# Large price adjustment for capitalization-weighted index

Assume we are calculating a value-weighted index of a set of stocks that have more or less the same capitalization. However, one of the stocks has substantially larger price than others (although market cap is still on the same level). For example:

Stock A: price 10, market cap 100 000
Stock B: price 15, market cap 120 000
Stock C: price 10000, market cap 110 000


Then value weighted index will be:

10 * (100 000/330 000) + 15 * (120 000/330 000) + 10000 * (110 000/330 000) = 3342


Now if Stock C gets excluded from the index and is replaced by Stock D with price 18 and market cap 110 000, then new value of the index is:

10 * (100 000/330 000) + 15 * (120 000/330 000) + 18 * (110 000/330 000) = 14.5


So the index would drop by 99.6% without any changes to the market cap. Am I missing something here ? Is there a way to adjust for that ? Fundamentally the index should represent average return on a universe of stocks and should not be affected so much by inclusion/exclusion of a single stock.

• The change of the index value in return space is NOT what an investor in the index is going to receive so it won't matter to the index holder if what you described happens. The dropping out of a stock from the index is kind of viewed as a "sell" of that stock by the person who owned the index so the return that the person receives is going to take into account that Stock C left the index. The investor doesn't "lose money" because stock C got replaced with a stock whose price is much less. Basically, it's all reflected in the accounting and a non-issue to an investor who owns the index. Feb 11, 2022 at 4:22
• Thank you mark - this is great insight. What about the futures on index then ? In this case return on index = return that investor gets. I am also curious how to adjust for stock drop out. From pure time series perspective you are calculating an average return on index. With such huge drop it will not be a good representation of the actual return that investor can expect. Feb 11, 2022 at 18:11
• No problem to help but I'm not clear on what you're looking for. What I can say is that an index change due to a deletion or an add will NEVER effect the return that an investor receives aside from the FUTURE performance of the stock that was deleted and the stock that was added. So, whether it's futures on the index or anything else, adds and deletions will only have an effect GOING FORWARD. The price difference between the deletion and add makes no difference. I might not be explaining this as clearly as I'd like to think so if someone else wants to chip in, feel free. Thanks. Feb 12, 2022 at 4:03
• Maybe think of it like this. The denominator in the calculation of the return to the investor is the new denominator with the new stock added and old stock deleted so the return takes the deletion and add into account. Does that help ? Feb 12, 2022 at 4:04