The law of One Price

BENEL D. LAGUA

In traversing the world of finance, it is not unusual to encounter terminologies and terms exclusively used by finance practitioners and economists which may confuse the man on the street. Allow me to share some of these concepts in a series of columns with the end view of breaking some myths finance people impose on the ordinary investor.

Let me start with this simple but powerful concept, the law of one price. Disciplines such as mathematics, physics and chemistry are characterized by well-defined laws. Economics has its share, and many are familiar with the law of supply and demand. Economists claim that not too far behind is the concept of “law of one price”.

Simply put, in competitive markets, identical goods must have the same price. An ounce of gold in Davao must have the same price as in Manila, because if there is disparity, the opportunists will move from one city to another to take advantage of price differential. What makes the law of one price to happen is arbitrage, a powerful idea in finance. Arbitrage is the purchase and immediate sale of equivalent assets in order to earn a sure profit from a difference in their prices.

In capital markets, identical securities with clearly the same payoffs must have identical prices. Otherwise, smart investors could make unlimited profits by buying the cheap one and selling the expensive one. The law of one price is enforced not by external parties, but by selfish profit motives. Decision makers are assumed to be rational agents with stable and well-defined concepts of risk and return.

The law of one price is a fundamental valuation principle. Understand that the law of one price has among its assumptions the absence of trade frictions, free competition and price flexibility. If the observed prices violate the law, we should suspect that something is interfering in the operations of the competitive market. Another possible reason is that there may be some differences, even if subtle and understated, between the assets. These so-called limits to arbitrage will derail the function of a competitive market.

The law of one price is illustrated in purchasing power parity, the concept that in the long run, exchange rates should adjust so that the price of an identical basket of tradeable goods is the same. The exchange rate between two countries is equal to the ratio of the currencies’ purchasing power. Stated differently, the difference in the rate of change in prices between two countries, or the difference in inflation rates, is equal to the change in depreciation or appreciation of the currencies.

A lighthearted guide to purchasing power parity is the Big Mac index created by the magazine “The Economist” 32 years ago. According to burgernomics, the difference in local prices for the standard Big Mac hamburger can suggest what exchange rate should be and how much a currency is under- or over-valued relative to another. Of course, one cannot buy all the cheap Big Macs in Manila and bring them over to say, Singapore, to take advantage of price differentials. There are too many barriers to arbitrage for a perishable like cost of travel, freshness of the burger, etc.

Still, three decades of the exercise shows it at least makes sense in principle. Since no two distinct assets are identical in all respects, we need to find assets that are comparable to the one we want to value. We can then use the logic of the law of one price to doing a valuation by comparables, which means the asset should have relative value in relation to other assets in its class.

Just like in equivalent assets, discrepancies in value give rise to arbitrage opportunities. This is the bedrock of valuation models. Models are attempts to evaluate the value of an asset from information about the prices of other comparable assets. A quantitative or numerical model is then developed to infer values using market interest rates, available data, and information about the prices of comparable assets.

Some valuation models can be as simple as using the price earnings ratio (ratio of stock price to earnings per share) of a listed company and multiply it by the earnings of a comparable firm we want to value. While other models may be more complicated, the principles are the same.

Specific types of valuation models are developed for different kinds of assets and for different purposes. All we need to know is that unknown asset values can be inferred from the prices of comparable assets whose prices are known. This is the essence of the law of one price and we now know it is not a legislated law, but one that relies on competition, information and the continuous search for arbitrage opportunities by market players.

And to the astute reader and investor out there, remember that making money out of arbitrage opportunities is the way to go. The ability to value assets accurately can only come from having the right information about comparable assets.

Investors who have a good sense of misalignment between price and value have the best chance of making money in any market.

(Benel D. Lagua is Executive Vice President at the Development Bank of the Philippines. He is an active FINEX member and a long time advocate of risk-based lending for SMEs. The views expressed herein are his own and does not necessarily reflect the opinion of his office as well as FINEX.)

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