Upper bound on forward settlement price

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Upper bound on forward settlement price발음듣기

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Let's see if there's a way to make a risk-free profit.발음듣기

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And let me just tell you right from the get-go there's usually not that many way to make risk-free profit in the world, so this is very theoretical.발음듣기

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If the spot price for gold was a thousand dollars...발음듣기

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So the spot price literally just means the market price.발음듣기

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If you were to buy or sell gold today and actually exchange hands, then you would pay or sell the gold for a thousand dollars per ounce.발음듣기

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And let's also say that the 1-year forward settlement price is $1200 per ounce.발음듣기

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So if you want to buy gold one year from now, you can agree right now to buy it for $1200.발음듣기

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Or if you want to sell gold one year from now, you could agree right now to sell for $1200 by entering into a forward or futures contract.발음듣기

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And just, the other details, the interest rate to borrow money is 10%.발음듣기

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And the carrying cost of gold is $50 per ounce per year.발음듣기

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And the carrying cost means if I had an ounce of gold, and I wanted to hold it responsibly, I wanted to store it, maybe someplace in a safe at a bank, and I wanted to insure it in case it got stolen or in case someone lost it, that would cost me $50 per ounce per year.발음듣기

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So that's what we mean by carrying cost.발음듣기

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And let's say you could also invest money risk-free in this type of a market...발음듣기

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(I've just made up these numbers) for 5% a year.발음듣기

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So how could you make the money?발음듣기

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Well, you could, and we're assuming you start with nothing, so you could literally just borrow $1000.발음듣기

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And then you use that to buy an ounce of gold in the spot market.발음듣기

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So you buy one ounce of gold.발음듣기

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And you also agree to sell it in the future.발음듣기

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So you enter into that forward contract.발음듣기

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So you enter into forward as the seller.발음듣기

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So you are, on the spot market, you are the buyer.발음듣기

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And on the forward market, one year from now, you agree to be the seller.발음듣기

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So let's just think about how this is going to play out.발음듣기

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So over the course of the year, you will have some cost.발음듣기

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You will have to pay the interest on this $1000. That's 10%.발음듣기

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So you're going to have to pay $100 in interest.발음듣기

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And you're going to have to pay the carrying costs.발음듣기

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$50 per ounce. So, $50 carrying cost. And so, when we end up a year from now, you can sell, you will sell the gold for $1200.발음듣기

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One year from now. And you know you can do that, because you entered into the forward agreement.발음듣기

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And then you can pay back the $1000 loan plus $100 interest.발음듣기

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And let's say you had to pay the carrying cost at the end of the year to the bank.발음듣기

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So plus the $50 carrying cost.발음듣기

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So how much did we profit?발음듣기

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Well, we get $1200 and we had to pay back $1150.발음듣기

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So we make... So, $1200 minus $1000 minus $100 minus $50...발음듣기

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We make a profit of $50.발음듣기

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So the big takeaway here is... that these type of things here normally don't exist!발음듣기

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If they did, people would do it all day and all night.발음듣기

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And this price would go up because everyone would want to buy on spot... and this price would go down because everyone would want to sell on the futures market.발음듣기

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Everyone would want to do this right here.발음듣기

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So the appropriate price is this one should not... this price, based on these numbers right here, should not be any higher than $1150.발음듣기

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So the correct market price here, if we didn't want risk-free profit, or essentially what the arbitragers would make happen by kind of taking advantage of this... it would eventually go to $1150.발음듣기

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So it's essentially the spot price, plus the cost to borrow money at that spot price, plus the carrying cost.발음듣기

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So that's essentially what would be the rational price for the futures contract, Or the forward settlement price.발음듣기

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