Cost of Carry Model: Audax At Fidelis.

This is part 2 of this Theory is Normal Backwardation thread posted yesterday.

Commodity Modeling

When considering consumption commodities or investment assets, the cost of carry model summarizes the relationship between the Spot price (S0) of the commodity and the Forward price (F0) of the commodity.

The current Spot price is the price in the cash market that we would pay today to purchase the commodity.

For example if I wanted to buy Corn No.2 yellow today I’d pay the spot price. On the other hand I may not want to buy the Corn No. 2 yellow today, I may want to buy the Corn in 3months or 6 months in the future, for instance.

In that case, I would enter into a forward or futures contract taking a long position, which would mean I promise to BUY that Corn No.2 contract (5,000 bushels) in the future but knowing the price today that will be paid in the future. (This being the forward price).

Note: the futures contract is one that trades on a standardized exchange, unlike that of a forward contract which is just an agreement between two counter parties.

This tees up the question of what sets this future/forward price? As we wrote yesterday about the theory of normal backwardation and learned that the price is mainly a function F(x) of the “cost of carry” or the cost to hold that asset. Holding the asset that has assumed systemic risk attached is denoted by the commodity beta. It being either positive or negative, nonetheless, a speculators appetite for risk is rewarded.

In other words, if we enter into an agreement to purchase the Corn contract in the future not today, someone will have to “carry” or hold the Corn in the interim and need to be compensated just like the speculator is for taking risk.

In a cost of carry model there are roughly four factors that determine the value of a commodity futures/forward contract.

The first, is the financing cost, denoted by (r) and correlated to that of the risk-free rate. This is an important determinant that drives up the forward/futures price up relative to the spot price. Thinking of it another way, in terms of the time value of money calculation.

Secondly, consumption commodities need to be stored, and (u) denotes the storage costs associated with doing so. And the higher (u) or the storage costs are, the higher the forward/ futures price will be relative to the spot price.

The two subsequent factors that influence the price of the forward /futures price are offsetting inputs to that of the risk-free rate (r) and storage costs (u).

In the case of either a consumption commodity or financial asset (q) denotes the income or dividend acquired through the ownership of the commodity contract. Income of course offsetting any costs, thereby lowering the price of the future / forward contracts price.

Lastly, the cost of carry model has a “catch-all” category that incorporates anything not incorporated with the other variables. It is denoted by (y) which represents the convince yield. The conscience yield is any other venue for tangible or intangible to owning or carrying the commodity asset.

It helps to visualize this is terms of what it would entail to own oil today or entering into a forward /futures contract to buy in the future. Weighing out the intangible or benefits to owning the oil now. Thereby, forgoing the risk of a storage in the future. Further to the point, we can think of the conscience yield as a negative or inverse storage costs, lowering the price of the forward or future contract.

Such that, the best biased or unbiased estimate for the forward/future price is the spot price (S0) * Euler’s constant ^ raised by our four-factor variables ( r+u-q-y) *T (⏰).

Noting again how both the risk-less rate and storage costs are additive, thereby there to increase the spot price (S0). However, offset by the other two factor variables, income or dividend received (q) and the conscience yield (y). These two variables being the benefit of carrying the commodity asset.



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