# 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?

• Google cost of carry model. – alexbougias Aug 8 '19 at 20:29
• If it's a stock index model, I'll need the dividend amounts if the ex-dividend date falls between now and the futures expiration date. For the interest rate, would it be the borrowing cost per stock (from the prime brokerage if we were shorting) or would it be the borrowing cost of capital i.e, if we had to finance a long position? – bloodynri Aug 12 '19 at 20:28

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