True/False: Mark (a) for true, (b) for false on the bubble sheet. (20 pts)

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1 Midterm Exam 2 11/18/ pts possible Instructions: Answer the true/false and multiple choice questions below on the bubble sheet provided. Answer the short answer portion directly on your exam sheet in the space provided. If you require additional space, paper will be provided at the front of the classroom. You have 90 minutes to complete the exam. Cell phone or laptop use of any kind is prohibited. You may use any standard calculator to perform computations; however, models with data storage capabilities are subject to search at the instructor s discretion. True/False: Mark (a) for true, (b) for false on the bubble sheet. (20 pts) 1) Selling a put is a strategy with limited gains and unlimited losses. False 2) The buyer of an option is required to post margin, while the seller of an option is not. False 3) A straddle is an option position that should profit when prices are highly volatile. True 4) For a call and a put written on the same underlying futures contract with the same strike price, they will never have positive intrinsic value at the same time. True 5) If the price of the underlying futures contract increases, the premium of both a put and a call for a give strike price, K, will increase. False 6) The price of a European option will always be at least as great as its American counterpart. False 7) You can create a synthetic short call option by buying futures contract and selling a put. False 8) If the basis is zero and futures commissions are zero, it is profitable to roll a hedge if the price spread F Distant Nearby ( t F t ) offered in the futures market is greater than your cost of storage of the underlying commodity. True 9) A put option is in the money when the futures price is greater than the strike price. False 10) The intrinsic value of an option is zero when the option is out of the money. True 1

2 Multiple Choice: Select only one answer. (15 pts) 11) To create a butterfly spread you: a. Buy a put and buy a call with the same strike b. Buy a low strike put, Buy a high strike put, and sell two puts with a strike in the middle. c. Buy a put and sell a call with the same strike d. Sell a low strike put, sell a high strike put, and buy two puts with a strike in the middle. 12) For two otherwise identical bonds, one having a small coupon and the other having a larger coupon: a. The size of the coupon does not affect the bond s price volatility. b. The affect of a bond s coupon size on price volatility cannot be determined from the information given. c. The small coupon bond experiences more price volatility than the large coupon bond. d. The large coupon bond experiences more price volatility than the small coupon bond. 13) To put on a bull spread you a. Buy a low strike call and sell a high strike put b. Buy a low strike call and buy a high strike put c. Sell a low strike call and buy a high strike call d. Buy a low strike call and sell a high strike call 14) Which statement is true: a. A seller of an option may choose to exercise in order to get out of their position b. The buyer of a call option has unlimited risk. c. The seller of a put option has unlimited risk. d. The buyer of an option may choose to exercise in order to get out of their position. 15) Generally speaking, the last day to trade or exercise on an option contract: a. is a few days before the last day to trade the underlying futures contract b. is a few days before the beginning of the delivery window of the underlying futures contract c. Coincides with the beginning of the delivery window of the underlying futures contract d. Coincides with the last day to trade the underlying futures contract 2

3 Short answer questions Use these option prices to answer the questions below. price F = $534 Option Strike Premium Call $530 $16.40 Put $530 $12.40 Call $535 $13.90 Put $535 $14.90 Call $540 $11.60 Put $540 $ ) Suppose you are bearish about this market. Describe a speculative option strategy (requiring more than one option) that allows you to profit if your market expectations are correct, but gives up some upside potential in order to reduce the cost of the position. List each trade in detail and provide profit diagrams of each option and the net position. (40 pts) Note: This question can be done with put or calls; they only need to do one of these. 3

4 Option 1: Buy high strike call; K=540, premium=11.60 Sell low strike call; K=530, premium $ Bought Call $16.40 $4.80 -$5.20 -$ F Net Sold Call Option 2: Buy high strike put; K=540, premium=17.60 Sell low strike put; K=530, premium $ $12.40 $4.80 Sold Put -$ F Net -$17.60 Bought put 4

5 17) Construct a synthetic long futures position with some combinations of the options above. a. List each trade in detail and provide profit diagrams of each option and the net position (30pts) b. Suppose that the current futures price is $535 instead of $534. Can you spot an arbitrage opportunity? If so, how do you do to capitalize on it? (15pts) a. Buy call option; K=535, premium=13.90 Sell put option; K=535, premium=14.90 b. If the futures contract was trading at 535 then there is an arbitrage opportunity. We created a synthetic long position at 534. Then we can sell the actual futures for 535 and lock in $1 riskless profit. 5

6 18) You have a spot position of crude oil in Cushing, OK and are considering hedging with the futures contract whose data for the past year is provided below. Given the statistics provided to you, determine the optimal hedge with this futures contract, and the effectiveness. Then determine if you want to hedge with this futures contract or not. Explain your answer; sice you are given the formulas, this question is more about explaining what they mean. (40pts) Cushing OK Spot S Crude Crude F 1/1/ /1/ /1/ /1/ /1/ /1/ /1/ /1/ /1/ /1/ /1/ Some statistics about these data: Covariance( S, F ) Variance of S Variance of F correlation ( ) ( ) cov S, F h = var F hedgingeffectiveness= correl( S, F) 2 Optimal hedge ratio is h=0.28; Hedging effectiveness ratio is he=0.095 The optimal hedge ratio is quite low at 28%. This means, for example, that if we have 18,000 bushels to sell we should roughly hedge only bushels. This small ratio indicates that the spot and futures are not very correlated.this is further indicated by a he of 9.5%. This means that only 9.5% of the variance of an outright position is the cash market can be eliminated by hedging with this futures contract. This indicates the spot and futures do not move together very reliably. We should only hedge 28% of our spot position in the futures market, and doing this will only reduce 9.5% of the variance associated with an outright position. Probably not a very good hedge instrument. 6

7 19) On November 1 you harvested soybeans and put 5,000 bushels into storage at the local elevator. You had not previously hedged any of this harvest. You decide to sell this grain on March 1 and hedge your price risk using the March futures contract. As expiration of the March contract approaches you must decide if you will sell, as was your original intention, or if you will roll your hedge forward and sell in May instead. Also assume that your local elevator is a delivery location of the futures contract so that you do not have to consider basis risk (i.e., S T = F T, or the spot price is equal to the futures price at expiration), and also assume that there are no commission charges for your futures transactions. (40pts) Date: Spot Price Price of March Price of May Cost of Storage (/bu/month) November March May Compare the profit of selling in March verses rolling the hedge forward to May. (40pts) Option 1: Sell in March Spot Nov NA Sell March for March Sell Buy March for Profit = (0.15*4)+( ) = $11.90 Option 2: Sell in May Spot Nov NA Sell March for March NA Buy March for 12.45, Sell May May Sell Buy May Profit = (0.15*6)+( )+( ) = $12.00 Option 2, rolling the hedge was profitable by $0.10 more because we were able to capitalize on a $0.40 price spread from March to May and it only cost an extra $0.30 to store the grain longer. 7