Law of one price
The principle that identical assets cannot trade at different prices in two markets, beyond the transaction costs between them — because arbitrageurs would close the gap.
In plain language
If the same asset sells for less in one market than another, someone can buy where it is cheap, sell where it is dear, and pocket a riskless profit. So in a working market, that gap should not last.
The workbook states the law of one price this way: two goods (assets) that are identical cannot trade at different prices in two different markets. If they did, one would buy from the cheaper market and sell in the costlier one and make riskless profits.
The buying and selling itself closes the gap: demand raises the price in the cheaper market, supply lowers it in the costlier one, until both are at the same level. Prices for the same tradable asset can differ only to the extent of transaction costs.
How it works
Who enforces it. Arbitrageurs — specialists who identify price differentials between two markets and trade in ways that reduce them (Chapter 5, section 5.4).
What counts as transaction costs. The workbook lists transportation, storage, insurance, interest costs and any other cost that affects buying and selling.
In derivatives (section 5.6). The underlying asset in the derivatives market is the same as in the cash market. But the price to buy it through a derivative can differ from the cash price because of other costs such as physical warehousing or interest. Derivative pricing takes these costs into account — so a futures price above spot is not, by itself, a violation of the law of one price.
The cash-futures arbitrage example (Chapter 18, section 18.12). Cash index at 10,000; one-month futures at 10,100. Buy in cash, sell in futures, and the ₹100 difference is locked in regardless of price movement. With 10:1 leverage, the margin is 1,010. From the gain, borrowing and transaction costs must be deducted.
Where it can fail. Chapter 14 notes that arbitrageurs face a synchronisation problem and differing incentives during bubbles, which lets mispricing persist.
A worked example
Illustrative figures. A stock trades at ₹1,000 in the cash market. Its one-month future trades at ₹1,025. A trader has access to funds at 12% a year and faces round-trip transaction costs of ₹3 per share. Lot: 500 shares.
Cost of carrying the stock for one month: ₹1,000 × 12% ÷ 12 = ₹10 per share
Arbitrage (buy cash, sell future):
| Per share | |
|---|---|
| Price gap (1,025 − 1,000) | ₹25 |
| Less interest cost | ₹10 |
| Less transaction costs | ₹3 |
| Net riskless profit | ₹12 |
On 500 shares: 500 × ₹12 = ₹6,000.
As arbitrageurs buy the stock and sell the future, the gap narrows. When the future falls to about ₹1,013 (₹1,000 + ₹10 interest + ₹3 costs), the profit disappears. That residual ₹13 difference is exactly what the law of one price allows: a gap only to the extent of transaction costs — here interest and trading costs.
Why NISM asks about it
Chapter 5 (Derivatives) states the law of one price twice — under arbitrage in section 5.4 (Purpose of Derivatives) and again in section 5.6 (Underlying concepts in derivatives) — and explains why derivative prices can differ from cash prices. Chapter 18 (section 18.12) gives the cash-futures arbitrage example. Questions test the definition and the transaction-cost qualification.
Common exam traps
- Prices can differ — but only to the extent of transaction costs. "Identical assets always trade at exactly the same price" overstates the law.
- Transaction costs include interest and storage, not just brokerage.
- Arbitrage closes the gap through demand in the cheap market and supply in the dear one.
- A futures price above spot is not automatically an arbitrage opportunity — carrying costs justify part of the difference.
- Arbitrage in this sense ≠ Arbitrage Pricing Theory. APT (Chapter 16) is a multifactor pricing model.
Where this is taught
- Series XXI-B · Chapter 5: Derivativesintroduced here
- Series X-A · Chapter 10: Understanding Derivativesintroduced here
Related terms
- Fair valueThe theoretical futures price — spot plus the cost of carrying the commodity to expiry — at which a buyer is indifferent between buying today and buying forward.
- ArbitragerA participant who locks a profit by entering opposite transactions in two markets at once — carrying no exposure and taking no view, and in the process pulling the two prices back together.
- ArbitrageSimultaneously 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.
- 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.
- Futures contractA standardised forward traded on an exchange, where the exchange fixes every term except the price and the clearing corporation guarantees settlement, so neither side carries the other's default risk.
- 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.