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Ketchup Economics and the Law of One Price – Guide Notes

November 25, 2011

Traditional finance is more concerned with checking that the price of two 8-ounce bottles of ketchup is close to the price of one 16-ounce bottle than it is in understanding the price of the 16 ounce bottle. Such is the view of Lawrence Henry (‘Larry’) Summers, currently Director of the White House’s National Economic Council, writing in the ‘Journal of Finance’ in 1985. “They have shown”, he went on, “that two quart bottles of ketchup invariably sell for twice as much as one quart bottle of ketchup except for deviations traceable to transactions costs … Indeed, most ketchup economists regard the efficiency of the ketchup market as the best established fact in empirical economics.” If so, this represents an example of the LOOP (‘Law of One Price’) principle in economics, i.e. identical goods should have identical prices.

But are they right? To find out, I checked the prices on offer at my local branch of a well-known local supermarket chain and found the following pricing structure. A 460g bottle of a leading brand of tomato ketchup was priced at £1.63, while the bigger (by 73.9%) 800g bottle sold at £2.19 (an extra 34.4%). According to the LOOP principle, one might have thought that the 800g bottle would have sold for 73.9% more than the 460g bottle, i.e. for £2.83. So is this a mispricing of 64p. Does this indicate that the market is inefficient? Well, the answer is pretty simple here. There is nothing wrong with the market, since there’s no clear way to exploit the mispricing, short of tipping the contents of the bigger bottle into the smaller bottles and selling them yourself. Summers would call this a “deviation due to transactions costs.” More fundamentally, the smaller bottle offers advantages that the larger bottle doesn’t have. Most obviously, it’s easier to store. Perhaps it also looks nicer on the table.

Trading financial assets, on the other hand, is a different issue altogether. Transactions costs are relatively small and assets trading in different markets are often identical, so in these cases one would expect the LOOP principle to more clearly apply. What’s the evidence? Well, one well-known apparent violation is the case of Royal Dutch Shell. Royal Dutch and Shell are separate legal entities but merged their interests in 1907 on a 60/40 basis. On this basis, the Royal Dutch shares should automatically have been priced at 50% more than Shell shares. However, they diverged from this by up to 15% until their final merger in 2005.

When the company 3Com spun off shares of its mobile phone subsidiary Palm into a separate stock offering, 3 Com kept most of Palm’s shares for itself. (Thaler and Lamont, 2003). So a trader could invest in Palm simply by buying 3Com stock. 3Com stockholders were guaranteed to receive three shares in Palm for every two shares in 3Com that they held. This seemed to imply that Palm shares could trade at an absolute maximum of 2/3 of the value of 3Com shares. Rather than being worth less than 3Com shares, however, Palm shares instead traded at a higher price for a period of several months. This should have allowed an investor to make a guaranteed profit by buying 3Com shares and shorting Palm – a virtual no-risk arbitrage opportunity, the equivalent of exchanging, say, $1,000 for £600 in the UK and almost simultaneously exchanging the £600 for $1,500 in the US.

How about prediction markets (speculative markets used for making predictions)? Is it possible to buy low and sell high across different prediction markets? Seems so! For an example, we need only point to the 2008 and 2012 US Presidential elections when it was for several days possible to back John McCain and Mitt Romney on the Betfair betting exchange at a healthy shade of odds against and simultaneously to do likewise with Barack Obama on the Intrade exchange. A guaranteed profit, even net of commission.

Professor Eugene Fama once defined an efficient market as one in which “deviations from the extreme version of the efficiency hypothesis are within information and transactions costs.” On this basis, there would appear to be some evidence that markets (in particular respect of the ‘Law of One Price’) are not always efficient.

 

Reading and Links

Lamont., O.A. and Thaler, R.A. (2003). Anomalies: The Law of One Price in Financial Markets. Journal of Economic Perspectives. 17, 4, 191-202.

On economics and finance. Summers, L.H. (1985). Journal of Finance, 40, 3, 633-635. http://m.blog.hu/el/eltecon/file/summers_ketchup%5B1%5D.pdf

Law of One Price. Wikipedia. https://en.wikipedia.org/wiki/Law_of_one_price

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