A stock index is a performance indicator or measure of a country's economy or of an industry sector. For example, Nasdaq 100 represents the largest 100 companies traded on the Nasdaq Stock Exchange. If, on average, the share price of these companies goes up, then the index will rise. Conversely, if they fall, the index will drop.
Most main indices are based on a basket of shares and are thus considered good measures of the current market sentiment. When you take a position on an index, you are effectively investing in the performance of these shares and thus avoid factors that influence the performance of individual companies (such as a lack of market volume).
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