1. Texoil Professor André Farber Solvay Business School
Université Libre de Bruxelles

2. Data October 15, 2005 Spot price of oil = $65 per barrel
Risk-free interest = 4% per annum with continuous compounding.
Difference between the storage costs and the convenience yield = -2%.
The contract that Mark had conceived would involve delivering 1,000 barrels every six month for the next 2 years at a fixed price of $70 per barrel payable at delivery.
Three price scenarios were considered: stable price, oil price increases, oil price drops.
t = 0 t = 0.5 t = 1 t = 1.5 t = 2 Scenario Scenario Scenario
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3. 1. Calculate the forward (futures) prices of oil for each maturity (6 months, 1 year, 1.5 year and 2 years)
Spot
0.5 year
1 year
1.5 year
2 year 65
65.65
66.31
66.98
67.65
Note: F > S for all maturities = contango Unusual for commodities
In general F < S: normal backwardation
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4. 2. Calculate P/L (Profit/Loss) for each scenario if the contract is hedged with forwards.
Texoil sells 1,000 bbl at a fixed price of $70/bbl Consider scenario 2 (oil price increase)
Year
Spot price
P/L contract
CF hedge
P/L hedged 65
0.5 75
-5,000
+ 9,347
+4,347 1
+8,687
+3,687
1.5
+8,020
+3,020 2
+7,347
+2,347
P/L hedged year t = Q(70 – St) Q(St – F0t) = Q (70 – F0t) P/L hedged year 1 = 10,000(70 – 75) + 10,000 (75 – 66.31)
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5. Scenarios
P/L hedged are identical in all scenarios
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6. 3. Calculate P/L for each scenario if the contract is hedged with futures (to avoid tedious calculation, assume that marking to market is semiannual).
Texoil would go long on 4 futures contracts. Consider what would happen at time 0.5 if the spot price = $75
Maturity
Futures prices
set at time 0
Maturity at time
t =0.5
Futures prices at time
t = 0.5
Payoff
Contract 1
0.5
65.65 75
9,347
Contract 2 1
66.31
75.75
9,441
Contract 3
1.5
66.98
76.52
9,536
Contract 4 2
67.95
77.23
9,631
Payoff on a contract = Q ×ΔF Payoff on contract 2 = 1,000 (75.75 – 66.31) = 9,441
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7. Payoffs under scenario 2
Huge profit on futures at time 0.5 followed by losses
But the TOTAL P/L hedged over the 2 years is the same as with forwards
The future value is slighly higher
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8. Comparing the scenarios
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9. Long futures position on 6-month futures
4. Suppose that only 6-month futures contracts are traded. Would it be possible to implement an effective hedge?
This could be done using a STACK HEDGE.
TIME
Long futures position on 6-month futures
4,000 bbl
0.5
3,000 bbl 1
2,000 bbl
1.5
1,000 bbl
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10. Stack hedge under scenario 2
The outcome is similar to a strip of futures.
Under scenario 1, a huge profit is created at time 0.5 followed by losses in later periods.
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11. Stack hedge: comparing the scenarios
This scenario correspond to what happened to Metallgesellschaft. Oil prices went down and the company had a huge loss on its derivative position.
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12. 5. What other risks should be considered?
The scenarios that we have analyzed are to simple. Many more paths of oil prices could happen than the one we considered.
Moreover, we ignore in the analysis changes in the convenience yield.
We could explore a larger set of possible future price by using the Monte Carlo technique.
Step 1: model the evolution of S and δ = u – y For the presentation, suppose:
Step 2: generate a large of future prices
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13. Result of simulation
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