April 2014 Q1ii Geometric mean

[Satya]

I have a question on how the geometric mean is calculated in this question.

The question says "The smoothed asset share will increase at the end of each year by the three year geometric average of the most recent and two preceding years' with-profits fund earned investment returns"

So let's say the returns for the last 3 years are 1%, 1%, 5%.
And let's say we start with £11,000 and want to accumulate it by one year.

The way ASET accumulates this for one year is as follows:
11000 * (1.01 * 1.01 * 1.05)^(1/3) = 11254

Whereas the way I did it was:
11000 * (1 + (5% * 1% * 1%)^(1/3) ) = 11188

These lead to different answers. I believe my way to be the correct way with reference to the question wording.
However would anyone be able to tell me where my logic is going wrong? Or are both answers likely to be acceptable?

 

[Lindsay Smitherman]

Hi - the way that the calculation is performed in ASET (and the Examiners' Report) is the correct method.

For compounding investment returns, as we have here, we need to add 1 to each of the returns before taking the geometric average. Otherwise, there would be problems with negative returns (eg consider what the results would be if the returns were -5%, -1% and 1%).

You may find the following a helpful reference:

https://www.investopedia.com/ask/answers/06/geometricmean.asp

Having said that, you would likely lose just a half mark, or possibly not even that, for such a small difference in approach - so don't worry about things like this. The examiners are looking more for understanding of how the asset shares and guaranteed benefits build up for such products.

Hope that is reassuring.

 

[Satya]

Thanks Lindsay! That clears things up.