Cp2 - April 2020 - Paper 2 - Summary Doc Q

[Darragh Kelly]

Hi,

I have a couple of questions regarding the IFoA's summary doc sol for the April 2020 paper 2.

My first question is regarding the following paragraph from the results section of the summary doc, specifically page 5 of 8:

Under the annual guarantee scenario if the guarantee was never hit then the mean fund value after the 10 years would be approximately $152,240 ´ 0.98510 = $130,885. As the mean return is higher than this it indicates the guarantee is hit in some scenarios.

These results indicate that the charges taken for the guarantees are greater in value than the average benefit expected to be gained by Mr White. How do we know that the results indicate that the charges are greater then the avg benefit? For example, for the annual guarantee option the average charge is worth $152,240 minus $130,885 = $21,355, whereas the benefit is $147,322 minus $130,885 = $16,437. For calculation of the average value of the guarantee charge, am I correct in saying this is just average fund value without guarantee charge minus average fund value with guarantee charge? The guarantee itself has to be stripped out as we are looking at the value of the guarantee charge in isolation? In the spreadsheet I tried to calculate the average charge a different way - I took the total fund value for each year and multiplied it by the guarantee cost (1.5%), and then summed all costs over 10 years. Then I took an average of this sum across all 100 simulations. My figure was 20,596 < $21,355, so wondering why they don't match. Similar reasoning for the calculation of the average value of benefit, it's the average fund value with guarantee minus average fund value without guaratee? Again I tried calculating the average value of the benefit a different way - I calculated fund value with guarantee minus fund value without guaratee for each year, then summed together for all 10 years, and then averaged across all 100 simulations. But I was quite away from the $16,437 value. This is reasonable as the investment company will expect to make a profit on the guarantee they are providing.

My second question is regarding the following paragraph from the results section of the summary doc, specifically page 5 of 8:

Similarly the overall guarantee option has an expected fund value after 10 years of approximately 97% of the value with no guarantee option. So whilst 15% of the fund is taken as a charge at the start of the investment, the expected result is significantly higher than 85% of the no guarantee option, which shows the value added by the guarantee provided. I dont follow the second sentence in this paragraph.

Many thanks,

Darragh

 

[Sarah Byrne]

Hi Darragh

Q1:
Here, the examiners are saying that the expected return without the guarantee is $152,240. Under the annual guarantee scenario, the charge is 1.5%. So, if the guarantee never bites, the only different between the no guarantee scenario and the annual guarantee scenario is the charge, which would reduce the expected return to $130,885.

We could say that the difference between these values is the 'cost' to Mr White of having this option, ie 152,240 - 130,885 = 21,335.

We can compare this cost to the difference in the expected return under the annual guarantee scenario of $147,322. This suggests that the expected benefit Mr White can expect from the option is 147,322 - 130,885 = 16,437.

So, it costs Mr White 21k but he is only expecting an increased return of 16k (so the charges are less than the benefit).

It sounds like you tried to do something similar with is good. Your numbers may have differed as these are very much estimates (which is fine in the exam). It isn't the end of the world if your values differ, the thought process and comments would have been more important as long as you did something sensible.

Q2:
For the overall guarantee scenario the charge is 15% at the start of the policy. So, with a 15% lower investment amount, if the return was the same as under the no guarantee scenario, we would expect the final value to be 15% lower (129,404). However, under this scenario the return is actually expected to be $148,407, which is 97% of the no guarantee scenario. This difference is being made by the guarantee (although the return is still lower than under the no guarantee scenario).

As always, remember that there were other comments/observations that could have been made without carrying out these exact calculation. We've presented a slightly different view in our ASET document. The important themes to note here were that whilst the overall return as lower under the guaranteed scenarios, the standard deviation was lower.

Sarah

 

[Darragh Kelly]

Thank you Sarah for the detailed reply! Was great!