4. Futures (30 points) Your firm will produce 10,000 exam-answering machines in one year's time. However, the price of exam-answering machines is very volatile. As CFO of the firm, you are tasked with hedging against this risk. For this problem, all prices of the exam-answering machines are quoted per machine. Of course, there are no futures contracts trading on exam-answering machines. After careful analysis, you determine that Treasury futures are the best asset to use to hedge the price risk. In particular, you will use 10-year Treasury-note futures with a delivery date in 1 year and 1 month (13 months) to hedge. Each Treasury futures contract is on $100,000 of face value of 10 -year notes, and as always, Treasury futures are quoted as a price per $100 in face value. From historical data, you calculate a standard deviation of annual price changes in examanswering machines of $1120 (per machine). You calculate a standard deviation of annual futures price changes of the Treasury futures contract you will be using of $5 (per $100 of face value). The correlation between these two price changes in 0.85. Note: many parts of this problem are independent of each other. (a) (10 points) What is the optimal number of contracts to minimize your risk? Make sure you show your work. Tell me both the number of contracts and which direction you would trade them (long or short). As always, do not "tail the hedge." (b) (5 points) Is there any basis risk involved in this strategy? Explain briefly. (c) (5 points) Before you enter into this arrangement, you want to double check that everything is priced correctly. You determine that in one year, the cheapest to deliver Treasury note is a note with a 0% coupon rate that currently has 8 years left to maturity. (Of course, at delivery this means it has 6 years and 11 months left to maturity.) What is the conversion factor on this note at delivery? Express your answer to four decimal places. (d) (5 points) Suppose the Treasury note that will be delivered currently sells for $92 (per $100 of face value). Calculate the price of the futures contract, ignoring the effects of daily settlement. If needed, use the following zero rates: 1.0% for one year, 1.1% for 13 months, 1.95% for 6 years 11 months, 2.0% for 7 years, and 2.05% for 8 years, all quoted per annum with continuous compounding. (If you were unable to do any required previous parts, tell me how you would use those values to answer this question.) (e) (5 points) Now, consider the effects of daily settlement. Do you expect the futures price to be below or above the value calculated in (d)? Briefly justify your answer ( 3 sentences maximum). 4. Futures (30 points) Your firm will produce 10,000 exam-answering machines in one year's time. However, the price of exam-answering machines is very volatile. As CFO of the firm, you are tasked with hedging against this risk. For this problem, all prices of the exam-answering machines are quoted per machine. Of course, there are no futures contracts trading on exam-answering machines. After careful analysis, you determine that Treasury futures are the best asset to use to hedge the price risk. In particular, you will use 10-year Treasury-note futures with a delivery date in 1 year and 1 month (13 months) to hedge. Each Treasury futures contract is on $100,000 of face value of 10 -year notes, and as always, Treasury futures are quoted as a price per $100 in face value. From historical data, you calculate a standard deviation of annual price changes in examanswering machines of $1120 (per machine). You calculate a standard deviation of annual futures price changes of the Treasury futures contract you will be using of $5 (per $100 of face value). The correlation between these two price changes in 0.85. Note: many parts of this problem are independent of each other. (a) (10 points) What is the optimal number of contracts to minimize your risk? Make sure you show your work. Tell me both the number of contracts and which direction you would trade them (long or short). As always, do not "tail the hedge." (b) (5 points) Is there any basis risk involved in this strategy? Explain briefly. (c) (5 points) Before you enter into this arrangement, you want to double check that everything is priced correctly. You determine that in one year, the cheapest to deliver Treasury note is a note with a 0% coupon rate that currently has 8 years left to maturity. (Of course, at delivery this means it has 6 years and 11 months left to maturity.) What is the conversion factor on this note at delivery? Express your answer to four decimal places. (d) (5 points) Suppose the Treasury note that will be delivered currently sells for $92 (per $100 of face value). Calculate the price of the futures contract, ignoring the effects of daily settlement. If needed, use the following zero rates: 1.0% for one year, 1.1% for 13 months, 1.95% for 6 years 11 months, 2.0% for 7 years, and 2.05% for 8 years, all quoted per annum with continuous compounding. (If you were unable to do any required previous parts, tell me how you would use those values to answer this question.) (e) (5 points) Now, consider the effects of daily settlement. Do you expect the futures price to be below or above the value calculated in (d)? Briefly justify your answer ( 3 sentences maximum)