> Suppose we have an S&P 5, if the top 5 companies remain the same, but they on average do worse, we'd see the S&P 5 go down. You seem to imply, if I understand correctly, that the S&P 5 is not down as much because 1 company did really well and stayed, 4 that did poorly left and got replaced by 4 companies that did really well, too. Thereby the S&P 5 changed its composition.
No that's not what's happening. Think of S&P 500 index as a basket of stocks. What does that basket look like? If I buy one "unit" of this basket, does it include 500 shares of stock, across the 500 companies? NO. The distribution of the basket is weighted, and it's weighted by market capitalization. So if all stocks were worth the same, you would have a unit amount of every single stock. But if, say, 5 companies do really well and 5 companies do really poorly, 1 "unit" of the S&P500 basket will actually include more of the "really well" stocks, and less of the "really poorly" stocks. The capital is automatically reallocated based on the market capitalization. Because of this, the market value of the S&P500 has stayed relatively stable.
> And that makes some sense. However, that would mean that if you had an all-world or all-us stock indexes, which did not exclude any companies dropping out of a top 100 or top 500 or whatever, would have to see a large drop.
Again, that's only true if this index is naive enough to not apply any sort of weighting. Most indexes in the world are weighted indexes, in fact we are generally instructed that indexes that do not apply any sort of weighting are bad indexes.