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Is the price of a share's future contract in the secondary market dependent on supply demand of the share in the secondary market or is it also influenced by the supply demand of the future's contract also.

I know theoretical values of futures using cost to carry model also affect the price which is once again function of the spot price of the share

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Futures prices and stock prices are driven by the same thing, aggregate expectations of what the stock's price will be in the future. Conceptually that is why they always move together.

If there is an exogenous shock in demand for one or other (like if a large buyer just decides to go long the futures contract) then arbitragers will work to make the prices match. That is, they will sell in the market where the exogenous demand happens and buy in the other market. That way they will make a small amount of profit and the prices will come back in line with each other.

Because the institutions that do this are extremely fast and efficient, we usually do not see large discrepancies between spot and and associated futures prices for liquid securities. This can break down for a short period during times when liquidity is poor or otherwise arbitrage is difficult, but for the most part it works well. A buy in the futures market large enough to move the price will cause arbitrageurs to buy in the spot market and sell in the futures. The net result will be a small increase in both the spot and futures price. The buy must be large enough to move both markets if it is to have more than a momentary effect.

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