Expectations model

There is more than one way to explain why a futures contract is priced the way it is. The cost of carry model says the futures price is built from today's spot price plus the cost of holding the asset until delivery. The expectations model says something different.

Under the expectations model, the futures price is not really about today's spot price at all. It is the market's collective guess at what the spot price will be when the contract expires. Every trader in the futures market is, in effect, voting on the future spot level, and the futures price is where those votes settle.

This matters most where the cost of carry model struggles — assets that cannot be stored, or cannot be sold short, where financing cost alone cannot explain the futures price.

The workbook (Chapter 15, section 15.7) frames the expectations model against expected, not current, spot and futures prices as the driver of the market — particularly useful when an asset cannot be sold short or cannot be stored. Under this model: futures can trade at a premium or discount to the current spot price, and the futures price signals the market's expected direction of the spot price.

If futures trade above spot, the market expects the spot price to rise — a state the workbook calls a Contango market. If futures trade below spot, the market expects the spot price to fall — a Backwardation market. Whatever the futures price implies today, futures and spot prices converge at expiry, because at that single point in time there can be no difference between them — which is also why every futures contract settles at the underlying cash market price on expiry.

The workbook's own illustration: on 14 May 2024, the May 2024 index futures contract trades at 22,308.70, while the spot index is elsewhere.

Under the expectations model, that 22,308.70 is read as the market's expectation of where the spot index will settle at the close on the last trading day of the contract — 30 May 2024 — not a statement about today's spot level at all.

If the futures price of 22,308.70 sits above the spot index on 14 May, the market is in contango, signalling an expectation that the spot index will rise to meet that level by expiry. As expiry approaches, spot and futures converge, and on 30 May itself both settle at the same number — whatever that turns out to be.

Put a rupee value on it. At an index lot size of 50, one futures contract at 22,308.70 carries a notional value of 50 × 22,308.70 = Rs 11,15,435. A fund holding 10 such contracts as a hedge is therefore carrying roughly Rs 1.12 crore of notional exposure, priced entirely off the market's expectation of where the index will settle on 30 May — not off today's spot index level.

Chapter 15 (Introduction to Forwards and Futures), section 15.7, presents the expectations model as the second of the workbook's two named futures pricing models, alongside the cost of carry model, and section 15.8 uses it to explain price discovery and convergence at expiry. Expect a question distinguishing contango from backwardation, and one testing what the expectations model says the futures price actually represents.

• Contango means futures trade above spot; backwardation means futures trade below spot. These two terms are frequently swapped by mistake.
• The expectations model and the cost of carry model are two different explanations for the same futures price — the workbook presents both without saying one is universally correct; cost of carry is described as more suitable for pricing forwards, while expectations dominates where storage or short-selling is not possible.
• Convergence at expiry is a separate fact from either pricing model — it holds regardless of which model is used to explain the price beforehand.