Reconstitution Algorithm

Key concepts

The governed definitions this build depends on. Read them first if a term is unfamiliar.

PrimaryIndex ReconstitutionIndex reconstitution rebuilds or materially refreshes index membership according to eligibility and selection rules.
PrerequisitePoint-in-Time DatasetA point-in-time dataset can reconstruct what information was valid and available to a specified user or system at a historical decision time.
PrerequisiteUniverse MembershipUniverse membership is an effective-dated assertion that a security belongs to a defined eligible set for a specified interval.
ImportantBenchmarkA benchmark is a governed reference value or series used to measure, price, allocate, or compare financial activity.
ImportantBuffer RuleA buffer rule reduces unnecessary index changes by applying retention zones or different entry and exit thresholds.
ImportantCorporate ActionA corporate action is an issuer or security event that changes rights, quantities, cash flows, identity, or trading terms.
ImportantEligibility RuleAn eligibility rule is a test that determines whether an instrument can enter or remain in a defined universe or index.
ImportantIndex ConstituentAn index constituent is an instrument included in an index for a specified effective interval.
ImportantIndex MethodologyAn index methodology is the governed rule set defining an index's objective, selection, weighting, calculation, maintenance, and review.
ImportantIndex RebalancingIndex rebalancing changes constituent quantities, factors, or target weights according to a scheduled or event-driven methodology.
ImportantIndex ReviewAn index review is a governed evaluation of constituents, data, factors, or methodology according to a declared schedule and process.
ImportantIndex TurnoverIndex turnover measures the amount of constituent weight or notional that changes between two portfolio states under a declared convention.

Reconstitution Algorithm helps practitioners trust what an index level means and helps builders rebuild membership from ranked candidates while controlling unnecessary turnover. The useful outcome is not merely a smooth chart—it is a value whose inputs, methodology version, time boundary, calculation, and invariant can all be audited.

Why this matters

Indices sit beneath funds, derivatives, mandates, performance reports, and market commentary. Yet the same securities can produce different valid indices because weighting, dividends, taxes, FX, capping, rebalancing, and governance differ. A benchmark engineer must therefore preserve both the market observation and the rule that transformed it.

Reconstitution Algorithm methodology overview

The diagram keeps the headline outcome below the title and learning promise, then gives the numerical marks their own stage. Nothing crosses the text region, and every shape represents canonical output rather than decoration.

Intuition before notation

Think of the index as a versioned calculation ledger. First freeze what was eligible and knowable. Then validate units and constraints. Only then calculate the level, weights, return, or membership state. Finally recompute the invariant independently. If continuity, feasibility, weight sum, or timing fails, publication stops.

Rendering system map…

Contract and formula

The canonical relationship is:

select top N with incumbent entry/exit buffers

Symbol	Meaning	Unit and timing
$I_t$	Published index or strategy level	Index points at timestamp $t$
$D_t$	Divisor or scale state	Effective at the same calculation boundary
$M_t$	Methodology-defined numerator	Base currency value
$P_i,Q_i,F_i,X_i$	Price, index shares, factor, and FX	Aligned point-in-time constituent state
$w_i,r_i$	Weight and return	Decimal fraction using the declared return variant

The shared fixture defines any additional topic-specific fields. Values must be finite; denominators and index levels must remain positive; factors, caps, and tax rates must satisfy their declared bounds; and arrays must align.

Step-by-step method

Freeze the constituent or time-series state at the decision cutoff.
Retain methodology version, source timestamp, currency, calendar, and return variant.
Validate dimensions, bounds, ordering, and constraint feasibility.
Run reconstitution using only current and prior state.
Recompute continuity, weight sum, positive level, or selection constraints.
Publish the result with diagnostics—or reject it with a specific reason.

Worked numerical example

The canonical fixture returns:

JSON

{
  "selectedIds": [
    "A",
    "B",
    "C",
    "D",
    "F"
  ],
  "additions": [
    "C"
  ],
  "deletions": [],
  "targetCount": 5
}

Canonical Reconstitution Algorithm values

Those are the exact rounded values asserted by both implementations. Rounding occurs only at the public boundary so iterative state and recursive levels do not accumulate display precision as calculation error.

Explore the methodology state

Open the guided light playground. It retains the full synthetic dataset and starts at a populated state. Choose the boundary scenario, change the constraint, step across the effective line, inspect the audit rows, then choose the rejected state. Reset always returns to the same observation and parameter.

The lab teaches one decision: what changed, why the rule changed state, and whether an output may be published. It does not imply that the illustrated method will outperform an alternative.

Implementation walkthrough

The Python implementation and TypeScript implementation expose the same calculate contract. A shared domain engine centralizes validated matrix, weight, capping, return, and rounding primitives, while each topic wrapper fixes the catalog calculation kind. The shared JSON fixture prevents language-specific examples from drifting.

The implementation deliberately favors explicit loops and diagnostics. Production administrators may use decimal arithmetic, distributed price engines, solver libraries, and exception workflows, but they should preserve the same visible invariants.

Compare nearby variants

Maintenance layer	Input evidence	Decision	Required audit output
Eligibility	Security attributes	Include or reject	Every rejection reason
Liquidity	Point-in-time trading history	Pass threshold	Window, median, missing months
Reconstitution	Frozen ranks and incumbency	Select membership	Adds, deletes, buffers
Rebalancing	Target and current weights	Trade to target	Index shares and turnover
Replication cost	Trade, spread, impact scenario	Estimate cost	Assumptions and sensitivities

The table shows why a nearby method cannot be substituted silently. A different tax assumption, cap sequence, covariance constraint, or review buffer changes the index definition even when the final numbers appear close.

Testing and validation

Topic tests verify canonical output, invalid-input rejection, input immutability, JSON finiteness, and cross-language parity. Domain checks additionally validate all package files, Mermaid source, SVG XML and bounds, data density, lab controls, keyboard behavior, deterministic reset, reduced motion, responsive layouts, embedded article behavior, links, and production builds.

Passing those checks establishes definition-level correctness for the educational convention. It does not establish tracking capacity, market impact, predictive value, administrator authorization, or compliance with every jurisdiction.

Failure modes

The central guard is to freeze the review universe and scores before applying deterministic buffers. Common failures include stale divisor or FX state, infeasible caps, singular covariance, missing dividends, future review data, mismatched calendars, excessive rounding, silent corrections, and exceptional corporate events handled with the wrong provider rule.

Reconstitution Algorithm publish-or-block guard

A rejected calculation should retain the raw inputs, methodology version, failed invariant, and time of decision. That evidence is more valuable than a plausible number with unknown provenance.

Evidence, governance, and scope

This topic belongs to Governance and Maintenance. The S&P DJI policies, MSCI methodology library, IOSCO Principles, and EU Benchmark Regulation frame reproducible maintenance and governance. Benchmark governance also requires transparent methodology quality, conflicts management, change procedures, complaints, auditability, and cessation planning. The package uses synthetic data and does not reproduce a branded provider index.

Summary and next topic

You can now calculate, implement, and audit Reconstitution Algorithm. Freeze dated state, make constraints explicit, recompute the invariant, and block unsafe output. Continue with Rebalancing Algorithm to extend the benchmark-engineering chain.

Asset map

Asset	Article placement	Video scene	Source	Static fallback	Status
Methodology overview	Opening	1–2	`visuals/static/article-hero.svg`	Same asset	Ready
Calculation flow	Intuition	3	`visuals/mermaid/calculation-flow.md`	Article steps	Ready
Canonical values	Worked example	5	`visuals/static/worked-example.svg`	Fixture JSON	Ready
Guided lab	Exploration	4–7	`visuals/animated/playground.html`	Worked-example SVG	Ready
Failure guard	Failure modes	7	`visuals/static/failure-guard.svg`	Text rejection rule	Ready

Full source records are in ../REFERENCES.md, and the canonical factual package is ../README.md.

Workflows

Rendered from the canonical Mermaid sources linked by this article.

Reconstitution Algorithm calculation flow

This diagram separates the dated methodology state from calculation and invariant checks.

Rendering system map…

Takeaway: reconstitution is publishable only after feasibility and post-calculation invariants agree.

Reconstitution Algorithm methodology state

This state machine makes review, calculation, exception, and publication boundaries visible.

Rendering system map…

Takeaway: Freeze the review universe and scores before applying deterministic buffers; a revision creates a new version instead of silently overwriting history.

References13 primary sources and evidence notes

Expand the source trail, evidence role, and limitations behind the engineering choices.

Accessed 2026-07-21. Examples and datasets are synthetic; no vendor index levels or constituent data are redistributed.

R1 — S&P Dow Jones Indices Index Mathematics Methodology

Organization or authors: S&P Dow Jones Indices
Source type: Official index mathematics methodology
Publication or effective date: 2026 accessed edition
URL or DOI: https://www.spglobal.com/spdji/en/documents/methodologies/methodology-index-math.pdf
Accessed: 2026-07-21
Jurisdiction: Global
Supports: Divisors, price and capitalization weighting, capping, return variants, currency, strategy, risk-control, decrement, and index-of-indices mathematics
Limitations: Provider conventions are authoritative for S&P DJI indices, not universal defaults

R2 — S&P DJI Equity Indices Policies & Practices

Organization or authors: S&P Dow Jones Indices
Source type: Official operations and maintenance methodology
Publication or effective date: March 2026
URL or DOI: https://www.spglobal.com/spdji/en/documents/methodologies/methodology-sp-equity-indices-policies-practices.pdf
Accessed: 2026-07-21
Jurisdiction: Global
Supports: Data hierarchy, corporate actions, additions, deletions, reviews, discretion, announcements, and recalculation
Limitations: Operational judgment and product rules still require the applicable index methodology

R3 — FTSE Russell Capping Methodology

Organization or authors: FTSE Russell, LSEG
Source type: Official capping guide
Publication or effective date: Version 5.0, January 2026
URL or DOI: https://www.lseg.com/content/dam/ftse-russell/en_us/documents/policy-documents/capping-methodology-guide.pdf
Accessed: 2026-07-21
Jurisdiction: Global
Supports: Single-level and multi-level capping, fast entrants, and corporate-event maintenance
Limitations: Targets and sequencing depend on the named FTSE Russell index

R4 — FTSE Russell Index Policy and Methodology Library

Organization or authors: FTSE Russell, LSEG
Source type: Official methodology library
Publication or effective date: Current accessed edition
URL or DOI: https://www.lseg.com/en/ftse-russell/governance/index-policy-and-methodology
Accessed: 2026-07-21
Jurisdiction: Global
Supports: Calculation, liquidity, free float, review, governance, and recalculation source hierarchy
Limitations: The library links multiple documents whose effective dates must be checked separately

R5 — MSCI Global Investable Market Indexes Methodology Library

Organization or authors: MSCI
Source type: Official methodology library
Publication or effective date: May 2026 calculation and GIMI editions
URL or DOI: https://www.msci.com/eqb/gimi/stdindex/methodology.html
Accessed: 2026-07-21
Jurisdiction: Global
Supports: Investability, free float, size and liquidity segmentation, reviews, corporate events, and index calculation
Limitations: MSCI data and branded production calculations can require licenses

R6 — MSCI Minimum Volatility Indexes Methodology

Organization or authors: MSCI
Source type: Official minimum-volatility methodology page
Publication or effective date: June 2026 accessed edition
URL or DOI: https://www.msci.com/msci-minimum-volatility-indexes
Accessed: 2026-07-21
Jurisdiction: Global
Supports: Optimization-based minimum-volatility construction and constraints
Limitations: The educational implementation demonstrates the mathematical core and does not reproduce proprietary production constraints

R7 — S&P Risk Control 2.0 Indices Methodology

Organization or authors: S&P Dow Jones Indices
Source type: Official strategy-index methodology
Publication or effective date: 2025 accessed edition
URL or DOI: https://www.spglobal.com/spdji/en/documents/methodologies/methodology-sp-risk-control-2-indices.pdf
Accessed: 2026-07-21
Jurisdiction: Global
Supports: Volatility-target exposure, dampening assets, rebalancing, and realized-volatility state
Limitations: This package uses a transparent cash implementation, not every Risk Control 2.0 variant

R8 — Principles for Financial Benchmarks

Organization or authors: International Organization of Securities Commissions
Source type: International benchmark-governance principles
Publication or effective date: Final report FR07/13, July 2013
URL or DOI: https://www.iosco.org/library/pubdocs/pdf/ioscopd415.pdf
Accessed: 2026-07-21
Jurisdiction: Global
Supports: Governance, methodology quality, accountability, conflicts, changes, and cessation
Limitations: Principles are not a substitute for applicable law or administrator procedures

R9 — Regulation (EU) 2016/1011

Organization or authors: European Union
Source type: Official consolidated regulation
Publication or effective date: Consolidated 1 January 2026
URL or DOI: https://eur-lex.europa.eu/eli/reg/2016/1011
Accessed: 2026-07-21
Jurisdiction: European Union
Supports: Accuracy, integrity, administration, input data, methodology, and use of regulated benchmarks
Limitations: Legal applicability depends on benchmark type, administrator, use, and jurisdiction

R10 — Portfolio Selection

Organization or authors: Harry Markowitz
Source type: Original peer-reviewed paper
Publication or effective date: 1952
URL or DOI: https://doi.org/10.1111/j.1540-6261.1952.tb01525.x
Accessed: 2026-07-21
Jurisdiction: General
Supports: Mean-variance foundations used by the minimum-variance topic
Limitations: Index-provider constraints and estimation choices are later implementation layers

R11 — On the Properties of Equally-Weighted Risk Contributions Portfolios

Organization or authors: Sébastien Maillard, Thierry Roncalli, and Jérôme Teïletche
Source type: Original peer-reviewed research
Publication or effective date: 2010
URL or DOI: https://doi.org/10.3905/jpm.2010.36.4.060
Accessed: 2026-07-21
Jurisdiction: General
Supports: Equal-risk-contribution definition and portfolio properties
Limitations: Convergence and covariance estimation remain implementation choices

R12 — Fundamental Indexation

Organization or authors: Robert Arnott, Jason Hsu, and Philip Moore
Source type: Original peer-reviewed research
Publication or effective date: 2005
URL or DOI: https://www.researchaffiliates.com/documents/FAJ_Mar_Apr_2005_Fundamental_Indexation.pdf
Accessed: 2026-07-21
Jurisdiction: General
Supports: Economic-scale weighting independent of current market price
Limitations: Metric selection, normalization, and data lags must be declared

R13 — FTSE Currency Hedging Methodology Overview

Organization or authors: FTSE Russell, LSEG
Source type: Official methodology overview
Publication or effective date: 2023
URL or DOI: https://www.lseg.com/content/dam/ftse-russell/en_us/documents/other/ftse-currency-hedging-methodology-cut-sheet.pdf
Accessed: 2026-07-21
Jurisdiction: Global
Supports: Currency exposure aggregation, hedge ratios, forward rolls, and quote conventions
Limitations: Production rates and calendars require licensed data and the full applicable calculation guide

Implementation

Full dependency-light reference implementations in both supported languages.

reconstitution_algorithm.ts

/** Reconstitution Algorithm (D03-F06-A05) reference implementation. */
import { calculateIndexTopic } from "../../../../shared/typescript/indexEngine.ts";

const KIND = "reconstitution";

export function calculate(data) {
  if (data === null || typeof data !== "object" || Array.isArray(data)) throw new TypeError("data must be an object");
  return calculateIndexTopic(KIND, structuredClone(data));
}

Playground

The embedded lab now expands to its full document height, keeping the article as the only scroll surface.

Full-height labplaygroundOpen full screen

Reconstitution Algorithm

Why this matters

Intuition before notation

Contract and formula

Step-by-step method

Worked numerical example

Explore the methodology state

Implementation walkthrough

Compare nearby variants

Testing and validation

Failure modes

Evidence, governance, and scope

Summary and next topic

Asset map

Reconstitution Algorithm calculation flow

Reconstitution Algorithm methodology state

R1 — S&P Dow Jones Indices Index Mathematics Methodology

R2 — S&P DJI Equity Indices Policies & Practices

R3 — FTSE Russell Capping Methodology

R4 — FTSE Russell Index Policy and Methodology Library

R5 — MSCI Global Investable Market Indexes Methodology Library

R6 — MSCI Minimum Volatility Indexes Methodology

R7 — S&P Risk Control 2.0 Indices Methodology

R8 — Principles for Financial Benchmarks

R9 — Regulation (EU) 2016/1011

R10 — Portfolio Selection

R11 — On the Properties of Equally-Weighted Risk Contributions Portfolios

R12 — Fundamental Indexation

R13 — FTSE Currency Hedging Methodology Overview

Related complete builds.

Eligibility Screen

Liquidity Screen

Free-Float Factor Calculation