Question

Assume that J&L went long 400 Jun HO futures contracts on 4/24/09, when by Exhibit 3 the futures price was F₀=1.386. (They would also have gone long 400 contracts for Jul, Aug,…, May to hedge June ’09 through April ’10 purchases, but we don’t need that here). At that time spot price of DF was S₀=1.38.

1. One week later, J&L closed 100 contracts (by shorting 100 Jun HO futures) when F_{1 week}=1.40, and purchased 4.2 million gallons of DF at the spot price of S_{1 week}=1.41. What was the profit/loss on the futures closed, and the cost of the DF net of this profit/loss?
2. One week later, J&L closed another 100 contracts when F_{2 weeks}=1.37, and purchased 4.2 million gallons of DF at S_{2 weeks}=1.37. What was the profit/loss on the futures closed, and the cost of the DF net of this profit/loss?
3. One week later, J&L closed another 100 contracts when F_{3 weeks}=1.39, and purchased 4.2 million gallons of DF at S_{3 weeks}=1.38. What was the profit/loss on the futures closed, and the cost of the DF net of this profit/loss?
   Exhibit 3 J&L Railroad NYMEX Heating Oil Exchange Futures (in dollars per gallon) April 24, 2009 Month May '09 Jun '09 Jul '09 Aug '09 Sep '09 Oct '09 Nov '09 Dec '09 Jan 10 Feb 10 Mar 10 Apr 10 May '10 Last $1.368 $1.386 $1.414 $1.443 $1.472 $1.502 $1.533 $1.563 $1.593 $1.614 $1.626 $1.629 $1.638 Spot $1.360 Each heating-oil futures contract was for the delivery of 42,000 gallons and matured on the last business day of the preceding month (e.g., the June 2009 contract expires May 29, 2009) Data source: New York Mercantle Exchange data.
   
4. One week later, J&L closed the final 100 contracts when F_{4 weeks}=1.42, and purchased 4.2 million gallons of DF at S_{4 weeks}=1.42. What was the profit/loss on the futures closed, and the cost of the DF net of this profit/loss?

Answer 1

Cost of 400 Futures = (400 * 42000) * Fo = (400 * 42000) * 1.386 USD

After Week 1:

Profit on Sale of 100 Futures = (100 * 42000) * (F1week - Fo) = 100 * 42000 *(1.40 - 1.386) = 58800 USD

Cost of the DF at S1week net of this profit/loss = 4200000 * 1.41 - 58800 = 5,863,200 USD (1.396 USD Per Gallon)

After Week 2:

Loss on Sale of 100 Futures = (100 * 42000) * (F2weeks - Fo) = 100 * 42000 *(1.37 - 1.386) = -67200 USD

Cost of the DF at S2weeks net of this profit/loss = 4200000 * 1.37+ 67200 = 5,821,200 USD (1.386 USD Per Gallon)

After Week 3:

Profit on Sale of 100 Futures = (100 * 42000) * (F3weeks - Fo) = 100 * 42000 *(1.39 - 1.386) = 16800 USD

Cost of the DF at S3weeks net of this profit/loss = 4200000 * 1.38 - 16800 = 5,779,200 USD (1.376 USD Per Gallon)

After Week 4

Profit on Sale of 100 Futures = (100 * 42000) * (F4week - Fo) = 100 * 42000 *(1.42 - 1.386) = 142800 USD

Cost of the DF at S4weeks net of this profit/loss = 4200000 * 1.42 - 142800 = 5,821,200 USD (1.386 USD Per Gallon)