Divisor Continuity Adjustment

Install and import#

npm install fintech-algorithms

import { calculate } from "fintech-algorithms/index-and-benchmark-engineering/index-initialization-and-continuity/divisor-continuity-adjustment";

Signature#

calculate(data)

Rescales the divisor when market value changes for a non-market reason — a share issue, a member swap — so the level does not jump. This is the mechanism that makes an index a continuous series rather than a sum of unrelated numbers.

Parameters#

Returns#

{ oldLevel, newDivisor, bridgedLevel, continuityError }

The new divisor plus continuityError — the residual difference between the level before and after. It should be zero or floating-point dust; anything larger means the inputs were not measured at the same instant.

Errors#

• When any market value or divisor is not positive — throws

Complexity: time O(1), space O(1).

Worked example#

verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

Input#

{
  "oldMarketValue": 100000000,
  "newMarketValue": 112000000,
  "oldDivisor": 100000
}

Call#

calculate(data)

Returns#

object with 4 fields: oldLevel, newDivisor, bridgedLevel, continuityError

{
  "oldLevel": 1000,
  "newDivisor": 112000,
  "bridgedLevel": 1000,
  "continuityError": 0
}

Diagrams#

Calculation flow#

flowchart LR
    A["Point-in-time inputs"] --> B["Validate units and timing"]
    B --> C{"Contract feasible?"}
    C -->|No| D["Reject with reason"]
    C -->|Yes| E["Calculate Divisor Continuity Adjustment"]
    E --> F["Recompute invariants"]
    F --> G{"Checks pass?"}
    G -->|No| D
    G -->|Yes| H["Publish audited output"]

stateDiagram-v2
    [*] --> FrozenInputs
    FrozenInputs --> Validated: contract passes
    FrozenInputs --> Rejected: missing or infeasible
    Validated --> Calculated: apply named rule
    Calculated --> Audited: invariants pass
    Calculated --> Rejected: invariant fails
    Audited --> Published: version and timestamp recorded
    Published --> Revised: approved correction
    Revised --> FrozenInputs: rebuild from retained source state

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

• S&P Dow Jones Indices Index Mathematics Methodology — S&P Dow Jones Indices
• S&P DJI Equity Indices Policies & Practices — S&P Dow Jones Indices
• FTSE Russell Capping Methodology — FTSE Russell, LSEG
• FTSE Russell Index Policy and Methodology Library — FTSE Russell, LSEG
• MSCI Global Investable Market Indexes Methodology Library — MSCI
• MSCI Minimum Volatility Indexes Methodology — MSCI
• S&P Risk Control 2.0 Indices Methodology — S&P Dow Jones Indices
• Principles for Financial Benchmarks — International Organization of Securities Commissions
• Regulation (EU) 2016/1011 — European Union
• Portfolio Selection — Harry Markowitz
• On the Properties of Equally-Weighted Risk Contributions Portfolios — Sébastien Maillard, Thierry Roncalli, and Jérôme Teïletche
• Fundamental Indexation — Robert Arnott, Jason Hsu, and Philip Moore
• FTSE Currency Hedging Methodology Overview — FTSE Russell, LSEG

The rest of the Index Initialization and Continuity family#

• Base-Date/Base-Value InitializationSets an index running: pick a base date and a base level, and the divisor follows from the market value on that date.
• Index Divisor InitializationThe divisor itself: market value divided by the target level.
• Corporate-Action Divisor BridgeApplies a corporate action to an index by routing its non-market value change through the divisor.
• Intraday Index-Level CalculationRecomputes the level from a live price snapshot using fixed index shares and float factors.