This is (or is becoming) a problem particularly with index funds/ETF's that use market-value to weight ownership. You can certainly find out the top 10 stocks in an index, and can probably get detained information on funds you are participating in. But avoiding market segments, countries, individual stocks, ... might be hard if the funds aren't interested in working with you. Although I could see boutique organizations creating more-acceptable investments as there's money in doing so.