Assignment X2.1

[almost_there]

It's not clear to me why the monthly compared to lump sum would have a higher effective charge % deducted over 5 years?
The initial charges on both would be the same amount, I understand that.
However when you pay monthly then the fund is smaller, so the fund growth is smaller, so smaller annual fund charges deducted compared to a lump sum. Therefore I don't get how it would be a 2.5%pa effective charge compared to 1.5%pa?

So if you pay monthly then it's £2000 invested in year 1 compared to £10,000 in the lump sum.
Initial charges ignored for now.
Growth of 5% on the £2000 makes it £2100. Fund charge of 1% = £21.
Lump sum £10,000, growth 5% makes it £10,500. Fund charge 1% = £105.

Do this over 5 years and clearly annual charges on lump sum are higher overall.

 

[almost_there]

Hi, I'd really appreciate the thoughts of an acted tutor here. It seems obvious to me more charges would be deducted from the lump sum rather than regular premium, with all else being equal. So why does the question say higher effective charge from the regular premium?

 

[David Wilmot]

Apologies for the delay in responding due to travel & teaching commitments. Have a look at the attached rough spreadsheet (that wouldn't pass CA2!) - which for simplcity is based in annual rather than monthly contributions. Does this clarify the point being made?

 

[almost_there]

Does this clarify the point being made?

Hi. OK yes I see the required calc now. However your answer falls short of the 1.55% that it states in the question? Also the lump sum effective charge is quite short of 2.5%... I can appreciate you've done it annually not monthly but still...?

I interpreted the situation in the question as saying you could replace the initial and annual charges with an effective 1.55% pa charge and get to the same place at t = 5. So you'd roll up the lump sum at a factor (1-1.55%)*1.05 each year.... in other words £10,000*[(1.05)(1-1.55%)]^5 = £11,804. This does not match the £11,856 in the question, which confused me.

It seems also only on the final roll up to t = 5 does the annual payment's charges exceed the lump sum charges. Not exactly intuitive... hang on, shouldn't cell B27 be applying the annual % charge i.e. D5 not D4? When I make that correction the lump sum deducts more charges than the annual... (907 vs 721)

 

[almost_there]

I think the question should have said 1.45% not 1.55% then?

 

[David Wilmot]

shouldn't cell B27 be applying the annual % charge i.e. D5 not D4? When I make that correction the lump sum deducts more charges than the annual... (907 vs 721)

Oops... yes... quite right - apologies for this error in my spreadsheet. Correction attached.

I've gone on to add another section to the spreadsheet, which looks at the effect (p.a.) of the initial charge on each of the annual investments in turn. I've then taken an average which comes out at 2.17%. Do you agree with these calcs? If I haven't made another slip, this illustrates the point being made in the solution where it says that "the average charge is higher than that quoted for a one-off invstment", because 2.17% > 0.95%.

So, in summary, I think that the 1.55% stated in the question is indeed wrong (see my post on another thread on this forum). However, I think that he solution is correct in making the statement quoted above. OK?

 

[almost_there]

Hi, sorry but I still find the statement "the average charge is higher than that quoted for a one-off investment" really unclear as that would seem to suggest we pay higher charges on the regular premium... but we don't as just £475 gets deducted as initial charges in both cases.

Anyway due to 907 > 721 then please confirm these parts in the question are also wrong then:

• Total charges for monthly contributions totalling £10,000 over 5 years have the effect of absorbing approximately 2.5% pa over the 5 year period
• Your manager has queried why , in respect of monthly investments, the effect of charges is so significant

 

[David Wilmot]

Hi, sorry but I still find the statement "the average charge is higher than that quoted for a one-off investment" really unclear as that would seem to suggest we pay higher charges on the regular premium... but we don't as just £475 gets deducted as initial charges in both cases.

Yes the amount deducted as a result of the initial charge is the same, but the effect of this charge is different for a single investment, when compared to a series of regular investments - as shown by the spreadsheet calculations. This statement you refer to would indeed be ambiguous if it hadn't ben preceeded in the solution by two lengthy explanatory paragraphs that make clear what is meant when referring to the "average charge".

 

[almost_there]

No sorry your question specifies charges absorbing 1.55% pa, then incorrectly states for monthly it absorbs 2.5%. Should have said 1.42% and 1.24% respectively. So the question is wrong.

 

[Anacts]

I think I can agree the numbers in the question (although we're not actually asked to check them and so for the time allowed in CA3 I think you would just go with them as they look reasonable to me). They are quoting reduction in yields.
11,856/10000 is the 5 year growth. Take the 5th root (and subtract one) and you get 3.46%. 5% less this is about 1.55%. Bingo.
Similarly, if you work out the projected fund value for an investment of £2000 pa paid monthly, with initial charge of 4.75% and annual charge of 0.5%, you get £10,755. Using a 5-year monthly annuity[s5(12)], the solution to 2000[s5(12)] =10755 is about i=2.5%. ie a reduction in yield of 2.5%.
Hope this helps.

 

[almost_there]

Anacts, yes that's the only way you can match the numbers in the question, thanks. However their sentence in the question which talks about charges absorbing % of the fund is very clumsy & misleading. You can only absorb what's there. As is the unnecessary effective charge % higher on annual premium talk, which overcomplicates the situation etc. no doubt all this & acted's solution generally would trouble the supposed manager in the actuary department , who wouldn't even get the terms premium and lump-sum.

 

[David Wilmot]

Thanks both – agreed!

My earlier spreadsheets are misleading as they implicitly assume a “simple” rate as opposed to a “compound” rate. I'll delete them to avoid confusing other students.

Having dug back into the history of X2.1, the phrase “absorbing approximately” was used in the original past exam question on which this question is based, and that is established terminology. However, we agree that this wording is ambiguous. The (compound) reduction in yield is arguably the most sensible interpretation, and we will look to improve the clarity of the wording of this question in the next edition of the materials – due very soon.

We’ve also discussed the specific jargon issues you raised and agree that “lump sum” could be considered as not being jargon in this situation (i.e. given the particular audience). We also don’t think that “premium” is generally jargon, but it is arguably not the most suitable word to use in this context given that this is an investment product. “Payment” or “contribution” might be better, but using "premium" shouldn’t be penalised heavily (if at all). Again we will reflect these changes in the new edition.

Apologies again for the confusion caused by the above, and thank you for raising these issues so we can make these improvements.