for traders and investors. Prices for NYMEX Henry Hub Natural Gas futures and NYMEX WTI light sweet crude oil futures contracts (both traded on CME) are presented in Table 1 below. In particular, futures contracts expiring up to July 2024 are provided. We also know that on 19 July 2022 the spot price of natural gas was USD7.531 per MMBtu (one million British thermal units) and the spot price of light crude oil was USD103.45 per barrel. Table 1: NYMEX Henry Hub Natural Gas futures prices and NYMEX WTI light sweet crude oil futures prices observed on 19 July 2022 Next, a small oil and gas producer located in Texas, USA has estimated that it will have approximately 2,000,000 barrels of crude oil and 800,000 MMBtu of natural gas ready for sale sometime around mid-October 2022. Naturally, given the volatility in the market, they are concerned that prices will fall before then and so they are considering locking in a selling price for their oil and gas now using the NYMEX futures contracts analysed above. They have approached you and your company to advise them on the hedge. Assume that today is 19 July 2022 and that you have estimated the following standard deviations of price changes: The correlation coefficient between the spot and futures price changes has also been estimated to be 0.915 and 0.842 for oil and natural gas, respectively. (e) Calculate the optimal number of futures contracts required (by tailing the hedge) and recommend an effective hedge for the oil and gas producer. Use the appropriate futures contracts from Table 1 and recall that one NYMEX WTI light sweet crude oil futures contract is written on 1,000 barrels of oil and one NYMEX Henry Hub Natural Gas futures contract is written on 10,000 MMBtu. 1 Finally, assume that the oil and gas producer is ready to sell their crude oil and natural gas in mid-October. At this time, the crude oil and natural gas spot prices have changed to USD92.50 per barrel and USD8.250 per MMBtu, respectively, and the futures prices for delivery in one month are USD91.42 per barrel and USD8.124 per MMBtu, respectively. (f) Calculate the outcome with and without the hedge. What is the producer's effective purchase price with and without the hedge? Did they benefit from this hedge? (g) Explain the main objective of the recommended hedge and the reasons why it cannot be a perfect hedge. for traders and investors. Prices for NYMEX Henry Hub Natural Gas futures and NYMEX WTI light sweet crude oil futures contracts (both traded on CME) are presented in Table 1 below. In particular, futures contracts expiring up to July 2024 are provided. We also know that on 19 July 2022 the spot price of natural gas was USD7.531 per MMBtu (one million British thermal units) and the spot price of light crude oil was USD103.45 per barrel. Table 1: NYMEX Henry Hub Natural Gas futures prices and NYMEX WTI light sweet crude oil futures prices observed on 19 July 2022 Next, a small oil and gas producer located in Texas, USA has estimated that it will have approximately 2,000,000 barrels of crude oil and 800,000 MMBtu of natural gas ready for sale sometime around mid-October 2022. Naturally, given the volatility in the market, they are concerned that prices will fall before then and so they are considering locking in a selling price for their oil and gas now using the NYMEX futures contracts analysed above. They have approached you and your company to advise them on the hedge. Assume that today is 19 July 2022 and that you have estimated the following standard deviations of price changes: The correlation coefficient between the spot and futures price changes has also been estimated to be 0.915 and 0.842 for oil and natural gas, respectively. (e) Calculate the optimal number of futures contracts required (by tailing the hedge) and recommend an effective hedge for the oil and gas producer. Use the appropriate futures contracts from Table 1 and recall that one NYMEX WTI light sweet crude oil futures contract is written on 1,000 barrels of oil and one NYMEX Henry Hub Natural Gas futures contract is written on 10,000 MMBtu. 1 Finally, assume that the oil and gas producer is ready to sell their crude oil and natural gas in mid-October. At this time, the crude oil and natural gas spot prices have changed to USD92.50 per barrel and USD8.250 per MMBtu, respectively, and the futures prices for delivery in one month are USD91.42 per barrel and USD8.124 per MMBtu, respectively. (f) Calculate the outcome with and without the hedge. What is the producer's effective purchase price with and without the hedge? Did they benefit from this hedge? (g) Explain the main objective of the recommended hedge and the reasons why it cannot be a perfect hedge