Ch 15 AOS doubts

[Actuary@22]

I have the following doubts in Ch 16 Anlaysis of Surplus as per Acted 2019 notes,

1. Under Return on Opening surplus section,pg5
"At the end of the year, balance sheet assets will have increased by 1.0% to 2,222 and
liabilities by 0.5% to 2,010."
Please explain why liabilities have increased by 0.5%.

2. Under Economic variance section,pg6,please explain how spread on insurers own assets is 2%-"The company would therefore use a discount rate of 0.5% + (2% – 0.3%) = 2.2% pa"

3.In the numerical on page 11,iii)c),"Expenses during the year have no effect on the liability at the end of the year."
Why would the expenses have no effect?

4.In practice ques 1,iv),

• please explain why assets are taken as 4090790 everywhere in the asset calculations and not 4.5 m?

Assets: [4,090,790 + 1,000  (800 – 30)]  1.06
– 1,000  0.004469  10,000 = 5,107,747

• Why new value is carried forward?
• And whats the difference if we go from expected to actual vs actual to expected

 

[Lindsay Smitherman]

I have the following doubts in Ch 16 Anlaysis of Surplus as per Acted 2019 notes,

1. Under Return on Opening surplus section,pg5
"At the end of the year, balance sheet assets will have increased by 1.0% to 2,222 and
liabilities by 0.5% to 2,010."
Please explain why liabilities have increased by 0.5%.

Would strongly recommend updating your notes. This example has been changed and it is now in Chapter 15 (so I have updated the title of this thread). Other forum visitors will not recognise these figures, but the basic example is still there (Section 2.3, page 6).

The increase is because this is the discount rate used for the liabilities (it is the 'expected' return) and so over the period the liabilities will increase by that amount to reflect one year's less of discounting (ignoring everything else that happens over the year - as is stated in the example).

 

[Lindsay Smitherman]

2. Under Economic variance section,pg6,please explain how spread on insurers own assets is 2%-"The company would therefore use a discount rate of 0.5% + (2% – 0.3%) = 2.2% pa"

Again, the figures are different in the current version of the CMP.
The rate used to discount the liabilities is as described in the earlier chapters on Solvency II: risk-free rate + matching adjustment, where matching adjustment = spread on portfolio of matching assets (= actual yield on matching assets minus risk-free rate) minus the fundamental spread. The figures are all as given in the question and are consistent with this expression.

 

[Lindsay Smitherman]

3.In the numerical on page 11,iii)c),"Expenses during the year have no effect on the liability at the end of the year."
Why would the expenses have no effect?

Because the liability valuation reflects what the company expects to happen in the future, ie what it expects the future expense levels to be, not what actually happened to expenses during the previous year.

 

[Lindsay Smitherman]

4.In practice ques 1,iv),

• please explain why assets are taken as 4090790 everywhere in the asset calculations and not 4.5 m?

Because the first thing we do is to separate out the assets backing the liabilities at the start of the year (4,090,790) and the surplus assets (409,210). The latter contributes to the surplus arising purely through the investment return earned on it, as is determined in the first step of the analysis. We now only have to consider the remaining assets, ie those backing the liabilities.

 

[Lindsay Smitherman]

Assets: [4,090,790 + 1,000  (800 – 30)]  1.06
– 1,000  0.004469  10,000 = 5,107,747

• Why new value is carried forward?
• And whats the difference if we go from expected to actual vs actual to expected

Apologies I don't understand the first question here - could you pls elaborate?

If we went from actual to expected instead, start with all as actual and then just change each element from actual to expected in turn, rather than starting with all as expected and then changing one-by-one from expected to actual.

 

[Actuary@22]

Apologies I don't understand the first question here - could you pls elaborate?

If we went from actual to expected instead, start with all as actual and then just change each element from actual to expected in turn, rather than starting with all as expected and then changing one-by-one from expected to actual.

By why the new value is carried forward I meant that,the reading states that
Now change each element from expected to actual in turn and, for each step, calculate the effect
on both assets and liabilities. Each time the value of assets or liabilities is changed, the new value
is carried forward to the next step.

So while calculating mortality surplus for instead (5,127,737 – 5,114,959) – (5,113,047 – 5,107,747) = +7,478
Why are we only not doing (5,127,737 – 5,114,959)?

 

[Lindsay Smitherman]

If working from expected to actual, we need to leave everything we have already changed to actual as actual for each step - and then change one more thing from expected to actual. That means that we are slowly converting each experience item from expected to actual, until we end up with everything converted to actual - which gives us the right finishing point. Otherwise, we won't get answers that add up to the correct amount overall.

For each step we are calculating the surplus arising from just the item we have changed for that step. So the contribution to surplus arising from just that item must be the new surplus (with that item now as actual) minus the surplus from the previous step (when that item was as expected).