Wealth based taxes: tax drag

[sfad]

With wealth based taxes:
Unlike accrual taxes, increasing return on investment → tax drag $ increases, tax drag % decreases. (Because wealth taxes apply to the capital base, the absolute magnitude of the liability they generate is less sensitive to investment return than taxes based on returns).
How does the tax drag $ increase, but tax drag % decrease?

 

[cpk123]

why don’t you put numbers to a problem, solve it, and cement the statement in your mind….

 

[kjsgbp]

because 1 out of 10 is 10% and 2 out of 40 is 5%… 2 is higher than 1 but the tax dollars dont increase proportionally to invesment returns.

 

[Carlo]

This is my intuition:
% tax drag = (GAIN - gain) / GAIN
where ‘GAIN’ is the gain assuming no taxes and ‘gain’ is the gain after wealth tax.
Now, per the wealth tax formula (assuming 1 year investment horizon to avoid the further complication of compounding):
1[(1 + r) * (1 - t)]
multiplying the terms in the brackets to make it easier to see what’s going on, we have:
1 * (1 + r - t - rt)
The intuition is in what happen to ‘gain’ vs ‘GAIN’ as ‘r’ goes up and ‘-t’ stays put.
As ‘r’ goes up and pushes up ‘gain’, the impact that ‘-t’ produces on ‘gain’ is less and less important as ‘-t’, differently from ‘r’, does not grow (i.e. it is assumed fixed).
To exemplify, let’s first assume r = 10% and t = 2%
‘GAIN’ will be [1 * (1 + 0.1)] - 1 = 0.1%
and ‘gain’ will be {1 * (1 + 0.1 - 0.02 - (0.1 * 0.02))] - 1 = 0 .078
gain/GAIN = 78% (i.e. gain is 78% of GAIN)
Pushing up ‘r’ to 50%
‘GAIN’ will be 0.5
and ‘gain’ will be {1 * (1 + 0.5 - 0.02 - (0.5 * 0.02))] - 1 = 0.47
gain/GAIN = 94%
In other words, with ‘r’ increasing, the relative difference (‘GAIN’ - ‘gain’) goes down which causes the % tax drag to decrease.
This is explained by ‘-t’ being fixed (0.02 in our example) which will diminish its negative impact on ‘gain’ in a rising ‘r’ scenario.
Good luck, Carlo

 

[sfad]

I have plugged numbers in and understand the math, but more don’t understand the explanation given:
(Because wealth taxes apply to the capital base, the absolute magnitude of the liability they generate is less sensitive to investment return than taxes based on returns)?

 

[daharmattan1]

Good thing you won’t need to understand the concept in 5 weeks you’ll just (maybe) need to know the fact

 

[FrankCFA]

Numerator: tax drag $ increases
Denominator: increase quicker
=> Ratio will be lower

 

[June06]

Any exception for this?
For wealth-based taxes, as investment return increases ⇒ tax drag $ increases; tax drag % decreases.

 

[JJ1337]

June06 wrote:
For wealth-based taxes, as investment return increases ⇒ tax drag $ increases; tax drag % decreases.

Nice, I have overlooked this issue.