Future Pricing

The futures price is the price at which a futures contract trades on an exchange. It represents the market's expectation of the spot price of the underlying asset at the contract's settlement date. However, the futures price is not simply a prediction of the future spot price. It's influenced by several factors, primarily the cost of carry.

Cost of Carry Model:

The most common model for pricing futures contracts is the cost of carry model. It states that the futures price should be equal to the spot price of the underlying asset plus the net cost of carrying (holding) that asset until the contract's maturity.

Formula: F = S + (Carrying Costs - Carrying Returns)

F = S(1 + r)^t + (Storage cost - Convenience Yield)

Where:

F = Futures price

S = Spot price of the underlying asset

r = risk free rate

t = time period

Carrying Costs: Costs associated with holding the asset, such as:
- Storage Costs: For physical commodities (e.g., warehousing fees for grain).
- Financing Costs: The interest paid on a loan to purchase the asset or the opportunity cost of tying up funds in the asset.
- Insurance Costs: To protect the asset against loss or damage.

Carrying Returns (Benefits): Income or benefits received from holding the asset, such as:
- Dividends: For stocks or stock indices.
- Coupon Payments: For bonds.
- Convenience Yield: A non-monetary benefit from holding a physical commodity, representing the value of having the asset readily available (e.g., a manufacturer holding inventory to avoid production delays). This is particularly relevant for commodities.

Example:

Suppose the spot price of gold is $1,800 per ounce. The annual risk-free interest rate is 2%, and the storage cost for gold is $5 per ounce per year. There is no convenience yield in this case. The futures price for a one-year gold futures contract would be:

F = $1,800 * (1+0.02)^1 + $5 = $1,841

Or, F = $1800 + $36 + $5 = $1841

The futures price is higher than the spot price because the cost of carrying gold (financing and storage) outweighs the benefits (none in this example). The price of a futures contract is determined by the forces of supply and demand in the market. The cost of carry model provides a theoretical framework for understanding the relationship between futures prices and spot prices. In practice, futures prices may deviate from the model due to various market factors and investor sentiment.