Limits to arbitrage

The last chapter showed that people make the same mistakes in the same direction, and that this can push prices away from what things are worth. But there was always a comforting answer to that. Milton Friedman gave it in the fifties: if some traders push prices to silly levels, smart traders will bet against them, make money, and push prices back. The silly ones lose money and eventually disappear. Wrong prices cannot last.

It is a beautiful argument and it is wrong, and the two papers in this chapter explain why. They are, for anyone who manages a family’s money, two very important papers, because they are not really about prices. What they are really about is money: where the money you invest comes from, and what happens on the day the people who gave it to you want it back.

De Long, Shleifer, Summers and Waldmann, 1990

Four economists, writing in the shadow of the 1987 crash, asked what happens if the traders who push prices around are not just wrong but unpredictable. Suppose a stock is trading well above what it is worth because a crowd of enthusiasts has decided it is the future. A sensible investor sees this and bets against it. Friedman says she will make money. But what if the enthusiasts get more enthusiastic next month? The price goes higher, her bet loses, and if she has borrowed money or has clients watching, she may have to close the position at a loss, right before she would have been proved right.

That is the whole paper in one paragraph, and its conclusion is unsettling. The mood of the crowd is itself a risk, and a sensible investor has to be paid for bearing it, so she attacks wrong prices timidly and only partially. Wrong prices therefore persist because correcting them is dangerous. The old trading-floor saying that the market can stay irrational longer than you can stay solvent finally had a mathematical proof. Stranger still, the paper shows the enthusiasts can survive and even do well, precisely because they bear a risk they created themselves.

The practical rule I take from it is a test I run before any position that depends on a price coming back to its senses: what happens if it first goes the wrong way by twice as much? What happens to the position, to whatever is financing it, and to the person making the decision? If the honest answer is that the position would be closed at the worst moment, then the position is too big, or the financing is too short, or I should not be in it. The paper is not against betting on mispricing. It explains why that bet is risky, and why, because it is risky, the opportunity is still there for the few who can afford to wait.

For a family the same paper contains a gift. The reason wrong prices persist is that most investors cannot wait them out. A family that truly cannot be forced to sell, that has no lenders who can call and no investors who can redeem, can collect a return that professionals have to walk past. That advantage is large. But it only exists if the family protects it. The moment it borrows against the portfolio, or commits to spending that cannot be cut, it has quietly become one of the investors who cannot wait, and the gift is gone.

Shleifer and Vishny, 1997

Seven years later Andrei Shleifer and Robert Vishny added the missing piece. In the textbook, the person who corrects wrong prices is a lone genius with her own money and unlimited patience. In reality she is a fund manager investing other people’s money, and the other people cannot see whether she is skilled. All they can see is her recent returns. So when her positions move against her, even if she is right, they take their money out, and she is forced to sell exactly when prices are most wrong and the opportunity is greatest.

Good managers know all this, of course, and they protect themselves in the only way they can. They keep more cash than they would like, so they are never forced to sell. They bet less than they believe, so a bad month does not become a phone call from a client. And they stay away from the prices that look most absurd, because those are exactly the ones that can get more absurd before they come back. Think about what that means. The most extreme mispricings, the ones with the most money in them, are the ones the smartest people leave untouched. And when a real crisis hits and prices go truly crazy, the capital that could fix them is busy being pulled out by nervous clients. The money shows up in the smallest amounts exactly when the opportunity is biggest.

The paper was published in March 1997. In September 1998 a hedge fund called Long-Term Capital Management, run by some of the smartest people in finance, including two Nobel laureates, acted out every page of it. Their positions were right, in the sense that the prices eventually converged. But they had borrowed heavily, the gaps widened first, their lenders and investors pulled back, and they were forced to sell at the worst possible prices, right before the market did what they had said it would do. Rarely has a theory been confirmed so quickly or so expensively.

What I take from it is a sentence I would put above the door of any family office: being right is not enough. You have to stay funded long enough for being right to matter. A strategy’s risk cannot be separated from the stability of the money behind it. The same trade is safe with capital that is locked up for five years and lethal with capital that can leave next month plus a loan on top.

And there are two sides to this for a family. As an investor in funds, look at who else is in the fund and on what terms, as carefully as you look at the strategy, because you can be right and still be liquidated by your neighbors. As a provider of capital, your willingness not to run in a bad year is worth money, and you should be paid for it, in lower fees, in access, in better terms. Most families give it away for nothing.

The exercise

There is one exercise from my reading that I think every family should do once a year. List every position that is either borrowed against or hard to sell, the way private equity or real estate is hard to sell. For each one, write down two dates. First, the date by which you honestly expect the investment to work out. Second, the earliest date on which the money funding it could be taken away against your will: a margin call, a loan covenant, a fund redemption, a spending need that cannot be postponed. Wherever the first date comes after the second, you have scheduled a Shleifer and Vishny accident in advance. Resize it or refinance it before the market does it for you.

What to keep

Structure comes before strategy. The right side of the balance sheet, who lent you the money and when they can ask for it back, is where survival is decided. Never fund a long wait with short money. If you borrow, borrow the amount that survives the position going the wrong way by twice as much, not the amount that works in a normal year. And avoid taking excessive loans against the portfolio: if the bet goes wrong, a margin call can force you to sell at the bottom and make the loss permanent.

Gala: it is not enough to be right. You also have to last until you are proved right. So before you take a risk, ask who can make you give it up, and when.