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joehogue

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tT
发表于 2011-7-11 15:25 | 只看该作者

Tax drag concept for wealth-base taxes

return, Investment
For wealth-base taxes, can anyone explain briefly why

1. as Investment horizon increases => Tax drag increases
2. as Investment return increases => Tax drag decreases

Thanks
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Windjam

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2#
发表于 2011-7-11 15:25 | 只看该作者
Measure of Wealth = (1+R)^N <-- 1 $ today growing at 10% becomes 1.21$ in 2 years (N=2).

Now you have a wealth tax of say 2%
so your ending wealth = 1.21 * 0.98 = 1.1858

tax drag = 1- [(1.1858-1)/(1.21-1)] * 100 = 11.52%

say time became 3 years

1.331 * .98 = 1.30438
Tax drag = 1 - [0.30438/.331*100] = 8%

the wealth grows faster than the amount of tax applied (since it is a fixed portion of the ending wealth).

now if return increased as well -> the ending wealth is much higher, (you should be able to do similar calculations as above) but the tax applied is a much smaller proportion of the ending wealth.

CP



Edited 1 time(s). Last edit at Thursday, April 7, 2011 at 06:17AM by cpk123.

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bodhisattva

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3#
发表于 2011-7-11 15:25 | 只看该作者
Thanks, I totally forget how to calculate tax drag.

TaxDrag_w(TD_w)=(G_BT-G_AT)/G_BT=1-([(1+R)(1-tw)]^N-1)/((1+R)^N-1)

The above will look much neater on paper, so no worry.

Here is a trick I got today: no need to memorize anything, as long as we know TD%.

1). as Investment horizon increases => Tax drag increases?
-- set N=large number, then
TD_w ?? 1-(1-tw)^N ==> TD_w increases as N increases.

2). as Investment return increases => Tax drag decreases?
-- set N=1, then
TD_w = tw+tw/R ==> TD_w decreases as R increases.

I tried the partial derivative approach, it's just not worth it.

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liangfeng

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4#
发表于 2011-7-11 15:25 | 只看该作者
It's "TD_w roughly equals to 1-(1-tw)^N"

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Analti_Calte

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5#
发表于 2011-7-11 15:25 | 只看该作者
You guys have a trick for remembering the relationship between tax drag and horizon/return among the different types of taxes? without having to do the calcs. I realize that it is due to principal being/not being taxed...

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