page 1 of 4 HW 4 Due on Tuesday, FEB 23 in class. Study carefully the following article: Crude oil protective puts by the State of Texas Texas, Other Governments, Trade in Commodities Futures “Texas, along with other governments, is becoming a big-time player in the commodities market. But it’s not because they’ve become bored with their own lottery operations. Quite the contrary; their goal is not to take risks, but to reduce them. If the word hedging does not yet appear in the codification of government accounting standards, you can be certain that it will soon. Texas uses commodity options to protect its tax revenues from sudden drops in the price of oil. Texas expects to generate $500 million from its oil severance tax. For every barrel of the "black gold" produced in the state, the Treasury receives 4.6 percent of the sales price. A sharp drop in price, such as in 1986 when it nose-dived from almost $25.82 to 11.36, can play havoc with the state’s budget. To lock in a set price, the state is experimenting with oil options. Here’s how they work. The State purchases put options on crude oil. Each option permits it to sell (or “put”) a thousand (1,000) barrels of oil at an established (exercise) price to the party that sold the option on a specified (exercise) date. If on the exercise date the market price of crude oil is below the established price, then the option has value: the intrinsic value - the difference between the established exercise price and the market price. The state either exercises the option or sells it in the open market, thus making a “profit” and covering the cost of the oil itself. The greater the decline in market price, the greater the gain to the state from the put.. If, however, the oil market price on the specified date is above the established exercise price, then the option has no value and the state will allow it to expire worthless. Its loss is limited to the amount that it paid to acquire the option (the “premium” cost). The Texas Treasury can be viewed as the de facto owner of 4.6 percent (the severance tax rate) of all the oil produced in the state. Therefore, for each 1,000 barrels of oil that it wants to protect against a decline in revenue, it must buy puts on 46 barrels. Suppose that on June 1, the State buys puts on 100,000 barrels of oil, thereby protecting 2,173,913 barrels (100,000 divided by 4.6 percent). Since put contracts are written in units of 1,000 barrels, the State would be required to buy 100 contracts. Assume that on the date the puts are purchased the prevailing market price is S = $21 per barrel and that this is the price that the state wants to lock in for purposes of severance tax collection three months hence. Therefore it buys puts with X = $21 as the strike price and T = October 1 as the expiration date. The cost of each contract might be approximately $1,100 including commissions---$110,000 for the 100 contracts.

page 2 of 4 If, on the expiration date, the market value of oil has fallen to ST = $18 per barrel, then the market value of each contract can be expected to approximate $3,000 [($21-$18)(1,000)] barrels]-or $300,000 for the 100 contracts. This amount will be just sufficient to offset the loss on the severance tax revenue from the $3 per barrel price drop (2,173,913 barrels times $3 per barrel times the tax rate of 4.6 percent). The state will sell the options for the $300,000 and its net loss on the entire transaction will be $110,000, the cost of the options. If on the expiration date, the price of oil is $21 or more, then the options will have no value and the state will be out the $110,000 that it paid for them. However, the state will still reap the benefits from the increased tax revenue owing to the rise in oil prices, and this additional revenue may be sufficient to offset all or at least a part of the option cost.” _________________________________________

page 3 of 4 For the HW: Assume that today, Texas crude oil is selling for S t = $87.18/barrel (bbl). Also assume that today, calls and puts on Texas crude for Jan11 Expiration are traded for the following prices (premiums) per barrel: K calls puts $85.00/bbl$2.60/bbl$1.18/bbl $85.50/bbl$2.30/bbl$1.38/bbl $86.00/bbl$2.03/bbl$1.65/bbl $86.50/bbl$1.79/bbl$1.86/bbl $87.00/bbl$1.58/bbl$2.13/bbl $87.50/bbl$1.38/bbl$2.43/bbl $88.50/bbl$0.46/bbl$2.99/bbl The State of Texas expects the price of Texas crude to be between $86/bbl and $88/bbl in Jan11, but wishes to hedge its severance tax revenue in case the crude’s price falls below $85. Based on production data from the last 5 years, the Texas Railroad Commission figures that by the options’ Jan11 expiration date, it needs to protect the 4.6% severance tax revenue from the sale of 152,000,000 barrels of oil that are expected to be produced and sold between today and the expiration date on Jan11. For solving the problems below you must make: An important assumption All the 152,000,000 barrels are sold on the Jan11 options’ expiration day. Moreover, you must use the following: Important Hint: For Q1 and Q3 do not account for the underlying crude current price in the ICF. The cash flow associated with the crude oil sale should appear in the table only at Jan11 expiration.

page 4 of 4 Q1. The State buys the $85.50, Jan11 puts. Use a table of cash flows to describe the initial cash flow and the terminal cash flow in Jan11 from this long put strategy. Q2. Graph the P/L profile of the State from the strategy in Q1, using all possible prices per barrel at expiration. Q3. The State opens the following collar : Long the K 1 =$85.50, Jan11 puts and Short the K 2 = $87.50 Jan11 calls to finance the puts. Describe the initial cash flow and the terminal cash flow at Jan11 from the collar using a table format. Q4. Graph the P/L profile of the State from the strategy in Q4, using all possible prices per barrel at expiration. In Q5 – Q8 show the tables of cash flows and the P/L at expiration as well as the P/L graphs. Q a Q b Q c Q d