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Arbitraging futures contracts II

Arbitraging Futures Contracts II. Created by Sal Khan.

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Video transcript

Let's say that the settlement price for delivering 1,000 pounds of apples on October 20, which we're going to assume is one year from now, let's assume that it's $200. Let's also assume that the current market price for 1,000 pounds of apples is also $200. So that future settlement price is the same as the current market price. And we're also going to assume, like the last example, that these apples that we have never go bad. They're just things that they never rot or anything. So they're as good in a year as they are right now. Let's also assume, above and beyond the assumptions of the last video, that we can borrow and sell apples in the current market. That we can actually short apples. So I go to someone who's got 1,000 pounds of apples who doesn't really see any need for them over the next year, and I say, can I borrow those apples? And what I do is I say, I'll borrow those apples. I'll sell those apples in the market today. And of the interest that I get on those apples, I'm going to give you 1%, the person who actually owns the apples. And that person says, oh, sure, why not? That way I actually get some money on my apples that I had no intention of using for a year. And then I, as the borrower and seller, will get 4% net. I'll get 4% net on the apples. So given this reality, what could I do, once again, to make a risk-free profit? Well, as you could imagine, I can borrow and sell the apples for a year. So let me write this down. I'm going to borrow and sell 1,000 pounds of apples. So if I just borrow it today and sell it, today's market price is $200 for 1,000 pounds. So I'm going to get $200. Now on top of that, what I want to do is agree to be the buyer on this futures contract. So let me write that down. Agree, you could say to go long the futures contract, or agree to be buyer on futures contract. So I'm agreeing, a year from now, to buy 1,000 pounds of apples for $200. So let's fast forward. Let's fast forward one year. So what's happened? So of the $200 I got from shorting the apples I got 5% on that. But I had to give 1% to the person I borrowed the apples from. So I'm getting 4% net. 4% on $200 is $8. So now I now have $208 because I got that 4% interest. It was $210. I gave $2.00 to the person who lent me the apples. Now I can use $200 of that to essentially uphold my part of the futures contract, to buy the apples for $200, for that agreed upon price. So $200 to buy apples. And I know I can do this regardless of what the market price is because that was the delivery price on the futures contract. So now I have $8 net. And those apples that I've just bought, those 1,000 pounds of apples, I can then use those apples to return it to the person that I borrowed the apples from. So they got their apples back. And they got that 1% on the $200 over the course of the year. And I made a risk-free $8. So if you think about it once again, this is setting a lower bound on what the actual settlement price on the futures contract is. I should not be able to make this risk-free profit. If it's available, then people will do it. And what it will do is it will increase demand to be the buyer here. So this price should go up. And it would increase supply on the selling side here. And so maybe this price over here would go down.