Continuous Futures Back-Adjustment Calculator
Illustrate how one historical futures price changes when an old contract is aligned to a new contract at one roll boundary using a backward difference or backward ratio method.
Enter one futures roll boundary
Use old- and new-contract prices observed under one documented roll rule and time basis. The historical-price field demonstrates the effect on one earlier value, not a complete series.
Entered back-adjustment result
Entered Futures Curve Analysis 1.0.0
| Calculation step | Entered arithmetic | Derived result |
|---|
How continuous-futures back adjustment is illustrated
Backward difference price = historical price + raw roll gap
Backward ratio factor = new-contract roll price ÷ old-contract roll price
Backward ratio price = historical price × backward ratio factor
A continuous futures series joins expiring contracts even though the old and new contracts can trade at different prices. TradingView documents an additive back adjustment based on the difference between the new and old closes near the switch. The same coefficient is applied to prior history so the old roll observation aligns with the new contract.
Research distributed by CME Group describes backward ratio adjustment as multiplying prior history by the ratio of new-contract to old-contract price at the roll. Ratio adjustment preserves percentage changes within the adjusted history, while additive difference adjustment preserves absolute differences but can alter historical percentage returns.
The audited difference example uses an old price of 100, a new price of 105 and one earlier historical price of 80. Adding the +5 gap changes the illustration to 85. Under ratio adjustment, the 1.05 factor changes the same historical price to 84. Neither adjusted value is a traded fill or realized return.
Worked example from the audited fixture
How to interpret the result
Difference and ratio methods answer different data-construction questions. The displayed continuity check proves only that the selected one-roll arithmetic aligns the old roll observation to the entered new price. It does not prove the roll date, data vendor, complete history or backtest is correct.
A careful continuous-futures adjustment workflow
- Define the roll rule, such as an expiry, volume or open-interest transition, before selecting prices.
- Capture old and new contract observations under the same timestamp and price-field convention.
- Choose difference or ratio adjustment based on the downstream analytical requirement.
- Use the historical illustration to inspect how one earlier level changes.
- For a real series, apply each roll cumulatively with documented contract and timestamp records.
- Keep actual per-contract returns and executed roll P/L separate from adjusted chart levels.
Basis, calendar spreads and back adjustment are different
These calculations all compare price levels, but they answer different questions. Basis compares futures with a spot or cash reference. A calendar spread compares two delivery months and may support a two-leg P/L review. Back adjustment changes historical analytical levels so consecutive contracts can be displayed as one series.
| Quantity | Compared prices | Primary job | Not equivalent to |
|---|---|---|---|
| Futures basis | Futures versus spot or cash | Measure an entered price relationship | Fair value or arbitrage proof |
| Calendar spread | Nearby versus deferred futures | Measure a two-month spread and entered P/L | Spot basis or a guaranteed simultaneous fill |
| Back adjustment | Old versus new contract at one roll | Align analytical price history | Executed roll P/L or a tradable contract |
| Roll schedule | Contract dates and liquidity evidence | Choose when a data or position transition occurs | A universal date inferred from prices |
Assumptions and limits
- The calculator adjusts one entered historical price across one entered roll boundary only.
- No contract chain, roll date, price series, OHLC bar, volume, open interest or vendor methodology is retrieved.
- Ratio mode requires positive old, new and historical prices and rejects zero or negative levels.
- Difference adjustment can change historical percentage returns and can produce negative adjusted prices.
- Cumulative multi-roll offsets, forward adjustment, return chaining and backtest recomputation are excluded.
- An adjusted continuous series is analytical data, not an executable contract or trading P/L record.
Where to verify futures curve inputs
Start with the exchange product page and rulebook for the exact symbol and delivery months. Confirm the quotation unit, multiplier, outright and spread tick, settlement method, last-trading and notice dates, and the exchange convention for a listed calendar spread. For spot or cash references, document the source, grade, location, timestamp and conversion basis.
For continuous data, verify the data vendor’s roll rule and adjustment method rather than assuming every platform stitches contracts alike. Volume, open-interest, expiry and fixed-date roll rules can switch on different dates. Difference, ratio, backward, forward and unadjusted series can display different historical levels even when they use the same underlying contracts.
Frequently asked questions
- It changes earlier contract history so an old-contract observation aligns with a new-contract price at a documented roll boundary.
- Add new-contract roll price minus old-contract roll price to the entered historical price and old roll observation.
- Multiply the entered historical price and old roll observation by new-contract price divided by old-contract price.
- A zero denominator is undefined, while zero or negative levels make the simple multiplicative interpretation unsafe for this bounded version.
- No. They both align the entered old roll observation to the new price, but they change earlier absolute levels and percentage returns differently.
- No. It illustrates one entered historical price across one roll boundary and does not retrieve or transform OHLC, volume or open-interest data.
- No. It is the entered new-contract price minus old-contract price. Executed roll P/L depends on actual positions, fills, costs and contract behavior.
- No. Expiry, volume, open-interest, fixed-date and vendor-specific roll rules must be selected and documented outside this page.
Sources and methodology
- CME Group — FX Futures Pricing and Basis — Defines FX basis and futures-minus-spot interpretation.
- CME Group — Equity Index Basis — States the futures-minus-spot convention and carry context.
- CFTC — Futures Glossary — Defines commodity basis, basis risk and calendar spreads.
- CME Group — Calendar Spread FAQ — Documents two-month structure and a product-specific quote convention.
- TradingView — Continuous Futures Back Adjustment — Documents one additive difference-adjustment implementation.
- CME Group — Demystifying Time-Series Momentum Strategies — Discusses backward ratio and difference adjustments and their return effects.
The operational contract is Entered Futures Curve Analysis version 1.0.0. Independent fixtures cover both basis signs, simple annualization, monetary basis, two quote orientations, long and short spread P/L, entered costs, difference and ratio back adjustment, continuity identities and invalid inputs. Sources support definitions and methods; they do not endorse the site or verify user data.
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