Sequence risk

What the video says

1. Does the order of your returns change where you end up?

   It depends on exactly one thing, and it is not the returns.

2. One set of returns, run in two opposite orders.

   Worst years first, best years first. Both pots end at 444.

   Not close. Exactly the same number, down to the last decimal place, and it could not be otherwise — multiplying does not care what order you multiply in.

3. So shuffle them properly.

   200 orders of the same 20 returns, and every one lands on 444.

   Not approximately, and not on average. Exactly the same number, every single time. So far the order has done nothing whatsoever.

4. Now take a fixed sum out each year.

   Best years first ends at 360. Worst years first runs out.

   Same returns. Same withdrawal. The only thing that changed is which year came first, and one of these two has nothing left.

5. Shuffle those too.

   The same 20 returns now finish anywhere from 9 up to 314.

   That is a range of 306 on a pot that started at 100, and not one return moved. Bad years early cost the most, and they cost it twice: you sold more units cheaply, and had less left to recover with.

6. Now put the same sum in instead of taking it out.

   Worst years first ends at 736. Best years first ends at 84.

   The sign reverses. The order that emptied the pot on the way down is the better one on the way up, since bad years early let you buy cheap.

7. Three arrangements, one set of returns.

   Left alone the two orders tie. Taking out, they differ by 360. Putting in, by 651.

   Nothing about the returns moved between these rows. Only what you were doing with the pot alongside them.

8. So where does it actually come from?

   Take the very same withdrawal as a percentage, and all 200 orders land on one number again.

   It was never the returns and it was never the order. A percentage is another multiplication. A fixed sum is not, and mixing those two is the whole of it.

9. What this rests on.

   The returns are a draw, not a measurement. The reordering is exact.

10. Where this stops.

    The returns and the size of the cashflow are chosen: ASSUMED. The orders are a seeded shuffle, worth what that draw is worth: ASSUMED. And nothing here was measured: MISSING.

11. Nothing here was measured.

    Every case above is the same set of yearly returns in a different order, and the seed that drew them is printed under every frame. Not investment advice.

Evidence behind it

• The arithmeticCONFIRMED
• The returns and the cashflow usedESTIMATED
• The orders shown (a seeded shuffle)ESTIMATED
• Anything measuredMISSING

Marks open only as wide as each input’s evidence class allows. See Method.