Nicole Seaman

Director of FRM Operations
Staff member
Subscriber
Learning objectives: Compute the forward price of a commodity with storage costs. Explain how to create a synthetic commodity position and use it to explain the relationship between the forward price and the expected future spot price. Explain the impact of systematic and nonsystematic risk on current futures prices and expected future spot prices. Define and interpret normal backwardation and contango.

Questions:

22.22.1. The spot price of natural gas is $5.00 per million British thermal unit (MMBtu) while the riskfree rate is 3.0%. The storage costs is $0.40 per MMBtu every six months payable in advance. The convenience yield is 2.0% per annum with annual compounding. Which is nearest to the implied theoretical price of an eighteen-month (1.5 years) futures contract?

a. $4.88
b. $5.05
c. $6.27
d. $6.46


22.22.2. The spot price of oil is $100.000 per barrel while the riskfree rate is 3.0% and its storage cost is 2.0% per annum. Oil has positive systematic risk. Specifically, its beta with respect to the market, β(Oil, M) = 1.10. The market's expected return is 14.0%; i.e., the market's expected excess return is +11.0%. Finally, the expected growth rate of the oil price (aka, price appreciation) is +8.0%. All rates are per annum with continuous compounding. We are interested in the traded price of the fifteen-month (i.e., 1.25 year) forward contract, and we'll assume the traded price equals the theoretical price. Which of the following statements is true about (i) the slope of the forward curve and (ii) whether we expect normal contango or normal backwardation?

a. The forward curve is inverted, F(1.5) = $97.50, and we perceive normal contango, F(1.5)>E[S(1.5)]
b. The forward curve is inverted, F(1.5) = $95.00, and we perceive normal backwardation, F(1.5)<E[S(1.5)]
c. The forward curve is upward-sloping, F(1.5) = $105.00, and we perceive normal contango, F(1.5)>E[S(1.5)]
d. The forward curve is upward-sloping, F(1.5) = $102.50, and we perceive normal backwardation, F(1.5)<E[S(1.5)]


22.22.3. The spot price of oil is $100.00 per barrel while the riskfree rate is 3.0% per annum. Its storage cost is 1.0% per annum. Oil has positive systematic risk; specifically, its beta with respect to the market, β(Oil, M) = 0.90. The market's expected return is 10.0%; i.e., the market's expected excess return is +7.0%. Finally, the expected growth rate of the oil price (aka, price appreciation) is +7.0%. All rates are per annum with continuous compounding. Which of the following is nearest to the theoretical two-year oil futures price, F(2.0)?

a. $96.74
b. $99.00
c. $101.41
d. $103.65

Answers here:
 
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