Basis, cost of carry and convergence

In simple terms

A futures price is not just a guess about the future. It is tied to today's price of the underlying, the spot price, by simple arithmetic. If it drifts too far, traders can profit by buying one and selling the other, which pulls the prices back together, as the arbitrage lesson explains.

The cost of carry

Imagine two ways of owning a share in 30 days:

1. Buy it today, paying ₹1,000 now, giving up interest on that money, but receiving any dividends.
2. Buy a future today, paying nothing now except margin, and pay the futures price at expiry.

For neither to be clearly better, the futures price should equal the spot price plus the interest cost of holding the share, minus any dividends. This is the cost of carry.

Basis, contango and backwardation

Basis is the difference between the futures price and the spot price. Conventions differ; here it is futures minus spot.

• Contango: futures above spot. Normal when carrying costs exceed income.
• Backwardation: futures below spot. Can happen when large dividends are expected, when the underlying is in short supply, or when strong demand to sell futures pushes their price down.

Basis also moves with supply and demand for futures, and with interest rates.

Convergence at expiry

At expiry, a future and the underlying refer to the same thing at the same moment, so their prices must be the same. As expiry approaches, the cost of carry shrinks towards zero, and the basis shrinks with it. This is convergence.

Convergence matters for anyone rolling futures from one expiry to the next, who pays the basis each time, as the futures lesson notes, and for hedgers, whose hedge can gain or lose as the basis changes, as the hedging lesson explains.

Why basis matters to hedgers

A hedger who sells futures to protect a portfolio, as the hedging lesson describes, is exposed to changes in the basis before expiry. If the futures price falls further below fair value, the hedge gains less than expected; if it rises above fair value, the hedge gains more. This basis risk is one reason hedges are imperfect even when sized correctly.

Not a forecast

Because the futures price is mostly spot plus carry, a futures price above spot does not mean the market expects the price to rise. It mainly reflects interest costs. Treating futures prices as predictions misunderstands what they measure.

Why it matters

Fair value, basis and convergence explain why futures trade at a premium or discount to spot, what it costs to roll a futures position, and how arbitrage keeps futures and spot prices linked. They also guard against the common mistake of reading futures prices as forecasts.

Limitations

The formula is simplified: it ignores costs, taxes, margin funding and differences in borrowing and lending rates. Real futures can trade away from fair value for periods, especially when markets are stressed or liquidity is thin.

Common mistakes

• Reading futures prices as forecasts.
• Ignoring dividends in fair value.
• Forgetting rollover costs when holding futures across expiries.
• Assuming basis is constant before expiry.

Try it yourself

1. Calculate fair value for a share at ₹2,500, interest at 6.5% a year, 45 days to expiry, and no dividend.
2. Recalculate with a ₹20 dividend expected before expiry.
3. Compare your figure with a real futures price on an exchange website and note the basis.