Convergence of Spot and Futures Prices

The spot price is the current market price at which a commodity can be bought or sold for immediate delivery. In contrast, the futures price is the agreed‑upon price for delivery at a specified future date, as recorded on a recognised exchange such as MCX.

The difference between the futures price (F) and the spot price (S) is called the basis. Mathematically, Basis = F – S. A positive basis indicates that futures trade above spot, while a negative basis means futures trade below spot. Basis reflects the net effect of financing costs, storage costs, and the convenience yield of holding the physical commodity.

For the NISM exam, remembering the definition of basis and its sign is crucial because many multiple‑choice questions ask you to identify whether a given market condition will produce a positive or negative basis. A common trap is to confuse basis with the “cost of carry”; they are related but not the same.

• Spot price – price for immediate delivery.
• Futures price – price for delivery at a future date.
• Basis – difference (F – S) that can be positive or negative.

The cost‑of‑carry model quantifies how the futures price is derived from the spot price by adding all costs incurred in holding the commodity until delivery and subtracting any benefits earned from holding it. In the Indian context, the key components are:

r – risk‑free rate (usually the yield on a government bond), u – storage cost per annum, and y – convenience yield, i.e., the non‑monetary benefit of having physical possession (e.g., ability to meet unexpected demand).

Using these variables, the NISM syllabus presents the discrete‑time relationship: F = S × (1 + r + u – y)^{T}, where T is the time to maturity in years. This formula shows that if financing and storage costs dominate convenience yield, futures will trade above spot (contango); otherwise, futures may trade below spot (backwardation).

Exam relevance: Questions often give r, u, y and ask you to compute the theoretical futures price or to identify the market condition (contango vs backwardation). Forgetting to subtract the convenience yield is a frequent mistake.

As the contract approaches expiry, the time component T in the cost‑of‑carry formula shrinks, reducing the impact of financing, storage and convenience yield. Consequently, the futures price moves closer to the spot price, and the basis narrows toward zero. This phenomenon is called convergence.

When T is large, the basis can be sizable, reflecting accumulated carry costs. Near maturity, even a small change in spot price can cause a relatively larger percentage change in basis, which is why traders monitor basis volatility closely.

For the exam, remember the rule: At expiry, Basis = 0. Questions may present a scenario where the futures price is still above spot a few days before expiry; you must recognise that the basis will continue to shrink, not stay constant.

Mathematically, set T → 0 in the cost‑of‑carry formula: (1 + r + u – y)^{0} = 1. Hence, F = S × 1 = S. This demonstrates that irrespective of the magnitude of r, u or y, the futures price must equal the spot price at expiry.

In practice, the exchange enforces daily settlement (mark‑to‑market). As the contract nears expiry, daily price adjustments accelerate, forcing the futures price to mirror the spot price more closely. Traders who hold positions until the last trading day experience negligible basis.

Exam relevance: A typical NISM question will give a futures price 10 % above spot 30 days before expiry and ask what the basis will be on the last trading day. The correct answer is zero, because convergence is guaranteed by the contract specifications.

Indian commodity traders use convergence to lock in the physical price of a commodity. By buying a futures contract when the market is in contango and the basis is positive, they can hedge against price rises while anticipating that the basis will shrink, reducing the net cost of carry.

Distributors of agricultural produce often monitor the basis to decide the optimal time to take delivery. A narrowing positive basis signals that the futures price is aligning with spot, indicating lower storage costs or higher convenience yield, which may be a cue to roll over contracts.

For the exam, remember that convergence reduces basis risk, but it does not eliminate other risks such as price volatility before expiry. Questions may test your ability to choose the right hedging strategy based on the observed basis trend.