econ HW: the law of one price, can it survive the real world?

The law of one price (from wikipedia):

The law of one price is an economic law stated as: “In an efficient market, all identical goods must have only one price.”

Intuition

The intuition for this law is that all sellers will flock to the highest prevailing price, and all buyers to the lowest current market price. In an efficient market the convergence on one price is instant.

An example: Financial markets

Commodities can be traded on financial markets, where there will be a single offer price (asking price), and bid price. Although there is a small spread between these two values the law of one price applies (to each). No trader will sell the commodity at a lower price than the market maker’s offer-level or buy at a higher price than the market maker’s bid-level. In either case moving away from the prevailing price would either leave no takers, or be charity.

Does the law of one price make sense? Your book describes why this idea might not hold in reality. How significant are these potential reasons why it might not hold? Explain your answer, as well as the implications for the economy.

The law of one price (hereafter LOP) makes perfect sense as a theoretical construct and as a thought exercise. The text points out a few cases, services and not-perfectly-substitutable items, where it demonstrates weakness. However, a look around the real world paints a more complex picture of its strengths and weaknesses as an explanatory tool.

In certain cases, such as markets for discrete securities or commodities, which are highly equalized among participants with regards to information, transactional speed and the number of market makers, The LOP demonstrates robust consistency. In such markets as these, even the exceptions prove the rule. The first electronic stock trading system (SOES, or Small Order Execution System) created on the NASDAQ exchange in the wake of the 1987 stock market crash became a literal proving ground for the law of one price in the market for stocks. As a new innovation created to re-instill faith in the markets after many small stock traders were burned by market makers ignoring frantic phone calls from investors as their investments went up in smoke, the trading houses were required to honor orders of up to 1000 shares of stock per order placed through the new trading system. Using this new system, a new generation of arbitrageurs began to use the newly decreased time required to trade to visit harsh consequences on the complacent market makers. When one trading house was slow to update a stock price, say from $20.15 to $20.35 per share, the new trading houses using the system would immediately flood the seller with orders for 1000 shares at a time, hold them until the market settled at the price the other market makers had moved to and then resell for a quick $400 each. First dozens, then thousands of day traders began making hundreds of thousands of dollars a year with this new strategy.

These “SOES Bandits” as they were called, turned the sleepy, clubby world of phone and open outcry based stock trading on its head and proved a rigorous exercise in arbitraging away exceptions to the LOP. Today, “high speed trading” is the new SOES and the stakes are high enough for companies to spend upwards of $300 million dollars to gain land rights to tunnel a straight direct line from Chicago to literally next door to NASDAQ’s servers in New Jersey in order to shave 3 milliseconds off of the time required to execute a trade. Strands of such cable lease for over $1 million per year and can cost on the order of another $5 million dollars to put into operation. Only the speed of light is the current upper limit to the implementation of the LOP in stock trading.

However, once one moves away from this peculiar example the LOP quickly begins to fall apart.  A 2009 paper by three economists from Harvard and Yale, which had subjects allocate $1000 each across four S&P 500 indexed mutual funds, found that even though fees associated with investing in the different funds varied by more than an order of magnitude, the subjects overwhelmingly failed to seek the lowest fee funds. This was even though these funds, by their nature, simply follow a common stock index, delivering virtually identical returns.

The further one goes from the world of fully fungible financial instruments, the more poorly the LOP fares. A 2001 study of several hundred years of data on the prices of seven, fully substitutable commodities in England and Holland shows that, until price differentials reach greater than 25% to 30%, taking into account transportation and other transactional costs, fairly large price differences resist arbitrage even largely to the present day and don’t exhibit significant convergence even in the face of greatly decreased transactional costs. To take the example of wheat prices, as given hypothetically in our text, the graph below (taken from the study) shows the relationship between Shillings and Guilders as well as relative wheat prices between the two countries for a span of 600 years. Even well into the 1970s, significant price divergence is the norm rather than the exception.

This clearly shows a major breakdown in the predicted relationship between real and nominal exchange rates and the law of one price.

Conceptual frameworks such as the LOP simply cannot incorporate the incredibly messy reality of imperfect information, irrational behavior by consumers and other agents and all manner of inequitable power relationships and real world obstructions preventing effective arbitrage of even large price differences in all sorts of markets.

This past Spring I had occasion to visit Germany, Slovakia, the Czech Republic and Poland in the span of one week. There, tremendous price differences existed between perfectly substitutable and, indeed, easily transportable consumer items such as a bottle of soda or a can of beer. Such items exhibited greater than threefold price differences in most cases, even between Germany and Slovakia, who use a common currency and have virtually no effective tariff regimes on most consumer goods. These nations can all be traversed in several hours on open roadways, yet they all reflect price differences that much more accurately track their relative standards of living than anything else. While a small shop in Poland on the border of Germany might be able to arbitrage sodas and beer effectively, viewed expansively, the law of one price simply doesn’t survive the chaotic patterns of everyday life. Such learning tools can have value in understanding limited concepts, but they can just as often serve to inhibit understanding of the deeper underpinnings of market power and informational deficiencies which undergird nearly all examples of capitalism in the real world.

Sources:
Susan Antilla “Wall Street; A Small-Trade System Gone Awry” New York Times, May 30th, 1993.
http://www.nytimes.com/1993/05/30/business/wall-street-a-small-trade-system-gone-awry.html
Christopher Steiner “Wall Street’s Speed War” Forbes Magazine, September 27th, 2010.
http://www.forbes.com/forbes/2010/0927/outfront-netscape-jim-barksdale-daniel-spivey-wall-street-speed-war.html
James J. Choi, David Laibson, and Brigitte C. Madrian “Why Does the Law of One Price Fail? An Experiment on Index Mutual Funds” November 2009.
http://www.som.yale.edu/faculty/jjc83/fees.pdf
Kenneth Rogoffi Kenneth A. Froot, and Michael Kiml “The Law of One Price over 700 Years” IMF Research Dept Working Paper, November, 2001.
http://www.imf.org/external/pubs/ft/wp/2001/wp01174.pdf
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About theunlikelyeconomist

theunlikelyeconomist is in the midst of the long slog to attain a PhD in economics.
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