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Limits to Arbitrage and the 100 Dollar Bill on the Ground

The efficient market hypothesis suggests that whenever mispricing occurs, rational traders get an opportunity for low-risk profit.

Riskless profit opportunities do not exist, or only for a noticeably short time because arbitrage will eliminate them. Similarly, you can assume that there are no 100-dollar bills on the pavement, or only for a very short time because someone will pick them up.

But what if the best 100-dollar bills collectors (such as the arbitrageurs) are limited in their movements? It might become way more difficult to fully exploit this huge profit opportunity, and thus the bill (or part of it) will stay longer on the pavement.




Limits to arbitrage describe how these rational traders are constrained as to how much they can profit from mispricing in the market.

Lamont & Thaler (2003) ask if “the market can add and subtract”, and the answer is a clear NO. Their paper focuses on equity carve-outs of US technology stocks.

An equity carve-out, also known as a partial public offering, is defined as an IPO for shares in a subsidiary company. The subsidiary firm raises money by selling shares to the public and then typically giving some or all of the proceeds to its parent.

The stub value represents the implied stand-alone value of the parent company's assets without the subsidiary, a projection of what the company will be worth after it distributes these shares.

In the popular case of Palm and 3Com, after the first day of trading, the stub value of 3Com, representing all non-Palm assets and businesses, was estimated to be negative $63, a total of negative $22 billion. Since stock prices can never fall below zero, a negative stub value is highly unusual.


Several patterns are noted, such as stubs starting negative and gradually getting closer to zero (eventually becoming positive), and that market forces act to mitigate the mispricing, but slowly.

In theory, arbitrageurs would buy the parent company and short the subsidiary. However, in practice, we saw that the mispricing persisted because shorting costs for arbitrageurs were too high to be able to make a profit from correcting the mispricing.

This phenomenon is called the “carve-out puzzle” and represents a major example of a limit to arbitrage: short-sale constraints.

Shleifer and Vishny (1997) investigate another possible limit to arbitrage: PBA (Performance Based Arbitrage).

When the arbitrageur manages other people's money, and these people do not know or understand exactly what he is doing, they will only observe him losing money when prices diverge.

They may therefore infer from this loss that the arbitrageur is not as competent as they previously thought, refuse to provide him with more capital, and even withdraw some of the capital (even though the expected return from the trade has increased).

When arbitrage requires capital, arbitrageurs can become most constrained when they have the best opportunities, i.e., when the mispricing they have bet against gets even worse. Moreover, the fear of this scenario would make them more cautious when they put on their initial trades, and hence less effective in bringing about market efficiency.

This article argues that these features of arbitrage (short sale constraints and Performance-Based Arbitrage) can significantly limit its effectiveness in achieving market efficiency.

In conclusion, you can still be able to pick the 100-dollar bill from the ground (or at least part of it), but a good knowledge of your limits can always be useful.

 

 

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