Annualizing Futures Curve Slope to Compare Contango

Summary

The document gives a way to compare the steepness of futures curves across contracts with different times to expiry. It proposes taking the logarithm of the ratio between the later-dated futures price and the earlier-dated futures price, dividing by the time between their expiries, and annualizing the result using a 365-day convention. The same measure can describe backwardation when the price relationship is reversed.

The answer is a compact measurement suggestion rather than a broader treatment of term-structure analysis. It does not provide worked examples, data, or guidance on choosing contract pairs, day-count conventions, or delivery dates versus expiry dates; it allows either expiry or delivery dates for the time inputs. Comparisons also depend on using consistent price and date conventions across the instruments being studied. The measure expresses a log price change per year, making intervals of different lengths more comparable, but the document does not discuss whether this is sufficient to compare markets with different contract specifications or economic drivers.

Key ideas

• A futures curve’s contango or backwardation can be expressed as a log price ratio between two maturities divided by the time separating them.
• Annualizing the rate makes contracts with different maturity gaps easier to compare.
• Expiry dates or delivery dates can be used to measure the interval, provided the convention is applied consistently.
• The suggested calculation is a measurement convention and is not accompanied by empirical validation or discussion of contract-specific adjustments.

Tags

# How to measure contango?


# How to measure contango?












Is there any unit of measure for the magnitude of the contango (or backwardation) for futures, so you can compare the contango of many symbols.

## Answer by Ivan (score 11, accepted)

https://quant.stackexchange.com/a/7859

Just take something like

$$ \frac{\log{\frac{F_j}{F_i}}}{t_j - t_i} \times 365 $$

where $t_i$ denotes the expiry (or alternatively delivery) date of future $i$. The annualization is so you can compare different futures.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.