3. The limits of arbitrage: why a wrong price stays wrong

Level 8: What is priced in and what is not

We come to the module that most changes the way you look at the market. Up to here the discussion has been about whether the price contains the information. Now the question is a different and far more practical one: assuming the price is clearly wrong and that you know it, who corrects it, with whose money and for how long. The answer explains why obvious deviations survive for years in front of thousands of professionals.

Spotting the error is the easy part

In textbook theory, arbitrage is instantaneous, riskless and requires no capital: if two equivalent things trade at different prices, someone buys the cheap one, sells the dear one and takes the difference without being exposed to anything. That figure barely exists in reality.

Andrei Shleifer and Robert Vishny described in 1997 how arbitrage really works: it is not carried out by an anonymous crowd with unlimited resources, but by a small number of specialists managing other people's money, with limited capital, a limited horizon and answering to clients who judge on short-term results. As soon as you replace the ideal arbitrageur with that real arbitrageur, the conclusion changes completely.

Betting against a price costs money every day

Going against an overvaluation normally requires short selling, and short selling is not symmetrical with buying:

• You have to borrow the stock and pay for it. In a stock heavily in demand from short sellers, that borrow fee can be several percentage points a year, and in extreme cases tens of points.
• The lender can recall the stock whenever they like. Your position can be closed out just before you are proved right, with no decision of yours involved.
• The collateral grows when the price rises. If the share goes up, you are required to post more money to keep the position, which is to say more capital is demanded precisely when things are going worst.
• The potential loss has no ceiling. Buying, you can lose what you invested; short selling, there is no upper limit to the price.

Do the arithmetic. If the stock borrow costs 20% a year and the overvaluation takes two years to correct by 30%, you got the analysis right and you lost money. Being right late is indistinguishable from being wrong.

The risk of the deviation getting worse

Even if a price is wrong, nothing guarantees the next move is toward value. It can move further away, and for a long time. For an investor trading their own money with no deadline that is uncomfortable; for a leveraged professional it is lethal, because the interim loss triggers collateral demands forcing them to sell part of the position. And in selling, they push the price even further from value.

It is a self-reinforcing mechanism: the wrong price generates losses for whoever tries to correct it, and those losses force trades that widen the error. That is why deviations do not close smoothly, but tend to hold and then close all at once.

The money leaves exactly when the opportunity arrives

This is Shleifer and Vishny's subtlest contribution, and it is worth taking slowly. The manager exploiting deviations invests clients' money. The clients do not observe the deviation: they observe the fund's result. If the deviation widens, the fund loses, and the clients withdraw capital.

Note the perversity of the sequence: the opportunity is greatest exactly at the moment the deviation is widest, and that is exactly the moment when the manager has his money taken away. Instead of buying more cheaply, he has to sell. The corrective force weakens just when it is most needed, and sometimes it turns into an amplifying force.

Hence a conclusion that runs against intuition: the bigger and more obvious a pricing error is, the less capacity professional capital has to correct it, because big errors come with big losses and big redemptions.

Two identical assets, two prices, for years

The classic example is dual-listed companies. One and the same corporate group listed in two places under two companies, with the economic rights split in a fixed and known proportion. If the theory held, the two quoted prices would respect that proportion precisely.

In practice they did not. In the most studied case, that of a large Anglo-Dutch oil group, the deviation from the theoretical proportion reached tens of percentage points and persisted for years, until the corporate unification ended the problem by legal means, not market ones. It was no secret: the deviation was published and discussed in the academic literature. It was still there because closing it required tying up capital for an indefinite period while enduring it getting worse before it got better.

Something similar happened with the partial flotation of a technology subsidiary in the year 2000: for months, the market value of the stake the parent retained exceeded the market value of the whole parent, which implied the rest of the business was worth less than zero. The practical impossibility of borrowing the subsidiary's shares stopped anyone correcting the absurdity.

Real case: 1998

The fund Long Term Capital Management brought together first-rate traders and two Nobel laureates, and applied exactly this strategy: spot small deviations between near-equivalent assets and multiply them with very high leverage. For four years it worked brilliantly.

In 1998, after the Russian crisis, the deviations the fund was exploiting widened instead of closing. With leverage on the order of twenty-five to one, a small adverse move was enough to destroy the capital: the fund lost around 90% of its value in a matter of months and a rescue had to be organized, coordinated by the New York Federal Reserve among a group of large banks, for a figure close to 3.6 billion dollars.

The devastating part of the case is this: a good share of those positions would eventually have been profitable. The analysis was not wrong. What was missing was time and capital to see it through.