in this video we're going to take a look at futures pricing now ultimately futures prices are set by supply and demand in the financial markets you have people that want to buy futures contracts people that want to sell futures contracts and wherever the supply and demand meet that sets the equilibrium price and that's the price of the futures contracts in the financial markets theoretically we could take a look at two different ways to price futures contracts one is based on expectations theory sometimes referred to as expectations pricing the idea here is that the futures price should equal the expected spot price at the time of expiration for example let's take a gold contract if I think that at expiration gold is going to be $1,500 per ounce then I wouldn't want to pay fifteen hundred fifty dollars per ounce for it today on the other hand if investors thought that it was going to be fifteen hundred dollars per ounce at expiration they wouldn't want to sell it to me for $1400 per ounce today either so the price in the futures market should be equal to the expected spot price at expiration now this isn't each individual's expected spot price but the equilibrium expected spot price should set the value of the futures price in the financial markets however when we get into financial markets we might see that there are some other things to take a look at that introduces the arbitrage pricing approach to introduce arbitrage pricing let's start with an example let's assume that you can buy a barrel of oil for $80 today the current futures price for delivery three months from today was $85 how can you exploit this discrepancy between the spot and futures price in a world of no transactions costs so oil futures contracts are 1,000 barrels so let's say I go out and buy 1,000 barrels oil today at $80 per barrel I can then at the same time sell a futures contract and agree to sell that those 1000 barrels of oil for 85 I've just agreed to sell the 1,000 barrels of oil I bought today for $85 three months from now so three months later I deliver 1,000 barrels at $85 per barrel I make $5,000 profit now note on this $5,000 profit there was no risk to me I didn't care what happened to the actual price of oil after I bought it because when I sold that futures contract somebody on the other side was agreeing to take delivery of that oil for $85 I bought today locked in my sales price and guaranteed myself a profit of $5,000 now in that example reassumed world no transaction costs however let's try to move this to a more realistic setting one contract of oil for five is from 1,000 barrels what issues will I have when I try to take advantage of this pricing scenario well first of all remember my first step in the above example I had to go out and buy a thousand barrels of oil at today's price of $80 per barrel what am I going to do with the thousand barrels of oil can I put it in my backyard I'm guessing my neighbor's probably wouldn't appreciate that too much however a local thief might find it attractive and decided to come and take couple barrels and turn around and sell them so when I purchased my 1,000 barrels of oil I have to worry about storage I have to find a safe legal and secure storage place to hold that oil for three months and that's going to add to my cost also while I'm guaranteed that $5,000 profit what do I have to do first I have to buy a thousand barrels of oil at $80 so I have to spend $80,000 upfront now I know three months later I'm getting 85,000 but I still have to borrow that $80,000 today so I'm going to have to borrow money and pay interest so I've got storage cost that storage includes storage facilities as well as security and I've got interest now you might say well I don't have to borrow the money maybe I've got $80,000 I can invest that's true but there's an opportunity cost if I invest in that oil I'm not investing it elsewhere so I still have the interest cost associated with that an opportunity cost of interest if I'm not borrowing the money and a real cost of interest if I do decide to borrow the money so the storage and interest are going to take away from my profit if the storage and interests are less than five dollars a barrel I'm still going to be able to conduct my arbitrage and lock in a profit if the storage and interest are six dollars a barrel now it's no longer worthwhile for me I can't buy my oil at 80 and lock in the sales price of 85 and make a profit now we also might look at a convenience yield in our oil example we looked at cost to us of holding the physical asset but there might be benefits to holding the physical asset one thing to look at might be in the case of stocks where you get dividend payments for interest for example if you buy index futures the actual stocks would pay you dividends but your index futures contract doesn't so if you're holding the futures contract instead of the actual physical property you're giving up the dividends if you're holding the actual stocks you're receiving dividends that's going to lower your cost of holding the actual stocks because you're getting the dividend payments maybe it's currencies pretend that you're looking at buying currency futures maybe you want to look at buying euro futures pretend that in the US interest rates are 2% and in Europe they're 5% well if I actually held the physical currency I can be collecting that 5% interest on my Euros because I'm holding a futures contract get to do that so I'm giving up that interest differential so currencies sometimes have a convenience yield we might look at commodities could just be a preference for the actual physical asset for example gold there are some people that think the advantage of gold is in case of some type of Armageddon situation where the global markets collapse and if the global markets collapse while the value of a futures contract may go up what if there's no markets to trade in once you rather have actual physical gold that you can get your hands on so a lot of people investing in gold would actually prefer to own gold bars or gold coins something physical that they can possess that way if there is some type of market collapse they don't have to worry about trying to sell their futures contracts so these convenience yields instead of a cost of holding the physical asset like our storage and interest from the previous example may lower the cost of holding the physical asset when we combine those all together what we have from the arbitrage pricing approach is that the futures price should be equal to the current spot price times 1 plus the annual interest rate the annual storage cost and here we're talking about the storage cost as a percentage not as a dollar value minus the convenience yield and again as a percentage raised to the time so let's say that our interest was 2% storage costs were 1% and convenience yield was 0.5% and we had a 3-month position now remember when we're raising to time we always want to think of that in years so that would be 0.25 so now let's say our futures price is what we're trying to solve for our spot price in this example let's just say is 80 so our futures be equal to 80 times one plus one zero two interest costs storage costs and then subtract off the convenience yield raised to the point two five power now let's do the calculations on that real quick that would give us futures price of 80 dollars and 50 cents so we can use the arbitrage pricing approach to figure out what the value of a futures contract is by figuring in interest cost storage costs convenience yield and how long that futures contract has until expiration the last thing we're going to talk about in this video is some terminology that you might hear in discussing futures contango contango is just a situation where the futures price is higher than the current spot price in our example here our market was in contango the futures price was 80 dollars and 50 Cent's spot price was 80 so the futures was higher than the current spot price oftentimes we'll see markets in contango when there are storage costs and in many cases especially physical assets that's going to be the case you might also hear the term normal contango and unfortunately some people use these two terms interchangeably which leads to a big confusion normal contango ties back into our expectations theory a little bit and says that the futures price is higher than the expected spot price so a little bit different here contango the futures price is higher than the current spot price normal contango futures price is higher than the expected spot price you also might hear that the futures market isn't backward ization backward ization is just the opposite of contango futures price is less than the current spot price in this case the convenience yield is higher than the storage and interest costs so that futures prices are lower than the current spot price normal backward ization again like normal contango deals with not the current spot price but the expected spot price so normal backward ization the futures price is less than the expected spot price let's go through a real quick example let's say we have a situation for the futures price is 100 expected spot it's 101 the current spot price is $99 now what would we have there well if we look we have a situation where the futures price is higher than the current spot price futures price is 100 it's higher than the current spot so futures is greater it's spot so our markets are in contango on the other hand right now the futures are less than the expected spot which that is our definition for normal backward ization so here we have a market that's in contango and normal backward ization these terms can get a little bit confusing but that gives you a basic idea of futures pricing and some of the terminology you might hear with respect to futures pricing in 22
