A commodity front month future is 80.00 and the second month is 82.00. The curve rolls once a month and spot is expected to stay at 80.00. What is the annualised cost of holding a long position through twelve rolls?

A commodity front month future is 80.00 and the second month is 82.00. The curve rolls once a month and spot is expected to stay at 80.00. What is the annualised cost of holding a long position through twelve rolls?

Approach: Work out what one roll costs as a percentage of the amount invested when the contract bought converges to an unchanged spot, then compound that over twelve rolls.

-25.6%. Each month you hold the second contract at 82.00 and it converges to spot at 80.00 as it becomes the front, a loss of 2.00 on 82.00, which is -2.439%. Compounding twelve of those gives (1 - 0.02439)^12, which is 0.7435, an annualised roll yield of -25.6%. The loss comes from contango and convergence together: an upward sloping curve with unchanged spot means every contract bought rolls down to the same spot price. A long position needs spot to rise 25.6% over the year to break even, which is why a futures position in a steeply contangoed market and a spot exposure are different trades with different expected returns.

Follow-up: The curve flips to backwardation with the second month at 78.50. What is the annualised roll yield and what does the shape say about inventories?

Key concepts: contango, roll yield, convergence, annualised return.