Offer your thoughts or opinion on the input financial query or topic using your financial background.

Does an index have a currency?
In practice, most (maybe all) stock indices are constructed by taking a weighted average of stock prices denominated in a single currency, and so the index implicitly does have that currency - as you suggest, US dollars for the S&P 500. In principle you can buy one "unit" of the S&P 500 for $2,132.98 or whatever by buying an appropriate quantity of each of its constituent stocks. Also, in a more realistic scenario where you buy an index via a tracker fund, you would typically need to buy using the underlying currency of the index and your returns will be relative to that currency - if the index goes up by 10%, your original investment in dollars is up by 10%.