Two Prices, Two Kinds of Liquidity
The corporate-bond market has two different liquidity questions hiding behind familiar price data: how much does an immediate trade cost, and how much compensation does an investor require for the possibility that a future trade will be difficult? This chapter focuses on the bid-ask spread and the model's liquidity yield spread so the reader can interpret each measure on its own terms, then see why dealer inventory and customer trading needs connect them without making them identical.
The bid-ask spread records an encounter
A bond trade has two customer-facing prices. The ask is the price a customer pays to buy; the bid is the price a customer receives when selling. The difference between them is the bid-ask spread. All else equal, a smaller spread means a customer gives up less in an immediate round trip: buying at the ask and selling at the bid would involve a smaller gap.
That definition is useful precisely because it is narrow. It describes the terms available when a trade is actually arranged. It does not by itself say how long the customer searched, how many dealers could respond, how much inventory those dealers carried, or whether the same price would be available when many customers wanted to sell at once. The spread is a measure of the cost of an encounter, not a complete measure of the market's ability to keep providing encounters.
A simple hypothetical makes the boundary clear. Suppose a bond's reference price is 100. If a customer can buy at 100.40 and sell at 99.70, the gap is 0.70. If better competition later produces an ask of 100.10 and a bid of 99.90, the gap is only 0.20. That change tells us that the terms of those immediate exchanges improved. It does not tell us whether the customer found a counterparty in seconds or after a long search, whether the quotes would survive a rush of selling, or whether an investor who holds the bond is now less likely to face a costly delay. The numbers in this example are illustrative, not measurements from the paper; their purpose is to separate a quote comparison from a broader claim about market capacity.
The side of the trade matters as well. A buyer needs a dealer willing to sell inventory, while a seller needs a dealer willing to use available balance-sheet space to buy. A market can make buying easier without making selling equally easy. Reporting one average spread can conceal that directional difference, especially when voice and electronic trades involve different customer types, bond sizes, and competitive sets. The bid and ask are therefore not merely two ends of one ruler. They are outcomes of two related but distinct searches for a feasible dealer.
The distinction becomes sharper in an over-the-counter market. There is no single public order book matching every buyer with every seller. A customer may contact one dealer through a voice-based conversation, or may send an electronic request for quotes to several dealers. In a voice meeting, the customer and dealer bargain over a price when the customer's value of owning the bond is high enough to make a purchase worthwhile, or low enough to make a sale worthwhile. The dealer and customer divide the gains from trade rather than accepting one universal exchange price.
The electronic version changes the competitive set. A customer can contact a fixed number of dealers at the same time, but the number of replies is random because a dealer must be in the right inventory state to respond. A dealer holding the bond can quote to a customer who wants to buy. A dealer with room on the balance sheet can quote to a customer who wants to sell. Several names on an electronic request therefore do not guarantee several effective competitors.
When several dealers can respond, competition pushes offers toward the competitive inter-dealer price. When few can respond, the available dealer has more room to retain part of the customer's trading surplus. In the model, dealers use a range of possible quotes in electronic trading. The lowest possible quote lies above the competitive reference price, while the highest reaches the customer's reservation value—the most the customer is willing to pay, or the least they are willing to accept, given their desire to own the bond. The precise distribution is less important for a first reading than the mechanism: the spread depends on both the customer's urgency and the number of usable dealers.
The same logic applies in reverse on the bid side. A customer who wants to sell needs a dealer with capacity to buy. More such dealers can make bids more competitive. The set of dealers able to serve buyers need not match the set able to serve sellers, because inventory positions point in opposite directions. That is why a market can have a different electronic bid spread from its electronic ask spread, and why a voice spread need not match an electronic one.
This also explains why a falling average bid-ask spread is meaningful without being conclusive. It may show that a customer can execute more cheaply once they reach the market. It does not establish that every customer can execute quickly, that dealers can absorb every direction of order flow, or that an investor is indifferent to the possibility of needing to trade later. Those are separate questions about access, capacity, and time.
The yield spread records the possibility of waiting
The Philadelphia Fed paper gives the second measure a precise role inside its model. The bond trades at par in the competitive inter-dealer market. Its coupon is written as the risk-free discount rate plus a spread, and the spread is chosen so that the bond's price remains one. Because the model excludes default risk and ordinary asset risk, the remaining liquidity yield spread is the compensation generated by trading frictions and balance-sheet constraints.
This normalization is a modeling choice, not a claim that a real corporate bond has no credit risk. An observed corporate-bond yield can contain components that this model intentionally leaves out, including compensation for default and other forms of risk. The paper isolates liquidity so it can ask a cleaner question: if investors may need to trade but cannot do so instantly, how does that difficulty affect the return required to hold the bond?
It helps to keep the units of the two measures in mind. A bid-ask spread is attached to an exchange: it is paid or lost when a customer buys or sells. A yield spread is an annualized return difference that affects the economics of holding the bond over time. The measures can be compared as evidence about market conditions, but they are not interchangeable prices. A few basis points in a quote and a few basis points in an annual yield do not describe the same cash-flow event. The yield measure matters because the customer may bear a cost even during a period when no trade occurs: the possibility of a difficult future sale or purchase changes what ownership is worth today.
The par-price normalization also keeps the direction of the reasoning visible. The bond's coupon includes the discount rate plus the liquidity component needed to support a par price. If search became easier while all else stayed fixed, less liquidity compensation would be needed in the model. If customers became more likely to need an imperfectly liquid trade, or if dealers became less willing to carry inventory, more compensation could be required. The model is not saying that a real yield can be decomposed by looking at one quote. It is using a controlled environment to identify the channel through which trading frictions affect required returns.
To answer it, the model gives customers different and changing convenience yields from owning the bond. A convenience yield is the value of possession beyond the market price. It can be positive when owning the bond is especially useful and negative when holding it imposes a distress cost. Customers periodically draw a new value, so a person who is content to own the bond today may want to sell later, while a non-owner may later want to buy.
Each customer has a reservation value: the value of owning the bond rather than not owning it, given the option to trade when an opportunity appears. There is a marginal customer whose reservation value equals the competitive inter-dealer price. In the paper's notation, that customer has convenience yield ε★ and satisfies R(ε★) = P. Customers above that threshold prefer to buy if they do not own the bond. Customers below it prefer to sell if they do own it.
The threshold is not just a way to divide buyers and sellers. It captures an intertemporal decision. Imagine a customer exactly at the margin. They are indifferent between owning and not owning at the current reference price. But they know that a future preference shock may make ownership much more valuable. If that happens, search may prevent them from buying immediately. They also know that a future shock may make the bond a burden, yet selling may take time. Those possible delays reduce the value of ownership today. The liquidity yield spread is the compensation needed to make holding the bond worthwhile despite that possibility.
Now consider two customers who face the same current quote but different expectations about their next trading need. One is likely to keep the bond for a long time; the other expects a portfolio change soon. The second customer places more value on being able to transact at the needed moment. Even if both can eventually obtain the same bid or ask, the second customer's holding decision is more sensitive to search time and dealer availability. In the model, that difference is represented by the distribution of convenience yields and the rate at which customers draw new ones. It is not necessary for every investor to face a different quoted spread for the market to impose a different holding-period burden.
The marginal customer is useful because they summarize this collection of decisions at the point where ownership changes hands. Raising the threshold means fewer non-owners are eager enough to buy and more owners are willing enough to sell. Lowering it does the opposite. The threshold therefore affects both the flow of customer orders and the amount of the bond that must sit with dealers to clear the market. A yield response can emerge from that change in the population of potential traders, not only from a change in the price offered to the particular customer who completes a trade.
This is why the yield measure can react even when the price of an individual trade does not. A customer may receive a competitive bid or ask when they trade, but still demand a higher expected return because the opportunity to trade may not arrive at the moment it is needed. The bid-ask spread looks at the price concession conditional on a transaction. The liquidity yield spread incorporates the risk of having to wait, search again, or accept an unfavorable opportunity later.
Dealer inventory enters both paths. Suppose more dealers hold the bond. A customer who wants to buy is more likely to encounter a dealer able to sell, and the customer may receive more competing asks. But a customer who wants to sell may find fewer dealers with available balance-sheet space to buy. The reverse occurs when fewer dealers carry inventory. Thus, an inventory change can improve one side's access while weakening the other side's competition. It can also change the customer's expected future trading options even if the average spread observed among completed trades moves little.
The model translates these effects into trading intensities: the rate at which customers get a feasible opportunity to trade, adjusted for the share of the gains they receive. In voice trading, bargaining power changes how much of the surplus reaches the customer. In electronic trading, the number and inventory positions of queried dealers change the expected competitiveness of the quote. Both determine how quickly a customer can move from wanting the bond to owning it, or from owning it to selling it.
This creates two distinct ways for the same market to appear better or worse. Search can improve while the demand for immediacy rises. For example, more electronic RFQs may give a customer a better chance of receiving a competitive offer, reducing the cost conditional on trading. At the same time, a larger population of active funds may create more moments when customers need to trade. The first force presses down on a transaction spread; the second raises the value of reliable access and can press up the compensation for holding the bond. Looking at only one of those margins would assign both changes to the wrong cause.
The reverse combination is possible too. A market may show a stable average spread because the bid and ask sides reprice in opposite directions, while fewer dealers are willing to carry inventory. Completed transactions then provide an incomplete sample of the underlying capacity: they show what happened to customers who found a willing counterparty, not necessarily what would happen to every customer under a larger or more one-sided wave of demand. This is why the paper's dealer-indifference condition matters even for a reader who never uses its equations. It explains how the capacity supporting today's quote can be changing beneath the quote itself.
That is the practical interpretation rule. When reading a bid-ask statistic, ask what happened during the trade: Which side was active? Which venue was used? How many dealers could actually respond? When reading a yield-based liquidity measure, ask a different set of questions: How often do customers need to trade? How much inventory can dealers carry? What happens when the desired direction of trading is concentrated? A narrow spread answers only the first family of questions.
There is also a measurement boundary. The model is calibrated with data on investment-grade bonds and trades larger than $1 million from January 2017 through March 2021, excluding March 2020. Its parameters and implied yield spread are therefore not raw observations that can be generalized automatically to high-yield bonds, very large blocks, or crisis periods. Even the empirical counterpart of a bid-ask spread may average over customers with different convenience yields and different probabilities of finding a willing dealer. Precision in the number does not remove selection in the underlying market.
The distinction between the two prices is therefore not a semantic exercise. It changes the conclusion a reader should draw from a market that appears cheaper to trade. A lower bid-ask spread can indicate stronger search competition and better transaction efficiency. It does not prove that the expected cost of future illiquidity has fallen by the same amount. To understand why, we now need to examine the dealer's constrained choice between carrying inventory for customer buyers and preserving space for customer sellers.