Cost of Carry for Index and Commodity Futures

Summary

The note explains how to estimate fair value for a futures contract using the cost-of-carry relationship. For an index future, it relates the spot index level to financing over the contract term, adjusted for income such as dividends. The same idea can be expressed by subtracting the present value of expected dividends from spot before applying financing.

For physical commodities, the calculation also needs costs such as storage, freight, and insurance. The note offers a compact no-arbitrage framework, but does not provide a worked market example or discuss practical complications such as discrete dividend forecasts, convenience yield, or changing funding rates. Its formulas assume simplified carry inputs and are best treated as a starting point for fair-value analysis.

Key ideas

• Index futures fair value links spot, financing, dividends, and time to expiry.
• Expected dividend income reduces the futures price relative to a no-income underlying.
• Commodity futures may include storage, freight, and insurance costs.
• The no-arbitrage carry relationship is a framework whose accuracy depends on input assumptions.

Tags

# Basis calculation


# Basis calculation












How does one calculate a fair value for a futures contract whose underlying is an Index? For example, how would fair value for ES futures be calculated using the prices of the S&P 500 constituents? I know it's related to dividends and interest rate but not sure exactly how. Also, what if the index is based on commodities like precious metals or oil?

## Answer by alexbougias (score 2)

https://quant.stackexchange.com/a/47053

What your are looking is the cost of carry model. That is an equivalence relationship emerging from a no-arbitrage argument. The future price is linked to the current price with

$F=S_0 e^{(r-q)t}$

Where $q$ is the percentage of the income streams, in your case the continuously compounded rate of the dividends. Equivalently, you can substract the present value of dividends from the current price.

$F=(S_0-I) e^{rt}$

If you are dealing with commodities, then you should add the costs associated with storage, freight rates and insurance of the underlying.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.