KNOWING HOW AN INDEX IS CALCULATED CAN HELP INVESTORS UNDERSTAND HOW IT MEASURES MARKET PERFORMANCE.
Index values are calculated and disseminated as frequently as once every second throughout the trading day. Behind each of these index "ticks" is a set of standardized approaches, formulas, and calculations.
How is an Index Value Calculated?
Click to reveal how a typical market-cap index might be calculated.
STEP 1: Each stock's market capitalization is calculated by multiplying its current price by its number of shares outstanding.
STEP 2: The index market capitalization is calculated by summing the market caps of the constituents.
STEP 3: The index value is calculated by dividing the index market capitalization by the index divisor.
|Index Market Capitalization
|Index Divisor ÷
|Index Value =
An index's return can be calculated by comparing the index values from one period to the next. For example, if the index value were 1,878.48 at the close of trading one day and 1,894.86 at the close the next day, the difference of 16.38 would indicate a 0.87% gain in value.
BACK-TESTED PERFORMANCE DATA
THE DIVISOR IN ACTION
The divisor is key to index calculation. It’s an arbitrary, though usually publicly available, number that is set at the time an index is launched. The divisor is used as the denominator in the equation for calculating index level where the numerator is the cumulative market value of the securities in the index. Because the numerator value can easily be trillions of dollars, the first thing the divisor does is to scale, or reduce, that figure to a comprehensible number.
Even more importantly, the divisor is the means for maintaining a continuous measure of market valuation, even as the list of index components is modified and the floating shares for various securities are adjusted. This continuity is possible because the divisor is regularly adjusted to compensate for any changes other than share prices that would affect the index value. Such changes may include rights offerings, spin-offs, and special dividend payments.
In addition, any adjustment to the divisor is made after the close of trading. As a result, the closing value of the index before the change is the same as the opening value on the next trading day, assuming that the prices of the component securities stay the same.
Divisor adjustments to equal-weighted and price-weighted indices differ from those for cap-weighted indices. However, the principle of maintaining a constant index level irrespective of changes to index components remains the same. For example, in a market-cap-weighted index, an adjustment isn’t required for stock splits because the market value of the security remains the same. However, with a price-weighted index, an adjustment is required because price — which might be half or less of what it was before the split — is the operative factor.
TYPES OF RETURNS
Equity and fixed income indices are most typically calculated as either price or total return indices. Many indices, including the S&P 500, are calculated both ways.
In a price-only calculation, the changing value of the index reflects the changing prices of its component securities, or unrealized capital gains and losses. In a total return index, on the other hand, the changing value is determined by a combination of the price changes and reinvested income from dividends or other cash payouts. This means the total return on an equity index in which any of the components pay dividends will always be higher than the price return.
Calculating the total return of an index differs from calculating the total return of an index-based product, such as a mutual fund, where dividend income is reinvested to buy additional shares. In an index, the dividends become an additional factor in calculating the changing level of the index.
Commodity indices may be calculated as total return or excess return, or as spot indices. For an example of how these return types are calculated, see the S&P GSCI methodology.