from these assumption changes. Ideally, the assumptions should only be changed from the new valuation date so that experience variances are relative to the start year best estimates. Taking this approach to the process will enable the company to identify ‘changes to insurance assumptions’ as a separate item from ‘insurance variances’"

I've just seen this in the notes which I think I understand - but why would we change the assumptions from the new valuation date?

Would you be able to provide an example to explain this please?
 
I'll try a simplified example and see if it helps (fingers crossed!)...

Imagine there's a payment of 121 to be paid in 2 years' time. Let's ignore mortality, expenses, .... ( I like my numbers easy!) and consider only discounting. Let's assume a discount rate of 10%.

At time 0, if we have Liability = 121 discounted for 2 years at 10% = 100.
Suppose time 0 Assets = 100, so the starting surplus is 0.

When we get to time 1, if actual investment return in the year had been 10%, then assets would be 110. And if we didn't change the assumption, the liability (now discounting for just 1 year) would also be 110. So, no surplus arising between time 0 and time 1.

So, let's consider instead the situation at time 1 if actual investment return in the year had been 12% and if we changed the discount rate assumption to be 7%. So, time 1 assets of 112 and liabilities of 121/1.07 = 113. Surplus arising of -1.

When doing the analysis, we want to break this down as an experience variance (difference between actual and expected experience during the year) item of +2 and a 'change in assumption' item of -3. So, we want only want to change assumptions from the new valuation date and to compare the experience during the past year with the assumptions we had been making for that year.

Not sure how much any of that helps, but hopefully at least a little!
 
Hi Lynn,

Sorry just one more question on a Tutorial Day 2 Question 8ii. We perform an analysis of surplus here from expected to actual. I understand the main calculation but not 100% sure why this first bit was done?

Now set allocated assets equal to SoY liabilities. (especially this bit, why didn't we stick to 15million?)
Then if everything is as expected we find that EoY assets would have been:
(12,310,560 x 1.06) – (1,236 x 970 x (1.06)0.5) – (618 x 30 x (1.06)0.75) = 11,795,462

EoY liabilities would have been 970 x 1,236 x 9.8384 = 11,795,455

So as expected, there is virtually no change in surplus: zero on allocated assets minus liabilities at start of year, 7 at EoY.

Many thanks!
 
Hi

Allocating total assets held at the start of the year into {assets = start year liabilities} + {start year surplus assets} can be a really useful starting point for the analysis of surplus.

This is because you can now calculate the {investment return earned on surplus assets} component directly.

And because if you roll forward {assets = start year liabilities} to the year end using the 'expected' basis, you can check that this amount (roughly) equals year end liabilities. So it helps to validate the analysis.
 
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