Fixed	Variable
You	6%	Prime + 0.5%
Me	7%	Prime + 1.0%

Because you have a better credit rating than I do, you have an absolute advantage in both quotes.  However, the interest rate differentials are not the same.  You have a 1% advantage in the fixed rate, but only a 0.5% advantage in the variable rate.  Therefore, when we compare our possible mortgages, you have a comparative advantage in the fixed rate.  Are you ready for the curve ball?  I have a comparative advantage in the variable rate.  Why, because you have me beat by a larger degree in the fixed rate.

You happen to think that interest rates are certainly going to go down so you would prefer to buy the variable rate mortgage.  I, on the other hand, think that rates can go nowhere but up so will get a fixed rate.

You and I, being the creative types, engineer a swap to leverage our comparative advantages.

• You get the fixed loan (even though you want the variable)
• I get the variable (even though I want the fixed)
• You and I then agree to swap payments (we are called counterparties to this agreement):
  • I pay you 5.75% (I’ll explain this number later)
  • You pay me Prime

  

Therefore, when you add up what we pay in total:

We both end up with the type of loan that we wanted at a better rate than we were quoted.  That is the reason for the odd 5.75% payment that I promised that I would explain, it is where we make use of both our comparative advantages to give us both a better rate.

1. Find the difference between the two fixed rates: 7.0-6.0 = 1.0%
2. Find the difference between the two variable rates: (Prime +1.0) – (Prime + 0.5%) = 0.5%
3. Take the difference between the above two: 1.0% – 0.5% = 0.5%
4. That number is the rate advantage that we can share.  So divide it by two.  0.5/2 = 0.25%

Therefore, instead of a direct swap of payments, I pay you 0.25% less than what You are paying to the bank, and we both come out ahead.

The big risk in this is that we have to trust each other to honour our payments to each other regardless of how prime moves. This is the simplest type of swap, called a Plain Vanilla Swap, but one of its siblings has been implicated in the global economic woes – the Credit Default Swap

Arbitrage is taking advantage of a price difference in multiple markets.  In the futures market an arbitrage opportunity presents itself when the basis between the spot and futures prices deviates from the normal cost of carry.

There are times when a futures price is more expensive than it should be, i.e. costs more than the spot + the cost of carrying the asset.  During these times an arbitrager could sell futures contract and buy the asset.  This is know as Cash and Carry Arbitrage.

e.g.,
Gold currently costs $1000 / oz, and has an associated cost of carrying (storing, insuring, etc) of $10 / month.
A 3 month gold futures contract, for some reason, currently costs $1060
The arbitrager performs a Cash & Carry by purchasing some gold and selling a futures contract to deliver gold in three months.

cost of gold = $1000
cost of carry = $10/month x 3 months
Income from futures sale = $1060

Net = $30.  Mr Arbitrager made an easy $30.

There are other times when a futures price is cheaper than it should be, i.e., costs less than the spot + the cost of carry.  During these times an arbitrager could buy futures contract and sell the asset.  This is know as Reverse Cash and Carry Arbitrage.

hmm, this may not work quite as slick.  I cannot sell the asset today if I don’t own it!  Don’t worry, you may be able to borrow it from someone else and then sell it:)  Yeah, I know, they may not like you selling their gold, but you will get the gold back because you bought a futures contract.

e.g.,
Gold currently costs $1000 / oz, and has an associated cost of carrying (storing, insuring, etc) of $10 / month.  A 3 month gold futures contract, for some reason, currently costs $940.  The arbitrager performs a Reverse Cash & Carry by:

• borrowing the gold from his girlfriend
• giving her his prized stamp collection as collateral
• paying her rent
• selling the gold
• purchasing a futures contract to receive delivery of gold in three months.

Mr Arbitrager made $100 by selling the gold and buying a cheap futures contract.  However, he will still need to pay rent on the borrowed gold and he loses the enjoyment of his stamps until the gold is delivered.

The difference between the spot and futures price is called the basis.  In a normal market there are adequate supplies of the underlying asset for every futures contract (i.e., every delivery month) and the basis reflects a premium on the futures contract (for the cost to carry).  For a better explanation, see yesterday’s post

Occasionally the futures price will drop below the spot price which is said to be an inverted market.  Of course, such a simple term would not be fun, so I present to you… (drum roll please), “backwardation.”

Normal market = contango
Inverted market = backwardation

Backwardation may occur for a number of reasons:

• Seasonal fluctuations of asset.  In the winter, the demand for heating oil increases but by the spring the demand will have waned so the futures price will not increase.
• A sudden lack of the asset.  When a refinery breaks down the supply of gas starts to drop and the price goes up, but generally the refinery will be operational again in three months so the futures price doesn’t need to increase.
• Asset does not store well.  Gold keeps well in my basement, oranges don’t.  If the oranges are ripe now then it would be better to own the physical asset.
• Asset is difficult to short sell.  Assets that are hard to short are generally those that meet the above conditions as well.

In an inverted market people prefer to own the physical asset.  If I need oil to heat my house then I would place a high value on owning the asset during a blustery Canadian winter.  The value placed on the commodity is known as a convenience yield.  Isn’t it convenient that I actually own oil now so that I can use it to heat my home and I won’t freeze.

You can buy gold in one of two ways.

1. In the cash market, where you will pay the spot price.
2. In the futures market where you will pay the futures price.

The cash market is similar to a jewelry store.  You can go buy a gold ring today, pay cash for it and give it to your girlfriend immediately.

The futures market is sort of like going to the jeweler and saying that you will need to buy a gold ring in about three months time.  You don’t need it today, but you want to buy it today, just to make sure that you know what price you will have to pay and that they will have it for you.  What price should the jeweler sell the ring to you for?  The same price as the spot price?  No.  Remeber that the jewelry store will have to:

• store the gold for you (they promised you that exact amount and quality of gold so they have to make certain they have it when you go to collect),
• finance the cost they paid for the gold (they aren’t doing well enough to promise everyone a gold ring on the promise that they’ll buy it in the future)
• insure it (if it goes missing they still have to pay for it)

All of those are called the “cost of carrying” the physical asset.  Add all of those costs up and it may cost an extra $10/ month for them to hold onto the gold for you.  You agree because you cannot afford to buy the ring today.

Therefore,  in a normal “cost of carry market” the price for the gold ring in three months time will be the spot price plus the cost of carrying.  This normal market also has the fancy term , “contango.”

As the time goes by the futures price and the spot price will converge.  It costs 10 bucks per month to store it, so a three month agreement will cost an $30 over the spot price, but a two month agreement will only cost $20, one month is only $10, or you can buy it today without any carrying charges.

Of course, that is not always the  way it works.  Sometimes speculators get in the game, or there is a sudden shortage (or abundance) of gold, and the spot and futures prices will deviate from this contango pricing.