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Arbitraging futures contract | Finance & Capital Markets | Khan Academy - YouTube
Channel: Khan Academy
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Male voiceover: Let's say that the
current market settlement price
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for a Futures Contract
that specifies the delivery
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of a thousand pounds of
apples on October 20th
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and just for the simplicity
of the math in this example,
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let's assume that that is one year away
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and the current settlement
price, the current market price
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on the future exchange for
delivery on that date is $300.
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Let's also assume that
the current market price,
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if you were to buy or sell
apples today not on October 20th,
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which is a year away
but today, let's assume
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that the current market price is $200.
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Let's also assume that if you
were to take out a $200 loan
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that you would have to pay 10% interest.
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If you were to borrow $200 today,
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you would essentially have
to pay back $220 in a year.
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Now, given all of the
parameters that I've set up,
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is there a way to make risk-free profits?
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Is there way to kind of
arbitrage this situation?
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And as you can imagine, there is
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and what we can do is, we can borrow $200,
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Let me list it all out.
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We can borrow $200 and then use that $200
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to buy 1,000 pounds of apples.
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Then we buy 1,000 pounds of apples.
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We keep them in our garage
or some place like that
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and then we also sell
or I guess we could say,
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we become the seller on
this Futures Contract
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or we sell the Futures short,
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I guess is another way to think about it.
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We also become the seller
on the Futures Contract.
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Essentially, we are agreeing
to sell 1,000 pounds of apples
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on October 20th, a year from now for $300.
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So I wanna show you is
if we set it up this way,
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we are guaranteed to make money no matter
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what happens to the price of apples
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and that's why we're
calling it an arbitrage
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because if you fast forward one year,
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so let's fast forward one year.
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In one year, we definitely
have 1,000 pounds of apples
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and just for the sake of simplicity,
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let's assume that apples don't get bad
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that I've somehow freeze-dried
them or I don't know.
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These are apples that never spoil.
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(chuckles) Let's say a year from now,
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I have the thousand pounds of apples
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so I give the apples to
settle the Futures Contract.
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Give apples to settle the contract
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and then of course, I have my loan.
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I have my loan of $200 but guess what?
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When I settled the contract,
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when I settled the Futures
Contract, I got $300.
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So, I get 300 dollars and what do I owe?
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Well, I owe $220 on my loan.
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Let me subtract that out.
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I owe $220 and so I made
a guaranteed risk-free $80
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of profit in one year
and we're not thinking
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about how much money I might
have had to set aside for margin
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but this essentially, just free money
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and if you think about it,
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if this settlement price is anything,
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if the settlement price
is anything above the $220
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then I'm going to make a risk-free profit.
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One way to think about
Futures pricing is even
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if you think there's
going to be a cold snap
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and apples are going to disappear
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and there's going to be
the shortage of apples
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and so you might say, "Hey,
maybe the apple prices
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"will go up." a year ago,
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there's always going to be a way
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to arbitrage it if the settlement price,
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if the growth in price
is more than the cost
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of borrowing the same amount of money,
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the cost of borrowing $200.
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In this situation, the
cost of borrowing is $20.
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The settlement price really shouldn't be,
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if we assume that there's
no arbitrage opportunities,
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it really shouldn't be more than $220.
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