We will DO ALL THREE OF THESE PROBLEMS IN CLASS – please print out and bring to class
OLD HOMEWORK ASSIGNMENT
1. Suppose you are a chocolate maker and you need 5000 lbs of cocoa beans in December so that you can make chocolate in time for Valentine’s Day. As a risk averse person, you want to lock in a price per lb now via a futures contract. Suppose you can make an agreement, that is, enter into a futures contract for 5000 lbs with a cocoa bean farmer with an agreed upon price of $3.00 lb (which happens to be the current spot price).
a) (4 points) Explain the terminology of the transaction – that is, what exactly are you doing and why: what is the farmer doing and why?
b) (4 points) Now suppose, for whatever reason, the spot price of cocoa beans rises to $4.50 per lb at expiration (December). Who looks smart for acquiring the futures contract, the cocoa farmer or the chocolate maker? Explain.
c) (8 points) Now, let’s assume that they are both speculators. Plot the futures profit function for the speculator cocoa bean farmer, the bear, (in one graph) and the speculator chocolate maker, the bull, (in another graph). Locate the profit or loss for each with a label of point A (where price equals $4.50).
Now assume that instead that the speculators play the futures options market. In particular, the speculator cocoa bean farmer buys a (Dec.) futures options put for 5000 lbs of cocoa beans for $3000 (strike price = $3.00 lb) and the speculator chocolate maker buys a (Dec.) futures options call for 5000 lbs of cocoa beans for $3000 (strike price = $3.00 lb).
d) (4 points) Assuming that the price rises to $4.50lb as before, and that the futures options expire in December, which option is “in the money?” Explain.
e) (8 points) Add the profit function for each speculator to your diagram above (the futures options profit function).
f) (4 points) Finally, what is the profit / loss for each speculator in the futures options market (locate this as point B on your diagram above (show work).
g) (8 points) Find the break- even spot price (at expiration) for the farmer AND the chocolate maker and locate on these points on your diagram (label as “break even spot”) Show work as to why this is the break even point.
h) (10 points) Are these results consistent with a zero sum game (hint, there are four players here)? Explain and show all work.
Old Homework Assignment from - Fall 2009 –
2. 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 the current (spot) and futures price of crude oil, per barrel, is $100. Suppose also that the current (spot) and futures price of gasoline is $3.00 per gallon. Each futures contract in oil represents 1,000 bbl and each futures contract in gasoline represents 50,000 gallons (its 42, 000 in the real world but we will use 50,000 since it is easier to work with). So you have this contract with Exxon, the user of the gasoline, to sell them 500,000 gallons of gas at the end of December. In order to produce the 500,000 gallons of gasoline you need 10,000 barrels of oil. The producer of crude oil is Saudi Arabia. We also assume that you can ‘turn’ oil into gas immediately (there is no lag).
a) As the manager of the oil refinery, you want to hedge against ‘bad things’ happening as in really high oil prices and really low gas prices (at the end of December). Explain exactly how you would hedge against these ‘bad things’ happening in the futures market.
b) Now let’s consider Exxon. What position (bullish or bearish) do they have (in gasoline) naturally and how would they hedge this natural position (explain in detail!)
c) Now let’s consider Saudi Arabia. What position (bullish or bearish) do they have (in oil) naturally and how would they hedge this natural position (explain in detail!)
d) Now explain why a futures market will naturally form between you and Saudi Arabia and you and Exxon. That is, clearly explain why deals are naturally made in these futures markets for oil and gasoline.
e) True/False/Uncertain: Explain. Suppose you sell 10 contracts of December gasoline where the spot and futures price is $3.00 per gallon. If (spot) gas prices fall and end up at $2.80 at the end of December (expiration) then your boss wants to give you a bonus, since entering the futures contract was profitable for your company (as compared to not entering a futures contract at all). In your answer please be sure to identify the profit or loss incurred by entering futures contract as compared to not entering the futures contract.
f) True/False/Uncertain: Explain. Suppose you buy 10 contracts of December oil where the spot and futures price is $100 bbl. per gallon. If (spot) oil prices fall and end up at $90 bbl at the end of December (expiration) then your boss wants to give you a bonus, since entering the futures contract was profitable for your company (as compared to not entering a futures contract at all). In your answer please be sure to identify the profit or loss incurred by entering futures contract as compared to not entering the futures contract.
Let us suppose that all parties, there are three of them (Saudi Arabia, you, and Exxon), take the appropriate hedges with the current and futures prices of oil and gasoline equaling $100/bbl and $3.00/gallon respectively. Note that all players are either buying or selling 10 futures contracts since 10 oil futures contracts represents 10,000 barrels of oil which is just enough for you to (immediately as assumed) make 500,000 gallons of gas to sell to Exxon.
Let’s consider the plight of all the players if the spot prices, at expiration, for oil and gas are $ 90 bbl and $2.80 gallon respectively.
In the space below draw 4 profit/loss diagrams with the oil market on top and gasoline market on the bottom. As we do repeatedly in class, please put the bear profit loss function on left and the bull profit loss function on the right. Identify as point A, the profit /loss of each player when the spot prices at expiration are $90 bbl and $2.80 gallon for oil and gas respectively (please show all work). Is this a zero sum game, why or why not??
Now suppose all three players play the future options market. There are futures options (calls and puts) available on gasoline with a strike price of $3.00 per gallon for a premium of $3000. Each call or put represents one futures contract (50,000 gallons of gas). There are futures options (call and puts) available on oil with a strike price of $100 bbl for a premium of $5,000. Add the profit/loss functions for all these futures options (there are four) and identify each of the three players losses/profits given that they have conducted the appropriate hedge as discussed above. Please label these new points as point B on all four diagrams.
Finally, prove that this futures options market is a zero sum game. Make sure you discuss the zero sum nature of the gasoline market separately from the zero sum nature of the oil market. There are four players in each market 8 players total (you count as two)!
ANOTHER OLDIE BUT GOODIE!
3. The pic below is the actual path of the 10yr Dec 2008 Treasury Futures contract since August of this year…it will help us with this question.
Suppose you were bullish on this Treasury futures contract and you bought 10 futures contracts and the end of July for 113. Also suppose that the margin requirement was $1000 per contract. Please answer the following questions:
a) (5 points) Suppose you held your position until the price went to 118 (early Oct) and then you closed (your position). How would you close your position exactly?
b) (5 points) How much ($) would you make or lose?
c) (10 points) In viewing the graph above we see some pretty sharp increases in the prices of these futures contracts as well as some very sharp decreases in the prices of these futures contracts. Explain why the sharp upward movements and then use the same logic in explaining the sharp downward movements. Be as specific and complete as possible and use actual real world events in your answer (this discussion is worth 10 points!).
d) (10 points) Suppose your friend was a bear and sold 10 futures contracts at the beginning of September for 116. His/her fur started burning early as prices generally rose during the first half of September. He/she got out their crystal ball and the crystal ball worked perfectly. In viewing the graph, when would the bear close their position and at what price (i.e., what did the crystal ball say exactly)? How much money did your friend the bear make?
e. (5 points) Suppose otherwise, that is, your friend the bear did not have a crystal ball and really started to ‘sweat’ during the beginning of October. As a result, they actually closed their position at the same time you did….toward the beginning of Oct when the futures price was 118. Given that the bear sold 10 contracts at 116, how much money did the bear make/lose as a result of closing at 118?
f. (5 points) We now want to figure out what that crystal ball in part d) is worth. In particular, compare the difference in your results – i.e., the profit/loss in d) and the profit/loss in e). How much money did that crystal ball save your friend? Show all work.
g) (5 points) Give a real world example of what the crystal ball saw coming (as in a real economic event) that put your friend in the cash!!
We now move on to a related but separate analysis and that is the futures options market for these 10 year Treasury futures contracts. Suppose that it is the very beginning of September and that the current and (obviously) futures price of these Dec 2008 Treasury contracts is 116. One player Jane, who is the bull, buys 10 futures options calls for a price of $500 each with a strike price of 116. Panda, who is the bear, purchases 10 futures options puts for $500 each at a strike price of 116. Given this information, let’s answer the following questions:
h) (5 points) What do the ten futures options calls that Jane bought allow her to do (be specific) and under what conditions would she want to do it (refer to the what would have to happen to the price of these contracts)? Be very specific.
We now consider the plight of these two players given two different scenarios.
Scenario A: Treasuries rally and the price at expiration is 118.
Scenario B: Treasuries get battered and the price at expiration is 112
i) Draw two futures options profit functions side by side (one for each player) as we did many times in class depicting the situation facing the bear and bull respectively.
(Correct and completely labeled diagram is worth 20 points)
j) (10 points) Figure out the profit loss for each player given scenario A and locate this point as point A in both graphs. Please show all work.
k) (10 points) Figure out the profit loss for each player given scenario B and locate this point as point B in both graphs. Please show all work
l) (10 points)What is the break even price for each player (please show all work) and make sure you identify this breakeven point on each diagram?
m) (10 points) Assuming scenario A, prove that this ‘game’ is zero sum, that is, show that when you add up all the winners winnings and losers losings, they sum to zero (recall there are 4 players).
n) (10 points) We discussed that when bets go well, it is always better to play the futures market but when bets go bad, it depends. Given the bull above, what is the price range, assuming the bet went bad, where it would still pay for the bull to play the futures market rather than the futures option market (assuming the price of each futures options contract = $500)?
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