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

Spot natural gas trades at USD 3.00 per MMBtu. The continuously compounded risk-free rate is 3% per year and storage costs are 1% per year (continuous). The 1-year futures price is USD 3.00. What convenience yield, continuously compounded, is implied by the market?

The implied convenience yield is 4% per year. Because the one-year futures price equals spot, the net cost of carry must be zero, so the convenience yield must offset the 3% interest rate plus the 1% storage cost.

  1. A4%Correct
  2. B2%
  3. C3%
  4. D1%

Explanation

F = S*exp((r+u-y)T). With F = S and T=1, r+u-y = 0, so y = r+u = 3%+1% = 4%. Using 2% would omit storage costs wrongly; 3% would ignore storage.

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