Currency-Hedged Index

Install and import#

npm install fintech-algorithms

import { calculate } from "fintech-algorithms/index-and-benchmark-engineering/return-variants/currency-hedged-index";

Signature#

calculate(data)

Neutralises currency exposure with rolling forwards. Hedged and converted variants of the same index can diverge by double digits over a year — they are different products, not a formatting choice.

Parameters#

Returns#

{ hedgedReturns, levels, endingLevel, hedgeRatio }

Hedged returns and levels, with the ratio applied.

Errors#

• When hedgeRatio falls outside 0…1 — 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#

{
  "baseCurrencyReturns": [0.01202, -0.003004, 0.002982, 0.006008, -0.003997],
  "forwardOffsets": [-0.0018, -0.0009, 0.0027, -0.0036, 0.0009],
  "hedgeRatio": 1,
  "baseLevel": 1000
}

Call#

calculate(data)

Returns#

object with 4 fields: hedgedReturns, levels, endingLevel, hedgeRatio

{
  "hedgedReturns": [0.01022, -0.003904, 0.005682, 0.002408, -0.003097],
  "levels": [1000, 1010.22, 1006.276101, 1011.993762, 1014.430643, 1011.288951],
  "endingLevel": 1011.288951,
  "hedgeRatio": 1
}

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 Currency-Hedged Index"]
    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 Return Variants family#

• Price-Return IndexLevel series from price returns alone, ignoring dividends.
• Gross Total-Return IndexReinvests dividends in full, with no tax deducted.
• Net Total-Return IndexReinvests dividends after withholding tax.
• Excess-Return IndexTotal return less a cash return, giving the return over funding.
• Dividend-Point IndexExpresses dividends in index points rather than currency, which is how dividend futures and swaps are quoted.
• Currency-Converted IndexRestates an index in another currency by compounding local returns with FX returns.