Texoil

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Texoil

• Professor André Farber
• Solvay Business School
• Université Libre de Bruxelles

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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 2Scenario
  1 65 65 65 65 65Scenario 2 65 75 75 75 75Scenari
  o 3 65 60 60 60 60

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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 gt S for all maturities contango
Unusual for commodities In general F lt S
normal backwardation
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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/bblConsider scenario 2 (oil price increase)
Year Spot price P/L contract CF hedge P/L hedged
0 65
0.5 75 -5,000 9,347 4,347
1 75 -5,000 8,687 3,687
1.5 75 -5,000 8,020 3,020
2 75 -5,000 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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Scenarios
P/L hedged are identical in all scenarios
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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 0 75 9,347
Contract 2 1 66.31 0.5 75.75 9,441
Contract 3 1.5 66.98 1 76.52 9,536
Contract 4 2 67.95 1.5 77.23 9,631
Payoff on a contract Q ?FPayoff on contract 2
1,000 (75.75 66.31) 9,441
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Payoffs under scenario 2
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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Comparing the scenarios
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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
0 4,000 bbl
0.5 3,000 bbl
1 2,000 bbl
1.5 1,000 bbl
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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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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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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 d
u yFor the presentation, suppose Step
2 generate a large of future prices
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Result of simulation