Practice futures / futures options problems
Problem #1
(15 points total) Suppose you are a weaver and you need 10,000 pounds of cotton to
make handkerchiefs. Harvest time is six months from now and 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 10,000 lbs with a cotton farmer with an agreed upon price
of $1.00 lb (which happens to be the current spot price).
a) (2 points) Explain the terminology of the transaction – that is, what exactly are you
doing and why: what is the farmer doing and why?
b) (2 points) Now suppose, due to a trade war and a great growing season, cotton prices
plunge to 50 cents ($0.50) per pound at harvest time. Who looks smart for acquiring the
futures contract, the cotton farmer or the weaver? Explain.
c) (3 points) Now, let’s assume that they are both speculators. Plot the profit function
(futures profit functions) for the speculator cotton farmer (in one graph) and the
speculator weaver (in another graph). Locate the profit or loss for each with a label of
point A (where the price equals $0.50). Please use the space below for your diagram.
d) (3 points) Now assume that instead that the speculators play the futures options
market. In particular, the speculator cotton farmer buys a futures options put for 10,000
lbs of cotton for $1000 (strike price = $1.00 lb) and the speculator weaver buys a futures
options call for 10,000 lbs of cotton for $1000 (strike price = $1.00 lb). Assume that the
price per pound plunges to 50 cents ($0.50) as before and that the futures options expire
at harvest time. Add the futures option profit function for each speculator to your diagram
above. Locate the profit or loss for both players in the futures options game as point B.
Be sure to label your diagram with all the specific numbers that apply. Which option is
“in the money?”
e) (4 points) Are these results consistent with a zero sum game (hint, there are four
players here)? Explain.
Problem 2
1.(56 points total) 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
you know next to nothing about markets and so you need to hire someone 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 input…oil … and maximizing your
revenue…..selling gas. We assume away all costs except for the input oil and we have
the following production figures – each oil contract consists of 1000 barrels of crude and
with 1000 barrels we can produce 100,000 gallons of gas. Each gas contract is for 50,000
gallons so for every oil contract that we buy we produce the equivalent of two gasoline
contracts. We have a contract with BP for 500,000 gallons of gasoline for delivery at the
end of February 2011 (10 gasoline contracts worth) and we need to buy the oil (5
contracts), the input, at the end of November to give us time to refine it in time for
delivery. The charts below represent the two futures contracts we consider – the Dec
2010 oil contract that expires on 11/19/10 and the March 2011 gasoline contract that
expires on 2/28/2011.
Four different job applicants come in and you interview them….they all advise you a
little differently.
1) Future guy – this person simply plays the futures market – so they would advise you
buy oil futures and to sell gas futures.
2) Going naked – 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 – this person would advise you to buy futures options calls on oil
and futures options puts on gas.
4) The option writer – this person would advise you to write futures options puts on oil
and to write futures options calls on gas.
We consider the oil market first (see graph below). Suppose that the futures price of oil
is $80 per barrel and that futures options, both puts and calls, are available at a price of
$2,000 each (STRIKE PRICE = $80, 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.
Scenario #1: The spot price of oil is $80 per barrel at expiration. Recall, you need to
buy 5 contracts or 5000 barrels of oil to make the gas.
a) (9 points) Given Scenario #1, which of the four strategies is the best in terms of
minimizing the cost of obtaining the 5000 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!
Scenario #2: The spot price of oil is $75 per barrel at expiration. Recall, you need to
buy 5 contracts or 5000 barrels of oil to make the gas.
b) (9 points) Given Scenario #2, which of the four strategies is the best in terms of
minimizing the costs of obtaining the 5000 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!
We now consider the market for gasoline (see graph below). Suppose that the futures
price of gasoline is $2.00 per gallon and that futures options, both puts and calls are
available at a price of $4,000 each (STRIKE PRICE = $2.00, 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 in terms of maximizing revenue, given each scenario.
Scenario #1: The spot price of gasoline is $2.00 per gallon at expiration. Recall, you
need to sell 10 contracts or 500,000 gallons (10 X 50,000) of gas to sell to BP.
c) (9 points) Given Scenario #1, which of the four strategies is the best in terms of
maximizing your revenue and which strategy is the worst in terms of revenue. Be
specific and provide the revenue associated with each strategy for full credit. , Please
use real numbers and show all work!
Scenario #2: The spot price of gasoline is $2.20 per gallon at expiration. Recall, you
need to sell 10 contracts or 500,000 gallons (10 X 50,000) of gas to sell to BP.
d) (9 points) Given Scenario #2, which of the four strategies is the best in terms of
maximizing your revenue and which strategy is the worst in terms of revenue. Be
specific and provide the revenue associated with each strategy for full credit. , Please
use real numbers and show all work!
Graphing – In the space below, please graph the futures and futures option profit function
for the oil market given each Scenario (two diagrams – the bear on the left and the bull on
the right). Recall, Scenario 1(LABEL AS POINTS A) is when the spot oil price is $80
per barrel at expiration and Scenario 2 (LABEL AS POINTS B) is when oil expires at
$75 per barrel. Be sure to label diagram completely including the break even points! 10
points for completely labeled graph.
Graphing – In the space below, please graph the futures and futures option profit
functions for the gasoline market given each Scenario (two diagrams – the bear on the
left and the bull on the right) Recall, Scenario 1(LABEL AS POINTS A) is when the
spot price of gasoline is $2.00 per gallon at expiration and Scenario 2 (LABEL AS
POINTS B) is when the spot price of gasoline is $2.20 at expiration.. Be sure to label
diagrams completely including the break even points! 10 points for completely labeled
graph.