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ST4 April 2013 Q1

D

dominic

Member
Hello,

The alternate solution to part ii) states that the expected assets are calculated using the interest rate of 6%, i.e., 65×1.06^3+5×(1.06^2.5+1.06^1.5+1.06^0.5) =£93.8m and the actual assets are calculated using the investment return of 7%, i.e., 65× 1.07^3+5×(1.07^2.5 + 1.07^1.5+ 1.07^0.5) =£96.3m.

However, I was wondering why the investment return of 7% is not used in part i) instead of 6% when calculating the actual actives?
I am happy that the expected actives uses the 6% and gives £66.2m.
Whereas I thought that the actual actives should be something like:
( 50*1.07^3 )x(1.03/1.04)^3 +0.24x8x(1.03^0.5x1.07^2.5 + 1.03^1.5 x 1.07^1.5 + 1.03^2.5 x 1.07 ^0.5 ) =£66.2 ? Do you know why this 1.07 (7% investment return) is not used in the provided solution?

Many thanks

Dom
 
Hi Dom

Good question! Part (i) asks us for the actuarial gain / loss over the intervaluation period in relation to active member liabilities. We would typically consider this to be one element of an analysis of surplus (AoS) calculation. Full AoS is discussed in detail in Subject SA4.

When we conduct a full AoS we assess separately the financial impact of each element of experience (investment returns on the assets, salary increases, pension increases, mortality etc) deviating from what was expected. And the broad approach is to calculate for each element, "actual value minus the expected value".

So, for investment returns on the assets, we would calculate the expected value of the assets if they had returned the discount rate and compare this with the actual value of the assets.

Having calculated the financial impact of that element, we use expected figures, ie the discount rate, in calculating other elements, otherwise we can end up double-counting the impact of a deviation.

So when assessing the actuarial gain / loss on the active members liabilities, the examiners have used the discount rate. The impact of the actual return on assets of 7%pa being different from the discount rate would be assessed separately and would be considered to be an asset issue rather than a liability issue.

I hope that helps.
 
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