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.
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).
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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).
10/27/09 o/h/l/c = 115265 115265 115265 115265 +0-050
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.
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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).
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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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