| Field | Value | Source text | Reading (model) |
|---|---|---|---|
| G1 Scope, precedence and principles · 7 fields | |||
| Document date | 2026-09 | September 2026Open p.1 ↗ |
The document is dated September 2026. |
| Index categorizations | Market Capitalization Weighted, Non-Market Capitalization Weighted | At a broad level, indices are defined into two categorizations; Market Capitalization Weighted and Non-Market Capitalization Weighted Indices.Open p.5 ↗ |
S&P DJI broadly categorizes equity indices as market capitalization weighted or non-market capitalization weighted. |
| Covered indices | S&P DJI equity indices and other quantitative rules-based calculations, market capitalization weighted indices, capped market capitalization weighted indices, non-market capitalization weighted indices, price weighted indices, equal weighted indices, total return indices, leveraged and inverse indices, weighted return indices, dividend point indices, risk control, decrement, excess return, currency, currency hedged, domestic currency return, special opening quotation, turnover and fundamental data calculations | This document covers the mathematics of equity index and other quantitative rules-based calculations and assumes some acquaintance with mathematical notation and simple operations.Open p.5 ↗ |
The document covers the mathematics of S&P DJI equity indices and other quantitative rules-based calculations, including the index and calculation types listed in the introduction. |
| Precedence rule | Index-specific methodologies specify the pricing type, application, parameters, and family treatment; this mathematics document provides calculations largely excluded from individual methodologies, while corporate action details are found in supporting policies or the relevant index methodology. | 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.Open p.5 ↗ |
The mathematical rules supplement individual index methodologies, and index-specific methodologies or supporting policy documents govern the particular application, parameters, and corporate-action treatment. |
| Administrator | S&P Dow Jones Indices (S&P DJI) | S&P Dow Jones Indices’ (S&P DJI) index calculation and corporate action treatments vary according to the categorization of the indices.Open p.5 ↗ |
The rules are issued by S&P Dow Jones Indices. |
| Rulebook version | — | — (not found verbatim in the PDF) |
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| Effective date | — | — (not found verbatim in the PDF) |
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| G2 Calculation and publication · 13 fields | |||
| Divisor adjustment timing | after the close of trading | Divisor adjustments are made “after the close” meaning that after the close of trading the closing prices are used to calculate the new divisor based on whatever changes are being made.Open p.10 ↗ |
Divisor adjustments are calculated after the close using closing prices and the applicable changes. |
| Negative or zero end of day level rule | Publish an official closing value of zero when an end-of-day calculation is zero or negative. | In the event an end-of-day index calculation results in a zero or negative value, S&P DJI will publish an official closing index value of zero on that day.Open p.70 ↗ |
If an end-of-day calculation produces zero or a negative value, S&P DJI publishes an official closing index value of zero. |
| Formula type | Divisor | The numerator on the right hand side is the price of each stock in the index multiplied by the number of shares used in the index calculation. This is summed across all the stocks in the index. The denominator is the divisor.Open p.7 ↗ |
Capitalization-weighted indices are calculated using a divisor-based formula in which index market value is divided by the divisor. |
| Return variants | PR, GTR, NTR | The preceding discussions were related to price indices where changes in the index level reflect changes in stock prices.Open p.22 ↗ |
The document covers price indices, ordinary total return indices that reinvest dividends, and net total return indices that adjust dividends for withholding tax. |
| Dividend treatment | Daily cash dividends are converted into index dividend points and reinvested across the overall total return index rather than in the specific stock paying the dividend. | A total return index represents the total return earned in a portfolio that tracks the underlying price index and reinvests dividend income in the overall index, not in the specific stock paying the dividend.Open p.22 ↗ |
Total return indices reinvest dividend income across the index by converting the daily dividend into index points and applying the resulting daily total return to the prior total return level. |
| Withholding tax basis | Global indices use withholding tax rates from the perspective of a Luxembourg investor; domestic index families use rates from the perspective of a domestic investor. | The tax rates used for S&P DJI’s global indices are from the perspective of a Luxembourg investor. However, in domestic index families, tax rates from the perspective of a domestic investor will be applied.Open p.23 ↗ |
Net total return indices adjust dividends by the applicable withholding rate, with Luxembourg investor perspective for global indices and domestic investor perspective for domestic families. |
| Divisor adjustment rule | Multiplicative formula: Divisor_t = Divisor_(t-1) * MV_t / MV_(t-1); Additive formula: Divisor_new = Divisor_old + CMV / Index Level; Principle: The divisor is adjusted so the index level remains unchanged when constituent market values change at constant prices | Given these, it is easy to determine the new divisor that will keep the index level constant when stock r is replaced by stock s: MV t = Divisor ( Divisor 1)Open p.9 ↗ |
The new divisor equals the old divisor multiplied by the ratio of new to old index market value, or equivalently the old divisor plus the change in market value divided by the unchanged index level. |
| Divisor adjustment events | addition of companies, deletion of companies, changes in shares outstanding, changes to IWFs, changes to other factors affecting share counts, corporate actions that alter total index market value at constant prices, index rebalancing events, other non-market driven actions | 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.Open p.5 ↗ |
Divisor adjustments are triggered by additions, deletions, share-count and IWF changes, other share-count factors, rebalancings, and corporate or non-market actions that change total index market value at constant prices. |
| Calculation frequency | Real-time and end-of-day calculations are covered; the provided text does not state a specific real-time publication interval. | For indices calculated in real-time, in the event an intraday index calculation results in a zero or negative value, S&P DJI will publish the zero or negative value as calculated.Open p.70 ↗ |
The rules refer to real-time intraday calculations and official end-of-day calculations, but do not specify a real-time interval in the provided sections. |
| Calculation times | — | — (not found verbatim in the PDF) |
|
| Precision | — | — (not found verbatim in the PDF) |
|
| Currency | Index-specific; the formulas use applicable exchange rates and examples include US dollars, while indices may be published in other currencies. | ∗𝐹𝑥𝑅𝑎𝑡𝑒𝑖 𝐼𝑛𝑑𝑒𝑥𝑀𝑎𝑟𝑘𝑒𝑡𝑉𝑎𝑙𝑢𝑒= ∑𝑃𝑖∗𝑆ℎ𝑎𝑟𝑒𝑠𝑖∗𝐼𝑊𝐹𝑖 𝑖 To calculate a capped market cap index, the market capitalization for each stock used in the calculation of the index is redefinedOpen p.11 ↗ |
Calculation and publication currency varies by index, with exchange rates applied when applicable. |
| Publication channels | S&P Dow Jones Indices website, index vendors for alternative pricing | At each underlying index’s rebalancing, and using each stock’s weight at that time, a forward looking calendar of such dates is determined and posted on S&P Dow Jones Indices’ Web site at www.spglobal.com/spdji.Open p.40 ↗ |
S&P DJI posts certain index information on its website and may capture alternative pricing through vendors. |
| G3 Prices and market data · 10 fields | |||
| Special opening quotation untraded price | Previous day's closing price is used for any stock that has not traded during the regular trading session. | For any stock that has not traded during the regular trading session, the previous day's closing price is used for the SOQ index calculation.Open p.69 ↗ |
For the Special Opening Quotation, a stock that has not traded in the regular session is valued at its previous day's closing price. |
| Special opening quotation price | Primary exchange opening price at which each security first trades. | The special opening quotation (“SOQ”) is calculated using the same methodology as the underlying index except that the price used for each index constituent is the open price at which the security first trades upon the opening of the exchange on a given trading day.Open p.69 ↗ |
The SOQ uses the opening price at which each constituent first trades on its primary exchange. |
| Vwap definition | Sum of trade price multiplied by trade volume over the observation window divided by total trade volume in that window. | VWAP is calculated by multiplying the price of trades by their volume, summing that for the applicable time window, and then dividing by the total volume of trades within that time windowOpen p.69 ↗ |
VWAP is a volume-weighted average of trade prices over a specified window. |
| Twap definition | Simple average of price snapshots over a specified observation window. | TWAP is calculated by taking a simple average of various snapshots of the price throughout the time window, written formulaically below:Open p.69 ↗ |
TWAP is a simple average of price snapshots over a specified window. |
| Fair value price source | Fair value adjustment factors are provided by a pricing service and applied to adjusted-close constituent prices. | The indices are calculated using fair value adjustment factors applied on a stock by stock basis to each stock in the index. The factors are provided by a pricing service which calculates fair value adjustments.Open p.69 ↗ |
Fair Value indices multiply adjusted-close prices by stock-by-stock fair value adjustment factors provided by a pricing service. |
| Price source | Exchange-provided prices are used for official end-of-day calculations, with the relevant price type—such as last trade, auction, VWAP, or official close—specified by exchange in the Global Equity Close Prices guide. | S&P DJI leverages exchange provided prices for official end-of-day index calculations. For each exchange, S&P Dow Jones Indices will use the relevant price (e.g. last trade, auction, VWAP, official close) as defined in the S&P Dow Jones Indices' Global Equity Close Prices guideOpen p.68 ↗ |
Official end-of-day index calculations use the relevant exchange-provided price, which may be the last trade, auction price, VWAP, or official close depending on the exchange. |
| Closing price rule | The relevant exchange-defined close price is used; the exact type is specified in S&P DJI's Global Equity Close Prices guide. | For each exchange, S&P Dow Jones Indices will use the relevant price (e.g. last trade, auction, VWAP, official close) as defined in the S&P Dow Jones Indices' Global Equity Close Prices guide available on https://us.spindices.com/.Open p.68 ↗ |
For official closing calculations, S&P DJI uses the relevant closing price defined for each exchange, such as an auction, official close, last trade, or VWAP. |
| Suspended price rule | For SOQ calculations, M&A target stocks suspended or halted are synthetically priced using deal ratio terms and the acquirer's opening price for stock deals, or the lower of the previous official close and cash consideration for cash-only deals; spun-off stocks not yet trading also receive a synthetic SOQ. | For M&A target stocks that are suspended or halted from trading on an exchange but are still in indices, S&P Dow Jones Indices will synthetically derive an SOQ for the suspended security using the deal ratio terms and the opening price of the acquiring companyOpen p.69 ↗ |
For the Special Opening Quotation, suspended M&A targets receive synthetic prices from merger terms and the acquirer's open or cash offer, and untraded spin-offs also receive synthetic SOQ prices. |
| Exchange rates | FX rates are applied in index calculations; dividend correction FX uses the exchange rate on the ex-date, currency-index dividend adjustments use the FX rate on the effective date, and dividend points use the same exchange rate as the total return version. | Foreign exchange conversion, if applicable, is based on the exchange rate on the ex-date, calculated as: Correction Amount * FX on the Reference Ex-DateOpen p.24 ↗ |
Currency conversion uses the rates applicable to the calculation, including the ex-date rate for dividend corrections and the effective-date rate for currency-index dividend adjustments. |
| Data sources | Exchanges, index vendors, ICE Data Services, Virtu Financial, Inc., S&P DJI internal calculations | Alternative pricing may be captured through vendors or calculated internally by S&P DJI. The formulas defined in this section are specific to internally calculated alternative pricing.Open p.68 ↗ |
Prices and alternative prices may come from exchanges, vendors, or internal S&P DJI calculations, while fair value indices use ICE Data Services or Virtu Financial. |
Open points · 10Model-written, for reference
- 1No explicit rulebook version label was found.
- 2No explicit effective date for the rules was found; the document only shows September 2026.
- 3No specific real-time calculation interval or intraday publication times were found.
- 4No number of decimal places for published index levels was found.
- 5The sections do not provide a general rule for ordinary suspended-security pricing outside SOQ or fair value contexts.
- 6Not coveredG4 Corporate events: not covered by this edition
- 7Not coveredG5 Shares, free float and weight factors: not covered by this edition
- 8Not coveredG6 Disruption, emergencies and corrections: not covered by this edition
- 9Not coveredG7 Review and constituent changes: not covered by this edition
- 10Not coveredG8 Governance, changes and termination: not covered by this edition
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