ADMS4503-Assignment1-F10-Sol

ADMS4503-Assignment1-F10-Sol - ADMS4503 3.0 AP/ADMS 4503...

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ADMS4503 3.0 Assignment #1 Page 1 AP/ADMS 4503 3.0 Derivative Securities Fall 2010 Assignment #1 Solution Instructions: (1) This assignment is to be done individually . You must sign and submit the standard cover page supplied as the last page of this assignment. (2) This assignment is due on October 24 , 2010. (3) 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. (4) You must show your work to receive full credit. (5) This assignment contains 5 questions and carries a total of 30 points . Question 1 (6 marks) AAPL spot price is $250, and is expected to pay no dividend in the foreseeable future. The risk-free rate is 3% per annum continuously compounded. (a) What is AAPL theoretical 1-year futures price? (2 marks) (b) The 1-year futures price is $256. Show that there is an arbitrage and show how to benefit from it? Show all details . (4 marks) Solution (a) The theoretical 1-year futures price given by: ( ) () 6136 . 257 1 % 3 exp 250 exp 0 = × × = × × = T T F T r S F (b) Since the market underprices the contract, there is an arbitrage that consists in taking a long 1-year futures contract, shorting the stock and investing the proceeds at the risk-free rate. By doing this, you lock in a net profit of $1.6136 . Here are the details: Today, you must: - Long one 1-year contract to buy the stock at $256 in 1 year - Short one stock at $250 - Invest the proceeds at 3% In 1 year: - You buy one stock for $256 according to your futures contract and close out your short position - Your investment grows to $250 x exp(3%) = $257.6136
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ADMS4503 3.0 Assignment #1 Page 2 - Your profit is then (257.6136 – 256) = $1.6136 Question 2 (6 marks) GS stock is expected to pay a dividend of $0.35 per share in 1, 4 and 7 months. The stock spot price is $150, and the risk-free rate is 3% per annum continuously
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This note was uploaded on 12/17/2010 for the course ATKINSON adms 4503 taught by Professor Nabil during the Fall '10 term at York University.

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ADMS4503-Assignment1-F10-Sol - ADMS4503 3.0 AP/ADMS 4503...

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