Wealth based taxes: tax drag

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?

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

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.

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

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)?

Numerator: tax drag \$ increases

Denominator: increase quicker

=> Ratio will be lower

Any exception for this?

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

Nice, I have overlooked this issue.

May I know if this has any relations to the following statement from Schweser?

“The equity return is typically made up mostly of capital gains rather than dividend income and capital gains can be deferred. By extending the holding period, the tax drag% and TAE can be reduced even in the f ully taxable location to improve the equity after-tax return and generate tax alpha.”

If not, appreciate it if someone could explain the above? Thank you.