Mortgage Dollar Roll

Transcription

1 Mortgage Dollar Roll Zhaogang Song Federal Reserve Board Haoxiang Zhu MIT Sloan School of Management April 5, 2015 Abstract Mortgage dollar roll is the most important trading strategy for financing agency MBS. In a dollar roll, the roll buyer lends cash against MBS collateral but can return different MBS collateral upon the maturity of the loan, creating adverse selection. The dollar roll specialness is the extent to which the implied financing rate falls below prevailing market interest rate. This paper provides the first analysis of the economics of dollar roll specialness, using a proprietary dataset of dollar roll financing rates from July 1998 to July We show that dollar roll specialness increases in adverse selection and decreases in the liquidity of MBS. Dollar roll specialness is also negatively related to expected MBS returns. We find that the Federal Reserve s MBS purchases are associated with a higher adverse-selection component of dollar roll specialness but a lower liquidity component. Keywords: Dollar Roll, TBA, MBS, Specialness, LSAP JEL classification: G12, G18, G21, E58 First version: January For helpful discussions and comments, we thank Joyner Edmundson, Katy Femia, Song Han, Jean Helwege, Jeff Huther, Bob Jarrow, Matt Jozoff, Akash Kanojia, Ira Kawaller, Don Kim, Beth Klee, Arvind Krishnamurthy, Guohua Li, Debbie Lucas, Jessica Lynch, Nicholas Maciunas, Tim McQuade (discussant), John Miller, Linsey Molloy, Danny Newman, Greg Powell, Bernd Schlusche, Andrea Vedolin, Clara Vega, Min Wei, and seminar participants at the 3rd Annual Fixed Income Conference and Cornell University. The views expressed here are the authors and do not necessarily reflect those of the Federal Reserve System. Board of Governors of the Federal Reserve System, Mail Stop 165, 20th Street and Constitution Avenue, Washington, DC, [email protected]. MIT Sloan School of Management, 100 Main Street E62-623, Cambridge, MA [email protected].

2 Mortgage Dollar Roll April 5, 2015 Abstract Mortgage dollar roll is the most important trading strategy for financing agency MBS. In a dollar roll, the roll buyer lends cash against MBS collateral but can return different MBS collateral upon the maturity of the loan, creating adverse selection. The dollar roll specialness is the extent to which the implied financing rate falls below prevailing market interest rate. This paper provides the first analysis of the economics of dollar roll specialness, using a proprietary dataset of dollar roll financing rates from July 1998 to July We show that dollar roll specialness increases in adverse selection and decreases in the liquidity of MBS. Dollar roll specialness is also negatively related to expected MBS returns. We find that the Federal Reserve s MBS purchases are associated with a higher adverse-selection component of dollar roll specialness but a lower liquidity component.

3 1 Introduction The Federal Reserve Bank of New York on Tuesday said it has been conducting a type of mortgage-bond-repurchase transaction to aid the earlier settlement of its outstanding mortgage-backed securities purchases, which is supporting the larger market. In purchasing the dollar rolls, the Fed could be relieving liquidity bottlenecks for investors who need to borrow a security they are short but have contracted to deliver to a buyer... The Wall Street Journal, December 6, 2011 Agency mortgage-backed-securities (MBS) guaranteed by Ginnie Mae (GNMA), Fannie Mae (FNMA), and Freddie Mac (FHLM) form a major component of U.S. fixed-income markets. 1,2 The combined market value of outstanding agency MBS is about $5.75 trillion as of June 2013, around half of the outstanding $11.39 trillion of U.S. Treasury securities, according to SIFMA. The average daily trading volume of agency MBS is 20 times larger than that of corporate bonds, and close to 60% of that for Treasury securities in 2010, according to Vickery and Wright (2011). Besides its large size and trading volume, the agency MBS market also plays a prominent role in the implementation of U.S. monetary policy since the global financial crisis. The Federal Reserve has conducted several rounds of quantitative easing (QE) since 2009 and accumulated $1.74 trillion face value of agency MBS on its balance sheet as of January Furthermore, the Federal Open Market Committee has announced in its September 2014 statement that the Federal Reserve will continue to use its MBS holdings to conduct reverse repo transactions as a regular policy tool in the future (see Frost, Logan, Martin, McCabe, Natalucci, and Remache (2015)). 1 Throughout the paper, the term MBS refers only to residential mortgage-backed-securities rather than those backed by commercial mortgages, unless otherwise noted. 2 Ginnie Mae, Fannie Mae, and Freddie Mac stand for the Government National Mortgage Association, Federal National Mortgage Association, and Federal Home Loan Mortgage Corporation, respectively. Ginnie Mae is a wholly-owned government corporation within the Department of Housing and Urban Development. Usually called Government-Sponsored Enterprises (GSEs), Fannie Mae and Freddie Mac were private entities with close ties to the U.S. government before September 2008, and have been placed in conservatorship by the Federal Housing Financing Agency and supported by the U.S. Treasury department since then. 1

4 A trading strategy called dollar roll is a particularly important tool that has been actively used by the Federal Reserve in its operations of quantitative easing (see the Wall Street Journal quote above). A mortgage dollar roll is the combination of two forward contracts on MBS, one front month and one future month. These forward contracts are traded in the liquid to-be-announced (TBA) market, which comprises over 90% of agency MBS trading volume and all the Federal Reserve s MBS purchases. In a dollar roll transaction the roll seller sells an MBS in the front-month TBA contract and simultaneously buys an MBS in the future-month TBA contract, both at specified prices. A roll buyer does the opposite. Mortgage dollar roll is the most widely used trading mechanism by which investors finance their positions in agency MBS and hedge their existing MBS exposures. It accounts for more than a half of the trading volume in the TBA market and about a half of the trading volume in the whole agency MBS market (see Gao, Schultz, and Song (2014)). A unique feature of the TBA market is that on the trade date the two counterparties only agree on generic security characteristics, such as agency, coupon, and original mortgage term, but not the specific CUSIPs to be delivered. A dollar roll, as a combination of two TBA trades, inherits this important feature. For example, a particular dollar roll contract may specify that the deliverable MBS must be guaranteed by Fannie Mae, with the original loan term of 30 years and a coupon rate of 4% per year. But it does not specify the particular CUSIP of MBS to be delivered on the trade date. Thus, the short side has a strong incentive to deliver the cheapest CUSIP that satisfy these parameters, creating adverse selection. In particular, after the roll seller delivers an MBS in the front month of a dollar roll, he may (and is likely to) receive a different, potentially inferior MBS in the future month. 3 adverse-selection risk is reflected by the prices in the two legs of the dollar roll. This It is convenient and intuitive to view a dollar roll as a collateralized borrowing contract, with the roll seller being the cash borrower. Compared to a standard repo contract, however, the roll seller faces a substantial risk that the collateral redelivered at the end of the contract 3 The roll buyer is also subject to this adverse-selection risk between the trade date and the front-month settlement date, but this risk is limited because the roll buyer can always return the MBS that the roll seller delivers into the front month. By contrast, the roll seller s risk is much larger because the future-month date is farther away and the roll buyer has the last say on the delivered CUSIP. 2

5 are inferior to the original collateral lent out. To compensate for this risk, the roll seller, equivalently the cash borrower, pays a low implied financing rate. This rate can sometimes be negative. A dollar roll is said to be on special if this implied financing rate is lower than the prevailing market interest rate, such as the general-collateral (GC) repo rate on the MBS or unsecured rates like LIBOR. The specialness of a dollar roll is hence a key indicator of funding conditions in agency MBS markets, just as repo specialness is a key indicator of funding conditions in U.S. Treasury markets. This paper provides the first analysis of the economics of dollar roll specialness. We ask the following three questions: 1. What economic forces determine dollar roll specialness? 2. What is the relation between dollar roll specialness and the expected MBS returns? 3. How does the Federal Reserve s large-scale asset purchase of agency MBS affect dollar roll specialness, and through which channels? Answers to these questions would shed light on this important yet underexplored market in the academic literature (see the literature section). It also provides new evidence on the effect of unconventional monetary policy on market functioning. Our analysis starts with an analytic framework that encompasses two driving forces of dollar roll specialness. The first is associated with the key feature of a dollar roll transaction: securities changing hands in the two legs of a dollar roll need not be the same, but only substantially similar, as defined by a set of parameters. 4 We call the collection of MBS CUSIPs that satisfy a particular set of parameters a cohort. Therefore, the roll buyer can potentially (and generally will) deliver the cheapest MBS within a cohort to the roll seller (the cheapest-to-deliver option). An agency MBS is cheap mainly because it has inferior prepayment characteristics not specified in the TBA contract, such as the loan-to-value ratio, FICO score, past prepayment behavior, and location of the mortgage, relative to other 4 The criterion of substantially similar is defined in the American Institute of Certified Public Accountants State of Position 90-3 such that the original and returned MBS should be of the same agency, original loan term, and coupon rate, and both should satisfy Good Delivery requirement set by SIFMA. 3

6 agency MBS in the same cohort. 5 (The default risk is insured by the agencies.) This adverse selection lowers the interest rate that the roll seller is willing to pay and hence increases specialness. The second driving force of dollar roll specialness is a liquidity channel associated with search frictions. Specifically, if the MBS market is more illiquid, it is harder for the dollar roll seller to locate an MBS to lend to the dollar roll buyer. Hence, the buyer has to offer lower financing rates, which will lead to a higher specialness. 6 Based on this analytic framework, we empirically study dollar roll specialness using a proprietary panel dataset of dollar roll financing rates from July 1998 to July The dataset, provided by J.P. Morgan, contains daily time series of dollar roll financing rates for FNMA 30-year TBA contracts with twelve coupon rates ranging from 3% to 8.5%. We calculate dollar roll specialness as the difference between prevailing one-month interest rates, such as the 1-month general collateral repo rate of agency MBS or the 1-month LIBOR, and the dollar roll financing rates. We also use other data including mortgage interest rates, MBS issuance, and purchases by the Federal Reserve. Our empirical investigation consists of three parts, corresponding to the three questions above. Determinants of dollar roll specialness. According to our analytic framework, a key driving force of dollar roll specialness is adverse selection regarding the redelivered MBS. Through a simple, stylized model, we show that this adverse selection increases in the expected cohort-level prepayment activity as well as the heterogeneity of prepayment characteristics within the cohort. Since little data are available to measure the latter, we focus on two empirical measurements of the former, i.e., the cohort-level prepayment activity. First, a lower mortgage rate encourages homeowners to prepay existing, higher-interest mortgages 5 We emphasize that inferior prepayment characteristics do not necessarily mean higher prepayment speeds. A high prepayment speed usually implies a low value for a premium MBS with value above par, but a high value for a discount MBS with value below par (See Section 3 for details). Hence, MBS with inferior prepayment characteristics refer to those with high (low) prepayment speeds if the corresponding TBA cohort is at premium (discount). 6 This is consistent with search theories of Duffie, Garleanu, and Pedersen (2002) and Vayanos and Weill (2008) as well as evidence regarding repo specials and on-the-run premium in Treasury markets (see Jordan and Jordan (1997), Krishnamurthy (2002), and Graveline and McBrady (2011), among others). 4

7 and to refinance at lower rates, leading to a higher prepayment risk and hence a higher specialness. Second, the so-called burn-out effect implies that homeowners who did not refinance at favorable rates in the past may have impaired credit, low loan balance, low home equity value, or other considerations that make them less responsive to lower mortgage rates in the future. We measure the burn-out effect by the difference between the coupon rate of an MBS cohort and the primary mortgage rate conditional on the former being higher than the latter. A higher burn-out effect implies a lower prepayment risk and hence a lower specialness. Guided by the literature on over-the-counter markets, our analytic framework also suggests that dollar roll specialness should increase in the illiquidity of MBS market. We use the new issuance of agency MBS as a proxy of liquidity, consistent with the rationale that a tighter supply of MBS implies higher opportunity costs or search costs of the roll seller to deliver a scarce MBS; hence, the roll buyer must offer a favorable financing rates to compensate the roll seller, leading to a higher specialness. We test how adverse selection (measured by mortgage rates and burn-out effects) and liquidity (measured by new issuance) affect dollar roll specialness in panel regressions. All three coefficients are significantly negative, confirming our analytic framework. In particular, a one percentage point lower primary mortgage rate corresponds to an average dollar roll specialness that is 89 basis points higher. A one percentage point increase in MBS coupon rate is associated with a lower specialness by about 148 basis points. A one-standard deviation increase in MBS issuance lowers specialness by about 49 basis points. Taken together, over 30% of the variation in dollar roll specialness in our sample period can be explained by primary mortgage rates, burn-out effect, and MBS issuance. The significance of these three variables is robust to alternative model specifications. 7 While these variables do not exhaustively cover potential measures of prepayment risks and liquidity in MBS market, they are representative in illustrating the two main economic channels of dollar roll specialness: 7 These specifications include whether the GC repo rate or LIBOR is used to measure specialness, whether the Treasury or LIBOR term structure is used to measure the OAS, whether the regression is run on the level or the first difference of the data, and whether time- and coupon-fixed effects are included. 5

8 adverse selection and liquidity. 8 Dollar roll specialness and expected MBS returns. We follow Gabaix, Krishnamurthy, and Vigneron (2007) and use option-adjusted spreads (OAS) as a proxy for expected MBS returns. The OAS is the yield on an MBS in excess of the term structure of interest rates after adjusting for the value of homeowners prepayment options, conditional on the interest rate path. In principle, OAS reflects the deviation of the market price of an MBS from its expected value and hence the risk premium demanded by investors who are averse to prepayment risks for holding this MBS. Using monthly OAS for the same collection of FNMA 30-year TBA contracts, we find a pronounced negative relation between the OAS and dollar roll specialness. In particular, an MBS cohort that is on special has an OAS that is about 60 basis points lower than that of an MBS cohort not on special, controlling for coupon and time fixed effects. A one percentage point increase in specialness is associated with an OAS that is about 45 basis points lower. As a robustness check, we regress realized returns from rolling TBA contracts for January 2000 July 2013 on dollar roll specialness, and find a strong negative relation as well. These results are robust to a variety of empirical specifications, as well as to potential model misspecifications behind the OAS data. The effect of LSAP on dollar roll specialness. As one of the most important central bank actions since the 2008 financial crisis, the large MBS purchase by the Fed raises potential concerns of market distortion. As highlighted by Bernanke (2012), Conceivably, if the Federal Reserve became too dominant a buyer in certain segments of these markets, trading among private agents could dry up, degrading liquidity and price discovery. Our analytic framework points to two channels through which the LSAP can affect dollar roll specialness, the indicator of the financing conditions of agency MBS markets. First, LSAP can decrease mortgage rates, which will increase prepayment activities and hence 8 As further robustness checks, we consider complementary prepayment measures such as the S&P/Case- Shiller 10-City Composite Home Price Index, the Mortgage Bankers Associations Purchase Index, and the MBA Refinance Index. Results with these variables strengthen our main results. 6

9 dollar roll specialness through the adverse-selection channel. Second, the large size of MBS withdrawn by the Federal Reserve from the market may result in shortages of collateral supply and increase dollar roll specialness by the liquidity channel. Based on the regressions for the determinants of dollar roll specialness, we decompose dollar roll specialness into an adverse-selection component and a liquidity component. We separately regress the two components on measures of LSAP. Our results show that the Fed s purchase of agency MBS is associated with a higher adverse-selection component of dollar roll specialness, suggesting that LSAP puts a downward pressure on interest rate and encourages prepayment of mortgages. But the Fed s purchase is associated with a lower liquidity component, suggesting that the Fed intentionally purchases less special MBS. (The alternative interpretation, namely that the Fed s purchase makes MBS markets more liquid, is contrived and unlikely in the extreme but not unusual scenario that the Fed purchases all the new issues of MBS.) Since we do not have exogenous shocks to Fed purchases, we interpret results on the liquidity component as correlation, not causality. We emphasize that decomposing dollar roll specialness based on our analytic framework into two components is an important step. Simply regressing the total dollar roll specialness on the Fed purchase variables would deliver a negative coefficient, which fails to detect the positive effect of LSAP on the adverse-selection component of dollar roll specialness. Relation to the literature. To the best our knowledge, this paper is the first that analyzes dollar roll specialness. It contributes to three branches of literature: MBS markets, repo specialness, and the effects of the Federal Reserve s asset purchases. The literature on MBS market has predominantly focused on the pricing of MBS, whereas we focus on the financing of MBS. (This difference is analogous to the difference between the pricing of Treasury securities and the financing of them through repo transactions.) Such studies include Dunn and McConnell (1981), Schwartz and Torous (1989), Stanton (1995), Boudoukh, Richardson, Stanton, and Whitelaw (1997), and Kupiec and Kah (1999), among others. Two recent studies, Gabaix, Krishnamurthy, and Vigneron (2007) and Duarte, 7

10 Longstaff, and Yu (2007), document empirical patterns of the returns of MBS, but they do not connect these return patterns to dollar roll specialness or systematically analyze the determinants of specialness. 9 Our study is also related to the literature on special repo rates in Treasury markets, including Duffie (1996), Jordan and Jordan (1997), Buraschi and Menini (2002), Krishnamurthy (2002), Duffie, Garleanu, and Pedersen (2002), Cherian, Jacquier, and Jarrow (2004), Vayanos and Weill (2008), Pasquariello and Vega (2009), and Banerjee and Graveline (2013), among others. The economics of dollar roll specialness in agency MBS markets differs substantially from that of Treasury repo specialness in that a dollar roll involves a major adverse-selection risk that an inferior security is returned. Adverse selection is a key determinant of dollar roll specialness. Lastly, our analysis of the impact of LSAP on dollar roll specialness relates to Hancock and Passmore (2011), Gagnon, Raskin, Remanche, and Sack (2011), Krishnamurthy and Vissing-Jorgensen (2011), Krishnamurthy and Vissing-Jorgensen (2013), and Stroebel and Taylor (2012), who analyze the effect of LSAP on mortgage rates. Among these, Krishnamurthy and Vissing-Jorgensen (2013) highlight the importance of the cheapest-to-deliver option in TBA markets. Complementary to these studies that focus on the level of mortgage rates, we investigate the impact of LSAP on MBS funding markets. Kandrac (2013) finds that LSAP is associated with a lower dollar roll implied financing rates, which is also about the level of (collateralized) interest rate. He neither studies the determinants of dollar roll specialness nor distinguishes the two channels through which LSAP may affect MBS funding markets. Our analysis fills this important gap. 2 TBA Market and Dollar Roll This section discusses institutional details of the TBA trading convention in agency MBS markets and dollar roll transactions, which consist of two simultaneous TBA trades (see 9 Two other recent studies, Malkhozov, Mueller, Vedolin, and Venter (2013) and Hansen (2014), show that variables capturing the mortgage risk hedging have return predictive power for Treasury bonds. 8

11 Hayre (2001) and Hayre and Young (2004) for detailed industry references of MBS markets). 10 Additional institutional details and a worked-out example for the computation of dollar roll financing rates are provided in Appendix A. 2.1 TBA market A TBA contract is essentially a forward contract to buy or sell an MBS. In a TBA trade, the buyer and seller negotiate on six general parameters: agency, maturity, coupon rate, par amount, price, and settlement date. Different from other forward contracts, there is only one settlement date per month for TBA contracts, set by SIFMA. For example, for 30-year FNMA MBS, the settlement day is usually the eighth or ninth business day of the month. A single settlement date per month concentrates liquidity. We now demonstrate the trading procedure in TBA markets through a concrete and hypothetical example, illustrated in Figure 1. Trade and Confirmation Dates. On the trade date April 25, the buyer and seller decide on the six trade parameters. In this example, a TBA contract is initiated on April 25 and will be settled on May 16. The seller can deliver any MBS issued by Fannie Mae with the original mortgage loan term of 30 years, annual coupon rate of 5%, par amount of $1 million, and price at $(102+16/32) per $100 of par amount. The trade is confirmed within one business day, which in this case is April Hour Day. The seller notifies the buyer the actual identity (i.e., the CUSIPs) of the MBS to be delivered on the settlement date, no later than 3 p.m. two business days prior to the settlement date ( 48-hour day ), which is May 14 in the example. These MBS pools have to satisfy the Good Delivery requirements set by SIFMA. For example, for each $1 million lot, the contract allows a maximum of three pools to be delivered and a maximum 0.01% difference in the face value; that is, the sum of the par amounts of the pools can deviate from $1 million by no more than $100 in either direction. 10 All TBA-eligible MBS are so-called pass-through securities, which pass through the monthly principal and interest payments less a service fee from a pool of mortgage loans to owners of the MBS. Structured mortgage-backed-securities like CMOs, which tranche mortgage cash flows with various prepayment and maturity profiles, are not eligible for delivery in TBA contracts. 9

12 Figure 1: A TBA Example Settlement Date. The seller delivers the MBS pools specified on the 48-hour day, and the buyer pays an amount of cash equal to the current face value times the TBA price (i.e., in this example) plus accrued interests from the beginning of the month, given that the seller holds the MBS pools until the settlement date. Accrued interest is computed on a 30/360 basis. The unique feature of a TBA trade is that the actual identity of the MBS to be delivered at settlement date is not specified on the TBA trade date. By specifying only a few key MBS characteristics, this TBA trading design dramatically increases the set of deliverable MBS and substantially improves market liquidity. 2.2 Dollar roll A dollar roll transaction consists of two TBA trades. The roll seller sells an MBS in the front month TBA contract and simultaneously buys an MBS in the future month TBA contract with the same TBA characteristics, at specified prices. In particular, the two MBS 10

13 delivered into the two TBA contracts need not have the same CUSIP, as long as they have the same TBA characteristics. Figure 2 shows the time line of an example dollar roll trade. In this example, the roll seller sells an MBS for May 16 settlement and buys it back for June 16 settlement, for a par amount of $1 million Fannie Mae MBS with the original loan term of 30 years and annual coupon rate of 5%, and with the front and future month prices at and per $100 of par amount, respectively. The drop of this dollar roll, defined as the price difference between the front- and future-month TBA contracts, is positive for two reasons. (In this example, the drop is = 14 per $100 par value.) First, and most importantly, the returned MBS pool in the future-month TBA contract may have inferior prepayment behavior and hence lower value than the original MBS sold in the front-month contract. Second, after the front-month leg of the dollar roll transaction, the roll seller gives up the ownership of the MBS and any interest and principal payments. These two features, especially the redelivery uncertainty of the returned MBS pool in the future-month leg, differentiates the dollar roll from an MBS repo transaction. In an MBS repo trade the same MBS pool has to be returned, and the original owner collects principal and interest payments during the term of repo. 11 A dollar roll can be viewed as a collateralized borrowing contract, with the important feature that the returned collateral can differ from the original collateral. As in repo contracts, we can calculate the effective collateralized borrowing rate for dollar roll transactions. The borrowing rate of a dollar roll, which measures the benefit of rolling an MBS pool relative to holding it, can be computed based on the drop after adjusting for the principal and coupon payments the roll seller gives up over the roll period. As an over-simplified example, suppose that the front-month and future-month prices of the dollar roll transactions are P 0 and P 1, respectively, and the coupon and principal payments of the MBS received by the roll buyer 11 Additionally, the cash lender in a repo transaction is generally able to call margin from the cash borrower periodically (as often as daily), protecting the lender against counterparty risk associated with fluctuations in the underlying collateral value. 11

14 Figure 2: A Dollar Roll Example are c and d, respectively. Then, the effective financing rate of the dollar roll is r = P 1 + c + d P 0 1. (1) A worked example of calculating dollar roll specialness is provided in Appendix A. Participants in the TBA and dollar roll markets include MBS dealers, mortgage servicers, pension funds, mutual funds, endowments, hedge funds, commercial banks, and insurance companies. The Federal Reserve and foreign central banks with large dollar reserves (e.g. China and Japan) sometimes participate in MBS markets as well. Among them, commercial banks, insurance companies, and pension funds mostly use buy-and-hold strategies and only trade dollar rolls occasionally, due to accounting considerations. Much of the dollar roll demand comes from MBS dealers who need to cover their short MBS hedging trades or maintain their MBS inventories for market-making. 12 Mortgage servicers and money man- 12 Dealers short positions in MBS could be hedges against their long positions in CMOs, specified pools, 12

15 agers are main providers of dollar rolls, with the former enhancing their portfolios returns at desirable financing rates and the latter financing their MBS positions to hedge their interest rate exposure of the loans they service on their books. Hedge funds demand or supply dollar rolls for both hedging and speculation. 2.3 Dollar roll specialness We say a dollar roll is on special if the implied finance rate is lower than the prevailing interest rates, such as MBS repo rates or LIBOR. The specialness of a dollar roll, defined as the market prevailing borrowing rate less the implied finance rate in a dollar roll, provides a rent to the MBS owners and represents an effective reduction in the financing costs of MBS positions. A positive specialness, however, is not an arbitrage in any sense, as the dollar roll seller bears the redelivery risk, i.e., the risk of an MBS with inferior prepayment characteristics being returned in the future-month TBA contract. In other words, dollar roll specialness incorporates a risk premium demanded by the roll seller for the redelivery risk. The higher is the risk, the lower price the roll seller is willing to offer in the future month of the dollar roll, and the lower is the implied financing rate (see equation (1) and the example in the previous subsection). Hence, specialness is higher. To see the intuition more clearly, we consider this stylized example. Suppose that the implied dollar roll financing rate on an MBS (and other MBS in the same cohort) is 1%, but the repo rate of using this specific MBS for secured borrowing is 2%. An investor with $1 million cash can engage in the following trades. She lends the cash against the MBS in the repo market for one month at 2%, and subsequently rolling the MBS collateral for one month at the financing rate of 1%. If, by any chance, the same MBS is returned to the investor in the dollar roll market, she can return the same MBS to the repo counterparty and close the repo contract; this earns her the net profit of $(2%+1%)/12 million. If, however, a different and cheaper MBS is returned in the dollar roll contract, this different MBS cannot be used to close the repo contract, and she must buy or borrow the original MBS to close the certain non-agency MBS, or bonds they have purchased for delivery in future months from originators. 13

16 repo contract. In this process, she must make up for the price difference between the original MBS and cheaper MBS delivered back in the dollar roll. The specialness of 3% (relative to MBS repo rate), therefore, compensates for such risks born by the roll seller. In addition to being a compensation for adverse selection stemming from redelivery risk, dollar roll specialness also reflects the general supply and demand conditions in the TBA market. For example, if the MBS of particular characteristics are scarce in the market, a holder of such MBS can extract more rents in the repo market and security lending market. By rolling this MBS, the roll seller gives up not only the interest and principal payments, but also the rents associated with cheaper financing rates and lending fees. Therefore, the equilibrium implied financing rate in the dollar roll must fall, leading to a higher specialness. The scarcity of a particular class of MBS can be driven by the shorting and hedging activities of dealers and originators, as well as the amounts of newly issued MBS. 3 The Economics of Dollar Roll Specialness In this section we develop an analytic framework to study the economics of dollar roll specialness. We consider first the determinant of dollar roll specialness and then the relation between dollar roll specialness and expected MBS returns. 3.1 The determinants of dollar roll specialness Redelivery risk and adverse selection As we discussed in the previous section, a key feature of financing MBS by dollar roll, relative to financing by repo, is that the roll buyer (who lends cash and receives an MBS) has the option to deliver a substantially similar but different MBS in the future month of the roll contract. As a compensation, the roll seller offers a lower price to buy back the substantially similar MBS in the future-month leg. This low price, in turn, implies a lower effective financing rate, or a higher specialness. 14

17 To illustrate the formal link between dollar roll specialness and adverse selection imbedded in dollar roll contracts, we consider the following simple, stylized model. There are three periods, t {0, 1, 2}. The discount rate is r per period. Multiple MBS CUSIPs of the same cohort, indexed by i {1, 2,..., n}, trade in the market. Investors are risk-neutral. For simplicity, suppose that all MBS have the same coupon rate c > 0 and maturity at t = 2. These MBS, however, have heterogeneous prepayment characteristics. In particular, for MBS i, a random fraction λ i of the underlying mortgages will be prepaid at t = 1 and the remaining fraction 1 λ i will be paid at t = 2. This information is unobservable ex ante. Thus, the time-0 value of a generic MBS is [ ( 1 + c c P 0 = E λ i 1 + r + (1 λ i) 1 + r c )] (1 + r) 2 = c 1 + r c (1 + r) 2 c r (1 + r) 2 E[λ i]. (2) If c > r, prepayment lowers (premium) MBS value; if c < r, prepayment increases (discount) MBS value. Suppose that strictly between t = 0 and t = 1 all {λ i } become public information. Now consider a dollar roll contract. For simplicity, suppose that the front-month leg is transacted at t = 0 and the future-month leg is transacted at t = 1. Also for simplicity and to focus on the adverse selection channel, suppose that the MBS coupon and principal (if prepaid) are paid after the future-month leg of the dollar roll transaction, so all cash flows are paid to the roll seller at t = 1. At t = 0, the roll seller delivers the roll buyer an MBS with value P 0. At t = 1, the roll buyer delivers back a potentially different MBS with the time-1 value ( P 1 (λ i ) = λ i (1 + c) + (1 λ i ) c c ) = c c 1 + r 1 + r c r 1 + r λ i. (3) Clearly, since the roll buyer has the option to redeliver any MBS at t = 1, he would deliver the cheapest. That is, the redelivered MBS has value min i P 1 (λ i ). 15

18 The effective financing rate R implied from the dollar roll contract satisfies which gives P 0 = 1 [ ] 1 + R E min P 1 (λ i ), (4) i R = E [min i P 1 (λ i )] 1 = c + 1+c + E [ ( ) ] min 1+r i c r λi 1+r c P c c r 1. (5) E[λ 1+r (1+r) 2 (1+r) 2 i ] Depending on c > r or c < r, we have R = c+ 1+c c r ( 1+r 1+r)E[max i λ i ] c 1+r + 1+c (1+r) 2 c r c+ 1+c r c +( 1+r 1+r)E[min i λ i ] c 1+r + 1+c (1+r) 2 + r c (1+r) 2 E[λ i] 1 = r (1+r) 2 E[λ i] 1 = r c r 1+r (E[max i λ i ] E[λ i ]), c 1+r + 1+c (1+r) 2 c r (1+r) 2 E[λ i] r c 1+r (E[λ i] E[min i λ i ]) c 1+r + 1+c (1+r) 2 + r c (1+r) 2 E[λ i] if c > r, if c < r. (6) Generally, a positive specialness needs three conditions. First, the MBS are not priced exactly at par. Second, prepayment activity is nonzero, that is, not all λ i are zero. Third, MBS have heterogeneous prepayment activities, that is, not all λ i are equal. The latter two conditions create the cheapest-to-deliver option and adverse selection. To get more intuition, we further suppose that λ i = λα i, (7) where the random variable λ captures the common shock to the prepayment speed of the cohort, the scaling factor α i > 0 captures the individual prepayment characteristics of mortgages that underly MBS i, and λ and {α i } are uncorrelated. Without loss of generality, we can normalize the mean of α i to be one: E[α i ] = 1. Substituting these parametric specifications into the expression of R, we get the specialness r R = c r 1+r r c 1+r E[λ] (1+r) 2 c r c 1+r + 1+c E[λ] (1+r) 2 + r c c 1+r + 1+c (1+r) 2 E[λ] (E[max i α i ] E[α i ]), if c > r, (1+r) 2 E[λ] (E[α i] E[min i α i ]), if c < r. (8) 16

19 The expression (8) has a simple intuition. All else equal, the specialness of a particular MBS cohort in the dollar roll market increases in the expected cohort-level prepayment risk, E[λ], as well as the the heterogeneity of individual MBS prepayment characteristics under the same cohort, captured by E[max i α i ] E[α i ] or E[α i ] E[min i α i ]. The expression (8) also makes it clear that the positive relation between specialness and cohort-level prepayment risk E[λ] is valid for both premium and discount MBS. Intuitively, while an increase of the cohort-level prepayment risk implies a decrease and increase of the MBS value for premium and discount securities, respectively, it always leads to a larger value gap of the cheapestto-deliver MBS and other MBS under the same cohort, hence a higher redelivery risk and higher specialness Liquidity effect So far, we have discussed the effect of redelivery risk for the specialness of dollar roll, which is unique to the MBS market. Now, we turn to the generic effect of liquidity for determining dollar roll specialness. Specifically, the agency MBS market is over-the-counter (OTC), similar to Treasury, corporate bond, municipal bond, and repo markets. An important feature of OTC markets is the search friction: market participants must first locate a counterparty to execute a trade or borrow a security. Empirical studies in Treasury markets generally find that a lower liquidity is associated with a higher specialness (Jordan and Jordan (1997) and Graveline and McBrady (2011)). Closely related, Krishnamurthy (2002) finds a negative relation between on-the-run premium and issue size in US Treasury markets. Using a theoretical model with search frictions and heterogeneous beliefs, Duffie, Garleanu, and Pedersen (2002) show that a larger supply reduces the lending fee and price of an asset in two ways. First, a larger asset supply implies a lower valuation or belief of the marginal holder of the asset. Second, a larger asset supply makes it easier for pessimists to locate the asset for shorting, which, in turn, reduces the lending fee and the asset price. Since a smaller lending fee corresponds to a higher effective financing cost for the security lender (i.e. cash borrower), their model predicts that 17

20 specialness is lower if the asset supply is larger. 13 In a similar vein, dollar roll specialness should increase in the illiquidity of the agency MBS market. Specifically, when lending an MBS is associated with a higher search cost for the dollar roll seller, the roll buyer must offer a favorable financing rate to compensate the roll seller, leading to a higher specialness. Therefore, we expect that dollar roll specialness is negatively associated with MBS liquidity. 3.2 Relation between dollar roll specialness and MBS returns As we have discussed, a dollar roll can become more special for two reasons: a higher adverse selection associated with redelivery risk or a lower liquidity. For both channels, dollar roll specialness is negatively related to the expected MBS returns. The generic rationale is that a high specialness of an MBS gives its holders a convenience yield in the financing market, and these holders are willing to accept a lower expected return in the cash market, as illustrated in Duffie (1996) and Duffie, Garleanu, and Pedersen (2002). A unique feature of dollar roll specialness is that the adverse selection channel narrows down the effective supply and liquidity of the MBS cohort to the cheapest-to-deliver pool of MBS, as investors rationally redeliver the cheapest CUSIPs in the future-month leg of dollar roll contracts. By definition, this effective supply of an MBS cohort, comprising of cheapestto-deliver MBS CUSIPs, is smaller than the supply of all CUSIPs in the MBS cohort. Even if the total supply of MBS in a cohort stays constant (which implies zero specialness due to the general liquidity channel), a higher adverse selection can shrink the effective supply of the MBS cohort and make it on special. This endogenous feedback between adverse selection and supply is unique to dollar roll and different from the total supply channel that is also present in repo market, though both induce a negative relation between the specialness and 13 Not all theories of OTC markets generate unambiguous predictions about the relation between asset supply and specialness. For example, Vayanos and Weill (2008) characterize the endogenous concentration of liquidity and trading activity in one asset even if there is another identical asset. They show that, if the supply of Asset 1 exceeds that of Asset 2 by a sufficient amount, short sellers concentrate on Asset 1. In this equilibrium, a decrease in the supply of Asset 1 can lead to a higher or a lower specialness of Asset 1. This ambiguous prediction comes from the interaction between scarcity in the repo market and scarcity in the spot market. 18

21 expected MBS return as discussed above. 4 Data Our empirical analysis employs three main proprietary data sets. The first data set comprises observations of dollar roll financing rates for FNMA 30-year (generic) TBA contracts for the next two delivery months and with twelve coupon rates ranging from 3% to 8.5%. These financing rates are furnished by J.P. Morgan and available at the daily frequency from July 1998 to July We construct monthly time series of dollar roll financing rates by forming simple averages of daily values in each month, which reduces noise associated with microstructure effects and intra-month seasonality. (In Appendix B, we reproduce the main results using two alternative methods to construct the monthly series, and the results are robust. 14,15 ) The data are an unbalanced panel, with the common last observations in July 2013 but varying initial observations between July 1998 and August Panel A of Table 1 provides summary statistics of these dollar roll financing rates. We observe that the time series mean of dollar roll financing rates increases with the coupon rate, with negative figures at coupon rates from 3% to 4%. The minimum values of financing rates are uniformly negative, extending to as low as 13% for the 7% coupon cohort. We compute two versions of dollar roll specialness, DSP GC and DSP LIBOR, using the 1-month general collateral (GC) repo rate of agency MBS and the 1-month LIBOR as benchmark prevailing interest rates, respectively. 16 We obtain the ICAP GC repo rate of MBS from Bloomberg and LBIOR from Datastream. Panels B and C of Table 1 report summary statistics of DSP GC and DSP LIBOR, respectively. Overall, the average specialness lies between 30 to 100 basis points if positive, and the time-series mean of dollar roll specialness generally decreases with the coupon rate, which is due to the burn-out effect. (Specialness 14 These two alternative series are end-of-month series and first-friday series. 15 In unreported results, we also construct monthly time series of dollar roll financing rates by taking the average of daily financing rates from the day after the settlement day of the previous month to the settlement day of the current month. The results are similar. 16 We also use the GCF repo rates of agency MBS that are only available from May 2005, and obtain similar results. 19

22 Table 1: Summary Statistics of Dollar Roll Financing Rates and Specialness Coupon (%) CC A: Dollar Roll Financing Rates Mean Std Min Max B: DSP GC Mean Std Min Max C: DSP LIBOR Mean Std Min Max D: Ratio of On Special Begin 08/ / / / / / / / / / / / /1998 End 07/ / / / / / / / / / / / /2013 No Special % -GC 100% 100% 96% 80% 82% 72% 64% 69% 64% 31% 36% 20% 88% -LIBOR 100% 100% 95% 88% 90% 81% 71% 75% 70% 35% 36% 22% 94% Note: This table provides summary statistics of the financing rates, specialness relative to both the GC repo rate and LIBOR, and the ratio of dollar roll being on special in the time series, across coupon rates. The values of financing rates and specialness are denoted in basis points. The last column CC refers to current-coupon MBS, which is the MBS with a coupon rate that makes its price equal to par. The overall sample period is July 1998 to July 2013, with various starting dates that depend on coupon rates. 20

23 for coupon rates from 7.5% to 8.5% is generally negative.) Moreover, DSP GC is lower than DSP LIBOR as the GC repo rate of MBS is usually below the 1-month LIBOR. Panel D of Table 1 presents the ratios of dollar roll being on special over time. We observe that dollar roll specialness is positive in over 65% of the sample period for TBA contracts with coupon rates less than 7%. MBS with very low coupons, e.g., from 3% to 4%, and the current coupon MBS (with a coupon rate that makes its price equal to par) are almost always special. Figure 3 shows the time series behavior of the dollar roll specialness of FNMA 30-year MBS that are priced the closest to par. We observe large variations of dollar roll specialness over time, which reflects time-varying funding conditions in the agency MBS market. Specialness shot up to as high as 230 basis points recently. Figure 3: Financing Rates and Specialness of Near-Current Coupon Dollar Roll Specialness of Near Current Coupon Dollar Roll Dollar Roll Specialness LIBOR Dollar Roll Specialness GC Basis Points Jan 00 Jan 05 Jan 10 Jan 15 Date Note: This figure plots monthly time series of the specialness of FNMA 30-year MBS that are priced the closest to par, from July 1998 to July The dollar roll specialness is computed both relative to the 1-month GC repo rate of agency MBS and to the 1-month LIBOR. Our second main data set comprises daily observations of option-adjusted spreads (OAS) 21

24 from July 1998 to July 2013 for the same collection of FNMA 30-year (generic) TBA contracts, also provided by J.P. Morgan. The OAS is a spread added to the term structure of interest rates such that the present value of an MBS s expected cash flows, after adjusting for the value of the homeowner s prepayment option conditional on the interest rate path, equals the price of the security. 17 In principle, OAS measures the expected return an investor earns, relative to certain benchmark interest rates, by buying the MBS and hedging out the prepayment risks. 18 We use OAS based on both the LIBOR swap yield curve and Treasury yield term structure, denoted by OAS LIBOR and OAS T sy, respectively. Since the LIBOR and Treasury yields are benchmark interest rates used by financial market participants for debt borrowing, OAS LIBOR and OAS T sy can be regarded as spreads relative to their funding costs. 19 We form monthly OAS time series by taking simple averages of daily numbers in each month. Table 2 provides summary statistics of these OAS series. We observe that the time series means of OAS LIBOR range from 6 to 160 basis points, and those of OAS T sy range from 20 to 200 basis points. Both increase with the coupon rates roughly, with the monotonic increasing pattern more pronounced for OAS T sy than for OAS LIBOR. Figure 4 plots the monthly time series of OAS LIBOR and OAS T sy for current-coupon FNMA 30-year MBS. Finally, we obtain weekly observations of primary mortgage rates (PMMS) for 30-year 17 Specifically, let r t, t = 1,, T be the path of one-period interest rate with a realization of r jt, t = 1,, T under the economy state j = 1,, N. With a prepayment model that specifies the prepayment behavior of the homeowner conditional on the realized interest rate path under state j, the cash flow path from the MBS C jt, t = 1,, T can be calculated. Then the OAS is defined such that [ N T ] C jt V MBS = p j, (1 + r j1 + OAS) (1 + r jt + OAS) j=1 t=1 where p j is the probability of state j. That is, the OAS is the yield spread to the interest rate r t required to set the present value of the MBS expected cash flows based on the prepayment forecast equal to the market prices of this MBS. 18 Since the hedging of prepayment risks is based on a prepayment model, OAS may contain components due to misspecifications of the prepayment model or interest rate model. We conduct a number of robustness checks in Appendix B on OAS. 19 A few studies including Fabozzi and Mann (2011) and Belikoff, Levin, Stein, and Tian (2010) argue that the OAS LIBOR is a better measure as most investors use LIBOR as the benchmark borrowing rate and LIBOR swap rates are quoted more uniformly and densely. 22

25 Table 2: Summary Statistics of Option-Adjusted Spreads OAS LIBOR Coupon (%) CC Mean Std Min Max OAS T sy Mean Std Min Max Note: This table provides summary statistics of monthly series of OAS LIBOR and OAS T sy across coupon rates. The OAS values are denoted in basis points. The last column CC refers to current-coupon MBS, which is the MBS with a coupon rate that makes its price equal to par. The overall sample period is July 1998 to July 2013, with various starting dates that depend on coupon rates. 23

26 Figure 4: Option Adjusted Spreads of Current-Coupon MBS Option Adjusted Spreads of Current Coupon MBS LIBOR OAS Tsy OAS Basis Points Jan 00 Jan 05 Jan 10 Jan 15 Date Note: This figure plots monthly time series of OAS LIBOR and OAS T sy of current-coupon MBS, from July 1998 to July fixed-rate mortgage loans from the Freddie Mac primary mortgage market survey as a proxy for market-wide prepayment risk driven by interest rates. We also obtain daily observations of the current coupon (CC) rate for the 30-year TBA contract from J.P. Morgan., which we use to construct a measure of the burn-out effect. Figure 5 plots the monthly time series of the PMMS and CC rate, computed as the simple averages of observations in each month. As expected, there is a spread of around basis points between PMMS and CC due to the guarantee fee charged by the agency (Fannie Mae). Additionally, we obtain monthly new issuance and outstanding balance data of FNMA 30-year MBS pools across the twelve coupon rates ranging from 3% to 8.5% from embs. 5 Characterizing Dollar Roll Specialness This section presents the results on the determinants of dollar roll specialness and on the relation between specialness and expected MBS returns. Robustness checks are conducted in Appendix B. 24

27 Figure 5: Primary and Secondary Mortgage Rates 900 Primary and Secondary Mortgage Rate Primary Mortgage Rate Current Coupon Rate Basis Points Jan 00 Jan 05 Jan 10 Jan 15 Date Note: This figure plots monthly time series of primary mortgage rates (PMMS) for 30-year fixed-rate mortgage loans, from the Freddie Mac primary mortgage market survey, and current-coupon (CC) mortgage rate, from July 1998 to July What drives dollar roll specialness? Empirical measurement As discussed in Section 3.1, the specialness of a dollar roll depends on adverse selection and liquidity. Equation (8) shows that the adverse-selection component increases in the expected cohortlevel prepayment activity and the heterogeneity of prepayment characteristics within the cohort. Since little data are available on the heterogeneity of prepayment characteristics, we focus on the cohort-level prepayment speed in capturing redelivery risk. There are a number of ways to measure the cohort-level prepayment risk in the data. We focus on two: the time-varying market-wide prepayment risk that affects all MBS cohorts and the burn-out effect that is cohort specific. Our main time-series measure of market-level prepayment risk is the primary mortgage rate P MMS t. A lower mortgage rate implies a stronger incentive for borrowers to refinance and prepay mortgages, leading to larger revealed differences in 25

28 MBS values within the same cohort and hence a higher adverse selection. Therefore, we expect dollar rolls to become more special if mortgage rate becomes lower. Importantly, the mortgage rate can be interpreted as a leading indicator of prepayment activity because refinancing and prepayment take time to complete. Appendix B considers a few additional measures of prepayment activities, including house prices, transaction activities in real estate markets, and survey-based refinancing activity. Our second, cohort-level prepayment risk measure captures an important feature of the prepayment behavior, the burn-out effect. In particular, conditional on the coupon rate of an existing MBS being higher than the prevailing coupon of newly issued MBS, a higher coupon rate of the existing MBS implies a lower prepayment risk. To see why, consider the following example. Suppose that a household borrows at the mortgage rate of 6%, and the mortgage is packaged into an MBS that pays a coupon rate of 5%. Suppose, too, that the mortgage rate then declines from 6% to 5.5%. At this point, the household would refinance its mortgage at the lower interest rate of 5.5% as long as the 0.5% interest rate improvement on the remaining loan balance dominates the cost of refinancing. If, however, the household does not take this refinancing opportunity, it signals a higher effective cost of refinancing: the household could have an impaired credit, a low home equity value, or a small remaining loan balance, among other reasons. By this self-selection, households that forgo refinancing opportunity in the past are less responsive to lower rates and less likely to refinance in the future. By definition, these mortgage rate-irresponsive households are likely over-represented in mortgages pools underlying high-coupon MBS; thus, dollar rolls on high-coupon MBS are less special. Although our data do not contain the interest rates on the underlying mortgages, they do have the coupon rates. Because the primary mortgage rate and current coupon rate have a relatively stable spread over time (see Figure 5), we use the difference between an MBS coupon rate and the prevailing coupon rate as a proxy for forgone refinancing opportunities. Specifically, we measure the time-t burn-out effect of an MBS cohort with coupon rate CP i 26

29 as BO it = 1 {CPi >CC t} (CP i CC t ), (9) where 1 {CPi >CC t} = 1 if the MBS coupon CP i is higher than the current coupon CC t, and 0 otherwise. Conditional on CP i > CC t, the higher the coupon rate, the stronger the burnout effect and the lower the redelivery risk. We put a floor on the coupon difference at zero because prepayment risk is largely irrelevant if the MBS coupon is lower than the prevailing coupon. 20 To capture the liquidity effect, we use the time-t aggregate issuance ISU it for FNMA 30- year MBS with coupon rate CP i to measure the supply of MBS to the dollar roll. Because newly issued on the run MBS are more likely to circulate in the market than old off the run MBS that are held by institutional investors, ISU it may be a better proxy for the effective supply of MBS than the total outstanding balance. Moreover, conventional measures of liquidity such as bid-ask spread and price impacts are difficult to obtain because transaction data in agency MBS markets are only available from 2011 through TRACE. Specialness and OAS are measured in basis points, mortgage rates and coupon rates are in percentage points (e.g., 3 for a 3% annualized rate), and issuance is in millions of dollars Results Table 3 reports panel regressions based on the following model: DSP it = t α t D t + i γ i D i + β 1 P MMS t + β 2 BO it + β 3 ISU it + ɛ it, (10) where DSP it is either DSP GC it or DSPit LIBOR, and D i and D t are coupon dummies and time dummies, respectively, which control for coupon-specific effects or time-specific effects. We report robust t-statistics in parentheses that correct for serial correlation in the residuals clustered at the coupon level. Results in columns (1) and (4) of Table 3, using DSP GC it and DSPit LIBOR, respectively, 20 As a robustness check, we also define an MBS to be burned out if CP i > CC t + 1%, and the results are similar. 27

30 Table 3: Determinants of Dollar Roll Specialness DSP GC DSP LIBOR (1) (2) (3) (4) (5) (6) PMMS * * ** * * ** ( ) ( ) ( ) ( ) ( ) ( ) BO ** ** ** ** ( ) ( ) ( ) ( ) ( ) ( ) ISU ** * * ** * * ( ) ( ) ( ) ( ) ( ) ( ) N 1,666 1,666 1,666 1,666 1,666 1,666 R Coupon Effect Yes Yes No Yes Yes No Time Effect Yes No No Yes No No Note: This table reports panel regressions based on the following model: DSP it = t α t D t + i γ i D i + β 1 P MMS t + β 2 BO it + β 3 ISU it + ɛ it, where DSP it is either DSP GC it or DSPit LIBOR, and D i and D t are coupon dummies and time dummies, respectively. Robust t-statistics are reported in parentheses based on clustered standard errors at the coupon level. Significance levels: for p < 0.01, for p < 0.05, and + for p < 0.1, where p is the p-value. The overall sample period is July 1998 to July 2013, with various starting dates that depend on coupon rates. confirm our hypotheses on the determinants of dollar roll specialness: P M M S, BO, and ISU all have a significantly negative effect on specialness. The economic magnitudes are also large. In particular, a one percentage point decrease in primary mortgage rate increases dollar roll specialness by about 89 basis points; a one percentage point decrease in the MBS coupon rate increases specialness by about 148 basis points; and a $9.95 billion decrease in new issuance, which is roughly one standard deviation of MBS issuance across both time and coupon cohorts in our sample, increases specialness by 49 basis points (= ) Initially, it may appear surprising that ISU significantly affects dollar roll specialness, the difference between MBS repo rates and dollar roll financing rates. One might have expected that smaller new issuance of MBS would equally affect the MBS repo rate and the dollar roll financing rate, leaving specialness unchanged. New issues of MBS, however, concentrate on current coupons, which, as discussed above, tend to be more special and more likely the cheapest-to-deliver than the average MBS. Therefore, a lower new issuance is likely to disproportionately affect dollar roll financing rate than the MBS repo rate. 28

31 We also observe that the regression coefficients are almost the same for DSP GC it DSPit LIBOR, indicating the robustness of our results to which benchmark rates are used to compute specialness. The inclusion of coupon and time fixed effects inflates the R 2 in our baseline regressions in columns (1) and (4). Nonetheless, even after dropping some or all the fixed effects (columns (2), (3), (5), and (6)), P MMS, BO, and ISU still explain over 30% of the variation in dollar roll specialness. In Appendix B we conduct robustness checks by running regressions on the first difference: and DSP it = t α t D t + β 1 P MMS t + β 2 BO it + β 3 ISU it + ɛ it. (11) The results are broadly consistent with the specification (10), although the statistical significance is slightly weaker. Moreover, we conduct subsample analysis in Appendix B and find that the mortgage rates and burn-out effects are significant determinants before January 2009, but issuance is significant since January This could be a result of extraordinary market conditions since the financial crisis. 5.2 Dollar roll specialness and expected MBS returns In this subsection, we study the relation between doll roll specialness and expected MBS returns. We find a negative relation, as conjectured in Section 3.2. A commonly used measure of expected MBS returns is the option-adjusted spread (OAS) (see Gabaix, Krishnamurthy, and Vigneron (2007)). As we discussed in the data section, the OAS is effectively a model-implied yield spread of an MBS relative to a benchmark interestrate term structure, after adjusting for the value of homeowners prepayment options. Figure 6 plots the time-series averages of OAS LIBOR and OAS T sy together with those of DSP GC across coupon rates. A pronounced negative relation emerges. As coupon rate increases, specialness goes down, but OAS goes up. To examine the relation between dollar roll specialness and OAS across coupon rates and 29

32 Figure 6: Dollar Roll Specialness and OAS across Coupons 250 Specialness vs OAS Basis Points Roll Specialness GC Repo LIBOR OAS Tsy OAS 3% 3.5% 4% 4.5% 5% 5.5% 6% 6.5% 7% 7.5% 8% 8.5% Note: This figure plots time series averages of OAS LIBOR and OAS T sy together with those of DSP GC across coupon rates. The overall sample period is July 1998 to July 2013, with various starting dates that depend on coupon rates. time, Table 4 reports panel regression on the following model: OAS it = t α t D t + i γ i D i + β 1(DSP it > 0) + ɛ it, (12) where 1(DSP it > 0) is the specialness indicator function, taking on the value of 1 if an MBS cohort with coupon CP i is on special in period t and 0 otherwise, OAS it is either OAS LIBOR or OAS T sy, and D i and D t are coupon dummies and time dummies, respectively. Robust t-statistics are reported in parentheses that correct for serial correlation in the residuals clustered at the coupon level. Regression results with OAS LIBOR and OAS T sy are reported in Panels A and B of Table 4, respectively, using both DSP GC it and DSP LIBOR it in each panel. We observe from columns (1) and (4) that an MBS cohort on special has a significant negative premium of 60 basis points relative to an otherwise identical MBS cohort. The dollar roll special premium is around 54 30

33 Table 4: Regression of OAS on Specialness Dummy A: OAS LIBOR (1) (2) (3) (4) (5) (6) 1(DSP GC > 0) ** * ** (-4.13) (-2.74) (-3.43) 1(DSP LIBOR > 0) ** * ** (-4.15) (-3.10) (-4.01) N 1,666 1,666 1,666 1,666 1,666 1,666 R Coupon Effects Yes Yes No Yes Yes No Time Effects Yes No No Yes No No B: OAS T sy (7) (8) (9) (10) (11) (12) 1(DSP GC > 0) ** ** ** (-3.95) (-3.37) (-3.98) 1(DSP LIBOR > 0) ** ** ** (-3.94) (-3.56) (-4.44) N 1,666 1,666 1,666 1,666 1,666 1,666 R Coupon Effects Yes Yes No Yes Yes No Time Effects Yes No No Yes No No Note: This table reports panel regressions based on the following model: OAS it = t α t D t + i γ i D i + β 1(DSP it > 0) + ɛ it, where 1(DSP it > 0) is either 1(DSPit GC > 0) or 1(DSPit LIBOR > 0), OAS it is either OAS LIBOR or OAS T sy, and D i and D t are coupon dummies and time dummies, respectively. Robust t-statistics are reported in parentheses based on clustered standard errors at the coupon level. Significance levels: for p < 0.01, for p < 0.05, and + for p < 0.1, where p is the p-value. The overall sample period is July 1998 to July 2013, with various starting dates that depend on coupon rates. basis points using OAS T sy, from columns (7) and (10). From other columns of specifications dropping coupon and/or time effects, the dollar roll special dummy still explain 22% 30% of the variation in the OAS. Table 5 reports panel regressions using the magnitude of dollar roll specialness: OAS it = t α t D t + i γ i D i + β DSP it + ɛ it, (13) 31

34 Table 5: Regression of OAS on Specialness A: OAS LIBOR (1) (2) (3) (4) (5) (6) DSP GC -0.45** -0.47** -0.50** (-7.06) (-5.16) (-7.06) DSP LIBOR -0.45** -0.47** -0.50** (-7.11) (-5.37) (-7.34) N 1,666 1,666 1,666 1,666 1,666 1,666 R Coupon Effects Yes Yes No Yes Yes No Time Effects Yes No No Yes No No B: OAS T sy (7) (8) (9) (10) (11) (12) DSP GC -0.41** -0.43** -0.49** (-6.39) (-5.59) (-7.75) DSP LIBOR -0.41** -0.43** -0.49** (-6.44) (-5.65) (-7.84) N 1,666 1,666 1,666 1,666 1,666 1,666 R Coupon Effects Yes Yes No Yes Yes No Time Effects Yes No No Yes No No Note: This table reports panel regressions based on the following model: OAS it = t α t D t + i γ i D i + β DSP it + ɛ it, where DSP it is either DSPit GC or DSPit LIBOR, OAS it is either OAS LIBOR or OAS T sy, and D i and D t are coupon dummies and time dummies, respectively. Robust t-statistics are reported in parentheses based on clustered standard errors at the coupon level. Significance levels: for p < 0.01, for p < 0.05, and + for p < 0.1, where p is the p-value. The overall sample period is July 1998 to July 2013, with various starting date that depend on coupon rates. where DSP it is either DSP GC it or DSPit LIBOR. We observe highly significant impact of dollar roll specialness on OAS, regardless of which interest benchmark interest rates are used to compute specialness, which OAS measure is used, and whether coupon and time effects are included. The coefficient estimates are remarkably stable, ranging from 0.50 to Without coupon and time effects, dollar roll specialness can still explain around 60% of the variation in the OAS. 32

35 As in the previous subsection, we also run the first-difference regression: OAS it = t α t D t + β DSP it + ɛ it. (14) The results, reported in Appendix B, still reveal highly significant and negative relation between dollar roll specialness and OAS. We also conduct robustness checks on the potential misspecifications of OAS similar to Gabaix, Krishnamurthy, and Vigneron (2007) and find similar results. Regressing the OAS on dollar roll specialness may suffer an endogeneity problem as both are outputs from a prepayment model with the same inputs. To investigate the robustness of our results, we use another proprietary data set provided by J.P. Morgan that consists of monthly returns on FNMA 30-year TBA contracts from February 2000 to July The return series are calculated for a strategy of going long a one-month TBA, investing the TBA price in a riskless margin account, and then rolling the portfolio over every month on the monthly TBA settlement date. (Carlin, Longstaff, and Matoba (2013) employ a data set of return series with the same strategy.) By design, these return series do not depend on any model or assumption about mortgage prepayment rates or interest rate paths. We label this returns series the return on mortgages, ROM. Regressing ROM on dollar roll specialness is free of the endogeneity problem of regressing OAS on specialness. Columns (1) and (2) of Table 6 report panel regressions based on the model ROM it = t α t D t + i γ i D i + β DSP it + ɛ it, (15) whereas columns (3) and (4) report panel regressions based on the model ROM it = t α t D t + i γ i D i + β DSP it + ɛ it, (16) where DSP it is either DSP GC it or DSPit LIBOR, ROM it is the month-t return on the mortgage TBA with coupon rate CP i, and D i and D t are coupon dummies and time dummies, 33

36 Table 6: Regression of ROM on Specialness Variable (1) (2) Variable (3) (4) DSP GC DSP GC -0.48** (-2.05) (-3.42) DSP LIBOR DSP LIBOR -0.48** (-2.06) (-3.41) N 1,409 1,409 1,397 1,397 R Note: Columns (1) and (2) report panel regressions based on the model ROM it = t α t D t + i γ i D i + β DSP it + ɛ it, while columns (3) and (4) report panel regressions based on the model ROM it = t α t D t + i γ i D i + β DSP it + ɛ it, where DSP it is either DSP GC it or DSPit LIBOR, ROM it is the month-t return on the mortgage TBA with coupon rate CP i, and D i and D t are coupon dummies and time dummies, respectively. Robust t-statistics are reported in parentheses based on clustered standard errors at the coupon level. Significance levels: for p < 0.01, for p < 0.05, and + for p < 0.1, where p is the p-value. The overall sample period is February 2000 to July 2013, with various starting dates that depend on coupon rates. respectively. Columns (1) and (2) of Table 6 show that dollar roll specialness levels significantly affect the mortgage returns negatively, regardless of whether the GC repo rate or LIBOR is used to compute specialness. Moreover, using the first-differenced specialness to ease the concern on the time series persistence, we still observe negative impact of specialness on mortgage returns that is highly significant. Overall, these results confirm the documented negative relation between dollar roll specialness and mortgage returns using OAS as a proxy. 34

37 6 The Impact of Large-Scale Asset Purchases (LSAP) on Dollar Roll Specialness In response to the recent financial crisis, the Federal Reserve introduced a sequence of largescale asset purchase (LSAP) programs of agency MBS, as well as of Treasury securities, for the purpose of credit easing (Bernanke (2009)). The first LSAP program of agency MBS was announced in November The MBS purchases did not start until January 2009, and were finished in March 2010, with a total size of around $1.25 trillion as planed. Then, in September 2011, the Federal Reserve decided to reinvest principal payments from its agency MBS holdings into agency MBS markets, rather than into long-term Treasury securities as it has been doing since August Finally, in September 2012, another LSAP program of agency MBS began when the Federal Reserve announced that it will purchase additional agency MBS at a pace of $40 billion per month until the labor market and financial market conditions improve substantially. Together with the reinvestments from its agency MBS holdings, the Federal Reserve has been purchasing around $45 55 billion of agency MBS per month from September 2012 till the end of our sample period July The great majority of these purchases are newly issued 15- and 30-year agency MBS with production coupons, which vary over time with the primary mortgage rate. The Fed s MBS purchases are executed exclusively in the TBA market. Given the large size of the Federal Reserve s agency MBS purchases, one natural question is whether LSAP disrupts the functioning of the agency MBS market. In this section, we investigate this question by studying whether the Federal Reserve s purchases affected dollar roll specialness. According to our analytic framework in Section 3.1, there are two channels through which the LSAP can affect dollar roll specialness. The first channel is adverse selection associated with redelivery risk. As Section 3.1 suggests, the adverse-selection component of dollar roll specialness is driven by the average 22 On December 18, 2013, the Fed began tapering its asset purchases, with a reduction of $5 billion per month on MBS purchases. The scheduled MBS purchases ended in October 2014, although the Fed continues reinvesting in MBS the principal and coupon payments from its existing holdings. 35

38 prepayment speed of a cohort as well as the within-cohort heterogeneity in prepayment speeds. The Fed purchase affects both. On the one hand, as the Fed purchase exerts a downward pressure on mortgage rates, households are more likely to prepay, leading to a higher market-wide prepayment risk (a larger E[λ] in equation (8)). to increase specialness. This effect tends On the other hand, since the Fed purchases MBS through TBA markets, the Fed is likely to be delivered the CUSIPs that have the worst prepayment characteristics (see Krishnamurthy and Vissing-Jorgensen (2013)). This in turn suggests that the heterogeneity of prepayment characteristics among remaining CUSIPs not held by the Fed should fall (a smaller E[max i α i ] E[α i ] or E[α i ] E[min i α i ] in equation (8)). This effect tends to reduce specialness. The second channel is liquidity. The large size of MBS absorbed by the LSAP from the private sector may result in shortage of supply and increases dollar roll specialness. Differentiating the two channels is a distinct feature of our study. We obtain monthly series of the Federal Reserve s purchases of the FNMA 30-year MBS with different coupon rates Q LSAP it York. from the website of the Federal Reserve Bank of New We also use monthly aggregate issuance and outstanding balance data of FNMA 30-year MBS pools across coupon rates from embs to normalize the LSAP size. Figure 7 plots the LSAP purchase amount of FNMA 30-year MBS across coupon rates, along with amounts of the aggregate issuance and outstanding balance. Overall, the LSAP purchases included MBS with coupon rates between 3% and 6.5%. From the top panel, the average monthly purchase size as a ratio of the average monthly aggregate issuance is hump-shaped, peaking at the 5.5% coupon rate. 23 The same pattern is also observed for the total purchase size as a ratio of the outstanding balance as of July That is, the ratio of the total LSAP purchase size to outstanding balance is distributed unevenly across coupon rates, with the largest amounts for 5%, 5.5% and 6% coupon rates due to the concentration of the $1.25 trillion purchase from January 2009 to March 2010 in these coupon cohorts. It is worth pointing out that the total purchase size does not take into account the principal 23 The computation of the average monthly purchase size excludes the months when no purchase was conducted for a coupon cohort. 36

39 Figure 7: Size of LSAP Monthly Size of LSAP (left) Monthly Issuance (left) Size of LSAP vs Issuance Monthly LSAP Size/Issuance (right) Billion Dollars % 3.5% 4% 4.5% 5% 5.5% 6% 6.5% Total LSAP Size (left) Outstanding Balance (left) Total LSAP Size vs Outstanding Balance Billion Dollars Total LSAP Size/Outstanding Balance (right) % 3.5% 4% 4.5% 5% 5.5% 6% 6.5% 0 Note: The top figure plots monthly size of LSAP vs issuance across coupon rates. The bottom figure plots cumulative size of LSAP vs outstanding balance. The sample is from January 2009 to July payout, and accordingly the outstanding balance in Figure 7 is computed as the sum of the outstanding balance as of December 2008, the last month before the start of LSAP purchases, and the cumulative new issuance between January 2009 and July To differentiate the two channels through which LSAP can affect dollar roll specialness, 37

40 we employ the model (10) estimated in Section 5.1 using the sample of July 1998-July 2013, with both coupon and time dummies, and compute the adverse-selection component of dollar roll specialness and the supply component as DSP AS it = β 1 P MMS t + β 2 BO it, (17) DSP Supply it = β 3 ISU it, (18) respectively. We conduct this decomposition in the full sample to focus on the long-term dynamics of dollar roll specialness. We consider five measures for the Federal Reserve s MBS purchases LSAP it : the purchase size Q LSAP it (in billions of US dollars), the purchase size as a ratio of the month-t outstanding balance Q LSAP it /CB it, the purchase size as a ratio of the month-t aggregate issuance Q LSAP it /ISU it, the indicator 1(F low it ) of purchases in month t for coupon CP i, and the indicator 1(Stock it ) for the existence of MBS with coupon CP i in the Federal Reserve s holdings at month t. 24 Our investigation is based on the following regression: SP it = t α t D t + i γ i D i + β LSAP it + ɛ it, (19) where SP it can be the total dollar roll specialness DSP it, the adverse selection component DSP AS it, and the liquidity (i.e. supply shortage) component DSP Supply it, based on both the GC repo rate and the 1-month LIBOR as the benchmark interest rates. The regressions are estimated for the sample of January 2009 July Hence, we primarily explore the crosssectional difference of LSAP effects on dollar roll specialness, which avoids the caveat that including the longer sample before 2009 may mechanically capture the time series difference of specialness before and after the 2008 financial crisis. Columns (1), (2), and (3) of Table 7 report panel regressions (19) with DSPit AS, DSP Supply it, 24 We also define 1(F low it ) in terms of the settlement month t of the Fed s purchases for coupon CP i and obtain similar results. 38

41 Table 7: Impact of LSAP on Dollar Roll Specialness DSP GC (1) (2) (3) Adverse Selection Supply Total Q LSAP Est * t-stat (1.6412) ( ) ( ) R Q LSAP /CB Est t-stat (1.3714) ( ) (0.5358) R Q LSAP /ISU Est t-stat (1.2608) (0.5086) ( ) R (F low) Est * ** * t-stat (2.4677) ( ) ( ) R (Stock) Est ** * * t-stat (3.6449) ( ) ( ) R DSP LIBOR (1) (2) (3) Adverse Selection Supply Total Q LSAP Est * t-stat (1.6412) ( ) ( ) R Q LSAP /CB Est t-stat (1.3714) ( ) (0.5405) R Q LSAP /ISU Est t-stat (1.2608) (0.5086) ( ) R (F low) Est * ** * t-stat (2.4677) ( ) ( ) R (Stock) Est ** * * t-stat (3.6449) ( ) ( ) R Note: This table reports regressions based on the following model: SP it = t α t D t + i γ i D i + β LSAP it + ɛ it, where SP it is DSP AS it can be Q LSAP it, Q LSAP it, DSP Supply it, and DSP it in columns (1), (2), and (3), respectively. Moreover, LSAP it /CB it, Q LSAP i t/isu it, 1(F low it ), and 1(Stock it ), and D i and D t are coupon and time dummies, respectively. We report the coefficient estimate β, the robust t-statistic based on clustered standard errors at the coupon level, and the R 2 for each regression with only one LSAP variable. Significance levels: for p < 0.01, for p < 0.05, and + for p < 0.1, where p is the p-value. The sample period is January 2009-July

42 and DSP it, respectively. Both coupon and time effects are included, and robust t-statistics are reported in parentheses that correct for serial correlation in the residuals clustered at the coupon level. Regression results on the residual, DSP it DSP AS it as the coefficients there are not statistically significant. DSP Supply it, are omitted Column (1) of Table 7 shows that all the LSAP variables are positively associated with the adverse selection component of dollar roll specialness, with the two indicator variables statistically significant. In particular, results with the LSAP dummies 1(F low it ) and 1(Stock it ) suggests that the mere presence of the Federal Reserve s MBS purchases is associated with an increase of basis points of dollar roll specialness through the adverse selection channel. Given the earlier discussion, this result suggest that the increase in average prepayment is more important in the data than the potential reduction in the heterogeneity of prepayment characteristics across CUSIPs. Column (2) of Table 7 shows a negative relation between LSAP and the supply component of dollar roll specialness. This pattern may simply reflect the fact that the Fed purchases MBS cohorts with greater supplies in order to alleviate squeezes in the market, consistent with the Fed communication to the public. 25 Alternatively, the negative relation may suggest that the Fed s purchases of agency MBS improve market liquidity, leading to lower search costs and hence lower specialness. But this second possibility is unlikely in the extreme but unusual scenario that the Fed purchases all the new MBS issuance, in which case liquidity should dry up by definition. Combining these two components, Column (3) of Table 7 shows that all the LSAP measures are associated with a lower total dollar roll specialness, except Q LSAP it /CB it. This suggests that the endogenous selection by the Fed to purchase less special MBS coupon cohorts has a stronger effect in the data than the impact of the Fed s purchase on specialness through the adverse-selection channel. This column highlights that the decomposition is an important step in the analysis. Otherwise, the single negative coefficient may misleadingly suggest that LSAP has no negative impact on MBS funding market. 25 See faq.html for details. 40

43 7 Conclusion Mortgage dollar roll is the most widely used trading strategy for financing agency MBS, accounting for about a half of the trading volume in agency MBS markets. It is also an important tool that the Federal Reserve uses in conducting its monetary policy. A dollar roll is effectively a secured lending contract, but different from a repo contract, the cash lender who receives an MBS as collateral in a dollar roll transaction has the option to return a different MBS when the loan matures. Dollar roll specialness is defined as the extent to which implied dollar roll financing rates fall below prevailing market interest rates. Therefore, specialness is a key indicator of the funding markets of agency MBS. In this paper, we provide the first analysis of the economics of mortgage dollar roll specialness. Our analytic framework highlights two important determinants of dollar roll specialness: adverse selection that is unique to MBS markets and liquidity that is generic in OTC markets. The framework also suggests empirical measures of these two channels. Using a proprietary panel dataset from July 1998 to July 2013, we show that dollar roll specialness increases in adverse selection and decreases in MBS liquidity. In particular, a lower primary mortgage rate, a lower (burned-out) MBS coupon, or a lower MBS issuance is associated with a higher specialness. We also show that expected returns of the underlying MBS decreases in their specialness. These results are consistent with our analytic framework and robust to various model specifications. Our analytic framework suggests a natural decomposition of dollar roll specialness into an adverse selection component and a liquidity component. We employ this decomposition to evaluate the impact of the Federal Reserve s MBS purchase program on MBS financing markets since the 2008 financial crisis. Our results suggest that LSAP increases the adverseselection component of dollar roll specialness by putting a downward pressure on mortgage rates, but the large size of MBS absorbed by the Fed does not result in (detectable) supply shortages or market distortions through the liquidity channel. Instead, LSAP seems to be associated with a lower dollar roll specialness, suggesting that the Fed intentionally purchase less special MBS. 41

44 Appendix A Additional Details of TBA and Dollar Roll Markets A.1 Dollar roll financing rates: a worked example In this appendix we present a worked example for the calculation of dollar roll financing rates in Table 8, corresponding to the dollar roll transaction of Figure 2. In this example, an investor sells a May/June dollar roll of $1 million FNMA 30-year 5% coupon MBS, with the price drop of 14/32. We assume that the scheduled principal payment in May is $1000 and the annualized conditional prepayment rate (CPR) is 10%. (The CPR gives the expected prepayment in a way we detail shortly.) Moreover, the 1-month reinvestment rate over the roll tenor for the roll seller is r = 2%. According to the trading convention, the principal and coupon payments of May are made on June 25. Cash flows from holding on the $1 million FNMA 30-year 5% coupon MBS are presented in Panel B of Table 8. The investor will receive $13, in total on June 25, including coupon payments of $ , scheduled principal payments of $1000, and prepaid principal payments of (with a 10% CPR) $ The discounted proceeds as of June 16 is hence $13,892.99, using the 1-month short rate of 2%. Panel C tabulates the cash flows from rolling the $1 million FNMA 30-year 5% coupon MBS. The investor will receive $1,025,000 on May 16 by selling the MBS in the front month TBA contract at , along with 14 days accrued coupon payments of $ by holding the MBS until May 16, giving a total of $1,026, By reinvesting the proceeds at the rate r = 2%, the investor receives the cash inflow of $1,028, on June 16. Furthermore, on June 16, the roll seller buys back the amount left after the scheduled and prepaid principal payments, i.e., $990, at the price of 102-2, leading to a cash outflow of $1,010, A measure of monthly prepayment rate is the single monthly mortality rate (SMM), which equals the prepayment amount as a percentage of the previous month s outstanding balance minus this month s scheduled principal payment. The SMM can be computed from the CPR as SMM = 1 (1 CP R) 1/12. The $ prepayment is calculated as SMM (1, 000, 000 1, 000) given a 10% CPR. 27 In practice, the roll seller buys back more than the amount left after the scheduled and prepaid principal 42

45 Table 8: Dollar Roll Calculation A: Assumptions Security FNMA 5% 30-Year Principal Balance $1 million Conditioal Prepayment Rate (CPR) 10 Scheduled Principal Payment $1000 Front-Month TBA Price Future-Month TBA Price Roll Drop 14/32 Prevailing Interest Rate (e.g., LIBOR) 2% Implied Finance Rate r B: Cash Flows from Holding the MBS June 25 Receive coupon payments (5%*30/360*1,000,000) $ Receive Scheduled Principal $1000 Receive Prepaid Principal (with 10% CPR) $ $13, , June 16 Discounted Proceeds as of June 16 ( 1+(2%*9/360) ) $13, C: Cash Flows from Rolling the MBS May 16 Sell $1,000,000 FNMA 5% at $1,025, Receive 14 days accrued coupon payments (5%*14/360*1,000,000) $ $1,026, Reinvest the proceeds at r (30/360*r*1,026,944.44) until June 16 $ $1,028, June 16 Buy $990, (=1,000, ) FNMA 5% at $1,010, Pay 15 days accrued coupon payments to (5%*15/360*990,267.13) -$ $1,012, Net Proceeds from Rolling as of June 16 (1,028, , ) $15, D: Cash Flow of Rolling vs Holding the MBS 15, , $2, E: Dollar Roll Financing Rate Dollar roll implied financing rate=reinvestment rate at which rolling and holding the MBS are indifferent as of June 16 (Solve for r in 1,026,944.44*(1+r*30/360)-1,012,754.45=13,892.99) r=-0.35% Note: This table provides the calculation of a dollar roll example. The numbers are hypothetical. 43

46 Moreover, the roll seller delivers 15 days accrued coupon payments of $ to the roll buyer as the buyer holds the MBS from June 1 to June 16. In total, the roll seller has a cash outflow of $1,012, on June 16, with the net cash flow from the whole roll transaction as $15, on June 16. Overall, the investor earns an additional $2, by rolling her MBS instead of holding onto it, with the 1-month reinvestment rate equal to 2%. The effective dollar roll financing rate can be solved as the reinvestment rate r that equates the cash flows from rolling the MBS and those from holding onto it. That is, r solves 1, 026, (1 + r 30/360) 1, 012, = 13, , which gives r = 0.35% in this example. Since the roll seller may receive an inferior MBS in the future-month leg, the negative implied financing rate is not an arbitrage. Rather, it reflects redelivery premium, search costs, and other frictions in the market. A.2 Trading at Fail and negative financing rate The discussion of dollar roll markets in the main text is made under the assumptions that both counterparties of the dollar roll transaction deliver on time. In reality, the security borrower in a dollar roll transaction may fail to return the MBS to the roll seller on time in the future-month TBA contract. In this case, we say the roll is trading at fail. Fails could happen if there is a temporary shortage of MBS that satisfy the TBA delivery requirements due to, for example, a high volume of CMO deals. In the case of trading at fail, the dollar roll seller benefits by not having to pay the cash back to the security borrower until the MBS is delivered back. In addition, the roll seller is still entitled the principal and coupon payments of the MBS that the roll buyer fails to return. On net, the dollar roll seller receives extra interests earned on the funds that would be passed to the security borrower if a fail had not occurred. That is, while the dollar roll is trading at fail, the roll seller effectively payments due to the Good Delivery requirement that the returned MBS pool has a maximum principal difference of 0.01%. The simpler example here is just for the convenience of calculation. 44

47 borrows from the roll buyer at the 0% financing rate. Without a penalty on failure to deliver, a sufficiently negative implied financing rate in a dollar roll trade can encourage the MBS borrower in the roll transaction to fail strategically and charge a more desirable 0% financing rate, instead of the negative financing rate implied by the dollar roll. Assuming that the returned MBS is the same as the original one, this strategic incentive would bound the dollar roll financing rate at 0% from below. On April 29, 2011, the Treasury Market Practices Group (TPMG) proposed a fail charge of 2% for agency MBS markets, which would begin on February 1, By the same reasoning, this fails charge pushes the lower bound of the dollar roll financing rate to 2%, again assuming that the returned MBS is the same as the original one. However, given the redelivery risk in a dollar roll transaction, the implied financing rate can fall below the failing charges of 0% or 2% significantly, as a compensation to the roll seller (see Figure 3). This suggests that some security borrowers (roll buyers) view returning an MBS with inferior prepayment characteristics in the future-month TBA contract to be more advantageous than invoking a fail and holding onto the MBS. This usually happens when primary mortgage rate falls and new MBS issuance moves to lower coupon brackets, in which case holders of MBS with immediately higher coupons are subject to high prepayment risk and are better off delivering them. Reputation concerns may also prevent the security borrowers to fail excessively. B Robustness In this Appendix, we present five sets of robustness checks on our empirical results in Section 5. In unreported results, we have also conducted robustness checks using dollar roll specialness and OAS of the FNMA 15-year MBS and of the GNMA and FHLM MBS. Re- 28 The TMPG is composed of a group of market professionals from securities dealers, banks, and buy-side firms, and commits to supporting the integrity and efficiency of the U.S. Treasury market. Sponsored by the Federal Reserve Bank of New York, they meet periodically to discuss trading issues in Treasury, agency debt, and agency MBS markets. The TMPG has implemented a similar fails charge for transactions of U.S. Treasury securities since May 1,

48 sults are similar and available upon request. B.1 Additional variables for prepayment risk We use PMMS as the measure for market-wide prepayment risk in Section 5.1 because a lower mortgage rate encourages homeowners to refinance. To further understand how the prepayment risk drives dollar roll specialness, we consider three additional variables that are relevant for various aspects of the market-wide prepayment risk. The first is the S&P/Case-Shiller 10-City Composite Home Price Index (CS), which measures the total value of all existing single-family houses in 10 metropolitan areas of the U.S. 29 Although a low primary mortgage rate implies high refinancing activities in general, low house prices will lead to high loan-to-value ratios and prevent homeowners from refinancing, which may result in a low dollar roll specialness. We capture this effect by the interactive term P MMS CS in the regression: DSP it = t α t D t + i γ i D i +β 1 P MMS t +β 2 BO it +β 3 ISU it +β 4 P MMS t CS t +ɛ it, (20) where DSP it is either DSP GC it dummies, respectively. or DSPit LIBOR, and D i and D t are coupon dummies and time The second additional variable is the seasonally adjusted number of home sales (HS), measured by the Mortgage Bankers Associations (MBA) Purchase Index. The MBA Purchase Index is based on the number of nationwide home loan applications and covers about 75% of U.S. mortgage activity. This index is a leading indicator of home sales in four to six weeks, and is used by housing economists and homebuilders to forecast new and existing home sales. As an increase of home sales implies an increasing prepayment activity only conditional on a low mortgage rate, we include the interaction term P MMS HS in the 29 The Case-Shiller 20-City Composite Home Price Index is available only from January 2000, but tests using this shorter sample yield similar results. We do not use the Case-Shiller national index because it is only available at the quarterly frequency. 46

49 following model: DSP it = t α t D t + i γ i D i +β 1 P MMS t +β 2 BO it +β 3 ISU it +β 4 P MMS t HS t +ɛ it. (21) The third additional variable is the seasonally adjusted MBA Refinance Index (Refi), which measures the number of refinance applications and is hence a leading indicator of mortgage prepayment activity. Different from home prices and number of home sales, Refi directly measures the market-wide prepayment activity and has a high correlation with PMMS of We study how it affects dollar roll specialness in the model DSP it = t α t D t + i γ i D i + β 1 Refi t + β 2 BO it + β 3 ISU it + ɛ it, (22) where we do not include P MMS together with Refi due to colinearity concerns. Table 9 reports panels regressions of (20), (21), and (22). Results in columns (1), (2), (4), and (5) show that the interaction terms of PMMS with both CS and HS are highly significant and negative. This confirms our conjecture that conditional on a lower mortgage rate, a higher home price or home sales number further increases prepayment risk and hence dollar roll specialness. Moreover, results of columns (3) and (6) show that a higher Refinancing activity (Refi) is associated with a higher dollar roll specialness, with a significant t-statistics of 3.8. These results provide corroborative evidence that the prepayment risk, through various channels, is an important determinant of dollar roll specialness. B.2 Regressions of first difference The time-series persistence in the data may raise concerns about potentially spurious regression results. To address these concerns in this subsection we run the first-difference version of key regressions. Table 10 reports the results of the first-difference version of the regression on the deter- 47

50 Table 9: Determinants of Dollar Roll Specialness DSP GC DSP LIBOR (1) (2) (3) (4) (5) (6) PMMS ** * * ( ) ( ) ( ) ( ) BO * * * * * * ( ) ( ) ( ) ( ) ( ) ( ) ISU ** ** ** ** ** ** ( ) ( ) ( ) ( ) ( ) ( ) PMMS*CS ** ** ( ) ( ) PMMS*HS ** ** ( ) ( ) Refi ** ** (3.8753) (3.8092) N 1,544 1,544 1,544 1,544 1,544 1,544 R Note: Columns (1) and (4) report panel regressions for the model DSP it = t α t D t + i γ i D i + β 1 P MMS t + β 2 BO it + β 3 ISU it + β 4 P MMS t CS t + ɛ it, columns (2) and (5) for the model DSP it = t α t D t + i γ i D i + β 1 P MMS t + β 2 BO it + β 3 ISU it + β 4 P MMS t HS t + ɛ it, and columns (3) and (6) for the model DSP it = t α t D t + i γ i D i + β 1 Refi t + β 2 BO it + β 3 ISU it + ɛ it, where DSP it is either DSP GC it or DSPit LIBOR, and D i and D t are coupon dummies and time dummies, respectively. Robust t-statistics are reported in parentheses based on clustered standard errors at the coupon level. Significance levels: for p < 0.01, for p < 0.05, and + for p < 0.1, where p is the p-value. The overall sample period is July 1998 to July 2013, with various starting dates that depend on coupon rates. 48

51 Table 10: Determinants of Dollar Roll Specialness: First Difference DSP GC PMMS ( ) ( ) BO ( ) ( ) ISU (1.4362) (1.4344) DSP LIBOR N 1,654 1,654 R Note: This table reports panel regressions based on the following model: DSP it = t α t D t + β 1 P MMS t + β 2 BO it + β 3 ISU it + ɛ it, where DSP it is either DSPit GC or DSPit LIBOR and D t is the time dummy. Robust t-statistics are reported in parentheses based on clustered standard errors at the coupon level. Significance levels: for p < 0.01, for p < 0.05, and + for p < 0.1, where p is the p-value. The overall sample period is July 1998 to July 2013, with various starting dates that depend on coupon rates. minants of dollar roll specialness: DSP it = t α t D t + β 1 P MMS t + β 2 BO it + β 3 ISU it + ɛ it. (23) We still observe significant impacts of P MMS and BO on dollar roll specialness, but not ISU. 30 The coefficients estimates are lower for BO but higher for P MMS than those in Table 3. It is worth pointing out that the statistical insignificance of the supply variables in the panel regression (23) may be due to ISU it being a poor proxy, or that the supply effect is not quantitatively large. 31 Table 11 reports the results of the first-difference version of the regression on the relation 30 Since the change of ISU it will miss the payout of the MBS existing ahead of period-t, we also use the outstanding balance to measure the stock supply. Regression results are similar. 31 Interestingly, in the level regression, ISU is the only significant determinant of dollar roll specialness for the subsample of post-crisis. See the subsample analysis in this appendix for details. 49

52 Table 11: Regression of OAS on Specialness: First Difference OAS LIBOR OAS T sy (1) (2) (4) (5) DSP GC ** ** (-6.593) (-6.020) DSP LIBOR ** ** (-6.708) (-6.131) N 1,654 1,654 1,654 1,654 R Note: This table reports panel regressions based on the following model: OAS it = t α t D t + β DSP it + ɛ it, where DSP it is either DSP GC it or DSPit LIBOR, OAS it is either OAS LIBOR or OAS T sy, and D t is the time dummy, respectively. Robust t-statistics are reported in parentheses based on clustered standard errors at the coupon level. Significance levels: for p < 0.01, for p < 0.05, and + for p < 0.1, where p is the p-value. The overall sample period is July 1998 to July 2013, with various starting dates that depend on coupon rates. between dollar roll specialness and OAS: OAS it = t α t D t + β DSP it + ɛ it. (24) We still observe highly significant impact of dollar roll specialness on OAS, regardless of choices of dollar roll specialness measures and OAS measures. The coefficient estimates are even more stable than those in Table 5, ranging from to B.3 OAS misspecifications The OAS, our proxy of MBS expected returns, is calculated based on a Wall Street mortgage model that may be misspecified. We have shown in Section 5.2 that using directly observed mortgage returns leads to the same qualitative results. In this subsection, we conduct a few more robustness checks for the OAS results. We first obtain alternative OAS series for the FNMA 30-year MBS computed from Bar- 50

53 clays Capital, which are based on different prepayment and interest rate models from those by J.P. Morgan. In unreported results, we run the same regressions involving the OAS by these alternative OAS series, and obtain similar results. Hence, our results do not hinge upon a particular firm s prepayment model. As argued by Gabaix, Krishnamurthy, and Vigneron (2007), any bias that affects the OAS equally across MBS with various coupon rates has been controlled for by the time dummy D t and any bias that affects the OAS equally across time has been controlled for by the coupon dummy D i. Therefore, we only need to control for misspecifications that affect the OAS differently both across MBS with various coupon rates and over time. One possible concern is misspecified model-implied prepayment rate. As investors typically calibrate and recalibrate their prepayment models to historical data, model-implied prepayment rates can have biases that vary across coupon and time. To control for such a bias, we run the following regression: OAS it = t α t D t + i γ i D i + β 1 DSP it + β 2 SMM it + ɛ it, (25) where DSP it is either DSP GC it or DSPit LIBOR, and SMM it is the historical actual singlemonth mortality, which we compute for FNMA 30-year MBS with coupon rates from 3% to 8.5% by the historical CPR data obtained from J.P. Morgan. 32 Table 12 reports the panel regression of equation (25) in columns (1), (3), (5), and (7). While SMM it is significant, the coefficients on dollar roll specialness continue to be highly significant, regardless of whether DSP GC it OAS LIBOR or OAS T sy or DSP LIBOR it is used for specialness, and whether is used for OAS. Moreover, the regression coefficients range from 0.38 to 0.35, which are only slightly lower than those in Table 5, which range from 0.45 to 0.41 for the regression equation (13) without control variables. Another potential concern is misspecification in the term structure model and the interaction between the coupon rates and the level of interest rates, which affects the OAS 32 We also use the average single-month mortality for seven months centered around month t, following Gabaix, Krishnamurthy, and Vigneron (2007), and obtain similar results. 51

54 Table 12: Regression of OAS on Specialness: OAS Robustness OAS LIBOR OAS T sy (1) (2) (3) (4) (5) (6) (7) (8) DSP GC -0.38** -0.37** -0.35** -0.33** (-7.24) (-7.22) (-6.30) (-6.36) DSP LIBOR -0.38** -0.37** -0.35** -0.34** (-7.30) (-7.28) (-6.36) (-6.40) SMM ** ** ** ** (-5.42) (-5.43) (-4.79) (-4.79) CP*LIBOR -7.54** -7.50** -7.45** -7.41** (-6.50) (-6.52) (-6.35) (-6.37) N 1,666 1,666 1,666 1,666 1,666 1,666 1,666 1,666 R Note: This table reports regressions (in columns (1), (3), (5), and (7)) based on the following model: OAS it = α t D t + γ i D i + β 1 DSP it + β 2 SMM it + ɛ it, t i and regressions (in columns (2), (4), (6), and (8)) based on the following model: OAS it = t α t D t + i γ i D i + β 1 DSP it + β 2 CP i LIBOR t + ɛ it. where DSP it is either DSP GC it or DSPit LIBOR, OAS it is either OAS LIBOR or OAS T sy, SMM it is the historical actual single-month mortality, and D i and D t are coupon dummies and time dummies, respectively. Robust t-statistics are reported in parentheses based on clustered standard errors at the coupon level. Significance levels: for p < 0.01, for p < 0.05, and + for p < 0.1, where p is the p-value. The overall sample period is July 1998 to July 2013, with various starting dates that depend on coupon rates. differently both across coupon rates and over time. We control for such a bias by including the interaction term CP i LIBOR t into the regression: OAS it = t α t D t + i γ i D i + β 1 DSP it + β 2 CP i LIBOR t + ɛ it. (26) In fact, this regression with CP i LIBOR t also controls for other biases due to misspecifications of prepayment models that fail to capture the extent to which homeowners propensities 52

55 to prepay mortgages may differ across coupon cohorts. Table 12 reports the panel regression of equation (26) in columns (2), (4), (6), and (8). While CP i LIBOR t is significant, the coefficients on dollar roll specialness remain highly significant with values in line of those for the regression equation (13) without control variables. Overall, these results confirm that our empirical evidence on the impact of dollar roll specialness on expected MBS returns is robust to various types of misspecifications in the OAS. B.4 Subsamples Large market dislocations and many policy initiatives during the recent financial crisis suggest that the dollar roll markets may behave differently during the crisis than before. This subsection presents the empirical results of both the determinants of dollar roll specialness and the relation between MBS returns and specialness for two subsamples, July 1998 December 2008 and January 2009 July We use January 2009 as the cutoff date because the Federal Reserve began purchasing MBS in the first week of January 2009, though the plan to purchase was announced on November 25, Table 13 reports subsample panel regressions of equations (10) and (11) using level and first-differenced series in panels A and B, respectively. Both coupon and time effects are included, and robust t-statistics are reported in parentheses that correct for serial correlation in the residuals clustered at the coupon level. We observe that both P MMS and BO have a significantly negative effect on dollar roll specialness, as predicted by our hypotheses. The only exception is the level regression in January 2009 July One possible reason for this exception is that the shrink in housing assets and financial assets prevented a large fraction of homeowners from refinancing, even though they wish to take advantage of historically low interest rates. Federal initiatives such as the Home Affordable Refinance Program (HARP) can also have significant impact on homeowners refinancing activities in magnitudes that dominate the interest rate effect and burn-out effect. Interestingly, in the level regression, ISU is insignificant for the pre-crisis period but 33 We also use November 2008 as the breakpoint to account for the announcement effect, and use December 2007 as the breakpoint that is regarded as the beginning of the recent crisis. The results are similar. 53

56 Table 13: Determinants of Dollar Roll Specialness: Subsamples A: Level 7/ /2008 1/2009-7/2013 DSP GC DSP LIBOR DSP GC DSP LIBOR PMMS ** ** ( ) ( ) (0.4872) (0.6334) BO * * ( ) ( ) (1.5043) (1.4633) ISU * * ( ) ( ) ( ) ( ) N 1,025 1, R B: First Difference 7/ /2008 1/2009-7/2013 DSP GC DSP LIBOR DSP GC DSP LIBOR PMMS * * ( ) ( ) ( ) ( ) BO ( ) ( ) ( ) ( ) ISU (1.2786) (1.2762) (0.7478) (0.7462) N 1,014 1, R Note: This table reports regressions (in Panel A) based on the following model: DSP it = t α t D t + i γ i D i + β 1 P MMS t + β 2 BO it + β 3 ISU it + ɛ it, and regressions (in Panel B) based on the following model: DSP it = t α t D t + β 1 P MMS t + β 2 BO it + β 3 ISU it + ɛ it, where DSP it is either DSP GC it or DSPit LIBOR, and D i and D t are coupon dummies and time dummies, respectively. Robust t-statistics are reported in parentheses based on clustered standard errors at the coupon level. Significance levels: for p < 0.01, for p < 0.05, and + for p < 0.1, where p is the p-value. 54

57 Table 14: Regression of OAS on Special: Subsamples A: Level 7/ /2008 1/2009-7/2013 OAS LIBOR OAS LIBOR OAS Tsy OAS Tsy OAS LIBOR OAS LIBOR OAS Tsy OAS Tsy DSP GC -0.36** -0.30** -0.13** -0.08* (-8.55) (-7.73) (-3.55) (-2.42) DSP LIBOR -0.36** -0.30** -0.13** -0.08* (-8.55) (-7.73) (-3.57) (-2.43) N 1,025 1,025 1,025 1, R B: First Difference 7/ /2008 1/2009-7/2013 OAS LIBOR OAS LIBOR OAS Tsy OAS Tsy OAS LIBOR OAS LIBOR OAS Tsy OAS Tsy DSP GC ** ** ** (-3.664) (-3.782) (-6.091) (0.920) DSP LIBOR ** ** ** (-3.664) (-3.783) (-6.240) (0.902) N 1,014 1,014 1,014 1, R Note: This table reports regressions (in Panel A) based on the following model: OASit = t αtdt + i γidi + β DSPit + ɛit, and regressions (in Panel B) based on the following model: OASit = t αtdt + β DSPit + ɛit, where DSPit is either DSP it GC or DSP it LIBOR, OASit is either OAS LIBOR or OAS T sy, and Di and Dt are coupon dummies and time dummies, respectively. Robust t-statistics are reported in parentheses based on clustered standard errors at the coupon level. Significance levels: for p < 0.01, for p < 0.05, and + for p < 0.1, where p is the p-value. 55

58 is the only significant determinant of dollar roll specialness since the crisis. That is, the supply effect is quantitatively small pre-crisis but became much larger during the crisis. One possible interpretation is that investors flight to quality or the Federal Reserve s purchase of agency MBS tightened their supply, making a marginal increase in issuance especially important in reducing dollar roll specialness. The Federal Reserve s purchase is examined in Section 6. Furthermore, Table 14 reports subsample panel regressions of equations (13) and (14) in panels A and B, respectively. We observe highly significant impact of dollar roll specialness on OAS, regardless of whether level or first-differenced series are used in regressions, whether DSP GC it or DSP LIBOR it is used for specialness, and whether OAS LIBOR or OAS T sy is used for MBS returns. The coefficient estimates are remarkably stable across model specifications. B.5 Alternative construction of monthly series Our results in Section 5 use the monthly average of daily series to construct the month series. This was done to reduce noise associated with microstructure effects and intra-month seasonality. In this subsection, we reproduce the main results using two alternative methods to construct monthly series: the end-of-month series (taking the snapshot on the last day of a month) and first Friday series (taking the snapshot on the first Friday of a month). Table 15 reports the results on determinants of dollar roll specialness, and Tables 16 and 17 report results on the relationship between dollar roll specialness and OAS. The main results, both the sign and magnitude of the coefficients, are robust to these alternative methods. 56

59 Table 15: Determinants of Dollar Roll Specialness: Alternative Monthly Series A: End-of-Month DSP GC DSP LIBOR (1) (2) (3) (4) (5) (6) PMMS * ** * ** ( ) ( ) ( ) ( ) ( ) ( ) BO ** ** ** ** ( ) ( ) ( ) ( ) ( ) ( ) ISU ** * ** ** * ** ( ) ( ) ( ) ( ) ( ) ( ) N 1,666 1,666 1,666 1,666 1,666 1,666 R Coupon Effect Yes Yes No Yes Yes No Time Effect Yes No No Yes No No B: The First Friday DSP GC DSP LIBOR (1) (2) (3) (4) (5) (6) PMMS ** * ** ** * ** ( ) ( ) ( ) ( ) ( ) ( ) BO ** ** ** * ** ( ) ( ) ( ) ( ) ( ) ( ) ISU ** * * ** * * ( ) ( ) ( ) ( ) ( ) ( ) N 1,666 1,666 1,666 1,666 1,666 1,666 R Coupon Effect Yes Yes No Yes Yes No Time Effect Yes No No Yes No No Note: This table reports panel regressions based on the following model: DSP it = t α t D t + i γ i D i + β 1 P MMS t + β 2 BO it + β 3 ISU it + ɛ it, where DSP it is either DSP GC it or DSPit LIBOR, and D i and D t are coupon dummies and time dummies, respectively. Robust t-statistics are reported in parentheses based on clustered standard errors at the coupon level. Significance levels: for p < 0.01, for p < 0.05, and + for p < 0.1, where p is the p-value. The overall sample period is July 1998 to July 2013, with various starting dates that depend on coupon rates. 57

60 Table 16: Regression of OAS on Specialness: End-of-Month Series End-of-Month A: OAS LIBOR (1) (2) (3) (4) (5) (6) DSP GC -0.42** -0.45** -0.48** (-10.24) (-6.86) (-9.63) DSP LIBOR -0.42** -0.46** -0.50** (-10.24) (-7.80) (-10.94) N 1,666 1,666 1,666 1,666 1,666 1,666 R Coupon Effects Yes Yes No Yes Yes No Time Effects Yes No No Yes No No B: OAS T sy (7) (8) (9) (10) (11) (12) DSP GC -0.40** -0.41** -0.48** (-9.53) (-8.27) (-12.38) DSP LIBOR -0.40** -0.42** -0.49** (-9.53) (-9.14) (-13.71) N 1,666 1,666 1,666 1,666 1,666 1,666 R Coupon Effects Yes Yes No Yes Yes No Time Effects Yes No No Yes No No Note: This table reports panel regressions based on the following model: OAS it = t α t D t + i γ i D i + β DSP it + ɛ it, where DSP it is either DSPit GC or DSPit LIBOR, OAS it is either OAS LIBOR or OAS T sy, and D i and D t are coupon dummies and time dummies, respectively. Robust t-statistics are reported in parentheses based on clustered standard errors at the coupon level. Significance levels: for p < 0.01, for p < 0.05, and + for p < 0.1, where p is the p-value. The overall sample period is July 1998 to July 2013, with various starting date that depend on coupon rates. 58

61 Table 17: Regression of OAS on Specialness: The First Friday Series The First Friday A: OAS LIBOR (1) (2) (3) (4) (5) (6) DSP GC -0.44** -0.47** -0.50** (-10.78) (-6.47) (-8.92) DSP LIBOR -0.44** -0.47** -0.50** (-10.78) (-6.72) (-9.34) N 1,666 1,666 1,666 1,666 1,666 1,666 R Coupon Effects Yes Yes No Yes Yes No Time Effects Yes No No Yes No No B: OAS T sy (7) (8) (9) (10) (11) (12) DSP GC -0.41** -0.43** -0.49** (-10.14) (-7.81) (-11.15) DSP LIBOR -0.41** -0.43** -0.50** (-10.14) (-7.76) (-11.28) N 1,666 1,666 1,666 1,666 1,666 1,666 R Coupon Effects Yes Yes No Yes Yes No Time Effects Yes No No Yes No No Note: This table reports panel regressions based on the following model: OAS it = t α t D t + i γ i D i + β DSP it + ɛ it, where DSP it is either DSPit GC or DSPit LIBOR, OAS it is either OAS LIBOR or OAS T sy, and D i and D t are coupon dummies and time dummies, respectively. Robust t-statistics are reported in parentheses based on clustered standard errors at the coupon level. Significance levels: for p < 0.01, for p < 0.05, and + for p < 0.1, where p is the p-value. The overall sample period is July 1998 to July 2013, with different start dates for series of different coupon rates. 59

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