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Pricing Futures and the Cost of Carry Model

F=S e(r+c−y)TF = S\,e^{(r + c - y)T}

The futures price is determined by replication, not by anyone's opinion about the future.

The argument

Two ways to own the asset at time TT:

  1. Buy the future at FF and pay at delivery.
  2. Borrow SS now, buy the asset, pay financing rr and storage cc, and collect any yield yy along the way.

Both leave you holding the asset at TT with no risk taken. So both must cost the same, and that equality is the formula.

Key takeaway

The futures price is not a forecast of the spot price. It is today's spot adjusted for the cost of carrying the asset. A future above spot says storage and financing are expensive, not that prices are expected to rise.

This distinction matters because it is a frequent interview trap. If futures were forecasts, an upward-sloping curve would mean the market expects higher prices, and it does not.

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