Futures Price (Cost-of-Carry Model)
Futures Price (Cost-of-Carry Model)
The no-arbitrage futures price of a stored asset: the spot price grown at the cost of carry (financing plus storage less convenience yield) to delivery, with continuous compounding.
When to use: Use for commodity futures. For financial assets that pay income rather than incur storage, the forward price formula with an income yield is the same model with the signs arranged for that case.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| FuturesPrice | Futures Price | No-arbitrage futures price | $ |
| S | Stock Price | Current price of the underlying | $ |
| Rf | Risk-Free Rate | Continuously compounded annual risk-free rate as a decimal | % |
| StorageCost | Storage Cost | Annual storage and insurance cost as a fraction of the asset price | % |
| ConvenienceYield | Convenience Yield | Annual benefit of holding the physical asset, as a decimal | % |
| T | Time to Expiration | Time to expiration in years (e.g. 0.25 for 3 months) | years |
Real-Life Examples
Example 1: One-Year Commodity Future
Spot $80; financing 5%, storage 2%, convenience yield 1%; one year.
Given
Step-by-Step
The future sits $4.95 above spot, exactly the net cost of carrying the commodity for a year. Buy spot and sell the future above $84.95 and the carry is a riskless profit.
Example 2: Three-Month Gold Future
Gold at $1,900; financing 4%, storage 0.5%, no convenience yield; three months.
Given
Step-by-Step
Gold is almost pure carry: no convenience yield to speak of, small storage, so the future is spot plus a quarter of the financing rate.
Frequently Asked Questions
When the convenience yield exceeds financing plus storage, the cost of carry is negative and the curve is in backwardation. That is common in tight physical markets and is the market paying holders to keep inventory available.