# Carry Markets and Forward Prices

A commodity is said to be in carry when it is being stored rather than traded. The concept is similar to financial markets where this term is called the financial cost of carry. In the case of commodities this becomes more obvious since the process of producing and distributing them involves storing them as well.

The costs that are incurred in the carry markets affect the forward price of the commodity that will be traded in the future.

## Forward Price of a Commodity

The forward price of a commodity is derived using the following formula:

Where r is risk free rate at which the value of an asset grows in the market.

In financial markets δ is normally associated with the returns that arise from holding the asset. An example would be when an asset pays the dividend. This is called the dividend yield.

Commodities have the characteristic that they can be lent and bought back in the active market. This is called the act of leasing the instrument and the rate of return achieved from it is called the lease rate. The dividend yield in the financial markets is called the lease rate in the commodities market.

## Impact of Storage Costs and Convenience Yield

The price of the commodity calculated in the future must factor in both the financial cost of carrying the commodity as well as the physical cost of carry i.e. the cost of storing the commodity.

The impact of the storage cost is to make the graph of interest rates for commodities steeper than the normal interest rate structure. The advantage of lending a commodity is that the owner saves on the storage costs. However there is a disadvantage that the owner loses on the benefits of holding the commodity which in markets terminology is called the convenience yield.

In other words when a commodity is leased out, there is saving on storage costs but the benefits due to holding the commodity i.e. the convenience yield is lost.

This relationship is represented by the following equation –

Where δ is the lease rate, *c* is the convenience yield and λ indicates the storage costs.

The lease rate can also be represented as the difference between the commodity discount rate *α* and the expected growth rate of the commodity price *g*.

The commodity discount rate is the required rate of return on the commodity.

From the above relationships it becomes clear that the forward price moves in an opposite direction to the convenience yield and this is opposite for the storage costs.

## No-Arbitrage Trading Range

The convenience yield of the commodity cannot be earned by the average investor while trading in the no-arbitrage market. This results in a no-arbitrage trading range rather than a no-arbitrage price for the commodity.

The no-arbitrage trading range is the range of possible prices while factoring in the convenience yield for the pricing of the commodity.

## Example

The following details are available about corn:

- Spot price (Current price in the market) = $5 per bushel
- Rate of interest prevailing the market (r) = 6%
- Storage cost = 15%

The 1 year forward price is then calculated as follows:

If the convenience yield of holding the commodity is 4% then the forward price gets impacted:

From the relationships described, it can be deduced that the forward price is negatively impacted as a result of the introduction of the convenience yield i.e. it reduces in value.

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