Let's suppose we're interested in the pricing of a very simple index, with two stocks A and B. Both A and B have 2 outstanding (or floating) shares, and A is priced at 1 dollar per share while B is priced at 9 dollars per share.
By market cap, the weights of A and B in the index should be
w_A = 0.1 and
w_B = 0.9, so the price of our index is
0.1 * 1 + 0.9 * 9 = 8.20.
By the end of the day, we suppose that the price of A rises to $2, while B is unchanged. Then, our new weights should be
w_A = 2/11 and
w_B = 9/11, with an index price of
Mathematically, I understand this is happening because the total market cap of A is increasing, so the price of A is being weighted more heavily. However, I'm failing to grasp any financial intuition that allows a stock index to drop despite components trending upwards (or remaining unchanged).
How do stock indices like SPX/NASDAQ handle scenarios like this? Are they dynamically reweighted every time a component's price change (likely every tick)?
Thanks in advance!