Basic law

What Is the Law of One Price?

The Law of One Price (LOOP) is a fundamental concept in financial economics stating that, in efficient markets and absent trade frictions, identical goods or financial instruments should trade at the same price everywhere when prices are expressed in a common currency. This principle applies to both physical commodities and financial security types²⁷. The underlying idea of the Law of One Price is that any price discrepancies for an identical asset across different markets will be quickly eliminated by the actions of market participants seeking to profit.²⁶

History and Origin

The conceptual roots of the Law of One Price can be traced back to classical economists who explored the idea of price equalization through trade. Early discussions on how prices converge across markets due to arbitrage opportunities laid the groundwork for this principle²⁴, ²⁵. Its application became particularly prominent in the context of international trade and currency exchange as global markets became more interconnected. The law is a cornerstone of various economic theory models, including purchasing power parity (PPP), which extends the concept from individual goods to baskets of goods²³.

Christopher J. Neely's 2006 review for the Federal Reserve Bank of St. Louis highlights the enduring relevance of the Law of One Price in understanding financial markets and its implications for arbitrage²².

Key Takeaways

• The Law of One Price posits that identical goods or financial assets should have the same price across different markets, assuming no barriers or costs.²¹
• Its validity is often tested in the context of arbitrage opportunities, where traders exploit price differences to make risk-free profits.²⁰
• The principle is most applicable in highly liquid financial markets with minimal transaction costs.¹⁹
• Deviations from the Law of One Price are common in real-world scenarios due to various market imperfections.

Formula and Calculation

The Law of One Price can be expressed mathematically to compare the price of an identical good or asset in two different markets, adjusting for the exchange rate between their respective currencies.

Assuming two markets, Domestic (D) and Foreign (F), and an identical good 'i':

$P_{i,D} = S \times P_{i,F}$

Where:

• (P_{i,D}) = Price of good 'i' in the Domestic market
• (P_{i,F}) = Price of good 'i' in the Foreign market
• (S) = Spot currency exchange rate (domestic currency per unit of foreign currency)

This formula implies that if the Law of One Price holds, the domestic price of a good should equal its foreign price converted into the domestic currency using the prevailing exchange rate. If this equality does not hold, an arbitrage opportunity theoretically exists.¹⁸

Interpreting the Law of One Price

The Law of One Price is a foundational concept in asset pricing and market efficiency. When the law holds, it implies that markets are highly efficient and that price discrepancies are swiftly corrected. In financial markets, this means that a security should have a single price regardless of how it is created or where it is traded¹⁷. For example, if a financial instrument can be replicated using a combination of other assets (such as a call option being replicated by a stock and a bond), the Law of One Price suggests that the price of the original instrument and the replicated portfolio must be identical.¹⁶

Hypothetical Example

Consider a hypothetical scenario involving shares of "GlobalTech Inc.," a company whose stock is listed on both the New York Stock Exchange (NYSE) and the London Stock Exchange (LSE).

• Market A (NYSE): Shares of GlobalTech Inc. trade at $100.
• Market B (LSE): Shares of GlobalTech Inc. trade at £80.
• Current Exchange Rate: $1.25 per £1.

To apply the Law of One Price, we convert the LSE price into USD:
£80 * $1.25/£1 = $100.

In this scenario, the price of GlobalTech Inc. is $100 on both exchanges when expressed in a common currency. This illustrates the Law of One Price in action, as there is no price discrepancy to exploit. If the LSE price were, for instance, £75, then converting that to USD would yield $93.75 (£75 * $1.25/£1). This would create an opportunity for an arbitrageur to buy the shares on the LSE and simultaneously sell them on the NYSE for a profit, a practice that would theoretically continue until prices converge.

Practical Applications

The Law of One Price serves as a core concept in various areas of finance and economics. In portfolio management, understanding this principle helps in identifying potential mispricings or evaluating the fairness of valuation models for complex financial instruments like derivatives. For instance, in the derivatives market, the law dictates that financial instruments with identical cash flows, regardless of their structure, should command the same price.

In international finance, the Law of One Price is the theoretical underpinning for purchasing power parity (PPP), which suggests that exchange rates between currencies should adjust to equalize the prices of a basket of goods in different countries. Deviations from the Law of One Price are frequently observed in commodity markets, yet these discrepancies often reveal insights into market frictions and global supply and demand dynamics. For example, a Reuters analysis highlighted how regional factors can lead to price disparities for seemingly identical commodities like crude oil, demonstrating instances where the Law of One Price does not strictly hold due to logistical complexities.

Li¹⁵mitations and Criticisms

While conceptually powerful, the Law of One Price frequently faces challenges in real-world application due to various market imperfections and frictions. These limitations often lead to persistent deviations from the ideal "one price" scenario. Common factors that can prevent the Law of One Price from holding include:

• Transaction Costs: Brokerage fees, taxes, and other expenses associated with buying and selling assets can make arbitrage unprofitable, even if price differences exist.
• ¹⁴Transportation Costs: For physical goods, the cost of moving them between locations can create price differentials.
• Trade Barriers: Tariffs, quotas, and other governmental restrictions on trade can artificially inflate prices in certain markets.
• Information Asymmetry: Differences in access to information or the speed at which it disseminates can hinder rapid arbitrage.
• ¹³Quality Differences: Even seemingly identical goods may have subtle quality variations, branding differences, or warranty distinctions that justify price discrepancies across regions.
• ¹²Market Structure: Variations in the number of buyers and sellers, or the degree of competition within a market, can influence pricing power and lead to price dispersion.

Empirical studies frequently show that the Law of One Price does not strictly describe most markets, even as a rough approximation, particularly when considering international trade in diverse goods. The F¹⁰, ¹¹ederal Reserve Bank of St. Louis, for example, explores why prices for identical goods can differ across regions, citing factors beyond basic equilibrium forces.

Law of One Price vs. Arbitrage

The Law of One Price and arbitrage are deeply interconnected concepts in finance, but they describe different aspects of market behavior.

The Law of One Price is an economic principle that states that identical goods or financial instruments should trade at the same price in different markets, assuming no transaction costs or trade barriers. It's a theoretical ideal, suggesting that if all conditions are perfect, there should naturally be a single price for identical items.

Arb⁹itrage, conversely, is the practical act of exploiting deviations from the Law of One Price. It involves simultaneously buying an asset in one market where its price is lower and selling it in another market where its price is higher, thereby earning a risk-free profit. Arbitrageurs' actions are the primary mechanism through which the Law of One Price is enforced in real-world markets. When arbitrage opportunities arise, traders step in, increasing demand in the cheaper market and increasing supply in the more expensive market. This activity pushes prices towards convergence, ultimately eliminating the arbitrage opportunity itself.

There⁷, ⁸fore, while the Law of One Price describes a state of affairs (identical prices), arbitrage is the process or activity that drives markets towards that state. The existence of profitable arbitrage opportunities is, by definition, a violation of the Law of One Price, and the pursuit of these opportunities by market participants helps to restore the law's theoretical condition.

FAQs

What are the key assumptions behind the Law of One Price?

The Law of One Price relies on several key assumptions, including the absence of transaction costs (like brokerage fees or taxes), transportation costs, and trade barriers (such as tariffs or quotas). It also assumes free competition, perfect information, and immediate price flexibility across markets.

W⁵, ⁶hy doesn't the Law of One Price always hold true in practice?

The Law of One Price often doesn't hold perfectly in the real world because the ideal conditions it assumes are rarely met. Real-world markets have transaction costs, transportation expenses, trade restrictions, information lags, and other frictions that can create and sustain price differences for identical goods or assets.

H⁴ow is the Law of One Price related to financial markets?

In financial markets, the Law of One Price implies that financial security with identical future cash flows or payoffs should trade at the same price, regardless of how they are created or packaged. This principle is fundamental to the valuation of complex instruments like derivatives, where equivalent synthetic positions should match the price of the actual instrument.

W³hat is the connection between the Law of One Price and Purchasing Power Parity (PPP)?

The Law of One Price is a building block for Purchasing Power Parity (PPP). While the Law of One Price applies to a single, identical good, PPP extends this concept to a basket of goods and services. PPP suggests that exchange rates should adjust so that the same basket of goods costs the same in different countries when converted to a common currency, essentially being a broader application of the Law of One Price to overall price levels and international trade.

H²ow do deviations from the Law of One Price create opportunities for investors?

Deviations from the Law of One Price create arbitrage opportunities for investors. If an identical asset is priced differently in two markets, an investor can buy it where it's cheaper and sell it where it's more expensive, earning a risk-free profit. These actions, in turn, help to bring prices back into alignment, contributing to market efficiency.¹