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# Arbitraging futures contract

Created by Sal Khan.

Video transcript

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