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Studying for a test? Prepare with these 7 lessons on Options, swaps, futures, MBSs, CDOs, and other derivatives.

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# Upper bound on forward settlement price

Video transcript

Let'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. If 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. Or 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. 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. So 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. So 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. So 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. And 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? Well, 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. Everyone 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. So 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.