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Ch17 Q17.2 (AOS)

M

Mbotha

Member
Hi

Please can someone help me to understand why I don't get the same result if I work from expected to actual (the example works from actual to expected).
  1. Actual return on opening surplus = 86.08 x 4.5% = 3.87
  2. Expected assets at t=1: 200(1.005) - 5(1.005)^0.5 = 195.99
  3. Investment return variance (change expected return to actual): Assets are 200(1.045) - 5(1.045)^0.5 = 203.89; no change in liabilities
    • Hence investment return variance = 203.89 - 195.99 = 7.9
  4. Expense variance (change expected expenses tomavtual): Assets are 200(1.045) - 15(1.045)^0.5 = 193.67; no change in liabilities
    • Hence expense variance = 193.67 - 203.89 = -10.22
  5. Thus total surplus arising = 3.87 + 7.9 - 10.22 = 1.55
The problem seems to lie in my first bullet point - should I not be calculating actual return on opening surplus? I thought this was the E to A method (whereas A to E uses expected return on opening surplus)?
 
On a slightly different topic, does anyone know whether we need to learn the reasons for performing an AOS or AOEV? It no longer forms part of the core reading but it is one of the questions in the chapter (and I've seen it in several exam questions).
 
Mbotha said:
Hi

Please can someone help me to understand why I don't get the same result if I work from expected to actual (the example works from actual to expected).

The problem seems to lie in my first bullet point - should I not be calculating actual return on opening surplus? I thought this was the E to A method (whereas A to E uses expected return on opening surplus)?
Click to expand...

Hi - yes you are correct: that is where the problem lies.

The question specifically asks you to determine for analysis item (a) the expected return on opening surplus. Working from actual to expected (or expected to actual) is only relevant to the experience variance components, i.e. in (b) and (c).

Some companies base the "return on opening surplus" item of the analysis of surplus on actual return, and some base it on expected return. If the latter approach is taken, as has been asked for here, the excess of the actual over expected return is included in the next item, i.e. the investment return variance.

The point about working from actual to expected or expected to actual in terms of experience variances is about the process taken, and in particular it affects what assumptions are made for the other experience items that are not currently being analysed in that step. So here, for example, the solution in the course notes is working from actual to expected, therefore the expense value used in part (b) (analysing investment experience contribution) is based on actual. Your calculations above are exactly the same as in the course notes, other than that you are using expected expenses - because you are working from expected to actual, and so you haven't yet changed the expense value into its actual figure.

In both your own calculations and those in the course notes for part (b), the calculations need to be done twice: once using actual investment returns and once using expected investment returns. Whether this includes the actual return on the opening surplus or not would be a separate choice that the company makes, and isn't influenced by whether it is working from actual to expected or vice versa.

In this case, the question basically tells you what choice has been made in this regard, i.e. that the "return on opening surplus" analysis item is done using the expected return, so that the excess investment return achieved (i.e. actual less expected) falls into the next item: investment return variance.

It can be seen that you are including the excess of actual over expected investment return on the surplus assets in your answer to part (b) because you are calculating the value of actual and expected assets at the year end by using starting assets of 200, which is the total amount of assets held by the company at the start of the year and therefore includes the surplus assets. Hence if you include the excess of actual over expected investment return on the surplus assets in (a) as well (as you have done in your initial post), that is double-counting.

Consequently if you perform the calculation for (a) as stated (i.e. just the expected return on opening surplus), you will obtain the same overall surplus amount as in the solution.

Hope that is clearer?
 
Thanks, Lindsay. This makes a lot more sense now.

Just to check one more thing - it feels like the investment experience component will then always include the actual over expected return on opening surplus (because the equation used in the analyses would always consist of rolling forward the assets at time 0). Is that right?
 
Great - glad to have helped.

Re your second point: not necessarily. The company could calculate the "return on opening surplus" item using the actual investment return, and then for the investment experience variance item it could start the roll forward from assets which are equal in value to the start year liabilities (i.e. assets excluding surplus assets), rather than starting from the total assets including surplus.
 
So, in this case, the actual over expected investment return would be determined separately by comparing return on opening surplus calculated using actual return vs expect return? Or would we now not need to calculate this actual over expected source of surplus?

Sorry for all the questions! I really appreciate the help!
 
No problem!

If the company calculates the "return on opening surplus" item using actual investment return, then there is no need to calculate a separate "actual over expected return" for the surplus part of the assets, as this is already included within the return on opening surplus.

Broadly speaking a company can show the actual return on opening surplus in one of two ways within the analysis of surplus:

Return on opening surplus = actual return on opening surplus
Investment experience variance = actual minus expected return on assets excluding the opening surplus

OR
Return on opening surplus = expected return on opening surplus
Investment experience variance = actual minus expected return on all assets, including the opening surplus

All the best for the exam!

Lindsay
 
Sorry to come back to this topic but I'm a little confused by what the example on pg. 4 of chapter 17 is trying to say (relating to surplus arising from the matching adjustment)?
  • If assets achieve 2.5% (the GRY at time 0), noting that the discount rate is 2.2%, then the "extra yield reflects the difference between...actual experience and the 0.3% (fundamental spread) assumption".
I understand that it's reflecting the 0.3% (2.5%-2.2%) but what if actual return was 2.4%? Would that mean that the surplus arises out of only part of the fundamental spread?

Sorry, possibly a bit of a silly question....
 
Yes - you are correct. The company should not expect to earn the 0.3% fundamental spread because this represents the expected loss due to credit risk. However, if there are fewer defaults/downgrades etc than expected then the actual return might be 2.4%, say (i.e. credit events result in a 0.1% value reduction that year, rather than the 0.3% expected), in which case there would be surplus arising at a rate of 0.2% over the year (actual return minus the expected return of 2.2%).
 
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