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Define normal backwardation and contango and interpret each.

FRM® Part I · Financial Markets and Products · Commodity Forwards and Futures · FRM1.FM.11.k

The idea

Normal backwardation, in Keynes's sense, means the futures price is below the expected future spot price. Producers hedge by selling futures, so speculators take the long side and earn a positive expected return as payment for bearing the risk. This goes with a positive beta. Contango means the futures price is above expected spot, so the speculator is short and earns the premium, which goes with a negative beta. Practitioners also describe the shape of the curve. Backwardation is a downward-sloping curve, with spot above futures, and contango is an upward-sloping curve. Under cost of carry, contango occurs when r plus storage exceeds the convenience yield, and backwardation when the convenience yield is larger. The two usages are different questions, so check which one the exam asks.

A practice question

From the question bank, with the reason each wrong option is wrong.

In Keynes's sense, a commodity market is in normal backwardation when:

  1. the futures price is above the expected future spot price.Why not: This is contango in the expected-spot sense.
  2. the futures price is below the expected future spot price. - correct
  3. the futures price equals the expected future spot price.Why not: This is the unbiased case, which holds for zero beta.
  4. the spot price is below the futures price.Why not: This describes an upward-sloping curve (contango); it is not the definition of normal backwardation.

Normal backwardation: F < E(S_T). Long speculators earn a positive expected return as compensation for taking risk that hedgers wish to shed.

A harder one

Spot is USD 100, the one-year forward is USD 96, the risk-free rate is 3% and storage costs are 1.5% per year, continuous. Which statement is correct?

  1. The curve is in contango; the implied convenience yield is about 8.6%.Why not: Forward below spot is not contango; the sign of the slope matches backwardation.
  2. The curve is in backwardation; the implied convenience yield is about 4.1%.Why not: Reports the forward discount alone, forgetting r + lambda is added to it.
  3. The curve is in backwardation; the implied convenience yield is about 8.6%, above the carry cost of 4.5%. - correct
  4. The curve is in contango; the implied convenience yield is about 0.5%.Why not: Mislabels the curve and misses that the forward is below spot.

c = 0.045 - ln(96/100) = 8.58%, greater than r + lambda (4.5%), so the forward is below spot: backwardation.

The hardest tier

A one-year futures contract trades at USD 52 and the expected spot price at maturity is USD 55. The continuously compounded risk-free rate is 4%. Assuming no carry costs beyond interest, the commodity's implied expected return is closest to:

  1. 9.61% - correct
  2. 5.61%Why not: Reports only the excess return over the risk-free rate.
  3. -1.61%Why not: Subtracts the premium from the risk-free rate.
  4. 9.77%Why not: Mixes a simple return with a continuously compounded rate.

F = E x exp(-(alpha - r) x T) so alpha = r + ln(E/F)/T = 0.04 + ln(55/52) = 9.61%. The futures lie below expected spot, which is normal backwardation and implies positive beta.

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