Plate iv in print

The Inventory

the dealer who must hold what he buys before he sells it, and bear its price in the meantime; the part of the spread that is a premium for risk borne in inventory.

The dealer who stands ready to trade must own what no one yet wishes to buy, and want what no one yet wishes to sell; the spread is in part his wage for holding the difference, and bearing its price.

— the principle of this plate, after Hans Stoll, 1978

To stand ready to trade is to be willing to buy before one has found a buyer, and to sell before one has restocked — and therefore to hold, at almost every moment, an inventory of the thing one deals in, whose price can move while it sits in one's hands. The second component of the spread is the price of bearing that risk.

Consider the dealer who has promised to buy from anyone who wishes to sell. When a wave of sellers arrives — more eager to sell, at that moment, than others are to buy — the dealer absorbs the excess into his own holdings, and his inventory swells. He now owns more of the asset than he wishes to, and is exposed to the risk that its price falls before the buyers arrive to take it off his hands. Symmetrically, when buyers predominate, he sells from inventory and may run short, even owing the asset he has sold and does not hold, exposed to the risk that its price rises before he can replenish. Merely by standing between buyers and sellers whose arrivals do not match, the dealer is forced into a fluctuating, involuntary position in the asset, and that position carries price risk he did not seek.1

1. The inventory problem: by absorbing the mismatch between buyers' and sellers' arrivals, the dealer is pushed into a fluctuating long or short position and bears the risk that the price moves against it before it can be unwound. The risk is involuntary — a by-product of providing immediacy.

Bearing price risk, as the volume on the premium established, is not done for free; a risk-averse dealer must be compensated, and the compensation is built into the spread. The dealer sets his bid a little below, and his ask a little above, the price he believes fair, so that on the round trip — buying at the bid, later selling at the ask — he earns a margin that pays him for the risk his inventory bore in the interval. The wider the price swings of the asset, the greater the inventory risk, and the wider the spread must be to cover it: volatile assets carry larger spreads than placid ones, for the same reason that the premium of the fourth volume rises with risk. Part of the spread, then, is simply a risk premium in disguise — the price of the uncertainty the dealer holds on his books while he waits for the other side to arrive.2

2. The inventory-risk component: a risk-averse dealer widens his quotes around the fair price to earn, on the round trip, a premium for the price risk borne while holding inventory; the more volatile the asset, the wider the spread, exactly as the risk premium of The Premium rises with risk. Part of the spread is a risk premium in disguise.
⁂

The dealer does more than charge for the risk; he manages it, and the management leaves its mark on his prices. When his inventory grows uncomfortably large, he shades both his bid and his ask downward — pricing to discourage further selling to him and to encourage buying from him — so as to draw his position back toward the level he wishes to hold; when his inventory runs short, he shades both prices upward, to attract sellers and deter buyers. The dealer's quotes thus lean against his inventory, drifting to coax the order flow that will rebalance his book. This is why the prices a market shows at any instant encode not only what the asset is worth but where the dealers' positions happen to lie — a subtlety invisible to the trader, who sees only a price, but central to how the spread is actually set.3

3. Inventory management: dealers shade both bid and ask down when long and up when short, leaning their quotes against their positions to attract rebalancing order flow (Stoll; Ho and Stoll; Amihud and Mendelson). Quoted prices therefore reflect dealers' inventory positions as well as fundamental value.

No single dealer need bear the whole of the inventory risk, and the ways it is shared shape the modern market. A dealer can lay off an unwanted position onto other dealers, or hedge it in a related market, or hold it only briefly before the next wave of opposite trades arrives to clear it; the faster inventory turns over, the less risk is held at any moment, and the narrower the spread can be. This is why deep, active markets — where trades arrive thick and fast and inventory is held only seconds — have spreads a fraction of those in thin, slow ones, where a dealer may carry a position for days. The inventory component of the spread falls as the speed and density of trading rise, which is one reason the great liquid markets are so cheap to trade, and the obscure ones so dear.4

4. Inventory risk is reduced by laying off positions to other dealers, hedging in related markets, and rapid turnover; the faster inventory clears, the less risk is held and the narrower the spread. Deep, active markets hold inventory briefly and trade cheaply; thin, slow ones carry positions long and trade dear.

The inventory component, like immediacy, is an earned part of the spread, and its existence further answers the charge of parasitism. The dealer who carries inventory so that others may trade when they wish is performing a real and risky service: he warehouses the asset across the gaps in demand, bearing on his own books the price uncertainty that would otherwise fall on traders forced to wait. That he is paid a premium for it is no more an exaction than that an insurer is paid for bearing risk, or an entrepreneur for staking himself against an uncertain return. To this point, every component of the spread we have found is a fair price for a genuine service rendered, and the middleman stands vindicated. The turn comes only with the third component, and with the flagship — for not everything the spread must cover is so innocent.5

5. The inventory component is earned, like immediacy: the dealer warehouses the asset across gaps in demand and bears the resulting price risk, a real service compensated by a premium — no more an exaction than an insurer's or an entrepreneur's reward. The earned account holds until the adverse-selection component of The Informed, and the flagship.

The second component of the spread, then, is a risk premium: the dealer is paid for the price uncertainty he carries in inventory while he waits for the two sides of the market to balance, and the spread widens with the asset's volatility and narrows with the speed of trade, exactly as a premium for risk should. Together with the price of immediacy, it accounts for a spread that is wholly earned — the honest wage of warehousing and waiting. But there remains a third reason the dealer must charge, darker than the first two, and rooted not in the cost of his service but in the limits of his knowledge: the trader on the other side may know something he does not. The next plate takes up the menace of the better-informed.