This assignment
ADMS4503 3.0
Assignment #1 AP/ADMS 4503 3.0 Derivative Securities Winter 2013 Assignment #1
Instructions: (1)
(2) (3) (4) (5)
This assignment is to be done individually. You must sign and submit the standard cover page supplied as the last page of this assignment. Staple your assignment prior to handing it in. This assignment is due on February 10, 2013. The work can be typed or handwritten. If it is handwritten and too difficult to read due to messiness and poor handwriting, it will receive zero credit. You must show your work to receive full credit. This assignment contains 5 questions and carries a total of 30 points.
Question 1 (6 marks) IBM stock sells at $194.50 and is expected to pay dividends of $2 in 2 and 8 months respectively. The risk-free rate is 4% per annum continuously compounded for all maturities. We consider the 1-year futures contract on IBM. (a) What is the theoretical 1-year futures price? (2 marks) (b) The 1-year futures market price is $200. Show that there is an arbitrage and how to benefit from it? Show all details. (3 marks) (c) Based on the futures market price in part (b), what is the value of a short futures contract on IBM 10 months from now if the futures price in 10 months is $204? (1 mark)
Question 2 (6 marks) The S&P 500 spot is 1,472 and it is expected to pay a dividend yield of 2%. The risk-free rate is 4% per annum continuously compounded. Each contract is on $250 times the futures price. (a) What is the theoretical 1-year futures price? (2 marks) (b) The 1-year futures price is 1,490. Show that there is an arbitrage and show how to benefit from it? Show all details. (4 marks)
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ADMS4503 3.0
Assignment #1
Question 3 (6 marks) The palladium sells at $701 per ounce. It has a convenience yield denoted by y and a storage cost u = 2% (per annum continuously compounded). The risk-free interest rate is 4% per annum continuously compounded. The 6-month futures price is $710. A hedge fund takes 200 long positions in the 1-year futures contract on palladium today. Each contract is on 100 ounces. (a) What is the convenience yield? (2 marks) (b) Suppose that the hedge fund closes out its positions 9 months from now and makes a total gain of $100,000. What is the spot price of palladium 9 months from now if there is no arbitrage? (4 marks)
Question 4 (6 marks) Suppose the spot CAD/GBP exchange rate is 1.5937 and the Canadian risk-free rate is 4% per annum. Suppose the 6-month futures exchange rate is 1.6045. (a) What is the theoretical 1-year futures exchange rate? (3 marks) (b) Suppose the 1-year futures exchange rate is 1.62. Is there an arbitrage and if so how would you undertake it for 1 million in either currency? Show all details. (3 marks)
Question 5 (6 marks) The following table gives monthly data of the spot price and the futures price for commodities A and B respectively. A company expects to buy 125,000 units of commodity A in one month. The size of one futures contract on commodity B is 1,000 units. The company would like to hedge commodity A using commodity B futures contract. Month 1 2 3 4 5 6 7 8 9 10 11 12
Futures price 20.7 21.8 20.8 22.0 21.8 22.1 22.4 21.5 22.2 22.8 22.0 21.4
Spot price 21.4 21.8 21.1 21.7 21.9 22.2 21.9 22.2 22.3 22.7 22.0 21.7
Month 13 14 15 16 17 18 19 20 21 22 23 24
Futures price 21.6 22.5 22.4 22.6 21.3 22.0 22.5 22.4 22.5 23.2 22.5 23.2
Spot price 21.9 22.5 22.4 22.3 21.4 21.8 22.5 22.3 22.7 22.9 22.5 22.7
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ADMS4503 3.0
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(a) What position should the company take (long vs. short and number of contracts)? (Round the number of contracts to the nearest integer). (4 marks) (b) The 1-month futures price of the commodity is $23.2 today. If the futures price two weeks from now (when the hedging position is closed out) is $20.9 per unit and the spot price at the same time is $21.4 per unit, what is the effective price per unit paid or received by the company? (2 marks)
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ADMS4503 3.0
Assignment #1
Faculty of Liberal Arts and Professional Studies YORK UNIVERSITY Toronto, Ontario
AP/ADMS 4503 3.0 Derivative Securities Professor
Nabil Tahani M (Mon 7-10pm)
Section N (Mon 4-7pm)
Assignment #1 Due Date: February 10, 2013 Personal Work Statement I, the undersigned: • warrant that the work submitted herein is my work and not the work of others • acknowledge that I have read and understood the Senate Policy on Academic Honesty • acknowledge that it is a breach of the University Regulations to give and receive unauthorized assistance on a graded piece of work Name (typed or printed) York Student # Signature
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Assignment #1 AP/ADMS 4503 3.0 Derivative Securities Winter 2013 Assignment #1
Instructions: (1)
(2) (3) (4) (5)
This assignment is to be done individually. You must sign and submit the standard cover page supplied as the last page of this assignment. Staple your assignment prior to handing it in. This assignment is due on February 10, 2013. The work can be typed or handwritten. If it is handwritten and too difficult to read due to messiness and poor handwriting, it will receive zero credit. You must show your work to receive full credit. This assignment contains 5 questions and carries a total of 30 points.
Question 1 (6 marks) IBM stock sells at $194.50 and is expected to pay dividends of $2 in 2 and 8 months respectively. The risk-free rate is 4% per annum continuously compounded for all maturities. We consider the 1-year futures contract on IBM. (a) What is the theoretical 1-year futures price? (2 marks) (b) The 1-year futures market price is $200. Show that there is an arbitrage and how to benefit from it? Show all details. (3 marks) (c) Based on the futures market price in part (b), what is the value of a short futures contract on IBM 10 months from now if the futures price in 10 months is $204? (1 mark)
Question 2 (6 marks) The S&P 500 spot is 1,472 and it is expected to pay a dividend yield of 2%. The risk-free rate is 4% per annum continuously compounded. Each contract is on $250 times the futures price. (a) What is the theoretical 1-year futures price? (2 marks) (b) The 1-year futures price is 1,490. Show that there is an arbitrage and show how to benefit from it? Show all details. (4 marks)
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ADMS4503 3.0
Assignment #1
Question 3 (6 marks) The palladium sells at $701 per ounce. It has a convenience yield denoted by y and a storage cost u = 2% (per annum continuously compounded). The risk-free interest rate is 4% per annum continuously compounded. The 6-month futures price is $710. A hedge fund takes 200 long positions in the 1-year futures contract on palladium today. Each contract is on 100 ounces. (a) What is the convenience yield? (2 marks) (b) Suppose that the hedge fund closes out its positions 9 months from now and makes a total gain of $100,000. What is the spot price of palladium 9 months from now if there is no arbitrage? (4 marks)
Question 4 (6 marks) Suppose the spot CAD/GBP exchange rate is 1.5937 and the Canadian risk-free rate is 4% per annum. Suppose the 6-month futures exchange rate is 1.6045. (a) What is the theoretical 1-year futures exchange rate? (3 marks) (b) Suppose the 1-year futures exchange rate is 1.62. Is there an arbitrage and if so how would you undertake it for 1 million in either currency? Show all details. (3 marks)
Question 5 (6 marks) The following table gives monthly data of the spot price and the futures price for commodities A and B respectively. A company expects to buy 125,000 units of commodity A in one month. The size of one futures contract on commodity B is 1,000 units. The company would like to hedge commodity A using commodity B futures contract. Month 1 2 3 4 5 6 7 8 9 10 11 12
Futures price 20.7 21.8 20.8 22.0 21.8 22.1 22.4 21.5 22.2 22.8 22.0 21.4
Spot price 21.4 21.8 21.1 21.7 21.9 22.2 21.9 22.2 22.3 22.7 22.0 21.7
Month 13 14 15 16 17 18 19 20 21 22 23 24
Futures price 21.6 22.5 22.4 22.6 21.3 22.0 22.5 22.4 22.5 23.2 22.5 23.2
Spot price 21.9 22.5 22.4 22.3 21.4 21.8 22.5 22.3 22.7 22.9 22.5 22.7
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ADMS4503 3.0
Assignment #1
(a) What position should the company take (long vs. short and number of contracts)? (Round the number of contracts to the nearest integer). (4 marks) (b) The 1-month futures price of the commodity is $23.2 today. If the futures price two weeks from now (when the hedging position is closed out) is $20.9 per unit and the spot price at the same time is $21.4 per unit, what is the effective price per unit paid or received by the company? (2 marks)
Page 3
ADMS4503 3.0
Assignment #1
Faculty of Liberal Arts and Professional Studies YORK UNIVERSITY Toronto, Ontario
AP/ADMS 4503 3.0 Derivative Securities Professor
Nabil Tahani M (Mon 7-10pm)
Section N (Mon 4-7pm)
Assignment #1 Due Date: February 10, 2013 Personal Work Statement I, the undersigned: • warrant that the work submitted herein is my work and not the work of others • acknowledge that I have read and understood the Senate Policy on Academic Honesty • acknowledge that it is a breach of the University Regulations to give and receive unauthorized assistance on a graded piece of work Name (typed or printed) York Student # Signature
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