# Rebalancing Bands Math

So here’s one I noted last week to figure out but never quite found a firm answer. I have seen this two ways in different exam&mock questions.

Let’s say each asset class in an allocation has a TAA band of +/- 10%.

One asset class, Beer, is 45% in the SAA. At the periodic rebalancing date, Beer has dwindled to 40%. We need to decide whether to rebalance.

Is the tactical band 40.5% - 49.50% (which would be 45 +/- 10% of 45,) or is it 35 - 55 (45 +/- 10)?

Bands are whole numbers, why would someone complicate matters and put multiplicative targets?

clealry the case of percentage points difference versus % difference

It’s 2010 question 8 A.

I have always assumed the numbers ar additive/subtractive. In practice, this is what I use.

But 8A on this exam suggests rebalancing because a 40% weighted asset class with a +/-10 corridor hit 45.

I have also seen additive on other test questions.

Wow, just going through it now, and I’m struck. Should have been higher, since 45% is NOT outside the band.

It clearly says ± 10% of the SAA target.

I don’t know who I am anymore.

it is: “tolerance bands or corridor widths set at ± 10% of the target allocation” - so 45% is outside the 40 + 10% of 40

Saw it additive before, never seen this until now.

They don’t even show the maths for it.

agreed, but they said “+/- 10% of the TA” so I guess they are hedged here

Question is wrong, they most likely meant 5%.

Or the solution guide author mistook it for 10% on the whole range, which implies +/- 5% as well.

[quote=“cpk123”]

Now I came into this thread to argue this point above. But then I read the paragraph directly above it in the text

“For example, consider a three-asset class portfolio of domestic equities, international equities, and domestic bonds. The target asset proportions are 45/15/40 with respective corridors 45% ± 4.5%, 15% ± 1.5%, and 40% ± 4%. Suppose the portfolio manager observes the actual allocation to be 50/14/36; the upper threshold (49.5%)”

¯_(ツ)_/¯

Is this only for percentage-of-portfolio rebalancing, or is this approach universal across rebalancing methods cited in the curriculum?

Not one example or exercise in the book uses it that way.

Even if they did, at least state the “adhoc” approach, too ambigious.

In normal life (yes, there is a world outside your CFA books), ±10% means you add 10% and minus 10% from the initial allocation, in this case 45%, to arrive at an overall band of 35% to 55%.

Yes, because you have seen the asset allocation policy of every investment managment firm in the world ‘in normal life’.

Would love to see you write ‘in normal life’ during the AM exam on Saturday.

So whats the final decision here

35 - 55 (45 +/- 10)?

or

40.5% - 49.50% (45 +/- 10% of 45)

Read the question again.

The difference is in reading comprehension, Whether the corridor is a % of the TA, or an interval (of the portfolio).

I’d be surpised if they do that again.

I didn’t mean it in terms of asset allocation policies, but in terms of returns estimations, error margins, etc.

If they do throw a curveball like this on Saturday, I think they might give marks if it’s done either way, as long as the rest are correct.

there are certain key words they throw into the passage, gems hidden among the masses.

If you looked at that question - MOST people got it wrong, because they failed to read that important sentence.

===

Another example - 2012 Alonso IPS - 25,000 spent for charity – many people (self included) used that as a number in the Return calculation - and made the balance smaller - hence messed up the return requirement and lost points.

so be careful while you read the vignettes.

Just to be clear - because this thread really isn’t very - this method is only for percentage of porfolio rebalancing, correct? Is that what you mean by the important sentence?