Past Paper Discussion

A Thread to discuss past paper questions, answers, complaints and generally slag off the examiners.

I'll get the ball rolling then. 30 March 2006 paper; Qn 5 - attribution analysis.

Does anyoone agree the examiners answers? I can't see how they get a total fund return of 22.81%, there's a currency allocation but they didn't explicitly hedge the currency and I dont get the stock, currency splits etc etc etc etc.

(edit: I'm happy with 22.81 now having looked over it again but I still cant work out what all the columns are for and how they're calculated. I don't agree their end results and why is there two options for some of the answers?)

I thought I'd nailed this section but then this came along. Anyone able to offer a light for my very dark ST5 tunnel?

Cheers,
Olly

Incidentally, how come this forum isn't being used so much anymore? It was a hotbed of activity last time on the ST6 threads!

 

I agree that the examiners solution is hard to follow. I don't know how they got their benchmark returns, so if you figured that out please tell me. I guess
there are two options becuase you can either go via fund/actual or actual/fund.

The examiners reports for the past two sittings seem to fall well below the usual high standard.

 

Thanks for the reply PW. I'll get back to this evening with my calcs.

 

Examiners' approach - April 2006 Q5

Looking at the columns in the Examiners' answer and labelling column 1 as the column of asset classes:

Column 2 is the actual return on the fund.

The Examiners assumed cashflows occurred mid-year.

So for the USA asset class they solved the equation:

250x(1+i)-10x(1=i)^0.5=300

i = 24.49%

When the examiners calculated the overall return, they weighted each asset class by the investment at the start of the year, so the USA has a weight of 50%

Column 3 is the return on the benchmark fund.

So for the USA, the calculation is:

120/100 x 1.9/1.75 -1 = 30.29%

Column 4 is the currency return

For Asia this is 1.9/1.75-1=8.57%

Column 5 is the asset allocation profit

For Asia this is (50/500-5%)x(53.03-16.23)=1.84%

Column 6 is the currency profit

For Asia this is (50/500-5%)x(8.57-1.96)=+0.33%

Column 7 is the stock selection profit

For Asia this is 50/500 x (40-53.03)=-1.30%

 

Thank you Roadrunner that was extremely helpful. Are you a student / psychic / tutor or other? I ask as I cannot fathom how those formulas for currency and asset allocation profit work. They also do not appear to sum to the total profit which I might have expected.

For Asia I calculate the following returns (using my more basic method)

sector, stock
notional, notional: 0.05 * 53.03 = 2.65
actual, notional: 0.1 * 53.03 = 5.30
actual, actual: 0.1 * 40 = 4

Thus sector allocation profit is 2.65 and stock pick profit is -1.3, summing to total profit = 1.35.

I accept that if you introduce a currency profit you must divide these individual profits differently. But I would still expect them to sum to 1.35, however the examiners results (and your formulae which show them) do not.

So my questions are:-
1) Are those formulae that you used in the notes?
2) Would you agree that the asia profit is 1.35? If not, why not?
3) If so, how do you square those returns not summing to 1.35?
4) Why is there an alternative answer of 5.97% profit? Different contribution timings possibly?

Sorry for the grilling and if you don't have the time or the inclination to answer, fair enough, it's the busy season after all, but this question has put a massive bee in my bonnet as it seems to introduce a totally different approach to these types of questions that I've not seen before!

Cheers,
Olly

 

Sorry to bring this up again but I think it's worth revisiting in the light of the 2007 syllabus.

The 'Changes to the syllabus' document section on Unit 16, Section 3 notes that "a good example of what the examiners expect can be found in the examiners' report to the examination paper for ST5 April 2006, Question 5"

http://www.actuaries.org.uk/files/pdf/pastpapers/2006apr/st5r_a06.pdf

In light of this, I think it's important to discuss how the above results were arrived at. Anyone fancy answering my questions above?

Of course, the great irony of this is that the examiners report in question states, "whilst candidates were not asked for formulae it would be good practice to write out what formulae were used...". Well quite - it would be useful to know how the examiners arrived at their results seeing as the course didn't specify how they might have done it!

 

Bump

Bump.

Anyone?

 

The results you get for these attribution questions vary slightly depending on the assumptions you make, however the examiner has suggested to me that he is happy to accept any "reasonable" approach. What follows below is his preferred approach - although it actually differs slightly from his main solution on the Examiner's Report for the April 2006 question, as he calculated the actual weights slightly differently - i.e. just based on the opening fund values.

The actual returns are:

r(usa) = 24.49%
r(jaa) = 46.15%
r(eua) = -13.33%
r(asa) = 40.00%
r(caa) = 0.00%

These returns are calculated assuming that the cashflows are invested midway through the year and also the approximation (1 + i)^t = (1+ i*t).

The notional returns are:

r(usn) = 30.29%
r(jan) = 16.92%
r(eun) = -13.67%
r(asn) = 53.03%
r(can) = 0.00%

For example, the notional return for the USA (in £ terms) is calculated as:

(120/100) * (1.90/1.75) -1 = +30.29%

reflecting both the increase in the dollar value of the fund and the appreciation of the dollar.

The actual weights are:

w(usa) = 49%
w(jaa) = 19.5%
w(eua) = 21%
w(asa) = 10%
w(caa) = 0.50%

These weights are again calculated assuming that the cashflows are invested midway through the year - which is probably the most reasonable assumption to make unless the question suggests otherwise.

The US actual weight was therefore w(usa) = 245/500 = 49%.

Combining the actual weights and returns estimated in this way then gives:

r(aa) = sum of [actual weights x actual returns] = 22.20%

which is in fact "correct", in the sense that the fund grew by 22.2% from 500 at the start to 611 at the end, with no net cashflow at the halfway point.

The examiner's solution of 22.81% here is inconsistent as it is based on weights caluclated using opening fund values and returns based on mid-year cashflows.

Finally, the notional weights are:

w(usn) = 50%
w(jan) = 15%
w(eun) = 30%
w(asn) = 5%
w(can) = 0%

So, the overall returns are:

r(aa) = sum of [actual weights x actual returns] = 22.20%
r(an) = sum of [actual weights x notional returns] = 20.57%
r(nn) = sum of [notional weights x notional returns] = 16.23%

So, total stock selection profits = r(aa) - r(an) = +1.63%
total sector selection profits = r(an) - r(nn) = +4.34%

The stock selection profit contribution of the US is then found as:

= w(usa) x [r(usa) - r(usn)] = 0.49 x [24.49 - 30.29] = -2.84

Using the same approach for the other sectors then gives the stock selection contributions for each as: +5.70, +0.07, -1.30 and 0.00%, which sum to the total of +1.63%.

The sector selection profit contribution of the US is then found as:

= [w(usa) - w(usn)] x [r(usn) - r(nn)] = [0.49 - 0.50] x [30.29 - 16.23] = -0.14

Using the same approach for the other sectors then gives the sector selection contributions for each as: 0.03, 2.69, 1.84 and -0.08, which sum to the total of +4.34%.

In the April 2006 question, the currency contribution was found as part of the overall sector selection profit and it was found in an analogous way to that just described for splitting out the overall sector selection profit.

You first need to calculate the returns from investing purely in each currency, e.g. for US dollars this was:

r(us$) = 1.90/1.75 = +8.57%

which is positive as the US dollar appreciated over the year.

The corresponding figures for the other currencies are then: -5.00%, -6.67%, +8.57% & 0.00%. The weighted average currency return, based on the notional sector weights is then equal to:

r(cn) = sum of [notional weights x currency returns] = +1.96%.

The currency contribution of the US dollar to the overall sector selection profit was then found as:

= [w(usa) - w(usn)] x [r(us$) - r(cn)] = [0.49 - 0.50] x [8.57 - 1.96] = -0.07

The other currency contributions are then found in the same way and are -0.31, 0.78, 0.33 and -0.01.

However, I don't imagine that many people got this right, particularly as nothing like this had been asked before and it was not clear from the question that it was required.

Ignoring the currency element, the above approach has been exactly what has been required in each of the three ST5 performance attribution to date. I hope the above is reasonably clear - a complete solution is given in the ST5 ASET.

 

I believe that we must also calculate the return resulting from sector selection, but excluding the currency impact. For US, this can be calculated as:

= [w(usa) - w(usn)] x [r(us local index) - r(notional weights and local indices)] = [0.49 - 0.50] x [20 - 13.259] = -0.067.

Any comments?

 

The Examiners' Report doesn't does this. It only calculates the currency selection profit as part of the overall stock selection profit, without going any further. So, presumably that is as far as they wanted you to go.

 

Ok thanks.

 

Help

Hi all, one question on the April 06, Q5:

Why do they use the investment income figure in the calculations, I thought for MWRR you were meant to exclude investment figures?

Any help gratefully received! Thanks

 

(debating whether to start a new thread but as it's related)

I was just wondering if anyone uses any rules of thumb with regards to what consititutes as "too small to call" for the attribution questions.

The reason I ask is that depending on your method (eg notional stocks, actual sector or vice versa) the numbers would be different.

I think that both methods should give the same "answer" so if the sector profit is say 0.8% but doing it the other way gives -.5% (say) then we can't say much IMHO.

Of course I'm not going to do it both ways which is why I was wondering if there was a general rule of thumb which could be used.