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Strategic Financial Management · Forwards and Futures

Speculation and Arbitrage Using Futures: CMA Final SFM

Updated 11 October 2026 · Fact-checked

Speculation means taking an open futures position to profit from a price view. Profit or loss = (exit price − entry price) × lot size for a long, and the reverse for a short. Arbitrage means locking a risk-free gain when the futures price differs from its fair value: compare quoted futures with S₀ × e^(rT) or S₀(1 + r)^T, then buy the cheap leg and sell the dear one.

Understand Speculation and Arbitrage Using Futures

A futures contract is an agreement to buy or sell an asset at a fixed price on a fixed future date. It is traded on an exchange and marked to market daily. You put up only a margin, not the full value. That is why futures gains and losses are large compared with your capital.

A speculator has no position in the underlying asset. If you expect prices to rise, you go long (buy futures). If you expect a fall, you go short (sell futures). Your profit is the price move multiplied by the lot size. A long loses when price falls. A short loses when price rises. Risk is open-ended in both directions.

A spread (calendar spread) means buying one contract month and selling another on the same underlying. You are not betting on the direction of price. You are betting on the gap between the two prices. The gap changes less than the outright price, so risk is lower. If you expect the gap to widen, you buy the spread (buy far month, sell near month) and if you expect it to narrow, you sell it.

Arbitrage uses the cost of carry. Fair futures price = spot price plus the cost of holding the asset till expiry (interest) minus income received (dividend). If the quoted futures price is higher than fair value, futures are overpriced. You do cash and carry: borrow, buy spot, sell futures, hold, and deliver or square off at expiry. If futures are lower than fair value, they are underpriced. You do reverse cash and carry: sell spot (short), invest the proceeds, and buy futures. The gain is fixed at the start, whatever the spot price does later.

Key rules to remember

Profit or loss on a long futures position
(Sell price − Buy price) × Lot size × Number of lots
Positive means profit. Brokerage and margin interest are ignored unless the question gives them.
Profit or loss on a short futures position
(Sell price − Buy price) × Lot size × Number of lots
You sell first, so sell price is the entry price and buy price is the exit price.
Fair futures price (discrete compounding)
F₀ = S₀ × (1 + r)^T
T is in years. For a short period, S₀ × (1 + r × T) is often used. Follow what the question states.
Fair futures price (continuous compounding)
F₀ = S₀ × e^(rT)
Use when the question gives a continuously compounded rate or asks for it.
Fair futures price with known dividend
F₀ = (S₀ − PV of dividends) × (1 + r)^T, or S₀(1 + r)^T − FV of dividends at expiry
Both give the same result if the present value and future value are taken consistently.
Fair futures price with dividend yield
F₀ = S₀ × e^((r − q)T)
q is the continuous dividend yield. Used mainly for index futures.
Cash and carry arbitrage profit
Quoted F − Fair F (when quoted F is higher)
Per unit. Multiply by lot size and lots.
Reverse cash and carry arbitrage profit
Fair F − Quoted F (when quoted F is lower)
Per unit. Needs the ability to short sell the asset or hold it already.

How to solve Speculation and Arbitrage Using Futures questions

Use the same sequence for any speculation, spread or arbitrage question. Write units (per share, per lot) at each step.

  1. 1Identify the task: outright speculation, spread, or arbitrage. Note lot size, number of lots and the time to expiry.
  2. 2For speculation, write entry and exit prices for each leg. Decide long or short for each leg from the view given.
  3. 3Compute profit or loss per unit for each leg using (sell − buy), then multiply by lot size and number of lots.
  4. 4For arbitrage, compute the fair futures price with the given rate, time and any dividend. Keep T in years.
  5. 5Compare fair price with the quoted futures price. If quoted is higher, do cash and carry. If lower, do reverse cash and carry.
  6. 6List each cash flow: borrow or invest, buy or sell spot, buy or sell futures. Include interest cost or income to expiry.
  7. 7Compute the net gain at expiry. It should be the same whatever the spot price at expiry. State this as a check.
  8. 8Write a clear conclusion: the action, the amount, and whether the gain is risk-free.

Quickest way: Fair price gap method for arbitrage

When to use it: Use when the question asks only for the arbitrage profit and not for the full cash flow statement.

  1. Compute fair F₀ = S₀(1 + r)^T, adjusting for dividends.
  2. Take the difference between quoted F and fair F.
  3. If quoted F is higher, the profit per unit is that difference (cash and carry). If lower, it is the difference the other way (reverse).
  4. Multiply by lot size and number of lots.
  5. Check with one line of cash flows if the question asks for 'show the strategy'.

Common mistakes in Speculation and Arbitrage Using Futures

  • Using (buy − sell) for a short position, giving the wrong sign.

    Students memorise the long formula and apply it to both sides.

    Fix: Always write (sell price − buy price). For a short, the sell comes first, so it is the entry price.

  • Forgetting to multiply by lot size or number of lots.

    The working is done per unit and the last step is skipped under time pressure.

    Fix: Write 'per unit' at the top of the working and finish with a separate multiplication line.

  • Using T in months instead of years in the fair price formula.

    The question gives 3 months and the rate is annual.

    Fix: Convert first: 3 months = 0.25 years. Then compute the interest.

  • Ignoring dividends expected before expiry.

    The dividend is stated in a side line of the question.

    Fix: Scan the question for dividend, then subtract its future value from the cost of carry or its present value from spot.

  • Choosing the wrong arbitrage direction.

    Students do not compare quoted and fair prices before acting.

    Fix: Remember: futures too high, sell futures and buy spot. Futures too low, buy futures and sell spot.

  • Treating spread profit as depending on the direction of price.

    Students look at one leg only.

    Fix: Compute both legs separately and add them. The spread result depends on the change in the gap.

Worked examples

Example 1

A stock trades at ₹500 in the spot market. The 3-month futures contract is quoted at ₹520. The lot size is 1,000 shares. The risk-free rate is 8% per annum (use simple interest for the carry). There are no dividends. Is there an arbitrage opportunity? If so, show the strategy and the profit per lot.

Show the solution
  1. Time to expiry T = 3 ÷ 12 = 0.25 years.
  2. Fair futures price = 500 × (1 + 0.08 × 0.25) = 500 × 1.02 = ₹510.
  3. Quoted futures ₹520 is higher than fair ₹510, so futures are overpriced. Do cash and carry.
  4. Today: borrow ₹5,00,000 (500 × 1,000) at 8%, buy 1,000 shares at ₹500, and sell one lot of futures at ₹520.
  5. At expiry: deliver the shares against the futures at ₹520. Receipt = 520 × 1,000 = ₹5,20,000.
  6. Repay the loan with interest = 5,00,000 × 1.02 = ₹5,10,000.
  7. Net profit = 5,20,000 − 5,10,000 = ₹10,000, which equals (520 − 510) × 1,000.

Answer: Yes. Futures are overpriced by ₹10. Buy spot, sell futures, and borrow. The risk-free profit is ₹10,000 per lot.

Example 2

A trader expects the Nifty to rise and buys 4 lots of Nifty futures at 24,000. The lot size is 75. A week later the trader sells at 24,180. At the same time, another trader sells 2 lots of a stock futures at ₹1,200 (lot size 500) and buys back at ₹1,235. Find the profit or loss of each trader.

Show the solution
  1. Trader 1 is long. Profit per unit = 24,180 − 24,000 = 180 points.
  2. Units = 4 lots × 75 = 300.
  3. Profit = 180 × 300 = ₹54,000.
  4. Trader 2 is short. Profit per unit = sell − buy = 1,200 − 1,235 = −₹35.
  5. Units = 2 lots × 500 = 1,000.
  6. Loss = 35 × 1,000 = ₹35,000.

Answer: Trader 1 earns a profit of ₹54,000. Trader 2 incurs a loss of ₹35,000 because the price rose against the short position.

Exam tips

  • Read the question for the word 'risk-free' or 'arbitrage'. Then compute fair price first, before anything else.
  • Always check whether the question wants simple or continuous compounding. Use the form the question implies.
  • Show the full cash flow table at expiry. Examiners award marks for each leg: loan repayment, spot delivery, futures settlement.
  • In spread questions, write the gain or loss of each leg separately and then the net figure.
  • End with a one-line recommendation. SFM answers are marked on the decision as well as the working.

Practice questions from Forwards and Futures

Speculation and Arbitrage Using Futures in other exams

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

Speculation and Arbitrage Using Futures: frequently asked questions

What is cash and carry arbitrage?

It is used when futures are priced above fair value. You borrow money, buy the asset in the spot market and sell futures. At expiry you deliver the asset, repay the loan and keep the difference as a risk-free profit.

What is reverse cash and carry arbitrage?

It is used when futures are priced below fair value. You sell the asset (short or from holdings), invest the proceeds at the risk-free rate and buy futures. At expiry you take delivery and cover the position, keeping the gain.

How do I calculate profit on a futures position?

Use (sell price − buy price) × lot size × number of lots. A positive answer is a profit. For a short, the sell price is the entry price.

What is a calendar spread in futures?

It is buying one expiry month and selling another on the same underlying. Your result depends on the change in the price gap between the two contracts, not on the direction of the market.