Finally got round to modelling this.
Below are the results. (the spreadsheet is also attached0
The light blue background figures are the average annual growth in 1,000 simulations over 40 years with volatility of 15% p.a. and input growth parameter in the second line.
The yellow background figures are the same simulations but at 38% DD every 8 years.
The bottom line are then the annual tax equivalents of the 38%/DD8 regime.
On average it does not bear out your intuition, but of course the result in a particular experience will vary. I suppose the next step is to examine the actual spread of the annual equivalent.
I haven't gone through your spreadsheet yet, but I'm wondering: when you say "on average", what you are refering to?
Are you saying that if you model a particular outcome with and without deemed disposal overlaid on top, on average this is equivalent to the without case with ~33% applied at the end? That isn't terribly surprising, as its almost similar to the linear approximation case.
How many simulations are below this average, and have worse outcomes? How many are above? And, as you comments, what is the spread?
And what time duration did you use? I imagine the results will be impacted by whether the duration is a multiple of 8, so its probably interesting to sweep exts at 1, 2, 3, 4, 5, 6, 7 years also...
Even if the 38% DD every 8 years approximates CGT in the "average" case, this doesn't make it a fair or non-lazy modeling of the situation. A particular experience could be drastically impacted by the 38% DD if it had poor sequence of returns risk - as the credit for the DD isn't index linked or uplifted to cover missed growth (particularly over the best days)...