September 2014, Question 6

[MLC]

Hi,

My question is in two parts and relates to part iii) of September 2014, Question 6. My second question is the more pressing one.

Looking at part iii) in this question we have to compare the investment income earned in a fund to the investment income we would have earned had we instead invested in an index.

Question 1:

The answers in ASET calculate the income received at time t as:

= MV fund at time (t-1) x Index(t)/Index(t-1) x dividend yield (t)

In my solution, I calculated the income received as:

= MV fund at time t=0 x Index(t)/Index(t=0) x dividend yield (t)

So, for example, for Q3 I calculated income as

=3600 x 1797/1500 x (3.9%/4)

Would this be an acceptable approach and if not please could you explain why?

Question 2:

In the ASET solutions there is also a comment saying an alternative way of calculating the income received is as:

= [MV fund (t) - investment income (t)] x dividend yield (t)

e.g. for Q2) (4050 - 30) x 4.2%/4

However the comment goes on to say that in this particular question this approach was incorrect as investment income was received at the end of the quarter, but would have been ok if investment income were received evenly over the quarter. Please could you explain why this is the case.

Please can you also explain why investment return is deducted in the above calculation. I have seen similar questions where investment returns aren't deducted (for example question 5, April 2005 (question 14 in the day 2 Acted tutorial hand out)).

I'm trying to figure out a consistent approach, any help would be appreciated.

Thanks,

Max

 

[Gresham Arnold]

Hi,

My question is in two parts and relates to part iii) of September 2014, Question 6. My second question is the more pressing one.

Looking at part iii) in this question we have to compare the investment income earned in a fund to the investment income we would have earned had we instead invested in an index.

Question 1:

The answers in ASET calculate the income received at time t as:

= MV fund at time (t-1) x Index(t)/Index(t-1) x dividend yield (t)

In my solution, I calculated the income received as:

= MV fund at time t=0 x Index(t)/Index(t=0) x dividend yield (t)

So, for example, for Q3 I calculated income as

=3600 x 1797/1500 x (3.9%/4)

Would this be an acceptable approach and if not please could you explain why?

Hi Max

I think some elements of your calculation are correct, but not all:

As part of your calculation, you have calculated Index(t)/Index(t=0) x dividend yield (t) /4

So for Q3 you calculated 1797 x 3.9%/4, which is essentially the dividends that would have been received over Q3 from the index. That's fine.

We then need to adjust this figure to reflect the fund has only a proportion of the market value of the index. The examiners did this by multiplying by MV fund (t-1) / Index (t-1). In other words they multiplied by a ratio of the fund and index values at the start of the quarter.

You have multiplied by a ratio of the fund and index values at the start of the year. In some ways this is reasonable, but it does assume that the fund and the index change equally between the start of the year and the start of the quarter in question. And in fact they don't and we wouldn't really expect them to - because of the contribution cashflows experienced by the fund during the year and differences in performance of the stocks held by the fund and those held by the index. So the Examiners' approach is more accurate here. Would your approach have been acceptable? I don't know how your approach would have been marked, but if I were to guess I would expect it to gain some credit but not full credit.

I hope that helps

Gresham

 

[Gresham Arnold]

Hi,

My question is in two parts and relates to part iii) of September 2014, Question 6. My second question is the more pressing one.

Looking at part iii) in this question we have to compare the investment income earned in a fund to the investment income we would have earned had we instead invested in an index.

Question 2:

In the ASET solutions there is also a comment saying an alternative way of calculating the income received is as:

= [MV fund (t) - investment income (t)] x dividend yield (t)

e.g. for Q2) (4050 - 30) x 4.2%/4

However the comment goes on to say that in this particular question this approach was incorrect as investment income was received at the end of the quarter, but would have been ok if investment income were received evenly over the quarter. Please could you explain why this is the case.

Please can you also explain why investment return is deducted in the above calculation. I have seen similar questions where investment returns aren't deducted (for example question 5, April 2005 (question 14 in the day 2 Acted tutorial hand out)).

I'm trying to figure out a consistent approach, any help would be appreciated.

Thanks,

Max

Hi Max

The 30 that is being deducted in the formula above is contribution income not investment income.

So the formula above is trying to estimate an end of quarter fund value just before the contribution income was received (as the contribution income arrived at the end of the quarter and so would have had no time to earn dividends). Then multiply that by the dividend yield /4 to estimate dividend income over the quarter.

I think this is consistent with the approach we discussed separately for A2005 Q5, where I also said we perhaps ought to allow for the contribution income (although arguably it was pretty immaterial to the conclusions in that question).

Why, in this instance, is this not a great method of estimating the investment income that we would have received if we had been invested in line with the index? I think that if we had been invested in line with the index we would have received income across the quarter, which would have been reinvested in the index and itself earned further returns by the end of the quarter. So this would have led to a different end of quarter value cf the 4020 you used above (as this is based on the fund receiving investment income only at the end of the quarter, at which point it would have no chance to earn further return that quarter).