Twice now this volume has set a middleman between two parties: the dealer between the buyer and the seller, the bank between the saver and the borrower. This plate sets one between two prices. The arbitrageur does not stand between persons who want to trade and cannot find each other, nor between persons who want to lend and to borrow and cannot trust each other; he stands between two prices for the same thing — the identical asset quoted cheap in one place and dear in another — and his whole work is to buy where it is cheap and sell where it is dear, taking the difference for himself. He is the most abstract of all the volume's intermediaries, for he deals in no good and serves no client, but only in a discrepancy between two numbers; and he is, in one light, the most admirable, for the effect of his greed is to make the two numbers agree. When he buys the cheaper, he raises its price; when he sells the dearer, he lowers its price; and he keeps buying and selling until the two have met. He enforces, by pursuing his own gain and nothing else, the law of one price — the principle that a thing can have but a single value, however many places it may trade — and his profit is the wage of that enforcement. The plate's task is to weigh that wage, and to find in it both a genuine service and two strange features that set it apart from every other price in the volume.
The law of one price is among the most fundamental principles in all of finance, and the arbitrageur is its enforcer. The law says that two claims to the very same thing must sell for the very same price, for if they did not — if the same asset were cheap in one market and dear in another — then anyone could buy it where it was cheap, sell it where it was dear, and pocket the difference at no risk, and the rush of such buying and selling would close the gap. The law holds, in other words, not as a law of nature but as a consequence of the arbitrageur's appetite: prices are equal because, the moment they are not, someone trades to make them so. So much of the architecture of modern finance rests on this principle that it is hard to overstate. The price of an option is fixed by the requirement that no riskless arbitrage exist between it and the stock it is written on; the relations among the prices of bonds, currencies, and their derivatives are pinned down by the same demand; whole theories of what assets may be worth are built on the single axiom that arbitrage is absent. And the axiom is true only because the arbitrageur makes it true — because he is always watching for the gap that the law forbids, and always ready to trade it shut. The law of one price is the arbitrageur's shadow, cast across every market he patrols.
In its pure form, the arbitrageur's trade is the nearest thing finance offers to a free lunch — a profit with no risk attached. Suppose the same share trades at a hundred in one city and a hundred and one in another. The arbitrageur buys it at a hundred and sells it at a hundred and one in the same instant, and has locked in a profit of one without ever owning the share long enough to be exposed to its price moving; the long purchase and the short sale offset, and the gain is certain. This is pure arbitrage, the riskless capture of a price discrepancy, and it is the textbook ideal of the arbitrageur's art. But its very risklessness is the reason it is so fleeting, for a certain profit lying in the open is a thing that every arbitrageur wants, and the competition to seize it is ferocious and fast. The gap is found and closed in moments, often in milliseconds; the hundred and the hundred and one become a hundred and a half on both sides, and the opportunity is gone. And it is gone because it was taken: the arbitrageur's profit destroys the very discrepancy it feeds on. He is paid for closing a gap, and once it is closed he cannot be paid again; the opportunity dies in the taking of it, and rewards him only once, for the single error he has corrected. Arbitrage is, uniquely among the trades in this volume, a thing that consumes its own occasion.
The arbitrageur profits from a gap between two prices, but his profiting closes the gap; the opportunity dies in the taking of it, and pays him only once, for the error he has cured.
That the arbitrageur consumes his own occasion is, from the market's side, precisely his usefulness. For each gap he closes is a mispricing he corrects, a place where the same thing wore two prices reduced to a place where it wears one, and the sum of all his closings is a market in which prices are consistent — in which a thing's value does not depend on which window one approaches, and the scattered quotations of an asset are reconciled into a single coherent truth. This consistency is no small thing. It is the precondition of prices meaning anything at all, for a price that differed from market to market would be no reliable signal of value but a mere local accident; and it is the mechanism by which markets earn the name of efficient, the arbitrageur's relentless pressing-together of discrepant prices being the very force that drives prices toward the values they are supposed to reflect. He performs this service, characteristically, without the least intention of performing it. He does not care whether prices are accurate or markets efficient; he cares only for the difference he can pocket. But the byproduct of his self-interest is the public good of coherent prices, and the discipline counts him, rightly, among the market's most important servants — the unpaid, or rather self-paid, agent of the efficiency that the whole edifice of finance presumes. His profit is the wage of a reconciling he never meant to do.
Yet the wage is earned in a manner worth looking at squarely, for the arbitrageur's gain is always someone else's loss, and the someone is the one who mispriced. When the arbitrageur buys the share at a hundred that is truly worth a hundred and one, he buys it from a seller who let it go too cheap; when he sells at a hundred and one a share truly worth a hundred, he sells to a buyer who paid too dear. The difference the arbitrageur pockets is drawn, to the last penny, from the pockets of those who traded at the wrong price — the mispricers whose errors he exists to correct. So arbitrage, like the informed trading of an earlier plate, is at bottom redistributive: it transfers wealth from those who get the price wrong to the one who gets it right, and the service of correction and the act of extraction are, once again, the same act seen from two sides. And the arbitrageur depends, for his very living, on a continual supply of such errors. In a world where no one ever mispriced anything, there would be no gaps to close and no arbitrage to profit from; the arbitrageur would starve. He needs the erring crowd as the informed trader needed the uninformed, feeding on their mistakes and, in the feeding, curing them — bound to the mispricers in a relationship of mutual necessity, the corrector and the erring, neither able to profit or to persist without the other.
The arbitrageur lives on the errors of others, and would starve in a world that made none; he is bound to the mispricers as the informed trader to the uninformed, feeding on their mistakes and, in feeding, curing them.
All of this has assumed the textbook's riskless arbitrage, the certain profit locked in by trading the identical thing in two places at once. But that pure case, though it anchors the theory, is rare in the life of real markets, and most of what is called arbitrage is a far chancier thing. Usually the two prices are not for the identical asset but for two assets that ought, on every reasonable view, to be priced alike — close substitutes, or a thing and the bundle that should replicate it — and the arbitrageur who buys the cheap and sells the dear is betting that the prices will converge, not knowing for certain that they must. And here a danger enters that pure arbitrage was spared: the gap, before it closes, can widen. The thing that was too cheap can grow cheaper still, the thing too dear grow dearer, as the same irrational currents that mispriced them in the first place press them further from each other; and the arbitrageur who staked his capital on convergence now sits on a mounting loss. This is the limit of arbitrage that Shleifer and Vishny made plain. The arbitrageur is not the infinitely deep-pocketed corrector of theory but a finite man with borrowed money and nervous backers, and when his position moves against him his losses mount, his lenders demand more collateral, his investors clamour to withdraw, and he is forced to sell out of the very trade that was about to come good — to liquidate at the bottom, crystallising the loss, exactly when he should be doubling down. He can be entirely right about the prices and wiped out before they prove him so, for the market, as the trader's proverb runs, can stay irrational longer than he can stay solvent.
The limits of arbitrage are not a footnote to the law of one price but a standing qualification of it, for they mean that the law is enforced only imperfectly — only as far as the arbitrageurs' nerve and capital and patience extend, and no further. Where a mispricing is small and sure to close soon, arbitrage erases it almost instantly, and the law holds tight. But where a mispricing is large, or stubborn, or liable to grow worse before it mends, arbitrage falters exactly when it is most needed: the arbitrageurs who would correct it are the ones being bankrupted by it, and as they fail and withdraw, the mispricing is left to stand, and may even widen for want of anyone able to bet against it. Famous cases litter the record — a parent company worth, by the market's own arithmetic, less than the subsidiary it owned; closed-end funds trading for years at prices their assets plainly did not warrant — flat violations of the law of one price that arbitrage, for all its appetite, could not close. So the verdict of this plate on the arbitrageur's wage must hold two things together. His profit is earned: it is the wage of a genuine and indispensable service, the reconciling of discrepant prices into coherent ones, and it is, in the risky case, also the premium for a real and sometimes ruinous hazard borne. But it is earned by feeding on the errors of others, it vanishes in each instance the moment it is taken, and it is never, in the aggregate, sufficient to make prices perfectly consistent — only ever to chase them in that direction, pressing the law of one price upon a market that never quite obeys it.
The arbitrageur is therefore the middleman of this volume in his most distilled form — stripped of the buyer and the seller, stripped of the saver and the borrower, stripped of every party, and left standing between nothing but two prices, with the single office of pressing them into one. His service is real and his risk is real, and his wage is earned in both; yet it is a wage that consumes its own occasion, that is drawn from the losses of the mistaken, and that can never finish its work, for the perfectly consistent market it labours toward is one in which the arbitrageur himself would have nothing left to do. No bridge runs from this plate to another volume, as bridges have run from others, for the arbitrageur belongs wholly and only to the price of standing between; he is its purest practitioner, the one intermediary who trades neither goods nor money nor credit but the bare difference between two numbers, and lives, always precariously, on the labour of making them agree. The next plate turns from the trader who closes a gap between two prices to a middleman of a newer kind — the platform that stands between the two sides of a market it has built, and charges each of them for the meeting it alone can host, pricing not a service exactly but its own indispensability. As the table says of every price, first to last: the argument remains open.