Explain using a formula how low orange cropping yields may influence the futures price of frozen orange juice concentrate?
This is an exam question of 20 marks and I need you to be able to achieve a minimum of 65%.
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INVE3000: Introduction to Derivative Securities Assessment 1: Total marks 20. This assessment counts towards 25% of your final mark. Student Name: Student Id: Due date: 5 pm, Friday, 25th August 2023, Perth time. Please make your submission via the electronic link on Blackboard. Unfortunately, due to academic integrity concerns all submissions must be typed and uploaded in word or pdf format. Formulas and calculations presented must use an equation editor (or equivalent). No handwritten formula or diagrams permitted. Exercise 1 (5 marks) Extreme weather events and citrus greening disease have negatively impacted orange (a type of citrus) cropping yields in Florida, one of the world’s largest producing citrus areas located in the United States of America. In April the futures price of Frozen Orange Juice Concentrate (FOJC) rose to a historical high of US $2.86 (or US 286 cents) per pound in April 2023. i. Explain using a formula how low orange cropping yields may influence the futures price of frozen orange juice concentrate? (1 mark) ii. In April you bought two futures contracts on FOJC when the futures price was US 286 cents per pound with an initial margin of US $5,000 per contract. Each contract is for delivery of 15,000 pounds. If your maintenance margin is US $3,750 what price change in FOJC would lead to a margin call? (2 marks) iii. Instead of futures contract, you entered a one-year long forward contract on FOJC in April 2023 when the forward price was US 286 cents per pound. Each contract is also for delivery of 15,000 pounds. After one month (t=1 month) the price of the forward concentrate was US 293 cents per pound. Assuming a risk-free rate of 5% with continuously compounding, what is the value of the forward contract after one month? (2 marks)
Exercise 2 (4 marks) An investor owns an ETF (Exchange Traded Fund) tracking the ASX 200 index as part of his portfolio, and this ETF can generate a continuously compounded dividend yield of 2% per year. Today, the investor can buy the ETF for $50 per unit and sell it for $49 per unit. Meantime, the investor can borrow funds at 7% per year and invest funds at 5.5% per year (both rates are continuously compounded). For what range of half-year forward prices does the investor have no arbitrage opportunities? Just assume there is no bid–offer spread on the forward market. (4 marks) Exercise 3 (6 marks) i. What are the 0.5-year and 1-year zero rates (continuously compounding) implied from the table below? Assume coupons are paid semi-annually for coupon bonds. (2 marks) Bond Principal ($) Time to Maturity (yrs) Coupon per year ($) Bond price ($) 100 0.50 0 97.43 100 1.00 4 98.97 100 1.50 6 101.62 100 2.00 8 106.28 ii. Suppose that the 6-month, 12-month, 18-month, and 24-month zero rates are 5.10%, 5.00%, 4.80% and 4.75%, respectively. What is the two-year par yield? Verify the solution is correct by showing the discounted cashflows at the par yield. Round all answers to 4 decimal places. (4 marks)
Exercise 4 (5 marks) i. On April 1, an investor holds 40,000 shares of a certain stock. The market price is $28 per share. The investor is interested in completely hedging against movements in the market over the next month and decides to use the June Mini S&P 500 futures contract. The index is currently 4,500 and one contract is for delivery of $50 times the index. If the beta of the stock is 1.2, what strategy should the investor follow to completely hedge their stock portfolio? (2 marks) ii. After a month, the investor wishes to partially unwind their hedge to reach an overall target beta of 1. Using your answer from above, what strategy should the investor follow to reach their target? They still hold 40,000 shares and the market price is now $27.5 per share. The June Mini S&P Futures index is still at 4,500 and one contract for delivery is of $50 times the index. What will be the residual remaining position in their futures contracts? (3 marks)
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