Gesetz vom einheitlichen preis

The "Gesetz vom einheitlichen preis," known in English as the Law of One Price (LOOP), is a fundamental concept in financial economics and market efficiency. It states that, in the absence of trade barriers, transaction costs, and under conditions of free competition, identical goods or financial assets should sell for the same price in different markets when expressed in a common currency.⁴⁷, ⁴⁸ This principle suggests that any price discrepancies for the same asset across markets would be quickly eliminated by market participants engaging in arbitrage.⁴⁶

History and Origin

The intellectual history of the Law of One Price can be traced back to economists in 18th-century France who applied the "law" to markets involved in international trade.⁴⁵ It was later formalized and named by William Stanley Jevons in the 19th century, who posited that "In the same open market, at any moment, there cannot be two prices for the same kind of article."⁴⁴ The intuition behind this law is deeply rooted in the concept of arbitrage, where traders exploit price differences by buying an asset in a cheaper market and simultaneously selling it in a more expensive one, thereby driving prices toward convergence. The Federal Reserve Bank of San Francisco has revisited this concept in various economic letters, exploring its implications for international price convergence and exchange rates.⁴³

Key Takeaways

• The Law of One Price posits that identical goods or assets should have the same price across different markets, assuming no frictions.⁴²
• Arbitrage is the primary mechanism that enforces the Law of One Price, as traders eliminate price discrepancies for risk-free profit.⁴¹
• It serves as a foundational concept for theories such as purchasing power parity and is central to discussions of market efficiency.³⁹, ⁴⁰
• Real-world factors like transaction costs, trade barriers, and imperfect information often lead to deviations from the Law of One Price.³⁷, ³⁸
• The principle is widely applied in financial markets for pricing derivative securities and assessing asset pricing.³⁵, ³⁶

Formula and Calculation

The Law of One Price can be expressed mathematically when considering two markets with different currencies. For an identical good or asset, its price in one currency, when converted to another currency using the prevailing exchange rates, should equal its price in that second currency.

Let:

• (P_A) = Price of the good/asset in Market A (in Currency A)
• (P_B) = Price of the good/asset in Market B (in Currency B)
• (S_{A/B}) = Spot exchange rate (units of Currency A per unit of Currency B)

The Law of One Price states:

$P_A = P_B \times S_{A/B}$

This formula implies that if you convert the price of the good in Market B to Currency A using the spot price of the exchange rate, it should be identical to the price of the good in Market A.

Interpreting the Gesetz vom einheitlichen Preis

The Gesetz vom einheitlichen Preis suggests a theoretical ideal where markets are perfectly integrated and efficient. In such a scenario, any deviation from this price equality would immediately present an arbitrage opportunity, which rational market participants would exploit. The rapid actions of these arbitrageurs, buying in the cheaper market and selling in the more expensive one, would cause supply and demand to shift, pushing prices back into alignment.³³, ³⁴

The extent to which this law holds in practice is often used as a measure of a market's efficiency and integration. When evaluating financial markets, the Law of One Price is interpreted as a benchmark against which actual pricing discrepancies are measured. Significant and persistent deviations often indicate market inefficiencies, transaction costs, or other barriers preventing the free flow of goods or capital.

Hypothetical Example

Consider a hypothetical scenario involving the trading of a standardized gold bar.

• In Market X, a gold bar is priced at €1,900.
• In Market Y, an identical gold bar is priced at $2,050.
• The current foreign exchange rate is €1 = $1.08.

According to the Law of One Price, if you convert the price of the gold bar from Market Y to euros:
$2,050 / $1.08 per €1 = €1,898.15 (approximately)

Here, the price in Market X (€1,900) is slightly higher than the converted price from Market Y (€1,898.15). An arbitrageur, observing this small discrepancy, could theoretically:

1. Buy the gold bar in Market Y for $2,050.
2. Immediately sell it in Market X for €1,900.
3. Convert the €1,900 back to dollars: €1,900 * $1.08/€1 = $2,052.

This would yield a small gross profit of $2,052 - $2,050 = $2 per gold bar, assuming no transaction costs or other fees. Such arbitrage activities, if easily executed, would increase demand in Market Y and supply in Market X, quickly narrowing the price difference until the Law of One Price holds.

Practical Applications

The Law of One Price is a cornerstone in various fields of finance and economics:

• International Trade and Finance: It forms the theoretical basis for understanding exchange rates and the concept of purchasing power parity, which compares the relative value of currencies based on the prices of a basket of goods. When the Law of One Price holds, it implies that the real cost of a good is the same across countries.
• Arbitrage Opp³²ortunities: In financial markets, the Law of One Price is crucial for identifying potential arbitrage opportunities. Traders constantly monitor for deviations in the prices of identical securities or commodities across different exchanges, especially in liquid markets like futures contracts, to execute simultaneous buy and sell orders for a risk-free profit. This is fundamental²⁹, ³⁰, ³¹ to the operation of many sophisticated trading strategies.
• Derivative Pricing: The principle is widely applied in the pricing of derivative securities. If two different financial instruments generate the same future cash flows, the Law of One Price dictates they must trade at the same price today, or an arbitrage opportunity would exist. This underpins mode²⁸ls for options and other complex financial products.
• Commodity Markets: In global commodity markets, the Law of One Price helps analyze price relationships between various locations. However, real-world factors like shipping costs and trade barriers can lead to deviations. For instance, global shipping rates can significantly influence commodity prices across different regions, impacting how closely the Law of One Price holds for physical goods. An article by Reute²⁶, ²⁷rs highlighted how global shipping rates can keep food prices in the spotlight due to increased freight costs.

Limitations and²³, ²⁴, ²⁵ Criticisms

While the Gesetz vom einheitlichen Preis is a powerful theoretical concept within financial economics, it faces several practical limitations and criticisms that cause real-world deviations:

• Transaction Costs and Trade Barriers: The most significant factors that prevent the Law of One Price from holding perfectly are transaction costs, such as transportation, tariffs, taxes, and other trade barriers. These costs can mak²¹, ²²e arbitrage unprofitable, allowing price differences to persist.
• Non-Homogeneous Goods: The law assumes identical goods. In reality, even seemingly similar products can differ in quality, branding, warranties, or local market preferences, which justifies price differentials.
• Information A¹⁹, ²⁰symmetry: Perfect information is rarely available. Buyers and sellers may not have immediate or complete knowledge of prices in all markets, limiting the effectiveness of arbitrage and allowing price disparities.
• Market Imperfections: Real markets are seldom characterized by perfect competition. Monopolies, oligopolies, or government interventions can lead to price manipulation or rigidities, preventing prices from freely adjusting.
• Currency Fluc¹⁸tuations: Volatile exchange rates can introduce risk and complexity, making it challenging to maintain consistent prices across borders, even for identical goods.
• Limits to Arb¹⁷itrage: Even when theoretical arbitrage opportunities exist, practical limits such as funding costs, liquidity constraints, and "noise trader risk" can prevent sophisticated traders from fully exploiting them, allowing mispricings to persist. The New York Times ¹⁵, ¹⁶has discussed how market anomalies can persist despite the theoretical opportunity for arbitrage.

Gesetz vom einh¹³, ¹⁴eitlichen Preis vs. Arbitrage

The Law of One Price and arbitrage are inextricably linked concepts, but they are not interchangeable.

• The Law of One Price is a principle or condition that describes an idealized market state. It states that if certain conditions (no transaction costs, free competition, identical goods) are met, then identical assets or commodities should have the same price across different markets when converted to a common currency. It is a theoretical benchmark in economic theory.
• Arbitrage is the mechanism or activity by which market participants exploit violations of the Law of One Price. It involves simultaneously buying an asset in a market where it is cheaper and selling it in another market where it is more expensive to make a risk-free profit. The actions of arbi¹²trageurs, driven by the profit motive, force prices to converge towards the state predicted by the Law of One Price.

In essence, the La¹¹w of One Price describes what should happen in an efficient market, while arbitrage describes how it happens (or attempts to happen) when that condition is not met. If the Law of One Price holds perfectly, there are no arbitrage opportunities. Conversely, the existence of arbitrage opportunities implies a violation of the Law of One Price.

FAQs

What ¹⁰are the key assumptions of the Law of One Price?

The primary assumptions are the absence of transaction costs (like transportation, tariffs, taxes), free and perfect competition, identical goods or assets, and no legal restrictions or barriers to trade.

Why is the Law⁸, ⁹ of One Price important in financial markets?

It's important because it serves as a foundational concept for pricing financial instruments, especially derivative securities, and for understanding how arbitrage opportunities can lead to market efficiency. It helps identify m⁶, ⁷ispricings that, in theory, should not persist.

Does the Law of One Price hold true in the real world?

Generally, no, not perfectly. While it's a useful theoretical benchmark, real-world markets are subject to various frictions like transportation costs, trade barriers, taxes, and imperfect information, which lead to deviations. However, in highly ⁴, ⁵liquid and efficient financial markets with low transaction costs, it tends to hold more closely.

How does infla², ³tion affect the Law of One Price?

Inflation itself doesn't directly invalidate the Law of One Price, but differences in inflation rates between countries can cause exchange rates to adjust over time, which in turn influences whether the Law of One Price appears to hold for internationally traded goods. Sustained inflation differentials can lead to deviations from purchasing power parity, a concept related to the Law of One Price.¹