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FRM Part I · FRM Exam Part I · Commodity Forwards and Futures

The forward curve for a commodity that can be lent at a lease rate is downward sloping (backwardation) at all maturities. Ignoring storage costs and assuming the forward prices are no-arbitrage prices with continuous compounding, what does this imply?

A downward-sloping forward curve implies the lease rate is greater than the risk-free rate. The forward price depends on the risk-free rate minus the lease rate, so forwards fall below spot only when that difference is negative, meaning the lease rate is above the interest rate.

  1. AThe lease rate is less than the risk-free rate
  2. BThe lease rate exceeds the risk-free rateCorrect
  3. CThe lease rate is exactly equal to zero
  4. DThe forward price is above the spot price by the amount of the lease rate

Explanation

Because F = S e^{(r-l)T}, a forward price below spot requires r - l < 0, so the lease rate exceeds the risk-free rate. If l were below r, the curve would be upward sloping (contango). A zero lease rate would also give an upward-sloping curve, since r is positive.

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