Texoil Professor Andr Farber Solvay Business School Universit

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

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. 5 t = 2 Scenario 1 65 65 65 Scenario 2 65 75 75 Scenario 3 65 60 60 04 March 2021 Texoil 2

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. 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 04 March 2021 Texoil 3

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 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 – F 0 t) = Q (70 – F 0 t) P/L hedged year 1 = 10, 000(70 – 75) + 10, 000 (75 – 66. 31) 04 March 2021 Texoil 4

Scenarios P/L hedged are identical in all scenarios 04 March 2021 Texoil 5

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 ×ΔF Payoff on contract 2 = 1, 000 (75. 75 – 66. 31) = 9, 441 04 March 2021 Texoil 6

Payoffs under scenario 2 Under scenario 2: Huge profit on futures at time 0. 5 followed by losses 04 March 2021 But the TOTAL P/L hedged over the 2 years is the same as with forwards The future value is slighly higher Texoil 7

Comparing the scenarios 04 March 2021 Texoil 8

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. 04 March 2021 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 Texoil 9

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. 04 March 2021 Texoil 10

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. 04 March 2021 Texoil 11

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 04 March 2021 Texoil 12

Result of simulation 04 March 2021 Texoil 13