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Video transcript

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 way and the current settlement price the current market price on the future exchange for delivery on that date is three hundred dollars let's also assume that the current market price so if you were to buy or sell apples today not on October 20th which is a year way but today let's assume that the current market price is $200 let's also assume that if you were to take out a two hundred dollar loan that you would have to pay 10 percent interest so if you were to borrow $200 today you would essentially have to pay back two hundred and twenty dollars in a year now given all of the parameters that I've set up is there a way to make risk-free profit is there a 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 borrow $200 and then use that $200 to buy a thousand pot of thousand pounds of apples so then we buy one thousand 1,000 pounds of apples we keep them in our garage or someplace like that and then we also we also sell sell or I guess we could say we go we become the seller on this futures contract or we sell the futures short I guess is another way to think about it so we also become the seller the seller on the futures contract on the futures contract so essentially we are agreeing to sell 1,000 pounds of apples on October 20th a year from now for $300 so I want to 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 so in one year we definitely have a thousand pounds of apples and just for the sake of simplicity let's this let's assume that apples don't get bad that I've somehow freeze-dried them or I don't know these are these are apples that never spoil so 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 to settle the contract and then of course I have my loan I have my loan of two hundred dollars but guess what when I settled the the contract when I settled the futures contract I got three hundred dollars so I get I get three hundred dollars and what do I owe what I owe two hundred twenty dollars on my loan so let me subtract that out so I owe two hundred and twenty dollars and so I made a guaranteed risk-free eighty dollars of profit in one year and we're not thinking about how much money I might have to set up side for margin but this is essentially just free money and if you think about it if you think about it if this settlement price is anything if the settlement price is anything above the two hundred twenty dollars then I'm going to make a risk-free profit so if 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 this 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 if the growth in price is more than the cost of borrowing the same amount of money the cost of borrowing two hundred dollars so in this situation the cost of borrowing is twenty dollars so the settlement price really shouldn't be if we assume that there's no arbitrage opportunities it really shouldn't be more than two hundred and twenty dollars