ASET April 2015, 2iii

[studentactuary15]

Hi, I am really confused with the way the solution is wrote for this Q. What I would have written is the following (very draft points):

• Set assets using BEL assumptions at t.
• Set assets using actual mortality assumption at t.
• Project them to t+1.
• Find difference for the profit/loss.
• Repeat for other actual decrement assumptions and other non-economic assumptions like expenses, surrenders, etc.

The solution mentions "Assets are allocated to the contracts equal to the value of the BEL at the beginning of the year". Why don't we just call this the BEL then? If it's using the same assumptions as the BEL, i.e. the best estimate assumptions. These assets (with the BEL assumptions, and the BEL, are projected to the year-end. The profit would of course be zero... Then it says steps 2 and 3 are repeated and then it says 4 and 5 are repeated... It seems very confusing which I think might be because they are trying to be as clear as possible - but for me at least, it did the opposite and confuse me.

Is what I wrote for my version of the answer in the ballpark of the actual answer?

 

[Em Francis]

Hi, I am really confused with the way the solution is wrote for this Q. What I would have written is the following (very draft points):

• Set assets using BEL assumptions at t.
• Set assets using actual mortality assumption at t.
• Project them to t+1.
• Find difference for the profit/loss.
• Repeat for other actual decrement assumptions and other non-economic assumptions like expenses, surrenders, etc.

The solution mentions "Assets are allocated to the contracts equal to the value of the BEL at the beginning of the year". Why don't we just call this the BEL then? If it's using the same assumptions as the BEL, i.e. the best estimate assumptions. These assets (with the BEL assumptions, and the BEL, are projected to the year-end. The profit would of course be zero... Then it says steps 2 and 3 are repeated and then it says 4 and 5 are repeated... It seems very confusing which I think might be because they are trying to be as clear as possible - but for me at least, it did the opposite and confuse me.

Is what I wrote for my version of the answer in the ballpark of the actual answer?

Hi
‘Set assets using BEL assumptions’ doesn’t really make sense as you would only use assumptions when projecting.

The reason why assets are allocated to BEL is to ensure there are no surplus assets at the start of year and if they are both projected using BEL assumptions then assets will equal BEL at end of year with no year-end surplus.

The profit emerging is then the difference between BEL and actual assets (ie not due to start of year surplus).

This profit can then be analysed by changing each item (one at a time) from their expected start of year BEL assumption used, to actual experience, before projecting. After projecting, the new profit emerging will be deducted from the previous to calculate the experience's contribution to profit.

You also don’t need your second point (‘Set assets using actual mortality assumption at t.‘) as the company will already have the value of the year-end assets.


Hope this makes sense.


Thanks

Em

 

[studentactuary15]

Hi
‘Set assets using BEL assumptions’ doesn’t really make sense as you would only use assumptions when projecting.

The reason why assets are allocated to BEL is to ensure there are no surplus assets at the start of year and if they are both projected using BEL assumptions then assets will equal BEL at end of year with no year-end surplus.

The profit emerging is then the difference between BEL and actual assets (ie not due to start of year surplus).

This profit can then be analysed by changing each item (one at a time) from their expected start of year BEL assumption used, to actual experience, before projecting. After projecting, the new profit emerging will be deducted from the previous to calculate the experience's contribution to profit.

You also don’t need your second point (‘Set assets using actual mortality assumption at t.‘) as the company will already have the value of the year-end assets.


Hope this makes sense.


Thanks

Em

Hi, really sorry to ask a follow-up question on this. I don't think I still fully understand this concept. Is there any chance you could provide a simple numerical example please (for example in mortality profit)?

My guess would be, if finding the analysis of surplus, we can evaluate (say) 2019 to 2020.

• At end of 2019, the BEL was calculated to expect 4 deaths which is a BEL of 200 for the year of 2020.
• Then we need to do a restatement of this for end of 2020.
• Roll this 200 forward allowing for the risk free discount rate, matching/volatility adjustment.
• This then becomes X = 205 => this is the 2019 BEL reinstated for 2020.
• Then looking at actual experience, we see that at end of 2020 there was only 1 death, so the actual liability was (say) Y = 50.
• The surplus arising from BEL in 2020 for mortality is X - Y = 205 - 50 = 155.

Am I on the right lines or am I completely lost?