Determining Price Relationships

As noted in the fundamental section, a futures price is related to the cost of carry of the futures and cash price. The greater the cost of carry, the higher the future price versus the cash price. For most futures, contracts with longer expirations will have higher prices because the cost to carry increases with time. A trader may attempt to spread one month against another if a price discrepancy occurs between one month and another.

The calculations used to determine the value of a future are similar to those  covering the basis calculations. We will use them here for spreading evaluation. The trader is now concerned with the difference between the near and distant futures prices to determine if both are correctly valued. Let's look at an example.

July coffee is trading at $0.90 a pound. What should the September future be trading at? Assume a two-month holding time and carrying costs which include insurance, storage, and interest costs of 17%.

Cost to carry = cost of commodity' interest rate. holding time

= $0.90 x 0.17 x 2/12

= $0.025

 

The September future should be trading at approximately $0.925 a pound ($0.90 + $0.025). Assume the actual future price is trading at a slightly lower price of $0.92 a pound. A trader could buy the cheaper September future and sell the more expensive July future. But there is one more important consideration the trader must be aware of in this situation.

The cost of carry represents a "floor price" for most near-term futures. The near-term future will usually not sell below a certain price relative to the more distant future. The floor price is calculated as follows:

 

Floor price = further out month - carrying cost

 

If the September future remains at $0.92 a pound, the July future should not sell below this floor price which is the September future minus the cost to carry:

Floor price = $0.92 - $0.025

                = $0.895 a pound

 

Why does a floor price occur? An arbitrager would buy the July coffee contract at $0.895 a pound and take delivery of the coffee. This action would be cheaper than buying the coffee in the cash market. The spread should not widen to more than the cost of carry or $0.025 a pound.

Is there a ceiling price of the near-term future? There is generally not a ceiling price because the mechanics are different. If July coffee becomes temporarily scarce due to a frost or other problems, the price of the nearby future could increase much more than the longer­term future. The longer-term future might not even increase and could in fact drop in value if the supply or demand problem is of a short-term nature. Here, the inverted spread can be much greater than $0.025 because the cost of carry does not affect the relationship on the upside. The July contract could trade at $1.00 a pound and the September could be at $0.95 a pound.

Temporary supply and demand problems can cause the near-term future to change much more than the longer-term future. In the opposite case, where there is an excess supply of coffee, the arbitrageur will simply buy the near-term future and create a floor price. This buying will continue until the longer-term future drops or the near term increases to the appropriate cost of carry level.

The ceiling and floor pricing in futures of different months has important implications when a trader wishes to spread one future against another. When buying a spread (purchase near term and sell further out) the risk is theoretically limited to the floor price of the carrying cost. The near-term future should not sell below the cost of carry of the distant month. However, the reward is not limited because the spread can widen to any level irrespective of carrying charges.

When selling a spread (sell near term and buy further out) the opposite applies. The risk is not limited because the spread can widen to any price. The reward is limited because the near-term future can only drop to a floor price set by the carrying cost. In the previous example, the arbitrageur could sell the July at $0.90 a pound against buying the September at $0.92 and hope to make $0.005 a pound. That is the maximum profit obtainable, whereas the arbitrageur could lose much more than this if the July increased more than the September. Perhaps this is one reason why the September is so "cheap" and the July so "expensive" in the example.

If carrying costs, or more often, interest rates decrease, the carrying costs would drop and the spread difference of $0.025 would decrease. If carrying costs increase, the spread difference could increase beyond $0.025. Unless interest rates are extremely high or fluctuate greatly, the spread relationship is usually affected more by the supply and demand situation of the underlying commodity.