The forward price of a commodity is calculated much along the lines of that of a financial product except for the fact that by virtue of its physical form and characteristics a commodity incurs different types of storage and holding costs as compared to a financial product and the factors that affect the commodities forward price are much different from those that affect the price of a financial forward.

The Equations

The equilibrium formula for the calculation of the forward price of a commodity is as follows:

Where r is the risk-free interest rate in the market, δ is the lease rate and T is the time between the current date and the future date at which the transaction is supposed to take place.

In financial markets the lease rate is associated with the rate at which returns have been obtained for owning the asset i.e. the dividend yield.

In the commodities market the lease rate arises because the asset can be loaned out in the market as each and every commodity has physical characteristics.

Let’s assume that g is the rate at which the commodity price grows and α is expected rate of return on the commodity price. The lease rate is represented by the following equation:

There is another way of representing the lease rate. When it is lent out storage costs are saved but the benefits of holding the commodity i.e. the convenience yield is forgone. The borrower of the commodity pays a lease rate that is equal to the convenience yield minus the storage costs.

Let us assume that c is the convenience yield and λ are the storage costs. The lease rate is given by:

 

This is also called the cost of carrying the commodity.

The Derivation

If the actual storage cost of the commodity is eλT where λ is the storage cost rate and T is time to maturity then the storage cost can be derived from the spot prices in the market and the prices shown by the warehouses. If the futures price is such that: