“The accrual equivalent after-tax return moves closer to the pre-tax return as time horizon increases.”
Now why is this true?
This is 1) with tax deferral.
2). Your after tax portfolio value is closer to the value without taxes.
example
10% return 2 years, 30 %tax ->
End of period balance = (1+0.1)^2 = 1.21
Tax of (1.21 - 1) (0.3) - 0.063 is paid
After tax = 1.21 0.063 = 1.147
AE Return = (1.147 / 1)^(1/2) = 1.0709
===
same after 3 years
1.331 - 0.331 * .03 = 1.2317 (more)
AE return after 3 years = 1.2317 ^ (1/3) = 1.0718
(higher – and getting closer to 10% which is the actual return without taxes)
===
10 years
1.1^10 = 2.5937424601
tax = 1.5937424601 * 0.3 = 0.47812273803
after tax = 2.5937424601 - 0.47812273803 =2.11561972207
AE Return for 10 years = 7.78%
So this is true even if the tax drag % is unchanged?
tax drag = 30% in each case above. so yes it is true.
Cheers