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Student Name ________________________ Student Number ________________________ Bus 316 Final Exam, December 2011 CAUTION In accordance with the Academic Honesty Policy (T10.02), academic dishonesty in any form will not be tolerated. Prohibited acts include, but are not limited to, the following: - Making use of any books, papers, electronic devices or memoranda, other than those authorized by the examiners. - Speaking or communicating with other students who are writing examinations. - Copying from the work of other candidates or purposely exposing written papers to the view of other candidates. 1 Student Name ________________________ Student Number ________________________ Question 1: Multiple Choice (20 Total marks, 2 marks for each answer) Select the best answer for each of the following multiple choice questions. Enter your answers on the scantron bubble sheet. If more than one answer is given for any item, that item will not be marked. Incorrect answers will be marked as zero. Explanations provided beside the answers will not be considered. 1. A short forward contract on a non-dividend paying stock was entered into some time ago at a delivery price of $24. It currently has six months to maturity. The risk-free interest rate is 5% and the current stock price is $25. Find the current value of the forward contract. a) - $1.63 b) - $1.59 c) $1.59 d) $1.63 e) $24.00 2. On May 1, an investor takes a short position in ten December gold Futures contracts on the New York Commodity Exchange (COMEX). The current Futures price is $1,600, the contract size is 100 ounces, the initial margin is $2,000 per contract, and the maintenance margin is $1,500. If by the end of May 1 the Futures price has dropped to $1,598: a) the margin balance increases by $200. b) the margin balance increases by $2000. c) the margin balance decreases by $2000. d) the investor receives a margin call. e) the broker automatically closes out the position. 3. Consider a 1-year Futures contract to buy one corporate bond. The current spot price of the bond is $920.00, the continuous interest rate for 1-year is 10%. One coupon payment of $10.00 will be paid in 9-months. If the Futures price of the bond in the market is $1003, an arbitrage profit can be generated by: a) shorting the Futures contract and short selling one Bond. b) shorting the Futures contract and buying one Bond. c) taking a long position in the Futures contract 9-months from today. d) taking a long position in the Futures contract and buying one Bond. e) taking a long position in the Futures contract and short selling one Bond. 4. An investor has an asset that is currently worth $500, and the continuously compounded rate at all risk-free maturities is 3 percent. If the asset pays a continuous dividend of 3 percent, which of the following is the closest to the no arbitrage price of the 3-month forward contract? a) $496.26 b) $500.00 c) $502.00 d) $503.00 e) $503.76 2 Student Name ________________________ Student Number ________________________ 5. The three month interest rates in New Zealand and Canada are 6% and 4% per annum respectively, with continuous compounding. The spot price of one New Zealand Dollar is Canadian Dollars 0.80. (i.e. 1 NZD = 0.80 CAD). What is the theoretical value of the 3 month futures contract? a) 0.7960 b) 0.8000 c) 0.8040 d) 0.8080 e) 0.8162 6. A shareholder wants to use 1-year put options to hedge 50% of a portfolio containing 10,000 shares of USCorp, a US firm. We denote by ST the spot price in one year for one share of USCorp and by K the strike price of the options purchased by the shareholder. The total value of the hedged portfolio (neglect the option premiums paid upfront) in one year is: a) 10,000 K b) 10,000 max(K,ST). c) 10,000 ST + 5,000 max(K,ST). d) 10,000 ST + 10,000 max(K,ST). e) 5,000 ST + 5,000 max(K,ST). 7. Consider a European put option on a stock currently price at $50. The put option has an expiration of 6 months, a strike price of $40, and the risk-free rate is 5 percent. The price of the put option must be less than: a) b) c) d) e) $0 $1.23 $10 $10.99 $39.01 8. Is it ever optimal to exercise an American call option on gold early? a) Yes. You should exercise the option when the price of gold goes above the strike price. b) Yes. You should exercise the option when the price of gold drops below the strike price. c) Yes. You should exercise the option when the option's time value starts decreasing. d) No. You should not exercise the option since the later the strike price is paid out, the better. e) No. You cannot exercise the option early since only European options can be exercised early. 9. A three-month call with a strike price of $25 costs $2. A three-month put with a strike price of $20 costs $3. A trader uses these options to create a strangle. For which two values does the trader breakeven? a) II. and IV. b) I. and V. c) I. and IV. d) III. and IV. e) II. and V. I. II. III. IV. V. 3 $15 $17 $22.50 $27 $30 Student Name ________________________ Student Number ________________________ 10. An increase in which of the following will increase the value of an American call? a) I. only b) II. only c) III. only d) I. and III. only e) I. and III. and IV. only I. II. III. IV. 4 The stock price The strike price The volatility The time remaining before expiration Student Name ________________________ Student Number ________________________ Question 2: Option Pricing & Arbitrage (12 marks total) Consider a stock that is currently priced at $40. The stock is a non-dividend paying stock. The continuous riskfree rate of interest is 10% per annum. (3 marks) (a) If you own a 3-month European put with a strike price of $45, calculate the price of the put based on the \"lower bound\". Put = _______________ (3 decimals) (3 marks) (b) IF the current market price of a 3-month European call with a strike price of $45 was $0.50. Using the information at the very beginning of the question, calculate what the price for the 3month European put should be if there were no arbitrage opportunities. Put = _______________ (3 decimals) 5 Student Name ________________________ Student Number ________________________ (3 marks) (c) IF the current market price of a 3-month European put with a strike price of $45 was $4.25, based on your answer in part (b), describe the transactions would you enter into to earn a riskless profit? [If you were unable to answer part (b), you may use the price of $4.35] Transaction #1: _______________________________________________________________ Transaction #2: _______________________________________________________________ Transaction #3: _______________________________________________________________ Additional Transactions: (3 marks) (d) Now assume that the stock is expected to pay a dividend of $0.75 in two months. If the current market price of a 3-month European call with a strike price of $45 was $0.50. Using the information at the very beginning of the question, calculate what the price for the 3-month European put should be if there was no arbitrage opportunities (3 decimals) Put = _______________ (3 decimals) 6 Student Name ________________________ Student Number ________________________ Question 3: Option Trading Strategies (12 marks total) Consider a portfolio of options that consists of: Sell 3-month put with a strike price of $35 that priced at $4.50 Long 3-month put with strike price of $43 that is priced at $7.00 Currently the price of the underlying stock is $40. (2 marks) (a) Draw the PROFIT diagram based on the above portfolio. Clearly label the breakeven(s). (3 marks) (b) Complete the below table to Show Payoffs and Profit/Losses for the different possible price ranges of ST at expiration. Let ST denote the Stock Price at Expiration. Stock Price Total Portfolio Payoff Total Portfolio Profit/Loss ST 35 35