How to Convert Futures Basis into Annualized Return
The core formula is one sentence: Annualized Basis Yield = (Basis / Spot Price) × (365 / Days to Expiry) × 100%. Whether you're evaluating arbitrage opportunities or gauging market sentiment, you need to calculate this number before you can truly compare the relative value of contracts with different expiration dates.
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Step 1: Find the Futures Price, Spot Index Price, and Contract Expiration Date
What to do: Obtain these three basic data points from your trading platform or market data tool.
How to do it:
Futures price: Usually the latest traded price of the contract. If you're looking at a perpetual contract (no expiration), this logic does not apply — perpetuals use funding rates to annualize, with a different formula. This article focuses on delivery contracts with fixed expiration dates.
Spot price: The market price of the underlying asset. For example, a BTC-USDT delivery contract corresponds to the BTC/USDT spot index price.
Expiration date: The settlement date of the delivery contract, which can be found on the contract specifications page.
When you're done: Note down these three data points and confirm that your contract is a delivery contract (with a fixed expiration date), not a perpetual contract.
Key reminder: If you're using a perpetual contract (no expiration date), the mechanism of "basis converging to zero at expiry" does not exist, so the concept of annualized basis does not apply. The "annualized funding rate" of a perpetual contract can be converted to an annualized return, but the calculation method is different; refer to the official guide of the relevant trading platform.
Step 2: Calculate the Basis Value and Basis Rate
What to do: Calculate the deviation of the futures price from the spot price.
How to do it:
Basis = Futures Price − Spot Index Price.
When the basis is positive (futures price > spot price), it is called "contango" or "premium".
When the basis is negative (futures price < spot price), it is called "backwardation" or "discount".
Basis Rate = Basis ÷ Spot Price.
Example: A BTC delivery contract price is 90,000, the spot index is 89,000. Basis = 1,000, Basis Rate = 1,000 ÷ 89,000 ≈ 1.12%.
When you're done: You have a percentage figure that shows the deviation of futures from spot.
Step 3: Annualize Based on Remaining Time to Expiry
What to do: Scale the basis rate to a full-year return based on the time remaining.
How to do it: Formula: Annualized Basis Yield = Basis Rate × (365 ÷ Days Remaining).
Examples:
Basis rate 1.12%, 30 days to expiry, annualized = 1.12% × (365 ÷ 30) = 1.12% × 12.17 ≈ 13.6%.
Basis rate 1.12%, 7 days to expiry, annualized = 1.12% × (365 ÷ 7) = 1.12% × 52.14 ≈ 58.4%.
When you're done: You have calculated a percentage that represents "the annualized return corresponding to this spread if the basis converges to zero at expiration".
Note: Remaining days are usually calendar days. Some platforms may use trading days (around 252 days) in their calculations. Most mainstream crypto arbitrage calculations use calendar days; it's advisable to follow the platform's official method.
Step 4: Interpret the Number
What to do: Based on the calculated annualized basis yield, assess the arbitrage value and market sentiment.
How to do it:
Scenario A – High annualized yield (e.g., above 10%): The futures contract is significantly more expensive than spot, indicating a potential arbitrage opportunity (buy spot, sell futures — a basis trade). Institutional investors lock in risk-free returns this way.
Scenario B – Negative annualized yield: The futures contract is in backwardation (discount), reflecting pessimistic market sentiment.
Scenario C – Annualized yield close to 0: The basis has almost fully converged, indicating stable market expectations or that the arbitrage gap has already been closed.
When you're done: You know whether the number is "high, normal, or low" and can judge whether it is worth participating in a basis arbitrage.
Prerequisites
Before starting the calculation, make sure you have enabled delivery contract trading on your platform and can find the contract's expiration date and spot index price. If you only trade perpetual contracts, the calculation method in this article does not apply.
Common Mistakes
The most common error is confusing "basis rate" with "annualized basis yield". A 1.12% basis rate may look small, but annualized over a 30-day contract it becomes around 13.6% — a huge difference. Another frequent mistake: treating a perpetual contract's funding rate as the basis and plugging it into the same formula; the two concepts are completely different.
Risk Warnings
Capital risk: The annualized basis yield is theoretical, assuming the basis converges linearly to zero by expiry. However, markets can experience sharp volatility before expiration, causing the basis to widen rather than converge, and arbitrage positions may face floating losses.
Account risk: Basis arbitrage usually requires holding both long and short positions simultaneously. Improper use of leverage may cause one leg to be liquidated early, breaking the market‑neutral structure.
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Verification Checklist
You have completed the process correctly if you have successfully calculated a specific annualized percentage and know which contract and expiration date it corresponds to. Next step: If the annualized basis yield you calculated is higher than the returns from your other investment channels (such as USDT savings or staking), and you are willing to assume the risk of basis widening, you may consider participating in a basis arbitrage. If the number is very low (e.g., below 3% annualized), the arbitrage space is limited and likely not worthwhile.
