Limits to Arbitrage

The textbook argument for efficient prices is a threat: if a security is mispriced, someone will trade against it until it is not. The argument quietly assumes that the someone has unlimited capital, an infinite horizon, no borrowing costs and no investors. Real arbitrage is done by levered funds that mark to market daily, post margin to a prime broker, borrow shares from a lender who can recall them, and send quarterly statements to clients who redeem after bad quarters. Each of those is a lever the mispricing can pull to push the arbitrageur out. That is the whole subject.

The cleanest example: 3Com and Palm

On 2 March 2000, 3Com sold about 5% of its subsidiary Palm in an IPO and announced that the remaining shares would be distributed to 3Com shareholders later that year, at a ratio of 1.5 Palm shares per 3Com share. So a 3Com share was a claim on 1.5 Palm shares plus 3Com's own profitable networking business plus roughly $10 a share of cash.

Palm closed its first day at $95.06. So the Palm stake alone was worth

$1.5 \times 95.06 = 142.59$

per 3Com share. 3Com closed the same day at $81.81. Subtract, and the market was valuing everything else 3Com owned — the operating business, the cash — at

$81.81 - 142.59 = -60.78$

per share. Minus sixty dollars. Not a modelling assumption, not a discounted-cash-flow disagreement: arithmetic on two closing prices, with a distribution ratio that had been announced in writing.

The trade is obvious — buy 3Com, short 1.5 Palm, wait for the spinoff — and it did not get arbitraged away for months. The reason is mechanical. Only 5% of Palm's shares were floating, so there were almost no shares to borrow. Borrow costs on Palm ran to tens of percent annualised, locates vanished, and lenders could recall at will. The mispricing was not a failure of arithmetic. It was a shortage of borrow.

Performance-based arbitrage: losing money at the best moment

Shleifer and Vishny's core insight is that arbitrage capital is not the arbitrageur's own. It is other people's, and it is withdrawn on the basis of recent returns — which means it drains away exactly when the opportunity is largest.

Work through the mechanics. A fund has $100m of equity and runs a convergence book: $500m long the cheap leg, $500m short the rich leg, so $1bn gross at ten times equity. The prime broker requires 10% of gross as margin, which is exactly what the fund has. The spread is 5% wide, and the fund believes it converges to zero.

The spread widens to 8% instead. That is 3% on $500m of paired exposure, a $15m loss, or 15% of equity. Now:

• Equity is $85m, and at a 10% haircut that supports only $850m of gross. The fund must cut $150m of positions — selling the cheap leg and buying back the rich leg — at the widest spread it has ever seen.
• The quarter ends down 15%. Investors redeem 20% of remaining capital, another $17m. Gross must fall to roughly $680m.

The fund has been forced to shrink its book by a third while the trade got 60% more attractive. And every other fund in the same position is selling the same cheap leg into the same market, which widens the spread further. This is the loop that turned a fair-value gap into the September 1998 LTCM unwind and the August 2007 quant deleveraging.

The four frictions worth naming

• Fundamental risk. The "identical" legs are rarely identical. A merger breaks, an earnings restatement hits one leg, a relationship re-levels rather than reverts.
• Noise-trader risk. Even with a guaranteed terminal payoff, the path can go against you first. Royal Dutch and Shell were bound by a 1907 agreement splitting cash flows 60/40, so the price ratio should have been 1.5. It deviated by up to 35% for years, in both directions, and only converged when the companies formally merged in 2005 — decades after the trade first looked free.
• Implementation costs. Borrow fees, short recalls, locates, financing spreads, and the plain fact that the cheap leg is usually cheap because it is illiquid.
• Horizon and agency. The manager's horizon is the investor's redemption notice period, not the trade's convergence time.

In interviews

Use Palm/3Com: the numbers are unarguable and the explanation is borrow, not behaviour. Then give the general mechanism — arbitrage capital is levered, marked to market and redeemable, so it shrinks precisely when spreads are widest, and the resulting forced selling widens them further. Close by naming the four frictions and the practical implication: a mispricing that persists is telling you something about the cost of holding it, and your job is to find out what.