This document covers the mathematics of equity index and other quantitative rules-based calculations and assumes some acquaintance with mathematical notation and simple operations. The calculations are presented principally as equations, which have largely been excluded from the individual index methodologies, with examples or tables of results to demonstrate the calculations.
Different Varieties of Equity Indices
S&P Dow Jones Indices’ index calculation and corporate action treatments vary according to the categorization of the indices. At a broad level, indices are defined into two categorizations; Market Capitalization Weighted and Non-Market Capitalization Weighted Indices.
A majority of S&P Dow Jones Indices’equity indices are market capitalization weighted and float-adjusted, where each stock’s weight in the index is proportional to its float-adjusted market value. S&P DJI also offers capped versions of a market capitalization weighted index where single index constituents or defined groups of index constituents, such as sector or geographical groups, are confined to a maximum weight.
Non-market capitalization weighted indices include those that are not weighted by float-adjusted market capitalization and generally are not affected by notional market capitalization changes resulting from corporate events. Examples include indices that apply equal weighting, factor weighting such as dividend yield or volatility, strategic tilts, thematic weighting, or other alternative weighting schemes.
S&P DJI offers a variety of indices and index attribute data calculated according to various methodologies which are covered in this document:
- Market Capitalization Indices:
- Market-capitalization indices – where constituent weights are determined either by total or float-adjusted market capitalization.
- Capped market-capitalization indices − where single index constituents or defined groups of index constituents, such as sector or geographical groups, are confined to a maximum index weight.
- Non-Market Capitalization Indices:
- Price weighted indices − where constituent weights are determined solely by the prices of the constituent stocks in the index.
- Equal weighted indices − where each stock is weighted equally in the index.
- Derived Indices:
- Total return indices − index level reflect both movements in stock prices and the reinvestment of dividend income.
- Leveraged and inverse indices − which return positive or negative multiples of their respective underlying indices.
- Weighted return indices − commonly known as index of indices, where each underlying index is a component with an assigned weight to calculate the overall index of indices level.
- Indices that operate on an index as a whole rather than on the individual stocks − these include calculations of various total return methodologies and index fundamentals.
- Dividend Point indices − which track the total dividend payments of index constituents.
- Risk control, decrement, excess return, currency, currency hedged, domestic currency return, special opening quotation, turnover and fundamental data calculations.
The Index Divisor
The purpose of the index divisor is to maintain the continuity of an index level following the implementation of corporate actions, index rebalancing events, or other non-market driven actions.
The simplest capitalization weighted index can be thought of as a portfolio consisting of all available shares of the stocks in the index. While one might track this portfolio’s value in dollar terms, it would probably be an unwieldy number – for example, the S&P 500 float-adjusted market value is a figure in the trillions of dollars. Rather than deal with ten or more digits, the figure is scaled to a more easily handled number (e.g., 2000). Dividing the portfolio market value by a factor, usually called the divisor, does the scaling.
An index is not exactly the same as a portfolio. For instance, when a stock is added to or deleted from an index, the index level should not jump up or drop down; while a portfolio’s value would usually change as stocks are swapped in and out. To assure that the index’s value, or level, does not change when stocks are added or deleted, the divisor is adjusted to offset the change in market value of the index. Thus, the divisor plays a critical role in the index’s ability to provide a continuous measure of market valuation when faced with changes to the stocks included in the index. In a similar manner, some corporate actions that cause changes in the market value of the stocks in an index should not be reflected in the index level. Adjustments are made to the divisor to eliminate the impact of these corporate actions on the index value.
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