SA7 April 2019 - Question 2 (possible error in model solution)

Discussion in 'SA7' started by Mufaddal Jamali, Sep 25, 2019.

1. I'm marking my attempt at the paper. Came across the following issue, which I think is an error in the model solution. Please advise urgently.

Question 2.i:
• Benchmark return is calculated as a weighted average of the 4 categories, as expected, and gives an answer of 6.70%.
• Portfolio return is calculated as a [(sum of end values) divided by (sum of beginning values)], giving a return of 6.80%.
• The method used for the portfolio return is incorrect since it assumes equal weights to the 4 categories, which is not true, as per the data table in the question.
• Using the same method as for the benchmark return, I get a value of 6.85%.
Question 2.ii:
• Since this is using the previously obtained (and, I think, incorrect) value of alpha, the aggregate attribution must also be wrong? Though I haven't been able to verify where the solution is incorrect here.

Thanks for your post. I've just had a quick look at this question and the solution in the Examiners Report.

I think we are both happy with the benchmark return calc.

In order to work out the portfolio return, I think we agree the Examiners have summed the portfolio values at the end of the year and divided by the sum of the portfolio values at the beginning of the year ie (216+321+210+321)/(200+300+200+300) = 1068/1000 = a return of 6.8%.

I'm struggling to see why this method is wrong? Essentially we've calculated the values of the assets at the start and end of the year in \$m and calculated the return by dividing one by the other?

If I use the same method as for the benchmark return I still get 6.8%:

20% x 216/200 + 30% x 321/300 + 20% x 210/200 + 30% x 321/300 -1 = 6.8%

I hope that helps. Apologies if I am missing something obvious here?

Best wishes

Gresham

3. Hi Gresham,

Still struggling with this one. Here goes:

Benchmark Performance:
• Method 1 (sum divided by sum): (105 + 106 + 107 + 108) / (100 + 100 + 100 + 100) = 426 / 400 = 1.065 --> 6.5% return.
• Method 2 (weighted returns): (0.2 * 0.05) + (0.2 * 0.06) + (0.3 * 0.07) + (0.3 * 0.08) = 0.067 --> 6.7% return.
• Method 3 (weighted end value divided by start value): [(0.2 * 105) + (0.2 * 106) + (0.3 * 107) + (0.3* 108)] / [(0.2 * 100) + (0.2 * 100) + (0.3 * 100) + (0.3 * 100)] = 106.7 / 100 = 1.067 --> 6.7% return.
• As you can see, method 2 and 3 give the correct return figure of 6.7%, whereas method 1 does not (which is the method then used to calculate portfolio performance).
• Also, it should be fair to assume that the method used for the benchmark return calculation and portfolio return calculation should be the same, for the sake of consistency.
Portfolio Performance:
• Method 1 (sum divided by sum): (216 + 210 + 321 + 321) / (200 + 200 + 300 + 300) = 1068 / 1000 = 1.068 --> 6.8% return.
• Method 2 (weighted returns): (0.2 * 0.08) + (0.2 * 0.05) + (0.3 * 0.07) + (0.3 * 0.07) = 0.068 --> 6.8% return.
• Method 3 (weighted end value divided by start value): [(0.2 * 216) + (0.2 * 210) + (0.3 * 321) + (0.3* 321)] / [(0.2 * 200) + (0.2 * 200) + (0.3 * 300) + (0.3 * 300)] = 277.8 / 260 = 1.0685 --> 6.85% return.
It's possible that I'm doing something wrong, but I don't see it. Any thoughts?

Regards,

Here, under your 'method 1', you have assumed that the investment is equally weighted between the four possibilities. (By putting '100+100+100+100' in the denominator you have assumed that 100 is invested in each, which is not the case here.)

You cannot, therefore, compare the resulting 'benchmark performance' figure (of 6.5%) with the 'portfolio performance' that you have calculated under 'method 1' (of 6.8%), as the latter has been calculated using uneven weights.

Here you have taken what are already un-evenly weighted investment amounts (e.g. in the denominator 200, 200, 300, 300) and applied weightings to them. The result is that you have distorted the weightings away from the actual weightings to weightings which do not reflect the actual investment proportions (e.g. to 0.2*200, 0.2*200, 0.3*300, 0.3*300).

So, in summary:
• your 'benchmark performance method 1' uses equal weightings - which doesn't reflect the true (weighted) position
• your 'portfolio performance method 3' uses distorted weightings - which don't reflect the true weighted position
which is why the resulting figures do not correspond with your alternative (correct) approaches.

OK?

Best wishes

David

5. Hi David,

That makes perfect sense. Thanks for your explanation!

Regards,