A price-weighted index assumes that the investor holds an equal number of shares of each stock in the index. Since the number of stocks did not change, the investor would not need to change his holdings.

The other statements are true. A market value weighted index is most influenced by the stock with the largest market capitalization (Kurlew) and does not need to be adjusted for stock splits. A price-weighted index has a built-in downward bias because of the impact of stock splits. After a stock split, the denominator is adjusted downward to keep the index at the same level as before the split. Since high-growth companies tend to announce stock splits more frequently than low-growth companies, the larger, more successful firms lose influence on the index.