Compounding
Why does a string of weekly gains add up to more than their simple sum?
In plain words
Compounding means each period's return is applied on top of the return already earned, so gains earn further gains. Multiplying the weekly growth factors together gives the total, rather than adding the percentage moves.
Why it matters
Compounding also works in reverse: a large loss requires a much larger gain to recover. It makes the size of drawdowns and the order of returns matter, not just their average, when measuring what a position actually earned.
In a real week: BTC, week of 28 December 2020
In the week of 28 December 2020, BTC returned 25.56%, closing at 33000.05 from an open of 26281.54. The four prior weeks returned 6.46%, -0.95%, 22.32% and 12.05%, and prior_weeks_up counted three of them as up. Chained together, each week's growth applied on top of the last, so the sequence's combined effect exceeds what adding the individual figures would suggest.
A common mistake
Adding weekly percentage returns to estimate total performance. The sum ignores gains earned on earlier gains, understating the compounded result after a run of positive weeks.