The arbitrageur stands between two prices for the same thing. At one counter a share can be bought for a hundred; at another it can be sold for a hundred and two. If both offers can be taken together, the share can be delivered as promised, and the entire passage costs one, the remaining one is the trader's gain. He need have no opinion about what the company will earn next year. His opportunity lies in the relation between two commitments already available. Buying at the cheaper counter adds to demand there; selling at the dearer adds to supply. As others attempt the same passage, their competition presses the discrepancy toward the cost of crossing it. The arbitrageur is the middleman whose pursuit of a gap helps close it. The service is the reconciliation of prices, and its reward can disappear as that service is performed. Yet the conditions in the first sentence of the calculation carry much of the argument. Two numbers on a screen are a beginning; the trade between them still has to be possible.
The law of one price starts with claims that deliver the same thing under the same conditions. If two securities promise identical payments in every relevant future state, an investor able to buy the cheaper and sell the dearer can offset their future obligations and retain the initial difference. With unrestricted trading and no costs, such an opportunity puts pressure on the prices to agree. Delivery dates, currencies, rights, taxes and the possibility of default belong inside the comparison: a similarity of names or a close historical correlation cannot substitute for identical claims. Nor does the rule compare whichever quotations are most convenient. To buy, the trader must meet an available ask; to sell, he must obtain an available bid. A difference between two midpoints may leave no gain after those terms and the other costs are paid.1 The preceding plates' spread therefore survives inside the arbitrage calculation. In a market with costs, consistency permits a band within which a discrepancy is too small to pay for the trades that would remove it. The law acquires its force from an executable alternative.
The reward is self-extinguishing at the opportunity, rather than a promise that the occupation will disappear. Once competition has taken the available difference down to the costs of trading, another purchase and sale on the same terms supplies no additional excess. New orders, changed information, separate trading venues and the costs of keeping them connected can open another difference. The work must then be done again. Even in the simple example, there is no reason the two quotations must meet halfway: how far each moves depends on the orders and quantities available on its side. Agreement between the prices establishes consistency between the claims. Two claims can be priced consistently with each other while both rest on an optimistic assessment of their common future.2 Arbitrage can discipline relative prices without settling the whole question of fundamental value. Its contribution is consequential precisely because it is specific: a person need not know the final worth of the enterprise to show that one available route to the same entitlement is dearer than another.
The trader's capital can run out before the comparison is vindicated. Andrei Shleifer and Robert Vishny begin with nearly identical futures contracts traded on separate exchanges: even a position hedged at its final delivery date requires margin, and an adverse movement can call for more cash before the offsetting gain is collected. Their central model adds a separation between the specialist who understands the position and the investors who supply his funds. When a mispricing deepens, the specialist's reported performance worsens. Investors who cannot distinguish that deterioration from evidence of poor ability may withdraw, leaving him with less to invest just as the apparent opportunity grows.3 This mechanism does not require him to be wrong about the eventual value. It requires an intervening obligation that his final gain cannot yet discharge. Where the claims are only approximate substitutes, there is a further possibility: the relationship on which he relied may itself fail. A bet on convergence can carry both the risk of being mistaken and the risk of being unable to remain in the trade long enough to be right.
The obstacle can be as concrete as a share that cannot be borrowed. Lamont and Thaler studied technology-stock carve-outs in which a parent announced that it would distribute its remaining subsidiary shares. On March 2, 2000, Palm closed at $95.06, while 3Com closed at $81.81; the announced distribution ratio of about 1.525 Palm shares for each 3Com share valued the expected Palm entitlement alone at nearly $145. The rest of 3Com consequently had a sharply negative implied value. The tempting comparison was to buy the parent and sell the corresponding subsidiary shares short, subject to the distribution actually proceeding. But making the expensive sale required obtaining Palm shares to deliver, and shorting costs could be extremely high or borrowing unavailable.4 The authors' finding was a conspicuous discrepancy alongside a barrier to exploiting it. A calculation visible to ordinary arithmetic could persist because the missing part was the transaction. The example gives the law of one price a practical boundary: knowing which two claims to compare does not confer the means of exchanging them on both sides.
The service and its distributional effects have to be judged together. The trader's receipts come from the counterparties with whom he deals, but the gain does not by itself establish that both were mistaken about an independently known true value. They may face different needs, costs, information or access. The initial discrepancy likewise need not identify which quoted price will move. In the costless identical-claim case, the two terms are jointly inconsistent; selecting one of them as the uniquely correct price requires a further argument. Once passage has real costs, the trader may earn a return for locating the opportunity, arranging delivery and committing funds, while competition determines how much of the available difference he retains. The short-sale example also shows why the absence of an accessible profit cannot certify the correctness of the prices left behind.5 The volume's familiar question returns in a different form. A profitable intervention can improve the consistency of the market, yet the size of the private gain remains a separate object from the size and distribution of the benefit it creates.
Collecting the difference can help erase it, to the extent that the necessary trades can be made and sustained. That is the answer to the plate's question and the condition attached to its answer. The ideal comparison joins equal claims; the real passage has quotations, quantities, deadlines, borrowing terms and a balance sheet. Competition presses the return against those constraints, and a residual gap may reveal their force as much as another trader's neglect. The arbitrageur thus earns his place in the volume without becoming the guarantor of a perfectly coherent world. His most successful transaction can remove its own occasion; his most convincing calculation can still await a means of execution. The next plate turns to The Bank, whose intermediation also depends on keeping promises across time, but whose two sides seek different kinds of claims. One wants funds committed for years; the other wants a balance close at hand. There the gap cannot be closed by discovering that the promises are identical. The institution must make their difference serviceable.