Does the Federal Reserve Obtain Competitive and Appropriate Prices in Monetary Policy Implementation?

Abstract

Many of the Federal Reserve’s (the Fed’s) monetary policy operations involve trading with primary dealers. We find that, for agency MBS, dealers charge 2.5 cents (per $100 face value) higher selling to the Fed than to non-Fed customers. Controlling for the same dealer, same security, and same trading time, this discriminatory pricing likely arises from dealers’ market power rather than inventory costs. Further, matching trade size reduces the price differential by more than half, implying that dealers’ market power greatly relates to the Fed’s purchases in large amounts, whereas the Fed’s limited breadth of counterparty choice also plays some role.

The first objective is to obtain the securities at competitive and appropriate prices for the Federal Reserve, as doing so will ultimately benefit the U.S. taxpayer.

—Brian Sack, Executive Vice President of the Federal Reserve Bank of New York, at the Global Interdependence Center Central Banking Series Event, 2011

The U.S. Federal Reserve (hereafter the Fed) trades with around 20 primary dealers who the Federal Reserve Bank of New York appoints in its monetary policy operations. For example, in implementing conventional policies through which it adjusts the federal funds rate, the Fed buys or sells Treasury securities with primary dealers as direct trading counterparties. During the Great Financial Crisis, the Fed purchased huge amounts of Treasury securities and agency mortgage-backed securities (MBS), an operation known as quantitative easing (QE), also with primary dealers as direct trading counterparties. During the COVID-19 pandemic, the Fed again bought Treasury securities and agency MBS, as well as bought agency commercial mortgage-backed securities (CMBS) and corporate bonds for the first time, still with primary dealers as the main direct trading counterparties.¹

Does the Fed obtain competitive and appropriate pricing from primary dealers, which is of great importance to the benefit of U.S. taxpayers, as exemplified by the quote above? Existing studies have shown that dealers in over-the-counter (OTC) markets wield significant market power over regular (or non-Fed) customers, who are in a comparatively weak position (Bessembinder, Spatt, and Venkataraman 2020). The Fed is, however, likely to be in a much stronger position than non-Fed customers because of its unique role in the market. Yet, in this paper, we show that primary dealers charge discriminatorily higher prices selling securities to the Fed than to non-Fed buyers.²

Our analysis focuses on the agency MBS market, not only because of its importance and constant involvement in the Fed’s policies,³ but also because of the detailed data on this market that are available, making such an analysis feasible. In particular, we use two main data sets: supervisory-level MBS transaction data from the Trade Reporting and Compliance Engine (TRACE) and the Fed’s MBS trading records. Both data sets include dealer identifiers, which allow for accurate matching and enable us to compare a given dealer’s pricing schemes for the Fed with those applied to non-Fed customers. Specifically, in our sample period—which runs from October 2011 through March 2014 when the Fed purchased $1.5 trillion of MBS using the request-for-quote (RFQ) algorithm on the Tradeweb platform that selects four participating dealers for each trade—we find that the same primary dealer sells the same MBS on the same day to the Fed for about 2.5 cents more (per $100 in face value) than it charges non-Fed customers. This price differential is about half of dealers’ average gross profit margins.⁴

Our interpretation is that this striking finding on dealers’ discriminatory pricing against the Fed relative to non-Fed customers is likely due to dealers’ market power. A main alternative channel would be inventory cost difference—dealers need to hold larger inventory and incur higher inventory costs in selling to the Fed than to non-Fed customers—but our empirical design likely controls for it. Specifically, although different units of the same security may be purchased at different days and prices, our comparison—using the same dealer on the same day for the same MBS—likely ensures that the dealer’s selling to the Fed and to non-Fed buyers are based on the same inventory. A further finding that reinforces this same-inventory interpretation is that most of dealers’ inventory sold to the Fed, which we estimate by cumulating the trade flows, is built before the Fed operation day. We also look into intraday time windows and show that the discriminatory pricing against the Fed remains significant compared with non-Fed trades around the same trading time (within one hour, specifically), alleviating concerns related to intraday price movement. Overall, the results imply that dealers exert greater market power over the Fed than over non-Fed customers.⁵

In further analyses, we postulate two economic channels associated with the key features of Fed purchases that may cause dealers’ greater market power over the Fed than non-Fed customers. First, the Fed’s purchase is overwhelmingly large relative to an individual dealer’s inventory: on average, for a given MBS, the Fed’s purchase amount is about $3.7 billion and the amount of an average dealer’s inventory is only about $300 million. Hence, a dealer can monopolize the Fed’s residual demand that other dealers cannot satisfy, generating dealer market power (Kreps and Scheinkman 1983; Dunn and Spatt 1984); we call this the trade-size markup effect. Non-Fed customers’ purchase quantities are much lower, so they should suffer to a lesser extent from the trade-size markup effect. Second, the Fed uses primary dealers as exclusive trading counterparties and inclines to select a broad range of participating dealers in its RFQ sessions in the interests of equity, which constrains its flexibility, while non-Fed customers can solicit offers from both primary dealers and other dealers in a flexible way; we call this the constrained-counterparty-choice effect.⁶

We conduct three analyses to understand these two economic forces. First, we quantify how much of dealers’ discriminatory pricing against the Fed can be attributed to the trade-size markup effect and how much can be attributed to the constrained-counterparty-choice effect. Toward this goal, from the baseline sample of matched Fed and non-Fed customer trades, we further restrict our sample to mega-sized trades (defined as trades of $100 million or above) so that trade sizes for Fed and non-Fed buyers are within the same range. We find that the price differential between the Fed and non-Fed trades is reduced by a bit more than half using these matched mega-sized trades, implying that dealers’ discriminatory pricing relates greatly to the trade-size markup effect, though the constrained-counterparty-choice effect also plays a noticeable role.

Second, the trade-size markup effect is caused by a buyer’s large trade size, regardless of its identity. Hence even non-Fed customers would receive inferior pricing for large trades if the size of their large trades were to overwhelm the inventory capacity of individual dealers. We hypothesize that this is more likely on Fed purchase days, as Fed purchases remove a large quantity of MBS supply from the market. Indeed, we find that, on days when the Fed does not trade, a standard trade-size discount is present for trades of all different sizes. In contrast, on days when the Fed trades, while non-Fed buyers still receive pricing discounts for below-mega-sized trades, they pay markups for mega-sized trades.⁷

Third, we examine the dealer counterparties of Fed and non-Fed trades and provide support to the constrained-counterparty-choice channel. We find that the largest non-primary-dealer trading with non-Fed customers is comparable to a medium primary dealer, while several other nonprimary dealers are comparable to small primary dealers. Therefore, customers do indeed trade with a few nonprimary dealers nontrivially, but the Fed cannot select them into its purchase operations. Moreover, we find that compared with non-Fed customers, the Fed allocates a high fraction of its trades to medium dealers relative to large dealers, perhaps because the Fed intends to use a broad range of dealers in the interests of equity; this may also adversely affect the competitiveness of its pricing.

Substantial heterogeneity across dealers is observed in OTC markets, so our final analysis examines whether large dealers charge greater discriminatory pricing against the Fed than small dealers do. We first show that large dealers (measured by the market share of trading volume before the start of the Fed’s purchases in October 2011) acquire the bulk of MBS inventory in selling to the Fed. We then regress Fed purchase prices and amounts on dealers’ size and show that a dealer that is a one-standard-derivation larger in size (1) charges the Fed a price that is about one cent higher per $100 in face value and (2) sells |$4.8\%$| more MBS as a fraction of the Fed’s total purchase amount. That is, by controlling the bulk of the MBS inventory, large dealers sell greater amounts of MBS to the Fed at higher prices than small dealers do. Importantly, the opposite is true for non-Fed customers: on the same days when the Fed buys MBS, large dealers charge lower prices to non-Fed buyers than small dealers do. This further corroborates the discriminatory pricing effect.

Overall, we find that primary dealers exert strong market power over the Fed relative to non-Fed customers, which arises greatly from the Fed’s huge purchase size and constrained choice of trading counterparties. Hence, the Fed’s policy execution efficiency can be potentially improved by adjusting purchase speed while giving greater considerations to secondary-market conditions.⁸ Moreover, including certain nonprimary dealers as direct counterparties and flexibly choosing the set of participating dealers in trading sessions could also improve the Fed’s operation flexibility.⁹ However, potential changes in operational design should be comprehensively evaluated to avoid losing the benefits of policy implementation speed and the primary dealer system and to avoid incurring excessive counterparty risk when including new counterparties.

Our paper is related to the literature that studies the asset pricing effect of quantitative easing (QE), but we examine a distinct economic issue. Specifically, studies in that literature, including Hancock and Passmore (2011), Krishnamurthy and Vissing-Jorgensen (2011), D’Amico and King (2013), and Koijen et al. (2021), among others, focus on the extent to which the Fed’s asset purchases reduced interest rates. We differ by focusing on the implementation efficiency of QE, that is, whether the Fed can achieve competitive and appropriate pricing and avoid paying excessive execution costs. Whereas large decreases in interest rates (equivalently, increases in bond prices) are the objective of monetary policy per se, low execution costs are the objective of the policy implementation mechanism.

Because of the distinct research objectives, the discriminatory pricing effect that we document is incomparable with the interest rate effect of QE. Rather, the effect we document is related to the execution costs documented in the existing literature on U.S. Treasury issuance auctions and monetary policy implementation, including Bikhchandani and Huang (1989), Cammack (1991), Back and Zender (1993), Simon (1994), Nyborg and Sundaresan (1996), Malvey and Archibald (1998), Kremer and Nyborg (2004), Goldreich (2007), Han, Longstaff, and Merrill (2007), Bonaldi, Hortacsu, and Song (2015), Hortacsu, Kastl, and Zhang (2018), and Song and Zhu (2018), among others.¹⁰ In fact, the magnitude of the discriminatory pricing effect we document (about 2.5 cents per $100 face value) is comparable to the execution costs documented in these studies. For example, Hortacsu, Kastl, and Zhang (2018) estimate that the total allocative inefficiency is about 2 basis points in Treasury issuance auctions, and Song and Zhu (2018) find that the Fed’s auction cost in purchasing Treasury securities is about 0.7 to 2.7 cents per $100 face value.

Notwithstanding similar magnitudes in the measures of implementation efficiency, our paper differs from these studies in important ways. First, our analysis compares dealers’ selling prices to the Fed with their selling prices to private buyers. Doing so allows us to empirically identify the dealers’ discriminatory pricing toward the Fed versus non-Fed customers. In contrast, the literature does not compare the dealers’ trading price with the Fed and Treasury with the dealers’ trading with non-Fed customers on the same side. Rather, the literature compares the dealers’ trading price with the Fed and Treasury with a range of market prices such as bid-ask midpoint or average transaction price.¹¹Second, these studies mainly focus on auction design, for example, comparing uniform pricing rules with discriminatory pricing rules and analyzing dealers’ bidding strategies. Several recent studies, such as Hortacsu and Kastl (2012) and Boyarchenko, Lucca, and Veldkamp (2021), also analyze preauction information, for example, dealers’ use and sharing of customers’ order-flow information. Our analysis highlights the importance of the design of the entire purchasing operations, from the purchase speed to the choice of trading counterparties.

Several studies, such as O’Hara, Wang, and Zhou (2018), Hendershott et al. (2020), Hau et al. (2021), and Griffin, Hirschey, and Kruger (forthcoming), document dealers’ discriminatory pricing across different groups of regular customers in the corporate bond, municipal bond, and derivative markets. Moreover, Drechsler, Savov, and Schnabl (2017), Scharfstein and Sunderam (2017), Eisenschmidt, Ma, and Zhang (2021), and Wang et al. (2022) show that the market power wielded by banks over regular investors hurts the transmission efficiency of monetary policies. We complement these studies by showing that the Fed, which is a special and powerful trader, is still subject to dealers’ discriminatory pricing and market power. This points to a novel channel through which dealers’ market power hurts the transmission efficiency of monetary policies.

1. Institutional Background and Economic Framework

In this section, we introduce the institutional background and discuss the economic framework for our analysis.

1.1 Institutional background

As the Fed trades with primary dealers in various markets, we discuss mainly the institutional features that are ubiquitous and closely related to dealers’ strategic advantage in trading with the Fed. We then briefly discuss the agency MBS market. More details are provided in Appendix A.1.

The Fed’s monetary policy operations. As discussed in the Introduction, the Fed’s monetary policy operations often involve buying or selling Treasury securities and agency MBS. In doing so, the Fed usually relies on about 20 primary dealers as direct trading counterparties. All other investors who wish to buy from or sell to the Fed, for example, insurance companies, hedge funds, mutual funds, and pension funds, can do so by trading with primary dealers only. The Fed has long employed this primary-dealer system for implementation of various policies, including both the adjustment of the federal funds rate and the QE purchases that have become a regular tool over the last decade.¹²

Moreover, the Fed’s operations, especially QE purchases, are usually executed in huge quantities at rapid speed. For example, over just 15 months, from January 2009 to March 2010, the Fed purchased $1.25 trillion in agency MBS, while over 8 months, from November 2010 to June 2011, the Fed purchased $600 billion in Treasury securities. During the recent COVID-19 pandemic, the Fed purchased about $75 billion in Treasury securities and $50 billion in agency MBS on each business day in the week of March 23, 2020.

A typical timeline of the Fed’s purchase operations is as follows. The Fed publicly releases a monthly trading schedule, including the date, the securities to be purchased, and the expected amount involved in each upcoming purchase operation, which is fixed well ahead of the trade execution day.¹³ For each trade, the Fed solicits offers (or bids) from multiple dealers. For example, when purchasing Treasury securities, the Fed uses its own FedTrade system on which all primary dealers can participate for each trade (Song and Zhu 2018).

However, when the Fed started to purchase agency MBS in the secondary market for the first time, it “did not have either the systems or the market knowledge needed to execute MBS purchases efficiently” (Potter 2012). Therefore, the Fed followed market practice to use the Tradeweb electronic trading platform, which is a major trading platform for agency MBS and accounts for about 40|$\%$| of the dealer-client TBA trading volume (Schultz and Song 2019).¹⁴

Trades on Tradeweb are conducted through request-for-quote (RFQ) algorithms. For each RFQ session, a customer submits her trade request (TBA contract and trade size) nonanonymously to up to four dealers; after receiving dealers’ price quotes, the customer chooses one dealer (usually the one with the best price quote) to trade with. The Fed only trades with primary dealers, so for each trade the Fed selects four primary dealers to participate in its RFQ session. The participating dealers for a Fed trade are not pre-announced; hence, being chosen to participate in a Fed RFQ session is random from the perspective of a dealer. The Fed usually chooses different sets of four primary dealers for different RFQ sessions. Conceivably, the Fed has an inclination to be “fair” and involve all primary dealers in the interests of equity.

The Fed used Tradeweb until April 2014, after which it switched to the FedTrade system involving all primary dealers in each trade (Bonaldi, Hortacsu, and Song 2015). Our empirical analysis focuses on the RFQ period, during which the Fed and non-Fed customers used similar trading protocols.

Agency MBS market. We briefly introduce the agency MBS market, on which our empirical analysis focuses. Agency MBS, issued through Fannie Mae, Freddie Mac, and Ginnie Mae, are effectively default-free but subject to prepayment risk (Hayre and Young 2004). Trading in agency MBS occurs via both specified pool (SP) contract, under which an individual MBS is traded, and TBA forward contract, under which any MBS within an eligible cohort can be delivered (Gao, Schultz, and Song 2017). A TBA contract specifies, for example, a Fannie Mae 30-year fixed-rate MBS with a 4|$\%$| security coupon rate, but the particular MBS that a seller delivers needs to be identified only two days before the settlement day. TBA trading is remarkably liquid and incurs low transaction costs of only a few basis points (Bessembinder, Maxwell, and Venkataraman 2013; Gao, Schultz, and Song 2017).

Before 2008, agency MBS were involved only in the Fed’s operations in the short-term funding market (like repo and securities-lending contracts). In response to the 2008 financial crisis, in early 2009 the Fed began to conduct outright purchases of agency MBS for the first time in the history of U.S. monetary policy operations. Since then, purchases of agency MBS have become a regular and important toolkit for the Fed. For example, in March 2020 the Fed revived purchases of agency MBS in response to the COVID-19 pandemic. The Fed purchases agency MBS exclusively through TBA contracts because of their great liquidity.

1.2 Economic framework

As our analysis controls for dealers’ inventory cost differences when selling to the Fed and non-Fed customers, we consider economic forces associated with dealers’ market power to account for their discriminatory pricing against the Fed. Specifically, we consider two economic forces related to the two key features of the Fed’s asset purchases described above: the Fed’s constrained choice of trading counterparties and huge purchase amounts.

The Fed’s constrained choice of trading counterparties. As discussed above, the Fed exclusively uses primary dealers as its trading counterparties, which can constrain its operational flexibility. Specifically, the Fed loses outside options in trading with nonprimary dealers; this can grant primary dealers market power over the Fed. Although this effect is theoretically clear-cut, its impact on the price differential between the Fed and non-Fed customers may have been contained by institutional features of the market. In particular, primary dealers account for the bulk of MBS trading volume, so the Fed should compare favorably relative to most non-Fed customers. Therefore, the effect of using primary dealers as exclusive trading counterparties is relevant mainly relative to some large institutional customers who can reach to both primary and nonprimary dealers. Moreover, as also mentioned above, the Fed tends to involve all primary dealers in its operations in the interests of equity. Specifically, the Fed may “overselect” small primary dealers into its RFQ sessions, which could adversely affect the competitiveness of its pricing.

The Fed’s purchases in large amounts. The effect related to the Fed’s implementation of huge purchase amounts is less straightforward, which we demonstrate using a simple modification of the Bertrand-Edgeworth model of price competition with capacity constraints, as in Kreps and Scheinkman (1983). Specifically, we assume that a large dealer with high inventory capacity and a small dealer with low inventory capacity compete to sell a given type of asset to a buyer. The large and small dealers’ inventories are |$x_1$| and |$x_2$|⁠, respectively, with |$x_1 \geq x_2>0$|⁠.¹⁵ We take |$x_1$| and |$x_2$| as exogenously given, but they could be endogenized in the same manner as in the first-stage game in Kreps and Scheinkman (1983).

We normalize dealers’ reservation value for holding inventory to |$0$|⁠. The buyer seeks to buy some constant |$D \in (0,x_1 + x_2)$| units of assets.¹⁶ Each dealer |$i=1,2$| submits an offer to sell up to |$x_i$| units of assets at price |$p_i$|⁠. The buyer first takes the lowest offered price, and if necessary then the higher offered price, until purchase demand |$D$| is met.

The unique equilibrium has two cases.

1. If the buyer’s purchase demand is low (⁠|$D\leq x_2$|⁠), dealers engage in standard Bertrand competition. They sell the same amount of inventory at the same competitive price to the buyer.

2. If the buyer’s purchase demand is high |$(x_2 < D < x_1 + x_2)$|⁠, both dealers employ a mixed strategy, randomizing the offer price |$p_i$| on a common interval that is above the competitive price level. The large dealer on average sells a greater quantity to the buyer than the small dealer does.¹⁷ Furthermore, the large dealer’s offer price is higher than that of the small dealer in the first-order stochastic dominance sense.

In equilibrium, whether the buyer can obtain competitive prices depends on the magnitude of its purchase amount relative to dealers’ inventories. When the buyer purchases in small quantities, as in case 1, it obtains competitive prices. When the buyer purchases a quantity that exceeds the small dealer’s inventory capacity |$x_2$|⁠, as in case 2, both dealers exert market power and charge uncompetitive prices to the buyer. Intuitively, this happens because at least one dealer effectively monopolizes the residual demand that the other dealer cannot meet. Moreover, dealer market power clearly arises in case 2 even without dealer asymmetry (i.e., |$x_1=x_2$|⁠). But when dealer asymmetry is present, the large dealer has greater market power, selling greater quantities of assets at a higher price to the buyer, than the small dealer does.

Compared with the Fed, non-Fed buyers’ purchase quantities are much lower and more likely to be filled by most individual dealers’ inventories; hence, dealers’ pricing for non-Fed buyers is likely to be as in case 1, while their pricing for the Fed is likely to be as in case 2. Hence, the Fed should suffer to a greater extent from dealers’ market power and pay discriminatorily higher prices than non-Fed customers, accounting for the price differential we empirically document.¹⁸ Further, we note that this is a generic effect regardless of buyer identity. That is, any investor whose trade size overwhelms the inventory capacity of individual dealers would receive worse pricing; accordingly, we dub this the trade-size markup effect.¹⁹ This trade-size markup effect stands in contrast to the standard trade-size discount effect documented in studies of OTC markets (Bernhardt et al. 2004; Bessembinder, Spatt, and Venkataraman 2020).

2. Data and Summary

In this section, we introduce the data and summarize the Fed’s agency MBS purchases and dealers’ inventory buildup.

Data. We use two main data sets. The first is the TRACE data set of agency MBS transactions. Each trade record in the TRACE data set contains trade parameters, such as the security identifier, trade date, price, volume, and, importantly, dealer identifier. The second data set comprises Fed purchase data publicly released by the Federal Reserve Bank of New York. Each record of the Fed purchase data contains the TBA contract identifier, price, trading volume, and an identifier of the primary dealer who sells to the Fed. We apply a number of algorithms to clean the data sets, especially those regarding dealer identities (see Appendix A.3 for details).

Our sample period runs from October 2011 through March 2014, a period for which both data sets are available. During this period, the Fed maintained (1) the reinvestment program, which reinvests cash flows from its holdings of agency MBS and agency debt into agency MBS and runs throughout our whole sample period, and (2) the so-called QE3 program, which runs from 2012:Q4 through the end of our sample period (see Appendix A.1 for details of the Fed’s MBS purchase programs). The Fed executes 9,270 purchasing trades in total. These trades are reported as customer-dealer trades in the TRACE data set, for which customer identities are unknown. We match the Fed trades to the TRACE data using the TBA contract identifier, trade date, volume, price, trade direction (i.e., the customer buys from the dealer), and dealer identifier. We are able to match 9,264 Fed trades and exclude the six unmatched cases.

Summary of Fed purchases.Figure 1 plots the quarterly aggregate amounts of quantities involved in the Fed’s purchases, which consist of exclusively 15-year and 30-year agency MBS. On average, the Fed purchases about $88 billion in agency MBS per quarter from 2011:Q4 through 2012:Q3, and increases the purchase amounts to about $190 billion per quarter after the QE3 program starts in 2012:Q4. The Fed’s purchases concentrate in newly issued MBS, so in Figure 1 we also include the quarterly aggregate issuance amounts of these MBS for comparison purposes. On average, the Fed’s purchases account for 28|$\%$| of the issuance from 2011:Q4 through 2012:Q3. This fraction increases to 55|$\%$| for the 2012:Q4–2013:Q2 period, and to 70|$\%$| after 2013:Q3, when the mortgage rate spikes and new issuance drops significantly.

Table 1 breaks down the aggregate purchase amounts by MBS type and trade size. We observe that the Fed purchases tilt more toward Fannie Mae than Freddie Mac and Ginnie Mae MBS and more toward 30-year than 15-year MBS, which are compatible with their market shares (Liu, Song, and Vickery 2021). Moreover, the bulk of the purchased MBS have coupon rates ranging from 2.5|$\%$| to 4|$\%$|⁠, in line with the low mortgage rates that prevailed during this period. In terms of trading size, almost all of the Fed’s purchases are executed in large-integer quantities of $50 million, $100 million, $150 million, $200 million, or $250 million in face value; for comparison, non-Fed trade size ranges from slightly less than $1 million to slightly more than $200 billion and averages about $50 million (see Table 2 for more details).

Intraday timing of the Fed’s operations. Given the Fed’s unique role and huge trade size, it is also worth looking into the intraday timing of the Fed’s operations. First, we find that 62|$\%$| of the Fed’s operations involve one single purchase trade for the same TBA contract on the same day.

For the remaining 38|$\%$| that involve multiple purchase trades for the same TBA contract on the same day, we assess whether the Fed has an incentive to spread out the trades using two measures: in the left panel of Figure 2, we plot the histogram of the time gap between any pair of consecutive trades of the same TBA contract on the same day, whereas in the right panel, we plot the histogram of the time gap between the first and last of trades of the same TBA contract on the same day. From the left panel, we observe that about 80|$\%$| of trades are at least 30 minutes apart and 50|$\%$| are at least 1 hour apart. From the right panel, we observe that on about 80|$\%$| of the days, the first and last trades of a TBA contract are at least 1 hour apart. Hence, if multiple trades are conducted for a TBA contract on a day, the Fed deliberately spreads out the trades.

Primary dealers. Our sample period comprises 185 broker-dealers in total, 21 of which are primary dealers. Sixteen of these primary dealers made at least one sale to the Fed, whereas the remaining five may have participated in the Fed’s offer solicitations but never won a trade (they are small dealers in the agency MBS market, accounting in aggregate for less than 1|$\%$| of total MBS trading volume). Hence, we focus on the 16 primary dealers who have traded with the Fed; these dealers account for 85|$\%$| of the market trading volume in aggregate (see Table 9 for details).

3. Dealers’ Discriminatory Pricing against the Fed

In this section, we document the main finding on the discriminatory pricing that dealers charge the Fed relative to what they charge non-Fed customers.

3.1 Baseline analysis

To estimate dealers’ discriminatory pricing against the Fed, we need to remove the well-documented trade-size discount effect given that the Fed’s trade size is huge (see Table 1). In particular, similar to other OTC markets like those of corporate bond and municipal bonds, customers’ larger trades are executed at significantly better pricing in MBS markets, which may reflect lower per-unit order processing cost (Gao, Schultz, and Song 2017; Bessembinder, Spatt, and Venkataraman 2020). Similar to O’Hara, Wang, and Zhou (2018), we use a two-step procedure in estimating the Fed versus non-Fed price differential: in step 1, we estimate the trade-size discount effect; in step 2, we adjust the raw prices of the Fed and non-Fed trades based on the estimated trade-size discount and then calculate the price differential using the adjusted prices.

Estimation of the trade-size discount effect. We estimate the trade-size discount effect using trades on non-Fed-purchase days.²⁰ Specifically, for each day, we keep the non-Fed customers’ purchase trades for the TBA contracts the Fed does not purchase. We first report in the third column of Table 2 the changes of raw prices of these trades across size groups of |$<$|1M, 1M–5M, 5M–10M, 10M–100M, and |$\geq$|100M; they are estimated by regressing trade prices on size-group dummies, controlling for dealer|$\times$|TBA contract|$\times$|day fixed effects. We observe that the price change is negative across all size groups, showing a uniform presence of trade-size discount. The magnitude of the price change decreases with trade size, implying that the discount levels off with trade size.

To quantify this trade-size discount, we follow the literature to use the logarithm of trade size as the baseline functional form (Bessembinder, Spatt, and Venkataraman 2020). As prevalently used in studies of markets of corporate bond, municipal bond, MBS, ABS, and so on, |$log(trade \text{} size)$| can capture the leveling-off of the trade-size discount effect to certain extent. However, there is no guarantee that it is the “correct” specification and captures the leveling-off completely. We hence consider other specifications to confirm the robustness of our results. For example, we consider a reciprocal-function variant of the logarithm function, |$1/log(trade \text{} size)$|⁠, motivated by the simple case that trade-size discount reflects the spreading of a fixed order-processing cost.²¹ The first two columns of Table 2 report the estimates of regressing trade prices on |$log(trade \text{} size)$| and |$1/log(trade \text{} size)$|⁠, respectively. Both coefficients confirm a significant trade-size discount effect.

Estimation of dealers’ discriminatory pricing against the Fed. Our baseline analysis examines whether the same dealer charges a higher selling price to the Fed than selling to non-Fed customers for the same TBA contract on the same day; this empirical design is laid out in Figure 3. Accordingly, we consider the purchase trades of the Fed and non-Fed customers that are executed on the same day |$t$| for the same TBA contract |$m$| with the same primary dealer |$i$|⁠. As reported in the first column of Table 3, the matched sample contains 4,780 Fed purchase trades and 17,356 non-Fed purchase trades.²² The size of an average Fed purchase is about $172 million, four times as large as an average non-Fed-customer purchase, which is about $48 million.

Similar to O’Hara, Wang, and Zhou (2018), we first adjust the prices of both Fed and non-Fed trades in this matched sample using the estimated trade-size discount effects above. Specifically, we calculate the adjusted prices, when using the logarithm specification for trade-size discount, as

where |$Price_{i,j,m,t}$| is dealer |$i$|’s raw selling price of the |$j$|-th trade on day |$t$| of TBA contract |$m$| and |$\hat{\beta}$| is the coefficient estimated above in the first column of Table 2 (⁠|$-$|1.89). Similar calculations are done when using the |$1/log(trade \text{} size)$| specification.

We then run the following regression,

where the dummy |$\theta_{i,j,m,t}$| equals one if the trade |$j$| is a sale to the Fed and zero if it is a sale to a non-Fed customer, and |$\gamma_{i,m,t}$| is dealer|$\times$|TBA contract|$\times$|day fixed effects. Hence, the coefficient |$\alpha$| quantifies the difference between the selling price to the Fed and that to non-Fed customers by the same dealer for the same TBA contract on the same day.

We observe from the first two columns of Table 3 that the coefficients for the Fed dummy are significantly positive, showing that on average the same primary dealer charges about 2.5 cents higher (per $100 face value) to the Fed than to non-Fed customers.²³ This is about half of an average primary dealer’s gross profit margin when trading with the Fed (the average gross profit margin for a dealer is about 5 cents, as reported in Table A.2). It is also informative to compare our estimate with the discriminatory pricing effect estimated in other markets. Among them, O’Hara, Wang, and Zhou (2018) show that dealers charge a discriminatorily higher selling price to inactive insurance companies than to active insurance companies, which is about 2 to 10 cents and around 20|$\%$| of dealers’ gross profit margins in the corporate bond market.

Although the Fed versus non-Fed price differential estimated above is significant using different specifications to remove trade-size discount effects, one may still be concerned about potential misspecifications; after all, it is impossible to check all specifications for the trade-size discount effect. To further mitigate this concern, we look into evidence directly based on raw prices. In particular, the last column of Table 3 reports the changes of raw trade prices across size groups in the baseline matched sample, similar to those reported in the last column of Table 2 using trades on non-Fed-purchase days. We restrict the |$\geq$|100M group to Fed trades exclusively (the Fed trades mostly fall in this group), and all the other groups to non-Fed trades.²⁴ We observe that the Fed’s |$\geq$|100M trades is charged a markup of 1.32 cents relative to non-Fed customers’ 10M-100M trades, which is in contrast to non-Fed customers’ |$\geq$|100M trades receiving a discount of 0.22 cents on days with Fed operations (see the last column of Table 2).²⁵ This contrast provides raw-price-based support to dealers’ discriminatory pricing against the Fed, which is free of misspecification issues in estimating the trade-size discount effect.

Value differences. Because MBS of varying value can be delivered under the same TBA contract (as discussed in Section 1), dealers may have charged the Fed higher prices because they delivered higher-value MBS to the Fed than to non-Fed customers. In this section, we conduct analyses to compare the MBS received by the Fed with those not received by the Fed. We find that dealers actually delivered lower-value MBS to the Fed than to non-Fed customers.

In particular, from the Fed’s disclosure reports for the System Open Market Account (SOMA), we obtain its CUSIP-level MBS holdings as of April 2014. We retain only MBS issued on or after October 2011, which is the start of our baseline sample period.²⁶ From eMBS, we obtain the set of all TBA-eligible MBS for each TBA contract. By matching the eMBS and SOMA data, we categorize all MBS into Fed-held and non-Fed-held groups. We focus on 30-year MBS, which constitute over 80|$\%$| of the Fed’s purchases (see Table 1).

Because individual prices are not available for the MBS sold under a TBA contract, we use MBS characteristics for the comparison of Fed-held and non-Fed-held MBS. Specifically, we use the weighted-average original loan size (WAOSIZE), which is a key input for prepayment models and has been shown to possess the highest explanatory power for observed MBS trading prices, among other characteristics, such as a borrower’s FICO score and their loan-to-value ratio (Hayre 2001; Fabozzi and Mann 2011; An, Li, and Song 2020). The effect of WAOSIZE on prepayment risk is positive because savings from refinancing larger loans are higher and more likely to outweigh certain fixed refinancing costs; hence, a higher WAOSIZE is associated with lower MBS value.

To control for differences between the TBA contracts that dealers use to sell to the Fed and those they use to sell to non-Fed buyers, we consider the non-Fed-held MBS that belong to the same TBA contract cohort (agency|$\times$|loan term|$\times$|coupon) and are also issued on the same date as Fed-held MBS. The first column of Table 4 provides the result of regressing WAOSIZE of each MBS on the Fed-held dummy, controlling for cohort|$\times$|issuance-date fixed effects. We observe that the loan sizes of Fed-held MBS are significantly higher. Moreover, although the Fed purchases MBS only through TBA contracts, non-Fed customers can also purchase MBS through SP contracts and MBS issuers may retain some high-value MBS on balance sheet (Gao, Schultz, and Song 2017; Buchak et al. forthcoming)). To make sure that we compare MBS mainly traded through TBA contracts, in the second and third columns, we keep only MBS whose WAOSIZE falls into the top 50|$\%$| or the top 25|$\%$| within each cohort|$\times$|issuance-date group. These MBS are of relatively low values and are most likely to be traded through TBA contracts.²⁷ We find that the coefficient for the Fed dummy decreases naturally but, importantly, the coefficient remains positive.

In Appendix A.4.2, we also compare the realized prepayment rates and other characteristics of Fed-held and non-Fed-held MBS. We find that compared with non-Fed-held MBS, Fed-held MBS have similar FICO score and loan-to-value ratio; yet, they experience significantly faster prepayment rates and hence are of lower values than non-Fed-held MBS, given that interest rates stay at low levels and most newly issued MBS are in the money during our sample period. In addition, Fed-held MBS have a longer maturity (about 27 years) than non-Fed-held MBS (about 23 years), consistent with the Fed’s purchase concentration in newly issued MBS.

Overall, the comparison of Fed-held and non-Fed-held MBS further strengthens our finding on dealers’ discriminatory pricing against the Fed relative to what dealers charge non-Fed buyers. In short, dealers sell lower-value MBS at higher prices to the Fed than to non-Fed customers.

3.2 Differential inventory costs

One important concern on our interpretation—the discriminatory pricing reflects dealers’ greater market power over the Fed than over non-Fed customers—is that dealers may need to carry larger inventories in selling to the Fed than in selling to non-Fed customers, so the higher prices they charge the Fed may simply reflect higher inventory costs.²⁸ However, our empirical design likely controls for the potential inventory cost differences. In particular, although different units of the same MBS may be purchased at different days and prices, our comparison—of the same dealer’s selling prices on the same day for the same TBA contract to the Fed and non-Fed customers—likely ensures that the MBS the dealer sold to the Fed and to non-Fed customers are based on the same inventory.

A further finding that reinforces our interpretation is that most of dealers’ inventory sold to the Fed is built before the Fed operation day. Specifically, in Figure 4, we plot the cumulative inventory change for an average primary dealer under an average TBA contract that the Fed purchases (with multiple trades) within a window from 60 weekdays before to 60 weekdays after the Fed purchase date, which is set to zero.²⁹ We observe a salient run-up in dealers’ inventories, implying that primary dealers’ inventory used for their trading on the Fed-purchase day is indeed accumulated beforehand.³⁰ The MBS sold to the Fed and non-Fed customers are likely based on this same inventory.³¹

Moreover, we address two additional concerns on the same-day comparison by conducting same-intraday-window comparison.

First, the Fed’s purchases may affect intraday pricing on Fed operation days. In particular, just like the Treasury issuance auctions can result in a temporary downward price movement until the issuance time (Fleming and Liu 2014), the Fed’s purchases might lead to a temporary upward price movement until its purchase operation time, which would confound the same-day price differential estimate. To address this concern, we look into intraday time windows. Specifically, for each Fed trade, we keep the non-Fed trades for the same TBA contract by the same dealer that occur in a time window from one hour before to one hour after the Fed trade, denoted as |$[-1h,1h]$|⁠. We also consider time windows of longer lengths, including |$[-2h,2h]$|⁠, |$[-3h,3h]$|⁠, and |$[-4h,4h]$|⁠. Using the respective trades in these time windows, we then estimate the (Fed vs. non-Fed) price differential based on the same regression (2).

As reported in panel A of Table 5, the number of matched Fed trades is 4,180, 3,829, 3,221, and 2,279, smaller than the baseline same-day-matching sample with 4,780 trades. However, the average Fed or non-Fed trade sizes are fairly similar. Moreover, the average absolute time difference (weighted by non-Fed trade sizes) between the Fed and non-Fed trades is about 107, 85, 58, and 30 minutes, lower than that of the same-day sample (about 156 minutes). Most importantly, the price differential ranges from 1.66 to 2.23 cents, which is somewhat lower than the baseline estimate (2.5 cents) but still statistically significant and economically large.³²

Second, an inventory offloading effect may also confound our baseline estimate. Specifically, dealers with a larger inventory than needed may have to get rid of excess inventory at low prices after the Fed operation has taken place. The price differential estimates used so far may have included such non-Fed customer trades that help dealers offload their extra inventory. To alleviate this concern, we keep only the non-Fed trades that happen before the Fed trades, based on which we reestimate the price differential. As reported in panel B of Table 5, dealers’ discriminatory pricing against the Fed remains robust.³³

In addition, note that the above intraday analyses use cumulative-window groups because our main purpose is to show the significant price differential between the Fed and non-Fed purchase trades. As revealed in the lower price differential of shorter time windows, there seems to be an intraday price movement of non-Fed trades. Though not our focus, we investigate this interesting pattern with a window-by-window analysis. Specifically, we run the baseline regression (2) using the Fed trades and the non-Fed trades in nonoverlapping hourly time windows (the first is from the beginning of the day to four hours before the Fed purchase and the last is from four hours after the Fed purchase until the end of the day). Figure 5 reports the negative of the Fed purchase dummy, which is equal to the non-Fed buyers’ price minus the Fed’s purchase price. We observe that non-Fed trades exhibit a price run-up before the Fed trade and a (partial) reversal after the Fed trade, which is in similar fashion to the temporary intraday price movement around Treasury issuance auctions (Fleming and Liu 2014). Importantly, the hour-by-hour estimates also confirm that the Fed versus non-Fed price differential is robust to the intraday price movement and is significant using only non-Fed trades before the Fed purchase.

Overall, these intraday comparisons—using the same dealer, same MBS, and same trading time (before the Fed trade)—further control for the inventory cost differences, showing that the discriminatory pricing is likely because of dealers’ stronger market power over the Fed than over non-Fed customers.³⁴

4. Trade-Size Markup and Constrained-Counterparty-Choice Effects

The price differential estimated in the preceding section is obtained by comparing the prices of Fed trades (mostly |$\geq$|100M) and non-Fed trades (of all different sizes). Hence, it consists of both the trade-size markup and constrained-counterparty-choice effects, as discussed in Section 1.2. In this section, we conduct analyses on these two economic forces.

First, we quantify the relative contributions of trade-size markup and constrained-counterparty-choice effects to dealers’ discriminatory pricing. Among the Fed trades used in the baseline analysis (as reported in Table 3), we consider those that have matched non-Fed customer trades of $100 million or above in face value, which is the size range of most Fed trades (see Table 1). As shown in Table 6, the number of matched Fed trades is 1,727, 608, and 307 for the same-day, |$[-1h, 1h]$|⁠, and |$[-1h, 0]$| samples, respectively, which mostly account for less than one-third of the Fed trades that can be matched without reference to trade size (4,780, 2,279, and 1,363, as reported in Tables 3 and 5). The number of matched non-Fed trades is also lower, equal to 2,749, 731, and 348, respectively. The average size of these non-Fed customer trades is about $200 million, comparable to that of Fed trades (about $185 million).

We estimate the price differential between these mega-sized Fed and non-Fed trades, still based on regression (2), which now mainly captures the constrained-counterparty-choice effect. As reported in Table 6, the price differential is reduced from 2.5 to 1.13 cents (by about 55|$\%$|⁠) for the same-day sample, from 1.66 cents to almost zero for the |$[-1h,1h]$| window, and from 1.65 cents to 0.97 cents (by about 40|$\%$|⁠) for the |$[-1h,0]$| window. On balance, the results suggest that the trade-size markup effect accounts for a large fraction of dealers’ discriminatory pricing against the Fed while the constrained-counterparty-choice effect also plays a noticeable role.³⁵

Second, we conduct a further test for the trade-size markup effect.³⁶ As discussed in Section 1.2, trade-size markup is a generic economic effect regardless of the buyer’s identity, so even non-Fed customers would receive worse pricing for their trades that are large enough to overwhelm the inventory capacity of individual dealers. We conjecture that this is more likely on Fed purchase days, as Fed purchases remove a large quantity of MBS supply from the market.

As already shown in the last column of Table 2, the non-Fed customers’ |$\geq$|100M trades (similar to the Fed’s trading size) on non-Fed-purchase days indeed receive a discount (of 0.22 cents relative to 10M–100M trades). In the first column of Table 7, we report the price changes across size groups of non-Fed buyers’ trades on Fed-purchase days. In particular, for each non-Fed |$\geq$|100M trade, we keep the non-Fed purchase trades of smaller sizes for the same TBA contract, with the same dealer, and on the same day. We observe that non-Fed customers’ buying prices decrease for sizes up to $100 million, consistent with trade-size discount, but importantly, their buying prices increase for |$\geq$|100 million group, showing a trade-size markup of 0.55 cents. In the second column of Table 7, we further restrict the sample to the one-hour window around the non-Fed |$\geq$|100 million trades. We observe the same pattern: the trade-size markup effect for |$\geq$|100 million group on Fed trade days and the trade-size discount effect for smaller-sized trades. In fact, the trade-size markup effect for non-Fed |$\geq$|100 million trades is even stronger (1.28 cents with 1|$\%$| statistical significance).

Overall, consistent with our hypothesis, non-Fed buyers receive pricing discounts for moderately large trades but pay markups for extremely large trades when (and only when) the Fed’s purchases take a substantial fraction of assets out of the market and make dealers’ remaining inventory relatively limited.³⁷

Third, we provide some supportive evidence for the constrained-counterparty-choice channel by examining the dealer counterparties of Fed and non-Fed trades. In panel A of Table 8, we report a summary of different dealers’ average fraction of non-Fed purchases. Based on their total trading volume with non-Fed buyers, we classify primary dealers into large, medium, and small subgroups and also form three subgroups of nonprimary dealers—the largest one, the second to fifth, and the others.³⁸ We observe that the largest non-primary-dealer accounts for 4.2|$\%$| of all non-Fed purchases, comparable to a medium primary dealer; its trading fraction is higher than that of any small primary dealer. Moreover, the second to fifth nonprimary dealers are comparable to the smallest primary dealers. Therefore, customers indeed trade with a few nonprimary dealers nontrivially, but the Fed cannot select into its purchase operations.

We also compare the concentration of Fed purchases among primary dealers with that of non-Fed purchases. In particular, the first column of panel B in Table 8 reports the fraction of non-Fed purchases executed with the large, medium, and small primary dealers (as defined in panel A using dealers’ trading volume with non-Fed customers), whereas the second column reports the fraction of Fed purchases executed with the same three subgroups of primary dealers. We observe that the fraction of trading with large primary dealers is 51.04|$\%$| for Fed trades, lower than the 57.85|$\%$| for non-Fed trades; the reverse is true for the fraction of trading with medium primary dealers. That is, compared with non-Fed customers, the Fed allocates a high fraction of its trades to medium dealers relative to large dealers. These findings are consistent with the hypothesis that the Fed tries to use a broad range of dealers in the interests of equity, which may have adversely affected the competitiveness of its pricing. We caution that we do not have detailed data on the Fed’s selection of participating dealers in each RFQ session, which is important to fully substantiate this hypothesis.

5. Large and Small Dealers

In this section, we examine whether large dealers charge greater discriminatory pricing against the Fed than small dealers do.

Dealer heterogeneity. We measure the size of dealer |$i$| by the fraction of TBA trading volume for which it was responsible among all 185 dealers from May 2011 through September 2011, denoted as |$M_i$|⁠. We use this earlier sample to avoid confounding effects of Fed purchases after they start in October 2011. As shown in panel A of Table 9, the 16 primary dealers capture a dominating market share of 85|$\%$| and, importantly, exhibit considerable heterogeneity: the top-5 primary dealers account for 47|$\%$| of the market, while the top-10 account for 77|$\%$|⁠.

Dealer size is also stable over time. To show this, for these top-5 and top-10 primary dealers, we compute their market shares of all trades for each quarter from 2011:Q4 through 2014:Q1. As shown in panel B of Table 9, the (time-series) average market share is 45|$\%$|⁠, 80|$\%$|⁠, and 88|$\%$| for the top-5, the top-10, and all 16 primary dealers, respectively, and these figures are similar to those reported in panel A. Moreover, the (time-series) standard deviation and range are both tiny, confirming the remarkable stability of dealer size.

We also present, in Figure 6, the cumulative inventory change for an average large primary dealer (defined as primary dealers with top-5 |$M_i$|⁠) and an average small primary dealer (defined as other primary dealers) under an average TBA contract that the Fed purchases (the construction procedure is similar to that for Figure 4). We observe that the five large primary dealers control the bulk of MBS inventory for the Fed’s purchases. Furthermore, the total selling amount under an average TBA contract to the Fed by an average large dealer and by an average small dealer are $455 million and $134 million, respectively.

Dealers’ differential discriminatory pricing. We first examine large and small dealers’ differential selling amounts and pricing to the Fed. To quantify large and small dealers’ differential selling amounts to the Fed, we consider the following regression:

where |$M_i$| is the size of dealer |$i$|⁠, |$A_n$| is the Fed’s purchase amount in trade |$n$|⁠, and |$W_{i,n}$| is the selling amount to the Fed by dealer |$i$|⁠. For each Fed purchase |$n$|⁠, one dealer, out of several participating ones, wins the trade and sells to the Fed, so |$W_{i,n} = A_n$| when dealer |$i$| is the one who sells to the Fed and |$W_{i,n}=0$| for other dealers; the total number of observations is hence 148,224 (= 16 dealers |$\times$| 9,264 trades). We control for TBA-contract fixed effects |$\gamma_m$| to compare individual dealers’ selling amounts to the Fed under the same TBA contract. As reported in the first column of Table 10, the coefficient |$\beta$| on the product term between dealer size and the Fed’s purchase amount is positive and significant. Quantitatively, a dealer that is one standard derivation larger in size (⁠|$3.8\%$|⁠, from Table 9) sells |$4.8\%$| (⁠|$=1.27\times3.8\%$|⁠) more in MBS as a fraction of the Fed’s total purchase amount.

To quantify large and small dealers’ differential pricing to the Fed, we consider the following regression:

Similar to the baseline regression (2), |$Price^{adj}_n$| is the Fed’s trade-size-adjusted price for purchase |$n$|⁠, where we use the coefficient for |$log(trade \text{} size)$| in the first column of Table 2 (⁠|$-$|1.89). The size of dealer |$i$| who sells to the Fed in purchase |$n$| is |$M_i$|⁠. We also control for TBA-contract fixed effects |$\gamma_m$| to compare individual dealers’ selling prices to the Fed under the same TBA contract. Because multiple purchases |$n$| under the same TBA contract |$m$| can be executed on different days, we control for market conditions |$Z_{n}$| using the BBB spread, 2- and 10-year Treasury yields, and the VIX index.³⁹ The coefficients |$\psi_k$| (⁠|$k$| = loan term|$\times$|coupon of the TBA contract) allow for different loadings on the market-level variables for different types of TBA contracts.

The second column of Table 10 provides the results of regression (4). For each Fed purchase |$n$|⁠, we observe only the selling price of the dealer who sells to the Fed, so the number of observations for this regression is the number of trades in total (9,264). The coefficient for dealer size is positive and significant. Quantitatively, a dealer that is one standard derivation larger in size (⁠|$3.8\%$|⁠, from Table 9) charges the Fed a price that is about one cent (⁠|$=0.25\times3.8$|⁠) higher per $100 in face value. This is about 20|$\%$| of an average primary dealer’s gross profit margin when trading with the Fed.

We then examine large and small dealers’ differential pricing to non-Fed buyers under the same TBA contract on the same day when the Fed buys, following the baseline design as demonstrated in Figure 3. Specifically, in Table 11 we report the results of regression (4) using the sample of these non-Fed buyer trades, with trade sizes at all levels, of at least $1 million, $10 million, and $100 million, respectively. The results reported in the first column indicate that a dealer that is one standard derivation larger in size (⁠|$3.8\%$|⁠, from Table 9) charges non-Fed buyers a price that is about 0.3 cents (⁠|$=0.07\times3.8$|⁠) lower per $100 in face value. The magnitude becomes even larger for larger trades, as can be seen in the next three columns. We note that the columns lack statistical significance, but the negative point estimates provide a contrast to the significantly positive |$0.25$| in Table 10.

In a competitive pricing context, if larger dealers charge higher prices to the Fed (as reported in Table 10) only because of their higher inventory costs, we should expect them to charge higher prices to non-Fed customers as well, which runs against to the findings reported in Table 11. Hence, the opposite pattern of large and small dealers’ differential pricing to non-Fed customers and to the Fed lends support to large dealers’ stronger market power.

6. Conclusion

We provide novel evidence, in the agency MBS market, that the same dealer charges discriminatorily higher prices to the Fed than to non-Fed buyers when selling from the same inventory. By comparing the same dealer’s sales of the same security around the same time to the Fed and non-Fed customers, this discriminatory pricing is likely because of dealers’ stronger market power over the Fed than over non-Fed customers rather than due to inventory cost differences.

Further analyses show that dealers’ discriminatory pricing arises from the trade-size markup effect associated with the Fed’s purchases in huge amounts and also possibly relates to the Fed’s constrained counterparty choice. Hence, the implementation of Fed purchase programs could be improved by adjusting purchase speed by giving further considerations to secondary-market conditions and by choosing trading counterparties flexibly. One potential approach, for example, is to conduct small-sized purchases on the FedTrade platform: the small size for each purchase can reduce the trade-size markup effect and the FedTrade platform can include all primary dealers in each operation, both of which would promote competitive pricing. Including certain nonprimary dealers (like those uncovered in our analysis who account for a fair fraction of market trading) as trading counterparties may also bring in some improvements. Of course, trade-offs in the design of the Fed’s purchase operations in terms of reducing execution costs versus reaping the benefits of fast execution and the primary dealer system should be comprehensively evaluated.

Appendix

The appendix provides additional results and details.

A.1 Institutional Background on Agency MBS and Fed Purchases

Most agency MBS are issued as pass-through securities in which interest payments (subtracting credit guarantee and mortgage service fees) and principal payments on underlying mortgages are passed through pro rata to MBS investors. Agency MBS are effectively default-free, with credit guarantees from Fannie Mae, Freddie Mac, or Ginnie Mae, but subject to uncertainty regarding the timing of cash flows, which is known as prepayment risk (Gabaix, Krishnamurthy, and Vigneron 2007).

Trading in agency MBS occurs via both the SP contract and the TBA forward contract. By combining thousands of heterogeneous MBS into a consolidated cohort, TBA trading incurs low transaction cost and serves as the bedrock of market liquidity for the entire agency MBS market (Gao, Schultz, and Song 2017; Li and Song 2019).

Table A.1 lists the major events associated with the Fed’s operations in the agency MBS market since the 2008 global financial crisis. The Fed began conducting outright purchases of agency MBS in early 2009. After that, the Fed conducted multiple rounds of outright purchases of agency MBS until December 2014, when it began tapering its MBS purchases. In March 2020, the Fed resumed purchasing agency MBS in response to the COVID-19 pandemic.⁴⁰

A.2 Proof of Claims in Section 1.2

In case 2 of the equilibrium discussed in Section 1.2, we claim that the large dealer on average sells more assets to the buyer than the small dealer does. In this proof, we use the equilibrium construction of Osborne and Pitchik (1986), which generalizes Kreps and Scheinkman (1983), to verify this claim.

Specifically, we assume the buyer’s demand for the assets |$d(p)$| at price |$p\in[0,\infty)$| is |$d(p)=D$| if |$p\leq \bar{p}$| and |$d(p)=0$| if |$p > \bar{p}$|⁠, for some constant |$\bar{p}>0$| and |$D\in (x_1,x_1 + x_2)$|⁠. That is, the buyer demands |$D$| units of the assets if the price is less than |$\bar{p}$| and |$0$| units otherwise. By theorem 1 of Osborne and Pitchik (1986), in equilibrium the small dealer randomizes the offer price |$p$| on the interval |$(\underline{p}, \bar{p}]$|⁠, where |$\underline{p} = \bar{p}(D-x_2)/\min(x_1,D)$|⁠. The cdf of the small dealer’s offer price on the interval |$(\underline{p}, \bar{p}]$| is

while the small dealer’s equilibrium selling revenue is |$x_2 \underline{p}$|⁠. Therefore, the small dealer’s expected selling amount to the buyer is

where in Equation (A.2) we use the definition of |$\underline{p}=\bar{p}(D-x_2)/\min(x_1,D)$|⁠. Because the total selling amount to the buyer is |$D$|⁠, the above result implies that the large dealer on average sells more assets than the small dealer does.

A.3 Data Cleaning for TRACE Transactions and Fed Purchases

For the TRACE transaction data, we first apply the standard algorithm to correct trade revisions, cancellations, and reversals, and also account for the duplicated reports of interdealer trades (Gao, Schultz, and Song 2017). Furthermore, we address several issues regarding dealer identifiers.

First, for a give-up trade in which a reporting firm reports on behalf of the actual trading dealer (e.g., a clearing firm reports on behalf of a correspondent dealer), we assign the trade to the dealer who executes the trade. We do the same for interdealer locked-in trades in which a reporting firm reports to TRACE on behalf of both actual trading dealers.

Second, some dealers use multiple identifiers in TRACE. We merge all identifiers that are tied to the same underlying dealer using the link table from the Depository Trust & Clearing Corporation (DTCC).⁴¹

Third, we exclude an interdealer broker who maintains a trading platform to match dealers for trading. For a given TBA contract at the same trading time (in seconds) and at the same trading price, 99.3|$\%$| of trades intermediated by this interdealer broker are netted to 0. Our algorithm is as follows.

• For about two-thirds of the trading records, this interdealer broker buys from some dealer A and sells to some dealer B the same TBA contract at the same time (in seconds) in the same quantity and at the same price. In this case, we delete the two trades that are intermediated by this interdealer broker and record the real transaction in which dealer A sells to dealer B.

• For the remaining one-third of the trading records, this interdealer broker splits trading volume across dealers for a given TBA contract at the same time (in seconds) at the same price. For example, dealer A sells $10 million in MBS, dealer B sells $5 million in MBS, and dealer C buys $15 million in MBS from this interdealer broker, all at the same time at the same price. In this case, we delete all three trades by this interdealer broker and record two trades: (1) dealer A sells $10 million in MBS to dealer C and (2) dealer B sells $5 million in MBS to dealer C.

• The above two cases cover 99.3|$\%$| of trades intermediated by this interdealer broker. For the rare cases in which this interdealer broker fails to net within the same second at the same price, we find that most of the time this interdealer broker either charges an explicit markup or holds inventory for a very short period of time, usually a few minutes. These trades are most likely executed by a separate dealer desk within this interdealer broker, outside of its main electronic matchmaking business. We do not change these unmatched trades.

In addition, to align with Fed purchases that are executed in the TBA market, we keep only regular good-delivery outright TBA trades with standard fixed coupon payments and without stipulations for 15-year and 30-year MBS issued by Fannie Mae, Freddie Mac, and Ginnie Mae.⁴² We correct certain incorrect settlement dates for TBA contracts using the settlement schedule provided by the Securities Industry and Financial Markets Association. We also delete trades executed on weekends.⁴³ Following Gao, Schultz, and Song (2017), we exclude trades with size less than $10,000. The resultant data contain 2,593,151 TBA trades, including trades between the Fed and primary dealers.

For the Fed’s purchase records of agency MBS, we first remove canceled transactions. We retain only outright purchases and exclude dollar rolls that the Fed uses to facilitate settlements (Song and Zhu 2019). In addition, we exclude “small value exercises” that the Fed conducts for operational testing.⁴⁴

A.4 Additional Results and Robustness Checks

We present a number of additional results and robustness checks.

A.4.1 Dealers’ gross profit margins

Our main analysis focuses on comparing dealers’ selling prices to the Fed with their selling prices to non-Fed customers. This differs from dealers’ gross profit margins, which compare dealers’ selling prices to the Fed with their buying prices from non-Fed customers.

For completeness, we present some summary statistics for dealers’ gross profit margins. In particular, for each purchase |$n$| that the Fed executes, we calculate counterparty dealer |$i$|’s volume-weighted average buying price (including both dealer-customer and interdealer trades) from |$t$| weekdays before to one weekday before purchase |$n$|⁠, denoted as |$\tilde{P}_{n}^{\{-t\}}$| (index |$i$| is not added explicitly because there is only one counterparty dealer |$i$| for each purchase |$n$|⁠). We do this for various time windows up to 60 weekdays before the purchase date, given that dealers accumulate inventory prior to a Fed trade, as documented in Figure 4. We compute the gross profit margin earned from purchase |$n$| as

Table A.2 provides summary statistics for the gross profit margins. We observe that the average gross profit margin ranges from 3.8 cents to 5.9 cents per $100 in face value for various window lengths |$t$|⁠. The increasing profit margins that we observe as the window length expands imply the occurrence of a price run-up on days prior to Fed trading; see Lou, Yan, and Zhang (2013) and Sigaux (2020) for similar price trends around the Treasury issuance auctions.

A.4.2 Differing prepayment characteristics of Fed-held and non-Fed-held MBS

Similar to the difference of the Fed-held and non-Fed-held MBS in WAOSIZE (as studied in Table 4), we also examine their differences in realized prepayment rates and other characteristics.

The first column of panel A of Table A.3 reports the result of regressing the realized prepayment rate of each MBS within 12 months of issuance on the Fed-held dummy, controlling for cohort|$\times$|issuance-date fixed effects. We observe that the Fed-held dummy is significantly positive, showing that Fed-held MBS experience faster prepayment rates than non-Fed-held MBS that are issued on the same date and belong to the same TBA contract cohort; see Kandrac and Schlusche (2015) for related evidence. In the second and third columns, we keep only MBS whose prepayment rates fall into the top 50|$\%$|⁠, and the top 25|$\%$| of rates within each cohort|$\times$|issuance-date group. The coefficient for the Fed dummy decreases but the coefficient remains significantly positive. Because interest rates stay at low levels and hence newly issued MBS are in the money during most of our sample period, the faster prepayment rates imply that Fed-held MBS are lower in value than non-Fed-held MBS.

We then conduct similar analyses for two other MBS characteristics: WAOCS (weighted-average original credit score) and WAOLTV (weighted-average original loan-to-value ratio). We use the top percentile of WAOCS and bottom percentile of WAOLTV, because a higher WAOCS and a lower WAOLTV is associated with a lower MBS value (Fusari et al. 2022). As reported in panels B and C of Table A.3, there is no detectable significant difference in WAOCS or WAOLTV between the Fed-held MBS and non-Fed-held MBS.

In addition, we look into the seasonedness of the MBS as measured by weighted average maturity (WAM). In particular, for each quarter end and each cohort, we compute the issuance-amount-weighted average of WAM of Fed-held and non-Fed-held MBS, respectively.⁴⁵ As reported in Figure A.1 for Fannie Mae, Freddie Mac, and Ginnie Mae 30-year MBS separately, the average maturity of Fed-held MBS (about 27 years) is longer than that of non-Fed-held MBS (about 23 years).

A.4.3 Dealers’ inventory buildup for Fed purchases

We first provide details about the measure of dealers’ inventory buildup (in Figures 4 and 6). In particular, the Fed conducts multiple trades on separate days under the same TBA contract, and these trades are then settled together. Hence, we calculate dealers’ inventory buildup as follows.

1. For each trade |$n$| executed by the Fed under a given TBA contract |$m$|⁠, we calculate the daily inventory change (= total purchase amount minus total sale amount on each day) for each primary dealer |$i$| (whether or not it sells to the Fed in trade |$n$|⁠), excluding all trades with the Fed. We do this up to 60 weekdays before and after the day of trade |$n$| (these days are denoted in relative terms such that |$-1$| and |$1$| mean |$1$| weekday before and after the day of trade |$n$|⁠, respectively) and denote the measure as InvChg|$_{i, n, m,t}$|⁠.

2. We take dealer |$i$|’s average daily inventory change across multiple trades under each TBA contract |$m$| and each of the 121 days |$t$|⁠, denoted as InvChg|$_{i,m,t}$|⁠.

3. We subtract dealer |$i$|’s total selling amount to the Fed under TBA contract |$m$| from InvChg|$_{i,m, 0}$|⁠.

4. We take the cumulative sum from day |$-60$| to day |$t$| to measure dealer |$i$|’s inventory buildup under TBA contract |$m$| on the |$t$|-th day relative to the Fed’s purchase day, denoted as InvCum|$_{i,m,t}$|⁠.

Overall, we calculate a dealer’s inventory change at TBA contract |$m$| level instead of trade |$n$| level, because dealers build inventory under a given TBA contract |$m$| for the entire series of trades.⁴⁶

Next, in the spirit of a placebo test, we provide supportive evidence that dealers’ inventory buildup as shown in Figure 4 is indeed associated with their anticipation of the Fed’s purchases. Specifically, Figure A.2 plots inventory changes under TBA contracts that settle in 2011:Q3, when the Fed did not conduct MBS purchases. Our sample cannot go earlier because TRACE only started to collect MBS transaction reports in May 2011. In particular, within each settlement month of July, August, and September 2011, we retain the top-10 TBA contracts by total trading volume; these contracts are comparable to those that are purchased by the Fed. The inventory calculation is the same as that for InvCum|$_{i,m,t}$| except that day |$t$| is defined relative to the TBA settlement day. We observe that, in contrast to an inventory buildup prior to Fed trades, dealers continue selling MBS prior to the settlement date, which reflects their intermediation of new MBS issuances.⁴⁷

Finally, we discuss several measurement issues that might arise in connection with dealers’ inventory buildup. First, the trading data, which measure flow changes in dealers’ inventories, do not allow for precise measurement of dealers’ inventory levels. Our focus is, however, on dealers’ inventory buildup in anticipation of a Fed trade, so the inventory change measured using trading data suits our purpose. Second, although the Fed purchases MBS exclusively through TBA contracts, dealers may deliver MBS acquired on the SP market. However, MBS in the SP market are usually higher in value, so it is suboptimal for dealers to accumulate a large volume of SP MBS and deliver them to the Fed through TBA contracts. That being said, we find that including SP trades in inventory measurement delivers similar results.

A.4.4 Inventory shocks and offloading

In practice, there may be some random shocks to dealers’ inventory. A higher realized inventory leaves a given dealer with greater inventory risk if the inventory goes unsold; as a result, the dealer may charge a lower selling price and sell a greater amount of MBS to the Fed to offload the inventory. Note that this implication fixes the customer and varies a given dealer’s realized inventory, which differs from our main test in which we vary customers (Fed vs. non-Fed buyers) but fix a given dealer’s inventory.

In the first column of Table A.4 we report the results of regressing the total selling amount to the Fed by dealer |$i$| under TBA contract |$m$| on InvCum|$_{i,m, -1}$|⁠, which is dealer |$i$|’s realized inventory under a given TBA contract |$m$|⁠. We include dealer fixed effects so that the coefficient for InvCum|$_{i,m, -1}$| measures the impact of varying realized inventory for a given dealer |$i$| across multiple TBA contracts |$m$|⁠. The significant coefficient |$0.322$| implies that if a given dealer receives $100 million in additional MBS inventory, it sells $32.2 million more to the Fed. The sample size is 6,368 instead of the 9,264 trades, because a given dealer |$i$| sometimes sells the same TBA contract |$m$| to the Fed in multiple trades |$n$|⁠. In the second column of Table A.4 we report the results of regressing the selling price to the Fed by dealer |$i$| of trade |$n$| on the realized inventory InvCum|$_{i,m, -1}$|⁠. As in Table 3, we adjust the raw prices using the estimated slope on |$log(trade \mbox{} size)$| from non-Fed buyers’ trades on days when the Fed does not trade. We also control for market conditions using the BBB spread, 2-year and 10-year Treasury yields, and the VIX index. We observe that a higher realized inventory has a negative impact on the selling price to the Fed. Overall, the results show that the greater a dealer’s realized MBS inventory, the more MBS it sells to the Fed at lower prices.

A.4.5 Analysis on interdealer trades

In the main text, we compare the Fed purchase trades with non-Fed customers’ purchase trades and do not use interdealer trades. In this section, we conduct an analysis on interdealer trades. Specifically, it is possible that dealers who were chosen by the Fed to participate in its operations might not have the (enough) MBS and need to scramble for inventory from nonparticipating dealers just before the operation. If this were the case, the prices at which participating dealers purchase MBS from nonparticipating dealers would be pushed to a high level so that the difference between the Fed purchase price and its counterparty dealer’s purchase price in the interdealer market would be quite low.

In Table A.5, we report estimates of the difference between primary dealers’ selling prices to the Fed and their buying prices from other dealers still based on regression (2).⁴⁸ We adjust the raw prices using the trade-size discount estimate based on interdealer trades on days when the Fed does not trade. Similar to the baseline estimate of the Fed versus non-Fed price differential, this price difference is large and significant, showing that the “scramble” effect is unlikely to be large. This is potentially because these dealers have great experiences trading with the Fed and can manage their inventory well.

A.4.6 Variations across Fed purchase programs

In this section, we present an additional test of the trade-size markup effect by exploiting a variation in the size of distinct Fed purchase programs. Specifically, after the QE3 program started in September 2012, the monthly purchase amount increased from about $30 billion to roughly $65 billion (see Section 1 for details). Cast within our economic framework, this increase in purchase amount can boost the trade-size markup effect.

We define the pre-QE3 period as running from 2011:Q4 through 2012:Q3, and the QE3 period as running from 2012:Q4 through 2014:Q1. Table A.6 reports the results of regression (2) but with an added interaction term between Fed purchases and the QE3 dummy, which captures dealers’ discriminatory pricing against the Fed in QE3 relative to the pre-QE3 period. In column 1 for the sample of Fed and customer trades of all sizes, the coefficient for the interaction term is positive and statistically significant, showing that dealers’ discriminatory pricing against the Fed indeed becomes more pronounced with larger purchases. To check whether the greater discriminatory pricing mainly occurs through the trade-size markup effect, we further restrict the sample to trades with size |$\geq$|100M so that only the constrained-counterparty-choice effect remains. As reported in column 2, the coefficient for the interaction term is about half of the estimate in column 1. Overall, dealers’ discriminatory pricing becomes stronger after QE3 starts and both effects contribute to the strengthening.

A.4.7 The effects of switching from Tradeweb to FedTrade

As discussed in Section 1.1, in April 2014 the Fed switched from the Tradeweb platform to its own FedTrade system for agency MBS purchases. This switch allows the Fed to seek offers from all primary dealers for each trade; before, the Fed could only seek offers from four primary dealers for each trade.⁴⁹ Intuitively, this switch could weaken the constrained-counterparty-choice effect.⁵⁰

For the sample of 2014:Q2–2015:Q2 during which Fed purchases were executed on the FedTrade system, we consider matched mega-sized (⁠|$\geq$| $100 million) trades of the Fed and non-Fed buyers, following the same procedure as Table 6. We adjust the raw prices using the estimated trade-size discount effects based on the |$log(trade \text{} size)$| specification on days when the Fed does not conduct purchase operations. As shown in Table A.7, the Fed’s price markup relative to non-Fed buys is 0.89, 0.22, and 0.64 cents for the full day, |$[-1h,1h]$|⁠, and |$[-1h,0]$| window. Overall, the numbers slightly weaken relative to the 1.13, 0.08, and 0.97 cents estimated in Table 6 for the Tradeweb sample. We caution that we do not have enough statistical power to claim a significant difference in estimates between the FedTrade and Tradeweb sample. Nevertheless, the overall direction of the change is consistent with a weakening of the constrained-counterparty-choice effect after the Fed switched to the FedTrade platform that allows all dealers to bid in any given operation.

Acknowledgement

We are grateful to Francis Longstaff for stimulating conversations and discussions. We thank Ralph Koijen (the editor), an associate editor, two anonymous referees, Hank Bessembinder, Darrell Duffie, Michael Fleming, Thierry Foucault, John Griffin, Yesol Huh, Pete Kyle, Wei Li, Mina Lee, Yiming Ma, Paolo Pasquariello, Nagpurnanand Prabhala, Paul Schultz, Pierre-Olivier Weill, Milena Wittwer, Yiqing Xing, Anthony Lee Zhang, Alex Zhou, and Haoxiang Zhu and seminar participants at Columbia Business School, Dimensional Fund Advisors, Johns Hopkins University, Tsinghua University, Microstructure Exchange, WFA, and Central Bank Workshop on Microstructure of Financial Markets for helpful comments.

Footnotes

References