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Roll Yield and Commodity Yield Curve

July 19th, 2010 · 3 Comments · Data, Futures


We have seen previously that backwardation and/or contango can induce a fairly large drift between the performance of an instrument’s spot market and its corresponding futures market.

This phenomenon can be described as roll yield of futures trading and I suggested it was one of the four components in Trend Following returns. As per that last post’s conclusion, breaking down the returns should allow to focus, study and improve a trading system’s individual component – and this is what we are doing here with the roll yield, by looking into the Commodity Yield Curve.

The roll yield had a negative impact in the Crude Oil example, however let’s explore how it could be turned into an extra source of profit

Term Structure – or Yield Curve

Term structure best applies to interest rates analysis. If we take the example of US Treasuries; they cover a wide range of maturities, from T-Bills (one year or less maturity) , T-Notes (one year to ten years) to T-Bonds (up to thirty years). For any given date, each treasury is priced depending on its maturity and an implied yield can be derived for each maturity. Charting these yields for each maturity gives the yield curve, also called term structure of interest rates.

Below can be found a “normal” (upward sloping) yield curve for US Treasuries (from last Friday) showing that yields went slightly down in the middle of the curve whereas the short and long ends of the curve did not change much:


The yield curve, or term structures of interest rates is a major economic indicator, closely watched by many traders to gain insights in the market. You can read more about it at investopedia and wikipedia.

Application in Futures Trading

Term structure can be similarly transposed to futures trading, which deals with the same concept of trading the same instrument (i.e. where a commodity like Corn replaces money used in the case of the classic yield curve) with different maturities (all different contracts and their various expiry/delivery months).

Note that the term Commodity Yield Curve is a bit of misnomer as the concept could be applied to any instrument traded in different maturities (i.e. all futures for instance).

Commodity/Futures Yield Curve: How to Build it?

The futures yield curve is a representation of the backwardation/contango rate for the different maturities of futures contracts. The contango/backwardation rates are calculated by taking the price difference between the spot/cash market price and the futures contract price. This difference can be expressed as a percentage (for x number of days: time to expiration of the futures contract) and then annualised to calculate an annual contango or backwardation rate, representing an implied yield for the specific maturity.

For example, if the spot market trades at 70 and the October contract (expiring in 90 days) trades at 71, the yield can be calculated as follows:

  1. Price difference = 71 – 70 = 1
  2. Percentage price difference = 1/70 = 1.43% (for 90 days)
  3. Annualised contango rate (yield) = (1.43% + 1)^(365/90) – 1 = 5.92%

Performing this calculation for each contract/maturity would allow to chart a futures yield curve.

Volatility of the Yield Curve

I calculated and charted the Crude Oil yield curve in order to analyse and visualise the evolution of the contango/backwardation rates, both across the historical timeline and the range of contract maturities. This was done as discussed above for all contracts available for a given date.

Here is a sample chart using data from December 03 to January 04 where Crude Oil was trading in backwardation:


Each “ribbon” on the chart represents the yields for all 18 different maturities (1=short, 18=long) for a given date: each ribbon represents the yield curve for that day. All yields are negative because of the backwardated aspect of Crude Oil at the time. Backwardation rates have reasonable values (-15%/+5%) and the associated yield curves vary slightly across time, albeit maintaining a similar pattern.

However this snapshot was taken at relatively quiet times in the market. Fast forward to 2009 and you can see that the market now exhibits contango, with rates spiking to much higher values:


Adding any more dates to this chart would make it hardly readable, but to give an idea of how the term structure of Crude Oil can vary over a longer period of time, I have simply plotted the shortest end of the curve (i.e. yields for the contract with closest maturity), which you can imagine as a “vertical slice” of the 3-D chart alongside the date axis, where maturity = 1. Here is the chart:


There are spikes, alternation between contango and backwardation. It clearly displays some volatility and, for lack of a better term, a character of its own.

Note that because the yield is calculated as an implied value based solely on the price difference between contracts, some discrepancies in these contract prices (for whatever reason) would impact the curve in a more volatile and “artificial” way than if it did purely represent the fundamental yield factors (cost of carry, supply/demand and shortage, convenience yield, etc.)

Some Observations

The main observations are:

  • Yield curves and their associated contango and backwardation rates evolve in a fairly volatile fashion across time.
  • For any given date, different contracts and their associated maturities offer different yields, possibly within a wide range of values.

This can add an extra dimension to your trading decisions. The yield curve offers other opportunities (than the traditional front-month contract) when wanting to buy or sell any instrument via futures trading. These extra opportunities can be turned into an extra source of profit.

This is really an introduction to a next post, in which we will look into how we can use this information and apply it to a trading system to improve its roll yield component and enhance its overall performance.
Stay tuned…

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3 Comments so far ↓

  • James

    Thank you for the well written description of yield curves. I am interested in the use of yield curves and futures calendar spreads for trend prediction. Is this something that you have researched?



  • Jez

    I havent looked into that aspect of yield curves. Next post will be presenting an actual system enhanced by making use of yield curves computation and picking the best contract (in terms of roll yield). The other aspect that might be interesting is using yield curves as portfolio filter – which I might look into in the future

  • Matt

    For anyone wanting to reconstruct this with esignal you can use ((CL 1! – CL 2!) / CL 1!), the CL 1 is the current / spot contract, CL 2 is next expiring.

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