Profit Attribution by Sector and Stock Selection

[dannyp123]

Hi,

I am getting a bit confused with the answers within ASET to the SP5 April 2015 paper, on profit attribution. Some help would be greatly appreciated. Question 5 (ii)b) asks for relative contributions from stock and sector (asset allocation) selection, at asset class level.

From the course notes it states that: F_AA - F_AN = stock selection profits, which makes sense to me. (F_ij being F_sector,stock; A actual, N notional). It also states that F_AN - F_NN then equals your sector selection profits. I am clearly going to be wrong here, but what confuses me is this doesn't seem to hold up in the answers within ASET. Page 10 of the April 2015 solutions:

It gives the formulas used to calculate both stock and sector selection profits for the domestic equities, namely -0.88% and 1.50% respectively.
Now for the stock selection it uses:
0.25*(35.2% - 38.72%) = -0.88%
This makes sense as if you multiply that bracket out it is using F_AA - FAN for domestic equities.

What throws me is I don't have a clue how the formula for the sector selection profit for domestic equities is then derived. it is shown as:
{1} (0.25-0.4)*(38.72% - 48.75%) = 1.50%...
That isn't even close to being F_AN - F_NN (which to my mind would look something like: (0.25*38.72% - 0.4*38.72%)=-5.81% ). So my question is how is that formula derived (formula {1})? And also why is it not F_AN - F_NN??

I would really appreciate knowing a formula that I can apply to all these profit attribution questions, because currently I am winging it a bit (and not well) as it doesn't seem to fit with the formulas in the notes?

Thanks for any help!
Dan

 

[Joe Hook]

Hi Dan,

Your formula there is applicable if we consider the fund as a whole. In this question we are asked to work out the stock and sector selection by asset class. The problem with F_AN - F_NN is it doesn't consider the benchmark returns for each asset class relative to anything. In fact the formula you've used would give positive sector selection profits for any asset we're overweight in, regardless of whether that's been a good asset class.

If you look towards the end of page 25 of the course notes for chapter 16 you'll see the formula used above which is:

(actual weight of asset class - benchmark weight of asset class) x (benchmark return on asset class - overall benchmark return)

It's rationale is that we should get positive asset allocation profits if either
1) An asset class performs well relative to the overall benchmark and we are overweight in that class or
2) An asset class performs poorly relative to the overall benchmark and we are underweight in that class.

If we take a very simple numerical example, imagine a fund invested 50:50 in equities and bonds but the benchmark is 80:20 so we go overweight in equities, underweight in bonds.

Benchmark returns are 20% equities, 4% bonds. So the overall benchmark return is 80%*20%+20%*4% = 16.8%. Benchmark returns are boosted by equity returns and dragged down by bond returns. So the better asset class to be invested in was equities and the manager would make profits by holding more equities and less bonds than the benchmark. However, they've chosen to do the opposite, holding 30% less equities and 30% more bonds.

Hence asset selection for equities: (50%-80%)*(20%-16.8%) = -0.96%
Asset selection for bonds: (50%-20%)*(4%-16.8%) = -3.84%
Overall selection: -4.8%

Note that you could obtain the overall -4.8% using your formula (50%*20%+50%*4% - 16.8%) but we have to use a different formula when splitting them out.

Overall, my advice would be to focus on the more detailed formulae (they should always work, regardless of the question) but then if you can spot that you only need high level figures because of the question wording then you can revert back to F_AN - F_NN for example.

Joe

 

[dannyp123]

Thanks Joe that is really helpful. Think I follow that now.

 

[dannyp123]

As a follow-up from another paper, I have looked over question 5 from the April 2016 SP5 paper. As an alternative solution it provides the stock and sector selection profits by asset class (ASET page 15 from that paper). What I am finding confusing is that I thought:

the sum of the stock selection profits by asset class = the stock selection profit at fund level
similarly, the sum of the sector selection profits by asset class = the stock selection profit at fund level

Thus the sum of both stock and sector selection profits by asset class = overall outperformance at fund level.

This is the case in the answer to Question 5 of the April 2015 paper, but not in this 2016 paper.... the sum of stock/sector profits at asset level do not equal the overall outperformance. Could you explain why? Or is this an error in the alternative solution figures presented on page 15 of the ASET solutions?

Thanks again,
Dan

 

[dannyp123]

Sorry, another on attribution. October 2016, Question 7. Definitely understanding the process a bit better now but this threw me:
Page 27 of the ASET solutions:
-total (2 year) outperformance is calculated by MULTIPLYING the returns for each year.
Page 28 of the ASET solutions:
-total (2 year) stock and sector outperformance is calculated by ADDING the returns for each year

Why does one multiply, and the other add? I am really confused. Shouldn't both either multiply, or both add the returns to achieve the 2 year rate?

Thanks,
Dan

 

[Joe Hook]

As a follow-up from another paper, I have looked over question 5 from the April 2016 SP5 paper. As an alternative solution it provides the stock and sector selection profits by asset class (ASET page 15 from that paper). What I am finding confusing is that I thought:

the sum of the stock selection profits by asset class = the stock selection profit at fund level
similarly, the sum of the sector selection profits by asset class = the stock selection profit at fund level

Thus the sum of both stock and sector selection profits by asset class = overall outperformance at fund level.

This is the case in the answer to Question 5 of the April 2015 paper, but not in this 2016 paper.... the sum of stock/sector profits at asset level do not equal the overall outperformance. Could you explain why? Or is this an error in the alternative solution figures presented on page 15 of the ASET solutions?

Thanks again,
Dan

Hi Dan, I'm a little confused here but apologies it is probably just me.

The sum of stock selection by asset class 2012 = 2.72% and sector selection by asset class 2012 = 0.29%. Combined this is 3.01% which is the fund's outperformance from part (i).

The sum of sector selection by asset class 2012 = -2.43% and sector selection by asset class 2012 = 0.83%. Combined this is -1.6% which is the fund's outperformance from part (i).

So to me this all seems to tie up as you'd expect it to. Perhaps you could clarify if you still think there's an issue.

 

[dannyp123]

Hi Dan, I'm a little confused here but apologies it is probably just me.

The sum of stock selection by asset class 2012 = 2.72% and sector selection by asset class 2012 = 0.29%. Combined this is 3.01% which is the fund's outperformance from part (i).

The sum of sector selection by asset class 2012 = -2.43% and sector selection by asset class 2012 = 0.83%. Combined this is -1.6% which is the fund's outperformance from part (i).

So to me this all seems to tie up as you'd expect it to. Perhaps you could clarify if you still think there's an issue.

Nope that is totally me! Sorry! My mistake.

 

[Joe Hook]

Sorry, another on attribution. October 2016, Question 7. Definitely understanding the process a bit better now but this threw me:
Page 27 of the ASET solutions:
-total (2 year) outperformance is calculated by MULTIPLYING the returns for each year.
Page 28 of the ASET solutions:
-total (2 year) stock and sector outperformance is calculated by ADDING the returns for each year

Why does one multiply, and the other add? I am really confused. Shouldn't both either multiply, or both add the returns to achieve the 2 year rate?

Thanks,
Dan

Hi Dan,

A possibly unsatisfying response incoming but it's a very fair question that many students and us tutors have had to ponder over the years.

The approach we use to attribution analysis by stock and sector is known as the Brinson model. Under that model we sum stock and sector selections over multiple periods to arrive at total figures. Within a single period the Brinson model works well but has some issues over multiple periods because as you've probably noticed, summing stock and sector selection does not give you the total outperformance. Total outperformance is found by multiplying (as you would probably expect) and this allows for the compounding effect of returns. If returns are higher in the first period then returns in the second year will be magnified. This is not true of stock and sector selection. If stock selection is good in the first year it does not magnify stock selection in the second. It's the combination of stock and sector selection that matters and there will be interaction effects between them.

Some attempts have been made to overcome this issue by smoothing but naturally this falls outside of the scope of SP5.

So my possibly unsatisfying suggestion is to try to avoid worrying about this too much and simply recognise that this is the approach we take. However, hopefully you'll be able to recognise that your stock and sector selections won't sum to the overall outperformance but you'll know that that is reasonable.

Hope this helps
Joe