Use the three tables below to answer the following questions



Exam #1

Econ 351

Spring 2017

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1. (45 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 120 call option and one 120 put option at Table 1 and close both positions at Table 2. Calculate the profit or loss AND rate of return.

b) (5 points) Suppose that you wait and closed at Table 3 instead. Calculate profit / loss and rate of return.

c) (5 points) In the space below, on the SAME graph, draw the evolution of the premiums of the 120 call and 120 put until expiration assuming we freeze the spot price of AAPL as it is in Table 1. Be sure to label which line is the call and which is the put

d) (20 points for a correct and completely labeled graph) We are now going to graph the profit functions for the long and short straddle where we opened up the positions at Table 1. Recall that we are buying one 120 call and one 120 put. The player of the short straddle writes these two options. Along with locating the breakeven points, identify the profit / loss for both players for two points: point B where the spot price of AAPL at expiration is as it is at Table 2 ($121.32) and point C where the spot price of AAPL at expiration is as it is at Table 3 ($132.12).

e) (10 points) Consider point C only. Assume that the player of the long straddle is going to exercise the option that is in the money. Go through the costs and the revenue and show that the profit or loss for the player of the long straddle is the same, in absolute value, as the profit or loss for the player of the short straddle. Explain what the player of short straddle has to do when the player of the long straddle exercises the option that is in the money.

2. (35 points total)

a) (5 points) Suppose we play a long strangle by buying a 122 call and a 118 put on Table 1 and close at Table 3. Calculate the profit or loss and rate of return.

b) (20 points) We are now going to graph the profit functions for the strangle for both the buyer and writer of the strangle above where both players opened up their positions at Table 1. We are going to plot the profit / loss for both players for only one point-- point C, where the spot price at expiration is as it is at Table 3, spot = $ 132.12 (there are two points C's, one for player of the long strangle and one for the player of the short strangle). Be sure to label the break even points (there are two of them!).

c) (10 points) Consider your the smaller of the two break even points - prove that the player of the short strangle, the person who wrote both options, will break even. Again, assume that the player of the long strangle exercises the option that is in the money. What does player of the short strangle have to do exactly? Provide the math as to why the player of the short strangle makes breaks even.

3. (45 points) Let's go back in time to election day, November 8, 2016. The graphic below depicts the intraday movement of the Dec 16 E- Mini index from Nov. 6 until 8 am on Nov. 9, when much of the country woke up to hear that Trump had won. In viewing the graphic, you can easily see that 'the market' did not like this surprise initially but for whatever reason, recovered rather quickly during the 'wee hours' of Nov. 9.

When playing the stock market (last semester) game I was betting on a Hillary victory and thus, I went long by buying ten Dec 16 Dow E-Mini futures contracts when the futures price was as it is at point A = 18,200. The multiplier on these futures is 5 so that each contract is worth 5 x 18,200 = 91,000. The margin requirement in stock trak is $2,750.

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We consider two different scenarios:

#1: I stay up to watch the election results and start getting very nervous as this futures contract starts to plummet as soon as Trump won Pennsylvania in the very early hours of Nov. 9. As a result, I close at point B because I thought that the market was going to continue it's slide. The futures price at point B = 17,600.

#2: I go to sleep early on election day and do not find out that Trump won until 8 am the day after election where this futures contract recovered from it's plummet and returns to 18,200, the same futures price as when I opened up this long position at point A = point C = 18,200.

a) (5 points) Compare my fortunes at point B vs. point C. That is, calculate my profit or loss by closing at point B vs. my profit or loss by closing at point C. How much money did I save or lose by going to sleep (scenario #2) vs staying up and closing at point B (scenario #1)

b) (10 points) Suppose I had a friend that convinced me that a Hillary victory was not a sure thing and thus, suggested that I hedge my long position by buying futures options puts. In particular, they suggest that I buy 10 future options puts with a strike price of 18,000.... each put cost $1,000. In order to hedge my ten futures contracts I buy ten futures options puts for $1,000 each. Assuming that these futures and futures option contacts expire with the price at 17,600 (point B), calculate how much money the hedge, suggested by my friend, saved me.

c) (20 points) In the space below, on the same graph, plot the futures bet along with the futures option hedge. Recall, we are buying 10 futures contracts when the price is 18,200 and buying 10 FO puts with a strike price of 18,000 and a premium = $1,000 for each put. Label a s point B, where the price at expiration is 17,600 on both of your profit functions. Be sure to label the break even point for these FO puts.

d)(10 points) If you drew your two profit function correctly, they cross at one point, indicating that there is a price at expiration where the profit / loss on the long position is equal to the profit / loss on the short position (the hedge). Identify this as point Z on your diagram and prove that the profit or loss, whichever is the case, is the same for either position.

4) (30 points) In class we went over exactly what happened in the movie 'Trading Places.' Dan Aykroyd (DA) and Eddie Murphy (EM) (pic below) got a hold of the actual orange crop report, altered it, and gave it back to the 'two old guys' - the Duke brothers. Given the altered crop report, the Duke brothers thought that the freeze destroyed a portion of the orange crop and thus, believed that the price of orange juice would skyrocket given the bad orange crop (low supply!). Dan Aykroyd and Eddie Murphy knew the true report which indicated that the orange crop was just fine, the cold weather had a negligible (small if any) effect on the orange crop. Orange juice futures contracts are for 15,000 pounds of orange juice and are priced in cents per pound (i.e. 150 = $1.50 per pound) The margin requirement in Stock Trak is $1,100 per contract. In what follows we will re-create the scene using the March 2017 OJ futures contracts.

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a) (5 points) The Duke brothers open up their position at point A by buying thirty March 2017 OJ futures contracts when the price is 185. What is their leverage ratio when they opened up their positon?

b) (5 points) If the Duke brothers close at point B, when the price is 220, what is their rate of return? Use the leverage ratio to calculate the rate of return.

c) (5 points) Suppose the Duke brothers did not close at point B and waited until point C, where the futures price is 165. Calculate the profit loss and rate of return NOT using the leverage ratio….be sure to show all work.

Now let's add a little twist to the story. One of the Duke brothers isn't sure about the validity of the orange crop report that they received and thus is concerned that if the orange crop is fine, they can lose a lot of money (as they did in the movie). So he seeks out someone that knows his or her finance and that person is you.....they need to hedge their long position! So you instruct them to take their long position at open by buying 30 March OJ futures when the price is 185. You then tell them to buy 30 March futures options puts on OJ with a strike price of 205. Each put represents one futures contract and costs $2,000 per put.

d) (10 points) Assume the hedge as above. The Duke brothers bought 30 futures contracts at open where the price was 185 and also bought 30 March put options with a strike price of 205 for $2,000 per put. Both positions are closed when futures price of OJ is 165 (point C). Given both bets and assuming that 165 is the price at expiration, how much money did they make or lose?

e) (5 points) Suppose that the Duke brother that sought you out for your financial advice agreed to give you a check for 10% of the money that you saved them with the hedge, but only if the hedge worked. So compare the difference between your answers for part c) the profit or loss (no hedge) and the profit or loss with the hedge. How much is the check for?

PART 2: NEW GRADER

40 points total

5a) (15 points for correct and completely labeled graph) In the space below, on the same graph, plot the futures profit function and the FO profit function for the Duke brothers…recall they buy thirty futures contracts when the price is 185 and then close at point C, with the futures price = 165 …recall, they bought thirty futures options puts for $2,000 each with a strike price = 205. Now label as point C, the profit / loss on each profit function associated at point C. Be sure to label the breakeven point for the FO puts.

b)(5 points) Referring to your breakeven point that you labeled above, prove that it is in fact the breakeven point. Assume that the buyer of the FO puts exercise the puts - go through the math.

c) (10 points) We now turn to the plight of Eddie Murphy and Dan Aykroyd. They know the real report and started to sell when prices peaked at 220 as at point B in the graphic. They sell 30 futures at 220 and then close at point C where the futures price is 165. Calculate the profit or loss for Eddie Murphy and Dan Aykroyd AND the rate of return.

d)(10 points) Now graph the profit function for Eddie Murphy and Dan Aykroyd and label point C.

6. (38 points total) Let’s pretend that you are the CEO for an amusement park here in PA and you plan on buying a new ride in the fall of this year - you know a little about finance but not much and so you bring in four people to give you some financial advice. The four players are identical to previous refinery problems. The idea here is to buy 10 year Treasuries in June, when the park is making cash and then to sell them in September to buy the new ride. The first player, the futures guy (FG) tells you to buy June futures and then sell September futures. Going naked (GN) says to not worry about hedging and play the spot market. The option buyer (OB) tells you to buy FO calls for June and FO puts for September. The option writer (OW) tells you to write FO puts for June and to write FO calls for September. To simplify matters, we will be dealing with just one contract. [pic]

a) (8 points) Suppose that the June futures price is at 128 and FO calls and puts are available, with a strike price of 128 for $3,000 (the cost of one call or put). The price at expiration for this June futures contract is 124. Compare the cost of obtaining one Treasury contract for each player and rank them from best to worst.

FG:

GN:

OB:

OW:

b)(10 points) Name and explain 2 reasons why this June 10 - year futures contract fell like it did from point A in graphic - end of Oct. 2016 to point B in Feb 2017. We discussed this in class!

c) (20 points) Graphing – In the space below, please graph the futures and futures option profit functions for the FG, the OB, and the OW all on the same graph. Label each of your points as point A where the price at expiration is 124. Please be sure to completely label your graph including the breakeven points.

7) (38 points) The September Hedge:

a) (8 points) Suppose that the September futures price is 130 and FO calls and puts are available, with a strike price of 130 for $3,000 (the cost of one call or put). The price at expiration for this June futures contract is 130 (not a typo). Compare the revenue from selling one Treasury contract for each player and rank them from best to worst.

FG:

GN:

OB:

OW:

b) (20 points) Graphing – In the space below, please graph the futures and futures option profit functions for the FG, the OB, and the OW all on the same graph. Label each of your points as point A where the price at expiration is 130. Please be sure to completely label your graph including the breakeven points.

c) (10 points) Imagine a little company party celebrating the new ride you purchased for your amusement park. The four players show up, FG, GN, OB, and the OW. Defining profits as the revenue received when selling the September contract minus the cost of buying the June contract - which strategy, FG, GN, OB, or OW, resulted in the most profit and which strategy was the worst in terms of profits - please show your work.

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