Arbitrage
Also written Arbitrage opportunity · Arbitrage trade
Simultaneously buying and selling an asset, or a replica of it, in different markets to profit from a price discrepancy — a trade that aims to lock in a profit rather than bet on direction.
In plain language
If the same thing sells for two prices at the same moment, buy it where it is cheap and sell it where it is dear. That is arbitrage.
The workbook defines it in three places, each adding something:
- Chapter 1 — a deal that produces profit by exploiting a price difference in a product in two different markets.
- Chapter 3 — a deal that produces risk-free profits by exploiting a mispricing in the market.
- Chapter 3, later — the simultaneous purchase and sale of an asset or replicating asset to profit from discrepancies in their prices.
The word "replicating" is what makes arbitrage central to derivatives. A futures contract and "buy the stock today and carry it" are two routes to the same position. If they are priced differently, arbitrage is possible.
Such opportunities do not last. The moment arbitrageurs spot one, they trade on it — buying in the cheap market pushes that price up, selling in the dear market pushes that price down — and the gap closes. In an efficient market, arbitrage opportunities exist only briefly, or not at all.
How it works
The workbook names three types in the futures market:
| Type | Position | Triggered when |
|---|---|---|
| Cash and carry | Long cash, short futures | Futures price above fair price |
| Reverse cash and carry | Long futures, short cash | Futures price below fair price |
| Inter-exchange / inter-market | Same contract, two exchanges | Same contract priced differently on two exchanges |
Inter-market example from Chapter 3: August futures on stock Z trade at Rs 101 on NSE and Rs 100 on BSE — buy on BSE, sell on NSE, and reverse when the gap closes.
Why it matters to the market. Hedgers want to shed risk and traders take it on; arbitrageurs establish an efficient link between different markets. Their trading keeps futures prices aligned with the underlying, and the liquidity they bring means better price discovery, lower transaction costs and less manipulation.
It is not truly riskless. The workbook lists the risks: a time lag between the two legs; one leg failing to execute in an illiquid market, leaving a naked exposure; and unwinding risk where contracts are not cash settled. Practically, arbitrage is undertaken only if it gives a net cash inflow after transaction costs, brokerage and margin deposits.
A worked example
The workbook's end-of-day example (Chapter 3, section 3.9):
| Cash market price | Rs 100 |
| May futures price | Rs 110 |
| Lot size | 50 |
The arbitrageur buys in the cash market at 100 and sells one lot of futures at 110, locking in Rs 10 per share. Because futures converge to the spot price at expiry, the outcome does not depend on where the price ends.
Expiry price Rs 108:
Cash: buy 100, sell 108 → +8
Futures: sell 110, buy 108 → +2
Total = Rs 10 per share → 10 × 50 = Rs 500 for the lot
Expiry price Rs 95:
Cash: buy 100, sell 95 → −5
Futures: sell 110, buy 95 → +15
Total = Rs 10 per share → 10 × 50 = Rs 500 for the lot
Same Rs 500 either way. The workbook adds that transaction costs, impact cost, brokerage and STT are ignored here — in real life they must be deducted, and they may consume the gap entirely.
Why NISM asks about it
Chapter 1, section 1.4, introduces arbitrageurs among the three market participants and a sample question asks for arbitrage by description. Chapter 3, sections 3.7 and 3.9, ties arbitrage to the cost of carry model, no-arbitrage bounds and the three arbitrage types. Chapter 5, section 5.1, works cash-and-carry, reverse cash-and-carry and calendar spread arbitrage with numbers, and section 5.3 covers arbitrage using put-call parity.
Common exam traps
- Arbitrage is simultaneous. Buying today and selling next week is a directional trade, not arbitrage.
- Arbitrageurs lock in profit; traders run naked positions. The workbook contrasts the two explicitly.
- Arbitrage removes the mispricing that creates it. An answer saying arbitrage opportunities persist in an efficient market is wrong.
- Futures above fair value → cash and carry; below → reverse cash and carry. This pairing is examined constantly.
- "Risk-free" is the textbook ideal. The workbook itself lists execution lag, illiquid legs and costs as real risks.
Where this is taught
- Series XVI · Chapter 5: Uses of Commodity Derivativesintroduced here
- Series XXI-B · Chapter 5: Derivativesintroduced here
- Series XXI-A · Chapter 5: Derivativesintroduced here
- Series VIII · Chapter 1: Basics of Derivativesintroduced here
Related terms
- ConvergenceThe certainty that a futures price and the spot price of its underlying meet at expiry — because on the last trading day the contract settles at the cash market price, leaving no room for a difference.
- Cost of carryThe cost of holding an asset until a future date — financing interest plus storage, less any income it pays. It links spot to futures: fair futures price = spot + cost of carry − inflows.
- Cash and carry arbitrageBuying the underlying in the cash market and simultaneously selling futures when futures trade above their fair price, carrying the asset to expiry to lock in the mispricing.
- Naked positionA long or short position in a futures contract held without any position in the underlying asset or an offsetting contract — fully exposed to price moves in one direction.
- No-arbitrage boundsThe band around the fair futures price, created by transaction costs, taxes and margins, within which a mispricing is too small to arbitrage profitably — so prices can sit there undisturbed.
- Reverse cash and carry arbitrageSelling the underlying in the cash market and simultaneously buying futures when futures trade below their fair price — the mirror image of cash and carry, and it needs stock to sell.
- Convergence TradeA relative-value trade that buys relatively under-valued bonds and sells relatively over-valued ones, betting their prices converge. The gaps are tiny, so profits need heavy leverage — LTCM's undoing.
- BubbleIn Kindleberger's description, a sharp, continuous rise in an asset's price in which early gains create expectations of further rises and draw in speculators seeking trading profits.
- Law of one priceThe principle that identical assets cannot trade at different prices in two markets, beyond the transaction costs between them — because arbitrageurs would close the gap.
- Put-call parityThe arbitrage-free relationship binding a European call and put of the same strike and expiry to the spot and the discounted strike: c + X·e^(−rt) = p + S. Deviations create risk-free profit.
- Interest rate parityThe principle that a currency pair's forward or futures price differs from spot by the two currencies' interest rate differential, so borrowing in one and lending in the other earns no riskless profit.
- Triangular arbitrageExploiting a misalignment among three exchange rates by converting currency A to B, B to C and C back to A, ending with more of A than you started with.
- Carry tradeBorrowing in a currency with low interest rates and investing the money in assets of a currency with high interest rates, to earn the interest rate differential.
- Arbitrage fundA mutual fund that buys in the cash market and simultaneously sells in the futures market to lock in the price difference, giving low NAV volatility similar to a liquid fund.
- Calendar spreadA long position in futures of one maturity and a short position in futures of another maturity on the same underlying. It is a bet on the price gap between the two months, not on market direction.
- Cost of arbitrageThe financing cost an arbitrageur incurs while holding a cash-and-carry position until expiry, which reduces the gross arbitrage profit to the net gain actually earned.