If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Lower bound on forward settlement price

Lower Bound on Forward Settlement Price. Created by Sal Khan.

Want to join the conversation?

  • blobby green style avatar for user jeromy.gallant
    I am not sure that I understand the math on this one....
    If I buy 1oz of gold @ $1000 + $50 carrying cost, that equals $1050

    If I enter a futures contract at $1050 and I put my $1000 into a 5% bond at the end of the year I have paid $1050 for one ounce of gold.

    So is $1050 the rational lower bound of this future in 1 year?
    (6 votes)
    Default Khan Academy avatar avatar for user
    • spunky sam blue style avatar for user Mike Moyle
      Mr Vincent answerred yuor question correctly, but may not have made it clear. If you buy today, your total cost a year from now will have been $1050, because of the carrying cost.

      If you but the bond and the future, you get the gold for $1050, all of which you got from the bond that you paid $1000 for. You saved $50 on the carrying cost, so your net cost is still just your original $1000.
      (18 votes)
  • old spice man green style avatar for user pardijoe
    If a billionaire wanted to buy a lot of gold to own for 20 years or more, would they buy it in the futures markets and keep rolling over contracts to avoid being delivered on? Or would they buy it on the market, get delivery, and pay a bank or something like that to hold it? It seems like it would cost a lot of money to keep paying trading fees and carrying costs. Thanks in advance.
    (5 votes)
    Default Khan Academy avatar avatar for user
  • leaf green style avatar for user Ray
    I can imagine that the carrying cost would change depending on the resources that each buyer has available, but it seems that a fixed carrying cost is needed to be set in stone to define a clear lower and upper bound. How is the carrying cost set? And who sets it?
    (3 votes)
    Default Khan Academy avatar avatar for user
    • blobby green style avatar for user vdusina
      The carrying cost is dependent on the commodity. In the video example of gold, the carrying cost is function of the price of insurance and the bank deposit box. In a commodity like oil, the carrying cost is the cost of tankage (usually per barrel), the cost of transporting those barrels, and the cost of insuring those barrels if required.
      (4 votes)
  • leaf green style avatar for user Iain McMeechan
    Is the cost of carry published in real life or is this part of the speculation too?
    (3 votes)
    Default Khan Academy avatar avatar for user
    • ohnoes default style avatar for user Cameron Cotten
      This is a really good question. You can look at historical carrying costs, and I would imagine these do not fluctuate much or are speculated on much, compared to the fluctuations in commodity price. However, the one carrying cost that probably did change once upon a time is the carrying cost of pork bellies (yes that is a real commodity). Ozone-depleting refrigerants were banned and this increased the cost of refrigeration in the short term, presumably changing the carrying cost of pork bellies. I'm sure that those who secured futures contracts for pork bellies before the ban were pretty happy with themselves.
      (2 votes)
  • aqualine ultimate style avatar for user Tang  PengXing
    What are the upper bound and lower bound used for?
    (2 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Angela Guerrero
    He keep saying at the end of the videos that if that was true everyone would want to be the buyer or the seller at the same time, which the contract ends,so that will increase prices. So who end up wining? is it still a good idea to go on a forward contract, knowing that everyone would be selling at the same time?
    (1 vote)
    Default Khan Academy avatar avatar for user
  • male robot johnny style avatar for user jondrometa
    What about this:
    Say you were interested in buying a gold bond (at the mentioned price of $1000 with a 5% interest rate in 1 year), and at the end of the term, you did NOT buy gold because you didn't sign a futures contract.
    Wouldn't that leave you with $50 profit to move on to a different venture? Is that even possible? Or do bonds like the one in the example not exist without purchasing options as well?
    (1 vote)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user muhtarmurawut
    at , why the lower bound not include the 10 percent interest rate ? since it borrows the 1000 dollars.
    thanks.
    (1 vote)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Angela Guerrero
    he keep saying at the end of the videos, that if that was truth, everyone would want to be the sellers or the buyers at the same time when the contract finished, so prices would go up or lower. So how can one know not to sell at the same time, or for how long to set up their contracts. I am all confuse.
    (1 vote)
    Default Khan Academy avatar avatar for user
  • leaf green style avatar for user Vulndare
    Say there's an oil shortage and you can profit by selling oil now and buying a future with the right to buy in a year. And then let's say for some reason there's an economic disaster or something and many people can't deliver the oil on the contract due date. Is there any insurance against this? Will the exchange cover it through margin refunds?
    (1 vote)
    Default Khan Academy avatar avatar for user
    • leaf green style avatar for user Ryan
      Futures have no risk of default. If you default on your obligation, your broker would cover the cost. If your broker defaults, the clearing house would cover the obligation. A clearing house has never defaulted, but ultimately the government would cover the obligation and bail them out in order to insure a stable financial system.
      (2 votes)

Video transcript

In the last video we established a reasonable upper bound on the 1-year forward settlement price of gold. We established that at $1150 which is essentially the sport price plus the borrowing rate to borrow $1000, plus the carrying cost of the gold. What I want to do in this video is to think of a reasonable lower bound. To do that let's imagine a world where instead of the forward settlement price being $1150, let's imagine a world where the forward settlement price is $1050. It's still higher that the spot price. Let's think of it from the the point of view of someone who wants to hold gold in a year. Let's say that you are that someone and right now you have $1000 that you want to use to give you gold. You want to hold the gold for the long term. You have 2 options here. You could just buy gold now. Buy 1 ounce with your $1000 right now. When you go forward a year from then your going to have that 1 once of gold plus you're going have to pay the carrying cost. The safety deposit box and the insurance on the gold. You're going to have 1 ounce of gold minus $50. That's what you're going have to pay. The other option, you say hey look instead of putting my $1000 into gold right now, let me put my $1000 into a risk-free bond. Into a risk-free bond. Risk-free bond, and at the same time agree to be the buyer on the 1-year forward settlement. On the 1-year forward contract. I'm agreed to to be the buyer at $1050. If you go forward a year, your $1000 risk-free bond is going to give you 5% interest a year. You're going to have $1050. This is just the interest on your bond. Then you can use that to go and buy the gold. Which you all ready locked in the price by agreeing to be the buyer on the forward contract. Then you buy the gold. In both situations you end up with an ounce of gold a year from now starting with your $1000. In this situation you just have an ounce of gold and you didn't have to pay any carrying cost. In this situation you have the ounce of gold and you did have to pay carrying cost. So, clearly any rational person, assuming their buying the gold for the long term, would want to do this situation. They save $50 over the course of the year. Really, the rational price, if this were to happen everyone would want to be the buyers over here. We're talking about $1050 price. That's right over here. This was the price in the last example. Everyone would want to be the buyer on the futures contract or the forward contract. That would increase the price over there. Knowing you'd have less buyers on the spot contract. That would decrease the price over there. In general this price seems too low. The price at which people would be neutral is if this price was $50 higher. Then it becomes completely equivalent. A rational lower bound given all of this, would have been a price of $1100. $1100. In general just going back to the last video, a ration upper bound will be the spot price plus the carrying cost and the rate at which someone could borrow money. A rational lower bound will be the spot price plus the risk-free interest rate and the carrying cost. In general, the only difference between those upper and lower bound is this rate and this rate. This rate and this rate. If these were the same the rational price would be the same. If these both were 10%, then the rational price would $1150. These were both 5% the rational price, the upper and the lower bound would have been $1100.