Skip to content

NISM-Series-XV: Research Analyst · Fundamental Analysis of Commodities

Cost of Carry, Basis and Price Relationships in Commodities

Updated 11 October 2026 · Fact-checked

Cost of carry is the total cost of holding a commodity from today to futures delivery: financing, storage and insurance, less any convenience yield. Futures price ≈ spot price + net carry. Basis is spot minus futures. Futures above spot is contango; futures below spot is backwardation.

Understand Cost of Carry, Basis and Price Relationships

A futures contract promises delivery of a commodity on a future date. Instead of buying the futures, you could buy the commodity today and hold it until that date. Holding costs money. This cost is the cost of carry.

Cost of carry has three parts. Financing cost is the interest on money tied up in the stock. Storage cost covers warehousing, handling and wastage. Insurance cost covers loss or damage. Together they are what it costs to carry the physical commodity forward.

There is also a benefit. Convenience yield is the benefit of holding the physical commodity, such as keeping a factory running or avoiding a stock-out. It is not a cash payment. It reduces the net cost of carry. When the benefit is large, such as in a shortage, it can outweigh the costs.

This gives the link between spot and futures prices. In a well-functioning market, futures price ≈ spot price + cost of carry − convenience yield. If futures trade well above this level, arbitrageurs buy spot, store it and sell futures. If they trade well below it, the link breaks down for commodities that cannot easily be sold short. Storage limits and perishability also loosen the link.

Basis is the gap between spot and futures. In this chapter, use basis = spot price − futures price, unless the question defines it otherwise. When futures are above spot, the market is in contango and basis is negative. When futures are below spot, the market is in backwardation and basis is positive. Basis moves towards zero as expiry nears. This is called convergence.

Key formulas to remember

Cost of carry pricing (simple interest)
F = S + financing + storage + insurance − convenience yield
All items are for the period until futures expiry. F is futures price, S is spot price.
Cost of carry pricing (continuous compounding)
F = S × e^((r + u − y) × t)
r is interest rate, u is storage cost as a rate, y is convenience yield rate, t is time in years. Use only if the question gives this form.
Financing cost (simple)
Financing cost = S × r × t
t in years, for example 3 months = 0.25.
Basis
Basis = Spot price − Futures price
Check the question's definition. Some sources use futures minus spot.
Contango
Futures price > Spot price (basis negative)
Normal when carry costs are positive and convenience yield is small.
Backwardation
Futures price < Spot price (basis positive)
Often seen when supply is tight and convenience yield is high.
Convergence
Basis → 0 at expiry
Futures and spot prices come together on the delivery date.

How to solve Cost of Carry, Basis and Price Relationships questions

Use this order for any question on carry, basis or spot-futures relationships.

  1. 1Identify what is asked: a futures price, a basis, a market state, or a reason.
  2. 2List the given inputs: spot price, interest rate, storage, insurance, convenience yield, time period.
  3. 3Convert time to years (months ÷ 12) and keep all costs for the same period.
  4. 4Compute each cost. Financing = S × r × t. Add storage and insurance as given.
  5. 5Subtract convenience yield if it is stated. Then compute F = S + net carry.
  6. 6Compare F with S. If F > S it is contango; if F < S it is backwardation.
  7. 7Compute basis as spot − futures unless the question defines it differently.
  8. 8Check the sign and reasonableness of your answer against the options.

Quickest way: Compare, then add

When to use it: Use for MCQs where options differ in sign or size, or where the question asks about the market state.

  1. For concept questions, link the state to the cause: high convenience yield or tight supply means backwardation; high carry costs and ample stock means contango.
  2. For numerical questions, estimate financing as S × r × t first, add other costs, then match the closest option.
  3. Fix the sign: futures above spot gives negative basis (spot − futures).
  4. Eliminate options that show futures below spot when all carry items are positive and there is no convenience yield.

Common mistakes in Cost of Carry, Basis and Price Relationships

  • Treating contango as a sign of a shortage.

    Students link a higher price with scarcity.

    Fix: Contango means futures are above spot because of carry costs and ample stock. Shortage tends to produce backwardation.

  • Getting the sign of basis wrong.

    Different books define basis in opposite ways.

    Fix: Use spot − futures unless told otherwise. Then contango gives negative basis and backwardation gives positive basis.

  • Adding convenience yield to the futures price.

    Students treat it as another cost.

    Fix: Convenience yield is a benefit of holding stock. It is subtracted from carry costs.

  • Using months directly as the time in years.

    Rushing through the interest calculation.

    Fix: Convert first: 3 months = 3 ÷ 12 = 0.25 years.

  • Assuming the cost of carry formula holds exactly for every commodity.

    The formula looks like a fixed rule.

    Fix: It is a pricing relationship that holds closely for storable commodities. It is weaker for perishables or when physical stock is hard to hold or sell.

  • Thinking basis stays constant until expiry.

    Students ignore convergence.

    Fix: Basis narrows towards zero as expiry nears, because futures become the spot price on the delivery date.

Worked examples

Example 1

Spot price of a metal is ₹60,000 per unit. The interest rate is 8% a year. Storage and insurance together cost ₹600 per unit for the 3-month period. There is no convenience yield. What is the fair 3-month futures price, and is the market in contango or backwardation?

Show the solution
  1. Financing cost = 60,000 × 0.08 × 0.25 = ₹1,200.
  2. Add storage and insurance: 1,200 + 600 = ₹1,800 net carry.
  3. Futures price = 60,000 + 1,800 = ₹61,800.
  4. Futures (₹61,800) is above spot (₹60,000), so the market is in contango.
  5. Basis = spot − futures = 60,000 − 61,800 = −₹1,800.

Answer: Fair futures price is ₹61,800; the market is in contango with basis of −₹1,800.

Example 2

Spot price of a commodity is ₹5,000 per quintal and the 2-month futures price is ₹4,900. What is the basis (spot − futures), what is the market condition, and what does it suggest?

Show the solution
  1. Basis = 5,000 − 4,900 = ₹100.
  2. Futures (₹4,900) is below spot (₹5,000), so the market is in backwardation.
  3. Positive basis means spot is at a premium to futures.
  4. This usually suggests tight current supply or a high convenience yield, so holders value the physical commodity more than the carry cost.
  5. As expiry nears, basis will tend to move towards zero.

Answer: Basis is +₹100; the market is in backwardation, suggesting tight spot supply or high convenience yield.

Exam tips

  • Memorise the pairing: contango with futures above spot, backwardation with futures below spot.
  • Read the basis definition in the question. If none is given, use spot − futures.
  • Convenience yield reduces carry; never add it.
  • Expect conceptual MCQs on causes: storage cost, interest rates, shortages and convergence.
  • With negative marking, skip a numerical question only if you cannot fix the time period; most are a few lines of arithmetic.

Practice questions from Fundamental Analysis of Commodities

Cost of Carry, Basis and Price Relationships in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Cost of Carry, Basis and Price Relationships: frequently asked questions

What is the cost of carry model in commodity futures?

It says the futures price equals the spot price plus the cost of holding the commodity until delivery. That cost includes financing, storage and insurance, less any convenience yield.

What is the difference between contango and backwardation?

In contango, the futures price is above the spot price. In backwardation, the futures price is below the spot price. Contango reflects carry costs and ample stock; backwardation often reflects tight supply.

What is basis in commodity trading?

Basis is the difference between the spot price and the futures price. This guide uses spot minus futures. It narrows to zero as the contract nears expiry.

What is convenience yield?

It is the benefit of holding the physical commodity, such as keeping production going or avoiding shortages. It lowers the net cost of carry and can push futures below spot.