Law of One Price: Works for Berkshire, But Not Chipotle Mexican Grill

Arbitrage is the financial equivalent of a “free lunch”. In theory, an arbitrage is a trading strategy that requires the investment of no capital, with no risk of capital loss, and where there is some positive probability of making money.

There is a basic principle in economics called “the law of one price”. This states that identical goods should have identical prices. For example, an ounce of silver should cost the same in the New York and Paris, otherwise silver would flow from one city to the other. Of course, this law does not always hold in practice, unless there are competitive markets, no transaction costs and no trade barriers.

Economists have generally assumed that the law of one price can be applied in liquid financial markets because of the possibility of arbitrage. Unlike international trade, where it takes time and effort to move silver physically from New York to Paris, one might expect the law to hold, since you can buy and sell securities quite easily.

But in practice, there have been many violations of the law of one price with closed end funds, ADR’s, corporate spin-offs and dual share class stocks. I’d like to discuss two specific cases involving dual share classes with different voting rights—one where the law works well and one where it does not work.

Case I- Berkshire Hathaway Class A and B shares (BRKA), (BRKB) (the law works)
Berkshire Hathaway has two classes of stock- Class A and Class B. One B share has the rights of 1/30th of an A share, except that the Class B share has only 1/200th of the voting rights of a Class A share (rather than 1/30th of the vote). There is also a key provision that a Class A share is convertible at any time, at the holder’s option, into 30 shares of the Class B stock. This conversion privilege does not extend in the opposite direction. That is, Class B shares cannot be converted into Class A shares.

Because of the conversion privilege, the “rule of one price” has worked pretty well for Berkshire Hathaway shares. The Class B shares almost never sell for more than 1/30th of an A share except for extremely brief time periods. When it rises above 1/30th, arbitrage takes place where someone can buy the A and convert it into B shares, which pushes the prices back to the 1:30 ratio.

The B shares can sell at a discount from 1/30th of an A share and I have seen this discount rise as much as 6%. But most of the time, the discount is about 1% or less. Warren Buffett has said that when the B shares are at a discount of 2% or more, they offer a better buy than the A shares.

Case II- Chipotle Class A and B shares (CMG), (CMGB) (the law doesn’t work)
Chipotle Mexican Grill (CMG) had its IPO on January 27, 2006. Until late last year, the majority of the company shares were owned by McDonald's. There are two Chipotle share classes with different voting rights. The B shares have ten times the voting power of the A shares, but the two share classes are otherwise identical. In September, 2006, McDonald's distributed its 'B' shares to its shareholders, so a lot of additional B shares were added to the market float.

If the law of one price held, you would expect the B shares to sell at a premium to the A shares or at least at parity. But as I am typing this, the A shares trade at $63.97, while the B shares are at $59.78.

The key difference from the Berkshire Hathaway example is that the B shares are not immediately convertible into the A’s, so there is no forcing arbitrage. Someone who tries to arbitrage this (by going long the B’s and short the A’s) has no guaranteed time period where the gain would be realized, and the A premium over the B’s could conceivably widen even more before it narrowed again.

If I wanted to invest in Chipotle, I would definitely prefer buying the B shares to the A shares. If I owned the A shares in an IRA, I would definitely switch into the B’s. But if I owned the A shares in a taxable account, the decision to switch would depend on my tax cost basis. It may not be worthwhile to switch from the A shares to the B shares if it generates a large capital gains profit.

The Chipotle example shows that supply/demand considerations in the market often trump economic “logic”. The huge supply of Chipotle B shares that McDonald's distributed into the marketplace has caused a relatively long lasting discount in the pricing of the B shares.

Full Disclosure: I am long BRKA, but do not own CMG or CMG-B.

BRKA vs. BRKB 1-yr chart:

CMG vs. CMGB 1-yr chart: