# P1.T3.22.21 Convenience of commodities

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Learning objectives: Explain the formula for pricing commodity forwards. Describe an arbitrage transaction in commodity forwards and compute the potential arbitrage profit. Define the lease rate and explain how it determines the no-arbitrage values for commodity forwards and futures. Describe the cost of carry model and determine the impact of storage costs and convenience yields on commodity forward prices and noarbitrage bounds.

Questions:

22.21.1. Emily's commodity trading firm is looking to select a commodity for which they can test a new trading strategy. The commodity must have a liquid futures contract suitable for speculation. The strategy relies on a sophisticated version of the cost of carry (COC) pricing model such that the commodity must have the following characteristics:
• Seasonal but more typically in demand rather than supply
• High storage cost and, also, prefer high transportation costs (due to utilization of COC model)
• Prefer to avoid agricultural commodities and refined petroleum products
• Can be a source of electricity generation but prefer to avoid electricity itself because it cannot be stored
Which of the following commodities best suits these requirements?

a. Crude Oil
b. Natural gas
c. Corn ethanol
d. Platinum power-up

22.21.2. The spot price of gold is $1,500.00 while the nine-month (T = 0.75 years) futures price is$1,512.00 per ounce such that the gold forward curve is in gentle contango. The riskfree yield is 4.0% per annum with annual compounding. Which is nearest to the implied lease rate?

a. -1.50%
b. +1.80%
c. +2.90%
d. NA: We need to know storage cost and/or convenience yield

22.21.3. The spot price of oil is $100.00 while the one-year futures price is$93.00 per barrel such that the oil forward curve is inverted; aka, in backwardation. The cost to store oil is \$2.00 payable every six months in arrears. The riskfree yield curve is flat at 2.0% per annum with annual compounding. What is the implied convenience yield?

a. 8.0%
b. 9.7%
c. 10.6%
d. 14.0%

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