A security market index is a means to measure the value of a set of securities in a target market, market segment, or asset class. The constituent securities selected for inclusion in the security market index are intended to represent the target market.
There are usually two versions of the same index:
The value of a price return index is calculated as:
ni: the number of units of security i in the index portfolio.
Single Period Returns
The single-period price return of an index is the weighted average of the price returns of the individual securities:
Since the total return of an index includes price appreciation and income, we need to add the weighted average of income to the above formula to calculate the single-period total return:
The single-period returns should be linked geometrically.
Similarly, to calculate the total return over multiple periods: