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Lower bound on forward settlement price

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

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• 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?
• 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.
• 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.
• It is not uncommon for long term hedgers to sell the expiring contract and buy a non-expiring futures contract for the same product. There is even a special type of trade called a calendar spread ( http://en.wikipedia.org/wiki/Spread_trade#Calendar_spreads ) which allows a trader to simultaneously sell the near month and buy the far month!
• 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?
• 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.
• Is the cost of carry published in real life or is this part of the speculation too?
• 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.
• What are the upper bound and lower bound used for?
• 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)
• People who find the arbitrage opportunities "win". After the prices are the same, there is essentially no arbitrage opportunity, thus it will become just a matter of choice when it comes to whether to buy certain amount of gold via a forward contract, or to buy some now.
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)
• Sal is assuming you are interested in holding gold at some point. Otherwise, what you have described above is the best course of action in that scenario. :)
• at , why the lower bound not include the 10 percent interest rate ? since it borrows the 1000 dollars.
thanks.
(1 vote)
• Lower bound is the lowest possible price, therefore it is assumed you don't borrow any money - you already have \$1000
(1 vote)
• 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)
• 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)
• 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.