Upper bound on forward settlement price

0:00Let's see if there's a way to make a risk free profit. And let me just tell you right from the get go, there's usually not many ways to make a risk free profit in the world. So this is very theoretical. If the spot price for gold was $1,000-- so the spot price literally just means the market price.

0:16If you were to buy or sell gold today and actually exchange hands, then you would pay or sell the gold for $1,000 per ounce. And let's also say that the one year forward settlement price is $1,200 per ounce. So if you want to buy gold one year from now, you could agree right now to buy it for $1,200.

0:36Or if you want to sell gold one year from now, you could agree right now to sell it for $1,200 by entering into a forward, or futures, contract. And just the other details, the interest rate to borrow money is 10%, and the carrying cost of gold is $50 per ounce per year.

0:52And 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.

1:07So that's what we mean by carrying cost. Let's say you could also invest money risk free in this type of a market-- I've just made up these numbers-- for 5% a year. So, how could you make the money? We're assuming you start with nothing. So you could literally just borrow $1,000, and then you use that to buy an ounce of gold in the spot market, and you also agree to sell it in the future.

1:46So you enter into that forward contract. Let me write this way-- enter into forward as the seller. So, on the spot market you are the buyer, and on the forward market, one year from now, you agree to be the seller. So, let's just think about how this is going to play out.

2:10So over the course of the year, you will have some costs. You will have to pay the interest on this $1,000. That's 10%. So you're going to pay $100 in interest. And you're going to pay the carrying cost, $50 per ounce. So $50 carrying cost. And so, when we end up a year from now, you will sell the gold $1,200.

2:46And you know you can do that, because you entered into the forward agreement. And then you can pay back the $1,000 loan plus $100 interest. And let's say you have to pay the carrying cost at the end of the year to the bank. So plus the $50 carrying cost. So how much did we profit?

3:13Well, we get $1,200, and we have to pay back $1,150. So $1,200 minus $1,000 minus $100 minus $50, we make a profit of $50. So the big takeaway here is that these type of things normally don't exist. If they did, people would do it all day and all night. 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 in the futures market.

3:42Everyone would want to do this right here. So the appropriate price is, this price, based on these numbers right here should not be any higher than $1,150. So, the correct market price here, if we didn't want to risk free profit or essentially what the arbitragers would make happen by taking advantage of this, it would eventually go to $1,150.

4:04So it's essentially the spot price plus the cost to borrow money at that spot price plus the carrying cost. So that's essentially what would be the rational price for the futures contract, or the forward settlement price.