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NISM-Series-VIII: Equity Derivatives · Strategies using Equity Futures and Equity Options

Cash and Carry vs Reverse Cash and Carry Arbitrage

Updated 11 October 2026 · Fact-checked

Cash and carry arbitrage means buying in the spot market and selling futures when futures trade above fair value. Reverse cash and carry means selling spot and buying futures when futures trade below fair value. Fair value is spot × (1 + r × t) in the simple form. You lock in a near risk-free gain.

Understand Arbitrage: Cash and Carry and Reverse Cash and Carry

Arbitrage means earning a profit from a price difference without taking market risk. In equity derivatives, the difference is between the spot price of a stock and the price of its futures contract.

The link between the two is the cost of carry. If you buy a share today and hold it until the futures expiry, you pay interest on the money used. You may also receive dividends. Fair futures price = spot price plus the net cost of carrying the share to expiry.

Fair value, F = S(1 + rt) − D, is a single no-arbitrage price. It is one number and does not change with the strategy you choose.

If the futures price is above fair value, futures are overpriced. You buy spot and sell futures. This is cash and carry. At expiry the futures price converges to spot. You square off the spot position at expiry. Physical settlement applies only to certain stock derivatives under SEBI rules, so do not assume it for every contract. You receive the dividend D while you hold the share, which lowers your net cost. Your gain is the futures price minus the cost of carrying the stock, which is spot plus financing cost, less any dividend received: futures price − [S × (1 + r × t) − D]. With no dividend this reduces to futures price − S × (1 + r × t).

If the futures price is below fair value, futures are underpriced. You sell spot and buy futures. This is reverse cash and carry. You need to hold the shares already, or borrow them where permitted. You earn the interest on the sale proceeds, and you buy back through futures cheaply. As the seller of the spot share, you forgo the dividend. That is already built into the same fair value, so it is not a separate deduction in each strategy.

The price risk is hedged because the two legs offset each other. The gain is locked in if you hold the position to expiry. In practice, arbitrage activity pushes futures prices back toward fair value. That is why futures rarely stay far from it.

Key formulas to remember

Fair value of futures (simple interest)
F = S × (1 + r × t)
S = spot price, r = annual interest rate, t = time to expiry in years (days ÷ 365). Use this when no dividend is given.
Fair value of futures (continuous compounding)
F = S × e^(r × t)
Use when the question says continuous compounding.
Fair value with dividend
F = S × (1 + r × t) − D
D = dividend expected before expiry. This is a single no-arbitrage price. The holder of the share in cash and carry receives D, which lowers the net cost of carry. The reverse trader forgoes D, and that is already built into the same fair value. Subtract D once, when you compute F.
Cash and carry trigger
Actual futures price > Fair value
Buy spot, sell futures. Futures are overpriced.
Reverse cash and carry trigger
Actual futures price < Fair value
Sell spot, buy futures. Futures are underpriced.
Arbitrage profit per share
Profit = |Actual futures price − Fair value|
Before transaction costs. For cash and carry it equals futures price − [S × (1 + r × t) − D], which reduces to futures price − S × (1 + r × t) only when there is no dividend.

How to solve Arbitrage: Cash and Carry and Reverse Cash and Carry questions

Use this order for any question on cost of carry or arbitrage.

  1. 1Write down spot price S, futures price, interest rate r, days to expiry and any dividend.
  2. 2Convert time to years: t = days ÷ 365.
  3. 3Compute fair value F = S × (1 + r × t), then subtract any dividend.
  4. 4Compare the actual futures price with F.
  5. 5If futures > F, choose cash and carry: buy spot, sell futures. If futures < F, choose reverse cash and carry: sell spot, buy futures.
  6. 6Compute profit per share as the difference between actual futures price and F.
  7. 7Multiply by the lot size if the question asks for profit per contract.

Quickest way: Compare and name the trade

When to use it: Use when options ask which trade to do or whether arbitrage exists, and no full profit calculation is needed.

  1. Estimate fair value roughly: S × r × t gives the carry in rupees.
  2. Add the carry to spot, subtract dividend if given.
  3. If futures is higher, answer buy spot and sell futures. If lower, sell spot and buy futures.
  4. If futures equals fair value, there is no arbitrage.

Common mistakes in Arbitrage: Cash and Carry and Reverse Cash and Carry

  • Reversing the trades for the two strategies

    The names sound alike and students memorise them without logic.

    Fix: Overpriced futures: sell the expensive thing (futures), buy the cheap thing (spot). Underpriced futures: do the opposite.

  • Forgetting to subtract the dividend

    The dividend appears as an extra line and gets ignored.

    Fix: Dividends received by the holder lower the net cost of carry. Subtract D once from S × (1 + r × t) to get fair value. Do not subtract it again for each strategy.

  • Using months or days directly as t

    Rushing and skipping the unit conversion.

    Fix: Always convert to years. For 30 days use 30 ÷ 365.

  • Treating arbitrage profit as market-view profit

    Students think the trade depends on prices rising or falling.

    Fix: Arbitrage is locked in by the price gap. The direction of the market does not matter.

  • Applying the profit formula without comparing first

    Students jump to calculation and take the wrong sign.

    Fix: Compare actual futures with fair value first. The sign decides the trade.

Worked examples

Example 1

A stock trades at ₹500 in the spot market. The one-month futures (30 days) trades at ₹510. The interest rate is 12% per annum (simple interest). No dividend. Find fair value and the arbitrage action and profit per share. Use 365 days.

Show the solution
  1. S = 500, r = 0.12, t = 30 ÷ 365 = 0.08219.
  2. Carry = 500 × 0.12 × 0.08219 = ₹4.93 (approx).
  3. Fair value = 500 + 4.93 = ₹504.93.
  4. Actual futures ₹510 is greater than ₹504.93, so futures are overpriced.
  5. Trade: buy spot at ₹500 and sell futures at ₹510 (cash and carry).
  6. Profit = 510 − 504.93 = ₹5.07 per share (approx).

Answer: Fair value is about ₹504.93. Do cash and carry: buy spot, sell futures. Profit is about ₹5.07 per share.

Example 2

A stock trades at ₹1,000. The 73-day futures trades at ₹1,015. The interest rate is 10% per annum (simple) and a dividend of ₹5 is expected before expiry. Is there an arbitrage? Use 365 days.

Show the solution
  1. t = 73 ÷ 365 = 0.2.
  2. Carry = 1,000 × 0.10 × 0.2 = ₹20.
  3. Fair value = 1,000 + 20 − 5 = ₹1,015.
  4. Actual futures ₹1,015 equals fair value.
  5. No gap exists between futures and fair value.

Answer: No arbitrage. The futures price equals fair value of ₹1,015, so neither cash and carry nor reverse cash and carry earns a profit.

Exam tips

  • Questions often give a futures price and ask which trade to do. Compare with fair value first, then pick the trade.
  • Check if a dividend is given. Many trap options ignore it.
  • Remember the logic: sell what is overpriced, buy what is underpriced.
  • Know that reverse cash and carry needs shares to sell, so it is mainly done by holders of the stock.
  • Do not spend time on exact decimals. Options are usually far enough apart for an estimate.

Practice questions from Strategies using Equity Futures and Equity Options

Arbitrage: Cash and Carry and Reverse Cash and Carry: frequently asked questions

What is the difference between cash and carry and reverse cash and carry?

Cash and carry is buying spot and selling futures when futures are overpriced. Reverse cash and carry is selling spot and buying futures when futures are underpriced. Both lock in a gain from the gap to fair value.

What is the futures fair value formula in NISM?

The simple form is F = S × (1 + r × t), where t is in years. Subtract the dividend expected before expiry if one is given. Use e^(r × t) only when continuous compounding is stated.

Is arbitrage really risk free?

It is close to risk free because the two legs offset each other and the prices converge at expiry. Transaction costs, financing differences and execution gaps can still reduce the profit. Exam questions usually ignore these unless stated.

Why do futures prices converge to spot at expiry?

At expiry the futures contract settles against the spot price, so the cost of carry falls to zero. Any gap would give an immediate arbitrage profit, which traders remove.