Why Dealer Balance Sheets Are the Market's Hidden Switch
The corporate-bond market's hardest-to-see variable is not the quote on a screen but the dealer capacity behind it. This chapter focuses on how a dealer's inventory position determines whether they can buy from a customer or sell to one, and how those individual choices become market-wide prices, order flow, and liquidity compensation. The goal is to follow the mechanism from a customer's changing desire to own a bond to the equilibrium that keeps the dealer-intermediated market operating.
Inventory decides which side a dealer can serve
The Philadelphia Fed model uses a deliberately spare representation of the market. Customers and dealers can each hold zero or one unit of a representative bond. Customers have changing preferences for the asset; dealers have a stable preference that includes the benefit of holding the bond net of the cost of using balance-sheet space. The bond can be traded in a competitive inter-dealer market at a reference price, but customers must still search for a dealer.
The zero-or-one assumption is not a claim that an actual dealer's entire book contains one bond or that a dealer cannot hold a portfolio of positions. It is a way to isolate the direction of the capacity constraint. A dealer with the bond has inventory ready to sell to a customer who wants to buy. A dealer without the bond has room to buy from a customer who wants to sell. The same dealer cannot occupy both states for this representative position at the same time.
That last point is easy to miss because dealers can trade with one another at the competitive reference price. Access to an inter-dealer market tells a dealer what the bond is worth and lets them reposition before a customer meeting. It does not erase the customer-facing capacity choice. To sell immediately, the dealer must already be carrying the asset. To buy immediately, the dealer must have room to take it onto the balance sheet. The market's friction is therefore not just the absence of a price. It is the need for the right inventory state at the right moment.
A customer buyer tests the first state. If the customer's reservation value is above the inter-dealer price, owning the bond is worth more to them than the cash they would pay. They need a dealer holding the bond. In a voice meeting, that dealer bargains over the ask. In an electronic RFQ, several dealers may be contacted, but only the dealers with inventory can offer a feasible sale. More inventory-holding dealers can mean more potential asks and stronger competition among them.
A customer seller tests the opposite state. If the reservation value is below the reference price, the customer values cash or relief from holding the bond more than continued ownership. They need a dealer with balance-sheet space. More dealers in that state can make bids more competitive and increase the chance of a purchase. The market does not have one generic pool of “liquidity providers” that is equally available to both sides. It has dealers in different positions, each able to serve a different direction of customer demand.
This directional structure creates a trade-off for every dealer. Carrying inventory opens the ask side but uses space that could have been reserved for the bid side. Preserving space opens the bid side but means the dealer cannot sell the bond from inventory. The dealer is not simply choosing whether to participate. They are choosing which kind of customer opportunity to be ready for.
The diagram shows two coupled state systems rather than one literal sequence. Customer preference changes create a need to buy or sell. Dealer inventory determines whether that need can be met. When the match occurs, the customer changes ownership and the dealer's inventory position can change in the opposite direction. The model's central relationship is the link between these states: customer search is only productive when the dealer is in the feasible state for that side of the trade.
Consider the two directions in sequence. A non-owner whose convenience yield rises searches for a bond. If an inventory-holding dealer is available, the customer buys and the dealer gives up the bond, moving toward the space-preserving state. Later, an owner whose convenience yield falls searches for a buyer. If a space-holding dealer is available, that dealer acquires the bond and moves toward the inventory state. Each successful trade solves one customer's problem while changing the dealer capacity available to the next customer. The model therefore treats liquidity as a flow through states, not as a permanent stock of dealers who are always ready to do everything.
A failed search is economically meaningful even though it creates no recorded bid or ask. If a customer wants to buy but finds no dealer with inventory, the customer's preference has not disappeared; the opportunity to trade has simply not arrived. The same is true when an owner wants to sell but no dealer has room. The customer remains exposed to the inconvenience of waiting or to the possibility that the next quote will be less favorable. Completed trades can consequently look orderly while uncompleted demand is accumulating in the background. The theoretical model captures that accumulation through customer values and transition rates rather than by treating every desire to trade as an executed order.
The inter-dealer market still matters in this sequence. It supplies the common reference price and gives dealers a way to acquire or dispose of the bond before serving customers. But the timing of the customer meeting makes the inventory state relevant. A dealer cannot respond to a customer buy as though an asset were already available if the dealer has not chosen to carry it. Nor can a dealer absorb a customer sale without room to take the asset. The reference market coordinates valuation; balance-sheet space determines whether that valuation can be converted into a customer transaction at that moment.
This feedback is why the model solves for quantities as well as prices. More dealers holding the bond increase the pool that can answer customer-buy requests, but reduce the pool that can answer customer-sell requests. As the two customer populations trade, dealers move between inventory states. Those movements change future matching probabilities and the competitiveness of later quotes. A change in the market's structure can therefore alter the distribution of states even before a large change appears in an average spread. Inventory is both an input into liquidity and an outcome of the trading process.
The capacity choice also explains why an electronic platform can have many named participants but few effective competitors. If several dealers receive an RFQ from a customer who wants to buy, a dealer without the bond cannot create an ask simply because they received the request. The relevant competitive set is the subset with inventory. On a sale request, the relevant set is the subset with space. The platform changes how dealers are contacted; the balance sheet still determines who can respond.
From changing preferences to dealer indifference
The model turns these state changes into an equilibrium through customer heterogeneity. Each customer receives a convenience yield for owning the bond, and that yield is redrawn at random times. A positive convenience yield can represent a strong desire to hold the security; a negative one can represent a distress cost from continuing to own it. The important feature is not the exact shape of the distribution but the fact that customers who look identical in their holdings today can want opposite trades after their preferences change.
For any current convenience yield, the customer compares the value of owning the bond with the value of not owning it. That comparison is summarized by a reservation value. There is a marginal customer with convenience yield ε★ whose reservation value equals the competitive inter-dealer price, written in the model as R(ε★) = P. A non-owner above the threshold wants to buy. An owner below it wants to sell. Customers at the threshold are indifferent, and because they form a measure-zero group, their tie-breaking behavior does not determine aggregate outcomes.
The threshold links preferences to inventory. Suppose the threshold rises. Fewer non-owners have a high enough convenience yield to want the bond, while more owners fall below the threshold and want to sell. In a steady state, that change creates more customer-sellers and fewer customer-buyers. To clear the fixed supply, a larger share of the bond must be held by dealers. Conversely, a lower threshold expands the set of customer-buyers and shrinks the set of customer-sellers, reducing the dealer inventory share required by market clearing.
This is the market-clearing schedule. The paper establishes that the fraction of dealers holding the asset rises with the marginal customer's convenience-yield threshold. The direction is intuitive even without solving the flow equations. Customer preferences determine who wants to own the bond; search opportunities determine how quickly those desires become trades; the remaining supply must be divided between customers and dealers. Inventory is not an independent backdrop. It is one of the quantities the customer flows determine.
The dealer side supplies a second relationship. A dealer that owns the bond earns the liquidity benefit of holding it and can pursue ask-side opportunities. A dealer that does not own it preserves capacity and can pursue bid-side opportunities. The model summarizes the value difference between these states as
Δ = ℓ + εD + Π1 − Π0.
Here, ℓ is the liquidity yield spread, εD is the dealer's net convenience yield from holding the asset, Π1 is ask-side flow profit, and Π0 is bid-side flow profit. A dealer wants to hold the asset when this difference is positive, wants to preserve space when it is negative, and is indifferent when it is zero. The notation is compact, but its economic meaning is a balance of opportunities and costs.
Ask-side profit depends on the chance of meeting customers who want to buy, the surplus available from those customers, and the number of other inventory-holding dealers competing to sell. Bid-side profit depends on the chance of meeting customers who want to sell, the surplus available on that side, and the number of dealers with space competing to buy. The liquidity yield gives the holder an additional monetary benefit. The carrying-cost term works in the opposite direction when balance-sheet space becomes more expensive.
For an equilibrium with active trading on both sides, the dealer cannot prefer one state permanently. If holding inventory were too attractive, too many dealers would carry the bond and ask-side competition would erode the return to doing so. If preserving space were too attractive, too few dealers would hold inventory and customer buyers would face a different pattern of scarcity and profits. The condition of dealer indifference is the point at which these incentives balance.
The paper represents this balance with a dealer-optimality schedule: for each possible dealer inventory share, there is a marginal customer threshold that makes a dealer indifferent. When the dealer sector is sufficiently small, this schedule slopes downward. If more dealers hold the bond, they compete more intensely on the ask side and earn less per opportunity. To restore indifference, the threshold must fall, expanding the set of customers who want to buy and increasing the volume of ask-side opportunities.
The market-clearing schedule slopes upward in the space of the marginal threshold and dealer inventory share. The dealer-optimality schedule slopes downward under the paper's stated condition. Their intersection determines the equilibrium share of dealers holding the bond and the marginal customer's convenience yield. This picture matters because it shows how a change in one primitive can affect both prices and quantities. Higher carrying costs do not have to appear as a one-for-one change in a quote; they can move the intersection, changing inventory, customer flows, and the division of surplus at the same time.
It is useful to read the two schedules as two different accounting requirements. Market clearing asks, “Given who wants to buy and sell, how much of the bond must customers and dealers hold for supply to balance?” Dealer optimality asks, “Given the available customer flow and competition, which inventory position gives a dealer enough value to justify using or preserving capacity?” Neither condition alone is a market outcome. Market clearing without dealer incentives could assign inventory to dealers who would not want it. Dealer incentives without market clearing could describe profitable opportunities that cannot coexist with the available supply. The equilibrium is the point where customer demand, dealer capacity, and asset ownership are mutually consistent.
This also gives the model a useful feedback loop. Suppose an initially small group of dealers holds inventory. Customers wanting to buy may face a thin ask-side competitive set, while sellers may find several dealers with room to buy. If successful purchases reduce the number of inventory holders, future customer-buy opportunities become scarcer; if successful sales transfer bonds to dealers, future customer-buy opportunities can become more plentiful. The model does not assume that one direction of trade permanently dominates. It lets the steady-state flows determine how often each state is occupied. That is the sense in which the inventory distribution is an equilibrium quantity rather than a fixed market feature.
The distinction between spread and profit follows from the same logic. A dealer's profit on one side is not just the spread on one transaction. It is the spread multiplied by the flow of eligible customer trades per dealer. In the calibration, the relevant order flow is about 14 trades per year per dealer per side. A market can therefore preserve a dealer's incentive through more opportunities or a changed inventory distribution even when the per-trade spread moves only slightly. Conversely, a small change in the spread can represent a meaningful incentive change when order flow is thin.
This mechanism also clarifies why a falling or stable bid-ask spread should not be read in isolation. The quote describes the outcome for a customer who finds a feasible dealer. The equilibrium condition asks whether enough dealers remain willing to maintain the inventory and capacity that make those encounters possible. The two questions overlap, but they are not the same. A market can offer a competitive price in completed trades while its underlying allocation of balance-sheet space is becoming more strained.
The next step is to use this common map to compare the three structural changes in the corporate-bond market. A higher carrying cost, a more competitive search technology, and more frequent customer trading all disturb the dealer-indifference balance, but they do so through different terms. Seeing that difference before looking at the numerical results is what prevents a single spread statistic from becoming the whole story.