Econ 351 - spring 2014 - Practice futures / futures ...
Econ 351 - spring 2014 - Practice futures / futures options problems.
1. Let’s pretend you are the owner of a car dealership (and it is summer 2009 – we are going back in time!) and along with being the owner you are also in charge of the finances of the dealership. This summer (2009) your dealership participated in the ‘cash for clunkers’ program and it worked well, with sales picking up significantly. The bad news is that the Federal Government, with their seemingly never ending red tape, has not paid you the cash for clunkers. You just received a note in the mail from Uncle Sam and ‘he’ promised that the check will be in the mail by early December of this year (2009) and you will receive the money by mid December, 2009.
Now you know that tax time is in mid April, 2010 and therefore, you want to park these ‘cash for clunker’ funds in 10 year Treasuries for 3 months and then get hold of the cash at the end of March to pay the tax bill by mid April (of next year (2010)). Let’s suppose that you sold 500 cars during the cash for clunkers program and Uncle Sam will pay you $3,000 per clunker meaning that the check from Uncle Sam (arriving in Dec.) will be for 500 x $3,000 = $1.5 million.
a) It is the second week of August 2009 and you are thinking of three different hedges to protect against bad things happening. What do we mean by bad things happening and what in particular, could cause bad things happening? Give me two real world examples.
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The three hedges are as follows. Note, to simplify matters, we consider only one contract (makes the math easier!)
Scenario #1: You buy a Dec. future contract for 114 and the price at expiration is 116.
Scenario #2: You buy a Dec. futures option call with a strike price at 114 for $1,500 and the price at expiration is 116.
Scenario #3: You write a Dec. futures option put with a strike price of 114 for a price of $1,500 and the price at expiration is 116.
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1.b) (10 points) Suppose the price at expiration of these futures is 116. Compare the costs of acquiring the Treasury contract in Dec. for each scenario and rank them accordingly from lowest cost to highest cost.
Given that these Dec. 09 futures contracts expire at 116, please draw your profit functions for each of the three scenarios above. In particular, draw the futures profit function, the futures option call profit function and the profit function for writing the put 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. (20 points for completely labeled graph).
Let’s move on to the next hedge. As noted above, you need to pay the tax bill in April and thus, you decide to sell March futures contracts (i.e., to get the cash in March to pay the tax bill).
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Consider the following 3 scenarios:
Scenario #1 - You sold a March futures at 116 and the contract expires at 120.
Scenario # 2 - You bought a futures option put at a price of $1,500 with a strike price of 116 and the contract expires at 120.
Scenario #3 - You wrote a future option call at a price of $1,500 with a strike price of 116 and the contract expires at 120.
1.f) (10 points) Now compare the revenue that you receive to pay the taxes under each scenario and rank them 1st, 2nd and 3rd. Please show all work.
Given that these March 10 futures contracts expire at 120, please draw the profit function for each of the three scenarios above. In particular, draw the futures profit function, the futures option put profit function and the profit function for writing the call 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. (20 points for completely labeled graph).
Another futures practice problem:
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 $4.50 lb 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.
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