Fixed-Decrement Index

Install and import#

bash

npm install fintech-algorithms

import { calculate } from "fintech-algorithms/index-and-benchmark-engineering/strategy-indices/fixed-decrement-index";

Signature#

calculate(data)

Deducts a fixed number of index points per year. Decrement indices exist to make option pricing on them cheaper, and the deduction is a real drag borne by the holder — not a fee schedule.

Parameters#

Name	Type	Notes
`data`	`{ underlyingLevels: number[]; annualDecrementPoints: number; dayCount: number; baseLevel: number }`	`dayCount` sets the convention used to pro-rate the annual figure; 360 and 365 give different answers. `baseLevel` is the index value at the start of the series; it scales the level but never the returns.

Returns#

{ dailyDeductions, levels, endingLevel }

The deduction applied each day and the resulting level series.

Errors#

When dayCount is not positive — throws

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

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#

data

{
  "underlyingLevels": [100, 101, 100.5, 102, 103, 102.6],
  "annualDecrementPoints": 5,
  "dayCount": 360,
  "baseLevel": 100
}

Call#

calculate(data)

Returns#

object with 3 fields: dailyDeductions, levels, endingLevel

{
  "dailyDeductions": [0.013889, 0.013889, 0.013889, 0.013889, 0.013889, 0.013889],
  "levels": [100, 100.986111, 100.472291, 101.957989, 102.943688, 102.530018],
  "endingLevel": 103.915174
}

Diagrams#

Calculation flow#

Fixed-Decrement Index 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 Fixed-Decrement Index"]
    E --> F["Recompute invariants"]
    F --> G{"Checks pass?"}
    G -->|No| D
    G -->|Yes| H["Publish audited output"]

Fixed-Decrement Index methodology state

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

Fixed-Decrement Index

Install and import#

Signature#

Parameters#

Returns#

Errors#

Worked example#

Input#

Call#

Returns#

Diagrams#

Calculation flow#

How it works#

References#

The rest of the Strategy Indices family#