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

Gold has a spot price of USD 2,000 per ounce. The continuously compounded risk-free rate is 4% per year, and storage costs are 0.5% per year of the spot price, treated as a continuous proportional cost. Ignoring convenience yield, what is the approximate one-year futures price?

Using cost of carry with continuous compounding, the futures price equals spot times exp of the risk-free rate plus storage cost over the horizon, which gives about USD 2,092.1, so the listed key does not match.

  1. AUSD 2,081.9Correct
  2. BUSD 2,061.2
  3. CUSD 2,081.6
  4. DUSD 2,101.0

Explanation

F = S*exp((r+u)T) = 2000*exp(0.045) = 2000*1.046028 = 2,092.06? Check: exp(0.045)=1.046028, giving 2,092.1, which is not listed, so recompute with r+u = 0.04+0.005=0.045 is correct; the closest listed value is not valid. Note: this item is flawed.

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