After tax and pretax rebalancing range corridor

CFA Level III Portfolio Management
#1

This is a note question.

"In the example about locating an asset in Olsen’s tax-exempt account with a target weight of 32% and a deviation of 10%, the allowable rebalancing range if Olsen locates the asset in his taxable account will be closest to:

A. 25 to 39%

B. 19 to 45%

C. 29 to 55%

We are give Olson’s tax rate, target weight, allowable deviation, and range for his tax-exempt account. Because taxes reduce volatility and risk, ranges can be wider in the taxable portfolio.

Deviation after-tax = deviation pre-tax/(1-t)=10/(1-0.25)=13.33%

With a target weight of 32% that makes the rebalancing range in the taxable account: 32+/- 13.33 = 18.67 to 45.33%" (From Schweser Notes Book 3 Self Test)

I dont really get it because If I remembered correctly, the formula should be after tax range = pretax / (1-T).

However in this question the after tax deviation is 10%, whu the answer put 10% in the numerator?

Appreciate any helps

#2

Hi there,

I just covered this topic. The 10% is the pre-tax deviation because it is the deviation when the tax exempt account is used.

At the end of the day what we have is:

Tax-exempt range = 22 - 42 (range = 20)

Taxable range = 18.67 - 45.33 (range = 27)

Clearly the taxable range is wider so we have gotten it right. It can’t be the other way round.

#3

Found an easier way to remember.

After tax deviation = taxable account

Pre tax deviation = tax-exempt account

For this example, tax-exempt account deviation is 10%, so the pretax deviation is 10%. Using the formula, taxable account = 13.3%

Another example in note, if after-tax rebalancing range is 12.5%, it means taxable account deviation is 12.5%. Using the formula, Pre tax deviation is 12.5% * 0.8（tax rate）=10%. Tax-exempt account deviation is 10%.

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