Highlights
Task:
Question 1: (20 points) Canada’s primary aluminium industry is the fifth largest in the world with an annual production of 2.9 million tons of primary aluminium with the lowest carbon footprint. Alcoa, Aluminerie Alouette and Rio Tinto operate 9 plants in Canada (8 plants in Quebec and 1 in British Columbia). The industry supports more than 8,800 jobs in Canada generating CDN$8.3 billion in exports. It is February 1st. An aluminium plant in Quebec agrees to deliver 250 metric tons (MT) of aluminium in 9 months to a car part manufacturer in Guelph. The current spot aluminium price is $1,994 per MT, and the risk- free rate of interest is 5% per year with continuous compounding. The aluminium plant has just taken a short position in a 9-month forward contract on 250 metric tons (MT) of aluminium.
a. Suppose that there are no storage costs for aluminium. Calculate the 9-month aluminium forward price for the contract. Calculate the value of the forward contract on Febuary1st, 2021, at the time the contract is first entered.
b. Three months later, on May 1st, 2021, the spot price of aluminium is $1990 per MT, and the risk-free rate of interest is still 5% per year. Calculate the forward price and the value of the short forward position on May 1st, 2021?
c. In Question 1.a, suppose now there are storage costs. The storage costs are $144 per MT per year payable quarterly in advance. The risk-free rate of interest is still 5% per year. On February 1st, 2021, calculate the present value of the storage costs for the 9 months. Calculate the forward price of aluminium on February 1st, 2021.
d. In Question 1.a, suppose now there is a storage rate of 4.0% per year and the aluminium plant obtains a convenience yield of 1.0% per annum from holding inventory of aluminium. The risk-free rate of interest is still 5% per year. On May 1st, 2021 (three months later), the spot price of aluminium is $1990 per MT. Calculate the forward price of the contract on May 1st, 2021. Calculate the value of the long forward contract on May 1st, 2021.
Question 2. (20 points) It is January 31, 2019. A local brewery is a large producer of craft beer whose main ingredient is barley. The demand for craft beer is seasonal with the largest demand occurring mid-June through the end of August. Production schedules require the acquisition of 80 metric tons (MT) of barley in late May to meet the summer season demand. The management of the brewery is concerned about the possibility that a rise in the price of barley between now and the end of May could hurt profit margin. Barley must be acquired for $350 per metric ton (MT) or less to ensure profitability. On February 1, 2021, the ICE June 2021 Barley futures contract (20 MT per contract) is selling for $351.80 per MT. The standard deviation of the change in the spot price of barley is 0.80. The standard deviation of the change in the futures price of barley is 0.56. The correlation between the change in futures price and the change in spot price is 0.60. One contract of barley is 20 metric tons on ICE.
(a) Indicate whether the risk manager of the brewery should take a long or short futures position to hedge price risk. Why?
(b) Calculate the risk-minimization hedge ratio, h, and determine how many contracts the brewery must trade? If the standard deviation of the change in the futures price of barley doubles, what would happen to the number of contracts? Does it increase or decrease? Explain the intuition behind your last result.
(c) Determine the hedge effectiveness and comment. Determine and discuss the effects of the hedge effectiveness of (i) a 25% decline in the correlation between the changes in futures price and the change in sport price, ρ, (i) a doubling of the standard deviation of the change in the spot price of barley, σs, and
(iii) a doubling of the standard deviation of the change in the futures price of barley, σF?
(a) Suppose that the brewery follows your hedging recommendations in (a) and (b). On June 1st, 2021, the spot price of barley is $400 per metric ton and the June barley futures price is trading at $410 per metricton. What is the total gain or loss from the futures position(s)? What is the net (effective) price paid by the brewery? Any regrets from hedging? Why?
Question 3. (20 points) In is February. The operation manager of a new mining company reviews its platinum production plans. The production forecasts suggest that the company will have 20,000 ounces of newly mined and refined platinum available for sale the following June. The manager considers the current price of the July platinum futures contract at $1,132.80 per ounce favourable, given the company’s total production costs, including interest and depreciation, of $980 an ounce. As a result, on January 28, the mining financial manage decides to lock in a profit by hedging his anticipated production using the July platinum futures contract at $1,132.80 per ounce. On January 28, the spot price is $1,121.31 per ounce. The contract size is 50 troy ounces on the CME Group.
(b) Indicate whether the financial manager should use a long or short forward contract to hedge the risk exposure. How many contracts are needed for a full hedge?
(c) On January 28, the company trades July futures contracts at $1,132.80 per ounce. The initial margin deposit for CME Group is $8,100 per contract and the maintenance margin is $6,000. The next day, the July platinum futures price closes at $1136.80 per ounce. What is the balance in the margin account? Would the company get a margin call? Why? What if the July platinum futures price closes at $1127.50 per ounce?
(d) What price change would lead to a margin call from the initial futures price of $809.80 per ounce (up ordown)?
(e) On June 15, the company sells platinum at $1210.25 per ounce locally and it offsets the futures positions. Suppose that on June 15, the futures price is trading at $1125.50 per ounce. What is the company’s net (effective) selling price per ounce for platinum?
(f) What would be the company’s net selling price per ounce for platinum if the financial manager hedged only 75% of the forecasted production? What is the total gain/loss from the futures position(s)? Any regrets from hedging? Why?
Question 4. (20 points) According to IATA, “The COVID-19 crisis has disrupted global air travel resulting in a dramatic decrease in the consumption of jet fuel by airlines. Coupled with this decline was a deep and rapid decline in oil prices related to this decrease in demand and an increase in supply by some producers. As a result, airlines may have over-hedged their future jet fuel purchases with forward or futures contracts and find themselves with contracts that have significant negative values captured in equity.” Studies have shown that airline profits are most sensitive to the price of jet fuel.
It is July 2019 (before COVID-19). Suppose you are a trader for an airline, and you watch the price of jet fuel rise to $76 per barrel and worried that prices could go higher in the summer of 2020 if the current trend continues. The airline is expected to buy 840,000 gallons (20,000 barrels) of jet fuel in summer 2020. On January 10, 2020, you decided to hedge 80% of your jet fuel price risk exposure using crude oil futures contracts (i.e., cross-hedge). On January 10, 2020, the spot price of jet fuel is $1.78 per gallon ($74.76 per barrel) and the June 2020 crude oil futures contract is trading at $62.00 per barrel. One crude oil futures contract is 1,000 barrels.
(a) Indicate whether you should use a long or short crude oil futures contract to cross hedge the jet fuel price risk exposure. How many contracts are needed?
(b) On January 10, 2020, the airline follows your hedging recommendation and trades 16 June crude oilfutures contracts at $62.00 per barrel. The initial margin deposit for crude oil is $4,200 per contract and the maintenance margin is $3,150. The next day, the June crude fuel futures price closes at $65.00 per barrel. What is the balance in the margin account? Would you get a margin call? Why? What if the June jet fuel futures price closes at $60.00 per barrel?
(c) What price change would lead to a margin call from the initial futures price of $65.00 per barrel?
(d) On June 10, because of the decline in the demand for air travel, the airline purchases 210,000 gallons of jet fuel (i.e., 25% of the forecasted demand) at $0.98 per gallon locally and offset its June crude oil futures positions. Suppose that on June 10, 2020, the June crude oil futures price is trading at $39.70 per barrel. What is the total gain or loss from the crude oil futures contract? What is the airline’s net buying price per gallon for jet fuel? Any regrets from hedging? Why?
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