Use the three tables below to answer the following questions



Exam #1

Econ 351

Fall 2015

Good Luck!

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GOOD LUCK!!!

1 (30 points total) Use the three tables below to answer the following questions

Table 1

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Table 2

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Table 3

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a) (5 points) Suppose we play a long straddle by purchasing one 113 call option and one 113 put option at Table 1 and close both positions on Table 2. Calculate the profit or loss AND rate of return.

b) (5 points) Explain the intuition as to why you made a profit or loss, which ever applies, by playing this long straddle. Note that we opened this long straddle on August 20 (Table 1) for options that expire on 9/04 and closed our position on 9/01 (Table 2).

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c) (5 points) Would we have been better off waiting until 9/02 (Table 3) to close our long straddle (as compared to closing on Table 2 as in part a)? Explain the intuition underlying your answer.

d) (5 points) Suppose someone had a really good crystal ball and told you, correctly, that the spot price of NFLX would stay as it is in Table 3 = 105.44 until expiration. Would it be better to close your long straddle on Table 3 or wait until expiration. Make sure you give me the exact savings or losses, by waiting until expiration vs closing on Table 3.

e) (5 points) Explain the intuition underlying your answer in part d).

f) (5 points) Suppose you went long on NFLX by buying 100 shares on August 20 and being risk averse, you decide to hedge this long position. Assuming that you close both the long position and the hedge on Table 2 (9/01), would it have been better to hedge by 1) buying a 113 put or 2) by writing a 113 call?

Explain with real numbers!

2. (35 points total)

a) (25 points for a correct and completely labeled graph) We are now going to graph the profit functions for the long and short straddle as above where we opened up the positions at Table 1. Recall that we are buying one 113 call and one 113 put. The player of the short straddle writes these two options. Identify the profit / loss for both players for one point, let's call it point B, with the spot at expiration as it is in Table 2: spot = $107.76 (there are two points B's, one for the player of short straddle and one for the player of long straddle). Be sure to include the math as to how you calculated the payoffs for each player (at Point B) and prove that this is indeed a zero sum game! Be sure to label the break even points (there are two of them!). Also, be sure to label which profit function represents the long straddle and which profit function represents the short straddle.

b) (10 points) Assuming the spot price of NFLX is frozen at its value on Table 1 until expiration, plot the evolution of the premium on your 113 call AND 113 put starting from the conditions at Table 1 through expiration. Please make sure you plot these on the SAME graph labeling your graph completely (be sure to identify which line is the call and which is the put).

3. (30 points total)

a) (20 points) We are now going to plot the profit functions of the hedges that we played in question 1. part f). In particular, we bought one 113 put (this is one hedge) and wrote one 113 call (this is the other hedge). Note that we opened these positions at Table 1. Please be sure to include both profit functions on ONE graph being sure to label graph completely including the two breakeven points.

b) (10 points) The profit functions above cross at two points which implies that there are two spot prices at expiration such that you would be indifferent since both hedges would result in the exact same loss or profit, which ever applies. Label these two points as points ND, which stands for No Difference. There are two point ND's. Include the math as to how you found these two points of No Difference. That is, prove that both hedges result in the same profit or loss, whichever applies.

4. (36 points total) Suppose you are in charge of an oil refinery which means you, as in your firm, are a user of crude oil and a producer of gasoline. As we know, both crude oil and gasoline are part of a well developed financial market so that futures and futures options markets exist that are extremely liquid for these two commodities. Suppose that you know next to nothing about markets and so you need to hire someone to help you make decisions as to how to the ‘play the game’ and maximize profits. Naturally, you maximize profits by minimizing the cost of the input…oil … and maximizing your revenue…..selling gas. We assume away all costs except for the input oil and we have the following production figures – each oil contract consists of 1000 barrels of crude and with 1000 barrels we can produce 100,000 gallons of gas. Each gas contract is for 50,000 gallons so for every oil contract that we buy we produce the equivalent of two gasoline contracts. We have a contract with BP for 500,000 gallons of gasoline for delivery at the end of February 2016 (10 gasoline contracts worth) and we need to buy the oil (5 contracts), the input, at the end of November to give us time to refine it in time for delivery. The charts below represent the two futures contracts we consider – the November 2015 oil contract and the February 2016 gasoline contract.

Four different job applicants come in and you interview them….they all advise you a little differently.

1) Future guy (FG)– this person simply plays the futures market – so they would advise you buy oil futures and to sell gas futures.

2) Going naked (GN)– this person doesn’t hedge and would advise you to take your chances in the spot market – think of this person as having a high risk appetite.

3) The option buyer (OB)– this person would advise you to buy futures options calls on oil and futures options puts on gas.

4) The option writer (OW) - this person would advise you to write futures options puts on oil and to write futures options calls on gas.

We consider the oil market first (see graph below). Suppose that the futures price of oil is $46 per barrel (point A in graphic) and that futures options, both puts and calls, are available at a price of $4,000 each (STRIKE PRICE = $46, EACH CALL AND PUT REPRESENTS ONE FUTURE CONTRACT). We consider two different scenarios with regard to this oil market and you need to figure out which of the job applicants have the best strategy given each scenario.

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Scenario #1: The spot price of oil is $40 per barrel at expiration (point B on graphic). Recall, you need to buy 5 contracts or 5000 barrels of oil to make the gas.

a) (8 points) Given Scenario #1, which of the four strategies is the best in terms of minimizing the cost of obtaining the 5000 barrels of oil and which strategy is the worst in terms of the costs of obtaining the oil? Be specific and provide the costs associated with each strategy for full credit. , Please use real numbers and show all work!

Scenario #2: The spot price of oil is $50 per barrel at expiration (point C on graphic above). Recall, you need to buy 5 contracts or 5000 barrels of oil to make the gas.

b) (8 points) Given Scenario #2, which of the four strategies is the best in terms of minimizing the costs of obtaining the 5000 barrels of oil and which strategy is the worst in terms of the costs of obtaining the oil? Be specific and provide the costs associated with each strategy for full credit. Please use real numbers and show all work!

Graphing – In the space below, please graph the futures and futures option profit function for the oil market given each Scenario. Note that we are only graphing the profit functions for you, the refinery and not the oil producer (only one graph) Your graph will have 3 profit functions: FG, OB, and the OW, please label each. Recall, Scenario #1 (LABEL AS POINT A) is when the spot oil price is $40 per barrel at expiration and Scenario #2 (LABEL AS POINT B) is when oil expires at $50 per barrel. Be sure to label diagram completely including the break even points! 20 points for completely labeled graph.

5) (36 points total) We now consider the market for gasoline (see graph below). Suppose that the futures price of gasoline is $1.30 per gallon and that futures options, both puts and calls are available at a price of $5,000 each (STRIKE PRICE = $1.30, EACH CALL AND PUT REPRESENTS ONE FUTURE CONTRACT). We consider two different scenarios with regard to this gasoline market and you need to figure out which of the job applicants have the best strategy in terms of maximizing revenue, given each scenario.

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Scenario #1: The spot price of gasoline is $1.20 per gallon at expiration (point B on graphic above). Recall, you need to sell 10 contracts or 500,000 gallons (10 X 50,000) of gas to sell to BP.

a) (8 points) Given Scenario #1, which of the four strategies is the best in terms of maximizing your revenue and which strategy is the worst in terms of revenue. Be specific and provide the revenue associated with each strategy for full credit. , Please use real numbers and show all work!

Scenario #2: The spot price of gasoline is $1.48 per gallon at expiration (point C on graphic above). Recall, you need to sell 10 contracts or 500,000 gallons (10 X 50,000) of gas to sell to BP.

b) (8 points) Given Scenario #2, which of the four strategies is the best in terms of maximizing your revenue and which strategy is the worst in terms of revenue. Be specific and provide the revenue associated with each strategy for full credit. , Please use real numbers and show all work!

Graphing – In the space below, please graph the futures and futures option profit function for the gas market given each Scenario. Note that we are only graphing the profit functions for you, the refinery and not BP, the user of the gas (only one graph) Your graph will have 3 profit functions: FG, OB, and the OW, please label each. Recall, Scenario #1 (LABEL AS POINT A) is when the spot gas price is $1.20 per gallon at expiration and Scenario #2 (LABEL AS POINT B) is when gas expires at $1.48 per gallon. Be sure to label diagram completely including the break even points! 20 points for completely labeled graph.

6. (30 points) Let’s pretend that you graduated in May of 2015 and you scored a job as chief financial officer for a golf resort in New York in November of 2015. Your ‘season’ ended in the fall and the person that you replaced 'parked' all the cash made during the 2015 golf season in ten year Government securities. In particular, they purchased 10 ten year Treasury contracts during the fall of 2015. The CEO, let's call her Betty, tells you that you need to use those 10 ten year Treasury contracts to pay taxes in April of 2016.

a) (5 points) So Betty comes to you and tells you that she can't sleep because of this stress and asks you to buy insurance (make a hedge) against bad things happening (in terms of paying the tax bill). What are the bad things that could happen... give a real world example.

So here we are in the November of 2015 and you are considering three different hedges:

Scenario #1: You sell 10 March futures contracts for 125 and the price at expiration is 128.

Scenario #2: You buy 10 March futures option puts with a strike price at 125 for a price of $2,500 per put and the price at expiration is 128.

Scenario #3: You write 10 March futures option calls with a strike price of 125 for a price of $2,500 per call and the price at expiration is 128.

b) (10 points) Compare the revenue obtained to pay the tax bill under each scenario and rank them accordingly from highest to lowest. Please show all work.

c) (15 points) Given that these March futures contracts expire at 128, please draw your profit functions for each of the three scenarios above. In particular, draw the futures profit function, the futures option puts profit function and the profit function for writing the calls all on the same diagram. Be sure to label each profit function and label as points 1, 2, and 3 to coincide with each scenario. Be sure to label all the break even points.

7. (30 points total) We are going to evaluate two of the futures bets we made on Stock Trak using the dartboard account.... we went long on 10 year Treasury futures by buying 15 futures contracts when the futures price is 155.7 and we also went short on the S&P 500 mini-index by selling 10 futures contracts when the futures price was 1925. The multiplier on this contract is 100 so that each futures contract is worth $192,500.

The Margin requirement for the 15 Treasury futures is $4,125 per contract and is $3,850 for each of the 10 S&P 500 mini-index futures contracts.

As of Tuesday, 9/29/15 the price of the Treasury contracts is 157.3 and the S&P 500 mini-index was 1,883.

a) (5 points) Considering the bet on Treasuries, what is the leverage ratio (please take the leverage ratio to three decimal spaces) when I made the bet? Now use the leverage ratio to calculate the rate of return.

b) (5 points) Considering the bet on the S&P 500 mini-index , what is the leverage ratio (please take the leverage ratio to three decimal spaces) when I made the bet? Now use the leverage ratio to calculate the rate of return.

c) (10 points) Plot the profit function for the 15 Treasuries that we bought labeling the graph completely with the conditions associated with those on 9/29/15 as above - label this as point A

d) c) (10 points) Plot the profit function for the 10 S&P 500 mini-index futures contracts that we sold labeling the graph completely with the conditions associated with those on 9/29/15 as above - label this as point A

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