Ch16 pg5: Return on Opening Surplus

[kntg24]

Hi. Can anyone explain how the bold calculation below is done? And, what is the difference between 'difference between actual and expected return on assets backing the BEL vs. on total assets'?

Thank you.

Start year balance sheet:
Assets: 2,200
Liabilities: 2,000
Surplus: 200

Over the course of the year,
actual return: 1%
expected return: 0.5%

End of the year balance sheet:
Assets: 1% (=2,222)
Liabilities: 0.5%(=2,010)
Surplus: 212

Surplus arising over the year= 212 - 200 = 12
Actual return on opening surplus= 2
difference between the actual and expected return(on assets backing the BEL)=10
Expected return on opening surplus=1
difference between actual and expected return(on total asset)=11

 

[Lindsay Smitherman]

Hi - what this is saying is that these are two different ways of explaining the additional surplus of 12 that has arisen over the year.

First approach:
Split the total assets at the start of the year (= 2,200) into the assets backing the liabilities, which are the BEL in this case (= 2,000) and the surplus assets (=200).
The actual investment return earned on the opening surplus will contribute to additional surplus arising over the year.
This = 200 x 1% = 2 (200 = surplus assets at start, 1% = actual investment return earned).
There is also surplus arising from the fact that the assets backing the BEL were expected (in the BEL calculation, via the discount rate used) to earn 0.5% but have actually earned 1%. Hence this 'difference between actual and expected return on assets backing the BEL' component = {1% - 0.5%} x 2,000 = 10
This then explains the total surplus arising of 12 = 2 + 10

Second approach:
In this case, we don't start with the actual return on the surplus assets but the expected return, giving us 'expected return on opening surplus' = 0.5% x 200 = 1 (ie now we are using the expected return of 0.5% rather than the actual 1%).
But all of our assets in total (those backing liabilities and those that comprise surplus assets at the start of the year) actually earned 1% over the year, hence we have the 'difference between actual and expected return on total assets' component of {1% - 0.5%} x 2,200 = 11 (ie this time applied to total assets rather than just to the assets backing the liabilities)
This again explains the total surplus arising of 12 = 1 + 11, but this time splitting into slightly different components

Some companies do the former (ie start with actual investment return earned on opening surplus) and some the latter (ie start with expected investment return earned on opening surplus). If you do the former, you then have to consider the actual return over expected only on the assets backing the liabilities, otherwise you will be double counting. If you do the latter, you can consider the actual return over expected on the total assets held, including the opening surplus.

Hope that helps clear this up.

 

[kntg24]

Thanks! This does help a lot.
So does that mean the increase of liabilities of 0.5% at the end of the year is due to BE based on the expected return on asset?

 

[Lindsay Smitherman]

Yes, in this simplistic example that is exactly what has happened. The BEL has increased from start year to end year due to the effect of being discounted (at 0.5%) by one year less, hence has increased by the expected return of 0.5%.

[Of course, in reality the BEL would also change due to having different cashflows to value (one year's less for business in-force at the start of the year, but then extra cashflows for new business written during the year) - but this has been ignored in this simplified exercise.]