Exam #1Econ 351Fall 2019

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TOTAL POSSIBLE = 280 POINTS

55 + 70 + 45 + 30 + 40 + 40

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1. (55 points total) Use the four tables below to answer the following questions. Note importantly that Tables 1 and 2 pertain to options that expired on 9/27/2019 and Tables 3 and 4 pertain to options that expire one week later on 10/04/19.

TABLE 1

TABLE 2

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TABLE 3

TABLE 4

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a) (5 points) Suppose we play a long straddle by purchasing one 177.5 call option and one 177.5 put option at Table 1 and close both positions at Table 2. Calculate the profit or loss AND rate of return.

COST: 126 + 196 = $ 322 close: REV: 1 + 1180 = 1181 PROFIT = $ 859....RETURN = 266.77%

b) (5 points) Suppose we play the same long straddle but with options that expire on 10/04/19 by purchasing one 177.5 call option and one 177.5 put option at Table 3 and close both positions at Table 4. Calculate the profit or loss AND rate of return.- COST: 272 + 340 = $ 612 close: REV: 28 + 1194 = 1222 PROFIT = $610....RETURN = 99.67%

c) (10 points) In the space below, on the SAME graph, draw the evolution of the premiums of the 177.5 call and 177.5 put until expiration assuming we freeze the spot price of BABA as it is in Table 1. Be sure to label which line is the call and which is the put.

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d) (25 points for a correct and completely labeled graph) We are now going to graph the profit functions for our 2 long straddles ON THE SAME GRAPH. Note, we are not drawing profit functions for the corresponding short straddles, just the long straddles. The first profit function is where we opened up the positions at Table 1. Recall that we are buying one 177.5 call and one 177.5 put. Along with locating the breakeven points, identify the profit / loss where the spot price of BABA at expiration is as it is at Table 2 (Label as point A) ($165.91) The second profit function (same graph) is where we opened up the positions at Table 3. Recall that we are buying one 177.5 call and one 177.5 put. Along with locating the breakeven points, identify the profit / loss where the spot price of BABA at expiration is as it is at Table 4 ($165.91) and labels as point A (there are two points A).

e) (5 points) What is the vertical distance called between your two profit functions and what exactly determines the magnitude (size) of the vertical distance?

THE VERTICAL DISTANCE IS THE (SUM OF) TERM PREMIUMS AND IS DETERMINIED BY HOW MUCH TIME UNTIL EXPIRATION BETWEEN THE DIFFERENT OPTIONS (IN THIS CASE A WEEK) AND HOW VOLATILE THE UNDERLYING STOCK IS…THE MORE VOLATILE, THE BIGGER THE TERM PREMIUM!

f) (5 points) Table 2 is after expiration – the 177.5 put is selling for $1180. What should the premium of the 177.5 put be? Show work.

THE 177.5 PUT IS $11.59 IN THE MONEY AND SHOULD SELL FOR $1159. (177.5 – 165.91) = 11.59.

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2) (70 points) Suppose you were bearish on the market and decided to sell one Dow Futures E-Mini contract when the futures price was where it is at point A = 27,250. The margin requirement is $5,390 and the multiplier is 5.

a)(5 points) What is the leverage ratio when we open up our short position?

5 x 27,250 = 136,250/ 5390 = 25.27829

b) (5 points) Calculate the profit/loss at point B, where the futures price is 26,000.

5 x (27,250 – 26,000) = 6,250

c)(5 points) Calculate your rate of return using the leverage ratio.

%Δ in Dow Mini (26,000 – 27,250)/ 27,250 = - 4.587%

4.587 x 25.27929 = 115.956%

d)(5 points) Calculate your rate of return not using the leverage ratio.

6,250/5390 = 115.955%

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So you are chatting with a friend who is in econ 351. You are bragging about all the money you made with your short position on the market (from point A to B) and he/she suggests that you buy insurance to protect your gains...... that is, he/she suggests that you hedge your short position. Note that futures options, both calls and puts are available on this futures contract.

Suppose that we hedge our existing short position by buying one FO call at point B with a strike price of 26,000 for $4,000 each.

d)(10 points) We now consider the move from point B to point C, where the futures price of the Dow Futures E-Mini goes from 26,000 (point B) to 27,000 (point C). Calculate the total profit or loss given your long bet and your hedge. We assume that the futures price at expiration is 27,000. BE SURE TO SHOW ALL WORK!

FUTURES BET......5 x (27,250 – 27,000) = $1,250

HEDGE 5 x (27,000 – 26,000) = $5,000 – $4,000 (premium) = $1,000 PROFIT ON HEDGE

TOTAL PROFIT BOTH BETS 1250 + 1000 = $2250

Graphing: In the space below, plot the profit function of the futures bet along with the profit function of the hedge (the FO call) on the same graph. Label as point B, your profit on your futures bet when the futures price is as it is at point B = 26,000. Then label as points C, the profit/loss associated with the futures bet and the profit/loss associated with the hedge where the futures price at expiration is 27,000 (there are two point C's) . Make sure to label the breakeven point for the FO call.

25 points for complete and correctly labeled diagram

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e) (10 points) If you drew the profit functions correctly they cross at one point – what is that point and what is the profit associated with this point.

(26,800 + 27,250)/2 = 27,025

Profit: Futures bet: 5 x (27,250 – 27,025) = 1125Profit: Hedge: 5 x (27,025 – 26,000) = 5125 – 4000 = 1125

Total profit 1125 + 1125 = 2250

i)(10 points) Suppose the futures price at expiration is 27,250 – the same as when you opened the futures bet. Calculate the profit or loss given the futures bet and the hedge. How does it compare to your profit above? Explain the intuition!

Profit: Futures bet: 5 x (27,250 – 27,250) = zeroProfit: Hedge: 5 x (27,250 – 26,000) = 6250 – 4000 = 2250

SAME AS ABOVE!

THE INTUITION – ONCE YOU GET TO THE STRIKE PRICE OF THE CALL = 26,000 AND BEYOND (A HIGHER PRICE) – THE PROFIT STAYS THE SAME, THE LOSS ON THE FUTURES BET WILL EQUAL THE GAIN ON THE CALL SINCE BOTH PROFIT FUNCTIONS HAVE THE SAME SLOPE IN ABSOLUTE VALUE.

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c)(25 points) We discussed hedging quite a bit. Suppose you had a long position on say AAPL, and you wanted to hedge this long position. Explain how you would do it using a graph to support your answer. For example, suppose the spot price of AAPL is $225 and you want to hedge with options that have a strike price = $225. Suppose you hedged with only one option either a call or a put. Draw a graph depicting these hedges assuming that the call or put cost $500. Under what conditions would the put hedge work out better and under what conditions would the call work out better. Please give me actual number assuming that we are at expiration.

To hedge a long position – buy a put or write a call.

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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 November 2019 OJ futures contracts.

a) (5 points) The Duke brothers open up their position at point A by buying one Nov. 19 OJ futures contracts when the price is 96. What is their leverage ratio when they opened up their positon?

15,000 x .96 = 14,400/1100 = 13.0909

b) (5 points) If the Duke brothers close at point B, when the price is 108, what is their rate of return? Use the leverage ratio to calculate the rate of return.

% change in OJ = 12.5%............ 12.5 x 13.0909 = 163.63%

c) (5 points) Suppose the Duke brothers did not close at point B and waited until point C, where the futures price is 100. Calculate the profit/ loss and rate of return NOT using the leverage ratio….be sure to show all work.

15,000 x (1.00 – .96) = $600 600/1100 = 54.55%

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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 one Nov. 19 OJ futures when the price is 96. You then tell them to buy one Nov. 19 futures options put on OJ with a strike price of 108. Each put represents one futures contract and costs $400 per put.

d) (10 points) Assume the hedge as above. The Duke brothers bought one futures contract at open where the price was 96 and also bought one Nov. 19 FO put option with a strike price of 108 for $400. Both positions are closed when futures price of OJ is 100 (point C). Given both bets and assuming that 100 is the price at expiration, how much money did they make or lose in total?

Puts are worth 15,000 x (1.08 – 1.00) = 1200 MINUS THE 400 (premium) = $800

Profit on Futures: 15000 (1.00 - .96) = 600

Total Profit = 1400

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 (part d). How much is the check for?

.1 x 800 = $80

f) (25 points) In the space below, draw a graph with the futures profit function along with the put hedge – be sure to label the break even point for the put. Label as points A, the conditions in part d) making sure your results on the graph match the results in part d).

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5.(45 points total) Suppose you are the chief financial officer for an oil producing company in Saudi Arabia and you are to sell oil to an oil refinery. To make matters simple, you are going to sell 1000 barrels of oil to an oil refinery. Suppose that you need to hire an intern to help you make decisions as to how to the ‘play the game’ and maximize profits. Naturally, you maximize profits by maximizing the revenue for your oil.

a) (5 points) What is your natural position in oil and how would you hedge against bad things happening.

Natural position is LONG, need to hedge short:

Sell futures, Buy FO puts, write FO calls!

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 to sell oil 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 puts on oil.

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

We consider the oil market first (see graphic). The delivery date is December 2019. Suppose that the futures price of oil is $57 per barrel (as it is at point A) and that futures options, both puts and calls, are available at a price of $3,000 each (STRIKE PRICE = $57, 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 $62 per barrel (point B on graphic) at expiration. Recall, you need to sell one contract or 1000 barrels of oil.

a) (8 points) Given Scenario #1, which of the four strategies is the best in terms of minimizing the cost of obtaining the 1000 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!

FG $57K WORST

GN $62K BEST

OB -$3K + 62K = 59K THIRD

OW + 3K + 57K = 60K SECOND

Scenario #2: The spot price of oil is $54 per barrel (point C on graphic) at expiration. Recall, you need to see 1 contract or 1000 barrels of oil.

b) (8 points) Given Scenario #2, which of the four strategies is the best in terms of minimizing the cost of obtaining the 1000 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!

FG $57K WORST

GN $54K BEST

OB -3K + 57K = 54 K BEST

OW +3K + 54K = 57K WORST

Graphing – In the space below, please graph the futures and futures options profit functions for the oil market given each Scenario for you, the oil producer (one diagram) – Recall, Scenario #1(LABEL AS POINTS B) is when the futures price at expiration is $62 per barrel at expiration and Scenario #2 (LABEL AS POINTS C) is when oil expires at $54 per barrel. Be sure to label diagram completely including the break even points!

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24 points for correct and completely labeled graph.

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6)(40 points) 5.(45 points total) Suppose you are the chief financial officer for a gasoline station called Sheetz and you are to buy gasoline from an oil refinery. To make matters simple, you are going to buy 50,000 gallons of gas from the refinery. Suppose that you need to hire an intern 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 gasoline. .

a) (5 points) What is your natural position in gasoline and how would you hedge against bad things happening.

Natural position is short, hedge long – Buy futures, Buy FO call, write FO puts

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 to buy gasoline 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 gasoline.

4) The option writer (OW) – this person would advise you to write futures options puts on gasoline.

We consider the gasoline market (see graphic). The delivery date is December 2019. Suppose that the futures price of gasoline is $1.55 per gallon (as it is at point A) and that futures options, both puts and calls, are available at a price of $4,000 each (STRIKE PRICE = $1.55 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 given each scenario.

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Scenario #1: The spot price of gasoline is $1.70 per gallon (point B on graphic) at expiration.

a) (8 points) Given Scenario #1, which of the four strategies is the best in terms of minimizing the cost from buying the gasoline and which strategy is the worst in terms of cost? Recall, we are buyimg 1 contract (50,000 gallons of gas) Please use real numbers and show all work!

FG 77.5K BEST (50,000 X 1.55)

GN 85K WORST

OB 4000 + 77.5K = 81.5K

OW-4000 + 85K = 81K

Scenario #2: The spot price of gasoline is $1.55 per gallon (point C on graphic) at expiration.

b) (8 points) Given Scenario #1, which of the four strategies is the best in terms of minimizing the cost from buying the gasoline and which strategy is the worst in terms of cost? Recall, we are buyimg 1 contract (50,000 gallons of gas) Please use real numbers and show all work!

FG 77.5K

GN 77.5K

OB 4000 + 77.5K = 81.5K WORST

OW- 4000 +77.5K = 73.5K BEST

Graphing – In the space below, please graph the futures and futures options profit functions for the gasoline market given each Scenario for you, the gasoline user. (one diagram) –Recall, Scenario #1(LABEL AS POINTS B) is when the price per gallon of gasoline is $1.70 at expiration and Scenario 2 (LABEL AS POINTS C) is when the price per gallon of gasoline is $1.55 at expiration. Be sure to label diagram completely including the break even points!

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24 points for correct and completely labeled graph.

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