Special Repo Rates: An Introduction - Robert H. Smith .
Special Repo Rates:An IntroductionMARK FISHERThe author is a senior economist in the financial section of the AtlantaFed’s research department. He thanks Jerry Dwyer, Scott Frame, andPaula Tkac for their comments on an earlier version of the articleand Christian Gilles for many helpful discussions on the subject.he market for repurchase agreementsinvolving Treasury securities (known asthe repo market) plays a central role inthe Federal Reserve’s implementationof monetary policy. Transactions involving repurchase agreements (known asrepos and reverses) are used to manage the quantity of reserves in the banking system on a shortterm basis. By undertaking such transactions withprimary dealers, the Fed, through the actions ofthe open market desk at the Federal Reserve Bankof New York, can temporarily increase or decreasebank reserves.The focus of this article, however, is not monetarypolicy but, rather, the repo market itself, especiallythe role the market plays in the financing and hedging activities of primary dealers. The main goal of thearticle is to provide a coherent explanation of theclose relation between the price premium that newlyauctioned Treasury securities command and thespecial repo rates on those securities. The next twoparagraphs outline this relationship and introducesome basic terminology that will be used throughoutthe article. (Also see the box for a glossary of terms.)1Dealers’ hedging activities create a link betweenthe repo market and the auction cycle for newlyissued (on-the-run) Treasury securities. In particular,there is a close relation between the liquidity premium for an on-the-run security and the expectedfuture overnight repo spreads for that security (theTspread between the general collateral rate and therepo rate specific to the on-the-run security). Dealerssell short on-the-run Treasuries in order to hedgethe interest rate risk in other securities. Having soldshort, the dealers must acquire the securities viareverse repurchase agreements and deliver them tothe purchasers. Thus, an increase in hedging demandby dealers translates into an increase in the demandto acquire the on-the-run security (that is, specificcollateral) in the repo market.The supply of specific collateral to the repo marketis not perfectly elastic; consequently, as the demandfor the collateral increases, the repo rate falls toinduce additional supply and equilibrate the market.The lower repo rate constitutes a rent (in the form oflower financing costs), which is capitalized into thevalue of the on-the-run security. The price of theon-the-run security increases so that the equilibriumreturn is unchanged. The rent can be captured byreinvesting the borrowed funds at the higher generalcollateral repo rate, thereby earning a repo dividend.When an on-the-run security is first issued, all of theexpected earnings from repo dividends are capitalized into the security’s price, producing the liquiditypremium. Over the course of the auction cycle, therepo dividends are “paid” and the liquidity premiumdeclines; by the end of the cycle, when the securitygoes off-the-run (and the potential for additional repodividend earnings is substantially reduced), the premium has largely disappeared.Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W Second Quarter 200227
BOXGlossaryAnnouncement date: The date on which theTreasury announces the particulars of a new security to be auctioned. When-issued (that is, forward) trading begins on the announcement date.Auction date: The date on which a security is auctioned, typically one week after the announcementdate and one week before the settlement date.Fedwire: The electronic network used to transfer funds and wirable securities such as Treasurysecurities.Repo: A repurchase agreement transaction thatinvolves using a security as collateral for a loan.At the inception of the transaction, the dealerlends the security and borrows funds. When thetransaction matures, the loan is repaid and thesecurity is returned.Repo dividend: The repo spread times the valueof the security: δ ps p(r – R).Repo rate: The rate of interest to be paid on arepo loan, R.Forward contract: A contract to deliver something in the future on the delivery date at a prespecified price, the forward price.Repo spread: The difference between the general collateral rate and the specific collateral rate,s r – R, where s 0.Forward premium: The difference between theexpected future spot price and the forward price.Repo squeeze: A condition that occurs when theholder of a substantial position in a bond financesa portion directly in the repo market and theremainder with “unfriendly financing” such as ina triparty repo.Forward price: The agreed-upon price for delivery in a forward contract.General collateral: The broad class of Treasurysecurities.General collateral rate: The repo rate on general collateral.Haircut: Margin. For example, a 1 percent haircut would allow one to borrow 99 per 100 of abond’s price.Matched book: Paired repo and reverse tradeson the same underlying collateral, perhaps mismatched in maturity.Off the run: A Treasury security that is no longeron the run (see below).Old, old-old, etc.: When a security is no longeron the run, it becomes the old security. When asecurity is no longer the old security, it becomesthe old-old security, and so on.On special: The condition of a repo rate when itis below the general collateral rate (when R r).On the run: The most recently issued Treasurysecurity of a given original term to maturity—forexample, the on-the-run ten-year Treasury note.Reverse: A repo from the perspective of thecounterparty; a transaction that involves receiving a security as collateral for a loan.Settlement date: The date on which a new security is issued (the issue date).Short squeeze: See repo squeeze.Specific collateral: Collateral that is specified—for example, an on-the-run bond instead of someother bond.Specific collateral rate: The repo rate on specific collateral.Term repo: Any repo transaction with an initialmaturity longer than one business day.Triparty repo: An arrangement for facilitatingan ongoing repo relationship between a dealerand a customer, where the third party is a clearing bank that provides useful services.When-issued trading: Forward trading in asecurity that has not yet been issued.Zero-coupon bond: A bond that makes a singlepayment when it matures.Reopening: A Treasury sale of an existing bondthat increases the amount outstanding.28Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W Second Quarter 2002
CHART 1The next section describes what repos andreverses are, describes the difference between onthe-run and older securities, and discusses theways dealers use repos to finance and hedge. Thearticle then explains the difference between general and specific collateral, defines the repo spreadand dividend, presents a framework for determining the equilibrium repo spread, and describes theaverage pattern of overnight repo spreads over theauction cycle.The central analytical point of the article is thatthe rents that can be earned from special repo ratesare capitalized into the price of the underlying bond soas to keep the equilibrium rate of return unchanged.The analysis derives an expression for the price premium in terms of expected future repo spreads andthen computes the premium over the auction cyclefrom the average pattern of overnight repo spreads.Some implications of this analysis are then discussed.Finally, the article presents an analysis of a reposqueeze, in which a repo trader with market powerchooses the optimal mix of funding via a triparty repoand funding directly in the repo market. Two appendixes provide additional analysis on the term structure of repo spreads and on how repo rates affect thecomputation of forward prices and tests of the expectations hypothesis.Repos and Dealersrepurchase agreement, or repo, can be thoughtof as a collateralized loan. In this article, thecollateral will be Treasury securities (that is, Treasurybills, notes, and bonds).2 At the inception of theagreement, the borrower turns over the collateral tothe lender in exchange for funds. When the loanmatures, the funds are returned to the lender alongwith interest at the previously agreed-upon reporate, and the collateral is returned to the borrower.Repo agreements can have any maturity, but mostare for one business day, referred to as overnight.From the perspective of the owner of the securityand the borrower of funds, the transaction is referredto as a repo while from the lender’s perspective thesame transaction is referred to as a reverse repo, orsimply a reverse.AA Repo and a Reverse RepoA RepocollateralAt inception:DealerCustomerfundscollateralAt maturity:DealerCustomerfunds interestA repo (from the dealer’s perspective) finances the dealer’slong position (collateralized borrowing).At inception:A Reverse RepocollateralDealerfundsCustomercollateralAt maturity:DealerCustomerfunds interestA reverse repo (from the dealer’s perspective) finances thedealer’s short position (collateralized lending).For concreteness, the discussion will refer to thetwo counterparties as the dealer and the customereven though a substantial fraction of repo transactions are among dealers themselves or betweendealers and the Fed. Unless otherwise indicated, thearticle will adopt the dealer’s perspective in characterizing the transaction. Repo and reverse repotransactions are illustrated in Chart 1, which can besummarized by a simple mantra that expresses whathappens to the collateral at inception from the dealer’s perspective: “repo out, reverse in.”Since dealers are involved with customers onboth sides of transactions, it is natural for dealersto play a purely intermediary role. Chart 2 depicts amatched book transaction. In fact, the dealer maymismatch the maturities of the two transactions, borrowing funds short-term and lending them long-term(that is, reversing in collateral for a week or a monthfrom customer 1 and repoing it out overnight first tocustomer 2 and then perhaps to another customer).1. A number of sources provide additional material for anyone interested in reading more about the repo market. To read abouthow the repo market fits into monetary policy, see Federal Reserve Bank of New York (1998 and n.d.). For institutionaldetails, see Federal Reserve Bank of Richmond (1993) and Stigum (1989). For some empirical results, see Cornell andShapiro (1989), Jordan and Jordan (1997), Keane (1996), and Krishnamurthy (forthcoming). Duffie (1989) provides sometheory as well as some institutional details and empirical results.2. There is also an active repo market for other securities that primary dealers make markets in, such as mortgage-backed securities and agency securities (issued by government-sponsored enterprises such as Freddie Mac, Fannie Mae, and the FederalHome Loan Banks). In the equities markets, what is known as securities borrowing and lending plays a role analogous to therole played by repo markets, and as such much of the analysis of repo markets presented here is applicable to equities.Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W Second Quarter 200229
CHART 2A Dealer’s Matched Book TransactioncollateralAt inception:Customer 1collateralDealerfundscollateralAt maturity:Customer 1Customer 2fundscollateralDealerfunds interestCustomer 2funds interestA dealer’s matched book transaction involves simultaneous offsetting repo and reverse transactions. From customer 1’s perspective thetransaction is a repo while from customer 2’s perspective the transaction is a reverse. The dealer collects a fee for the intermediation service by keeping some of the interest that customer 1 pays.CHART 3Making a Market IToldSellerToldDealerbid pricePurchaserask priceA dealer purchases an old Treasury security (Told) and immediately finds a buyer, earning a bid-ask spread.Typically, customer 1 is seeking financing for aleveraged position while customer 2 is seeking asafe short-term investment.On-the-run securities. The distinction betweenon-the-run securities and older securities is important. For example, the Treasury typically issues anew ten-year note every three months. The mostrecently issued ten-year Treasury security isreferred to as the on-the-run issue. Once theTreasury issues another (newer) ten-year note, thepreviously issued note is referred to as the old tenyear note. (And the one issued before that is theold-old note, etc.) Similar nomenclature applies toother Treasury securities of a given original maturity,such as the three-year note and the thirty-yearbond. Importantly, the on-the-run security is typically more actively traded than the old security inthat both the number of trades per day and theaverage size of trades are greater for the on-the-runsecurity. In this sense, the on-the-run security ismore liquid than the old security.3Financing and hedging. A dealer must finance,or fund, every long position and every short positionit maintains. For Treasury securities, this meansrepoing out the long positions and reversing in theshort positions. In addition to financing, the dealermust decide to what extent it will hedge the risk itis exposed to by those positions. For many positions, if not most, the dealer will want to hedgeaway all or most of its positions’ risk exposure. The30example that follows illustrates what is involved infinancing and hedging a position that is generatedin making a market in Treasury securities.Suppose a dealer purchases from a customer anold (or older) Treasury security. The dealer may beable to immediately resell the security at a slightlyhigher price, thereby earning a bid-ask spread (seeChart 3). On the other hand, since older Treasurysecurities are less actively traded, the dealer mayhave to wait some time before an appropriate purchaser arrives. In the meantime, the dealer must(1) raise the funds to pay the seller and (2) hedgethe security to reduce, if not eliminate, the risk ofholding the security. The funds can be raised byrepoing out the security. An important way thatdealers hedge such positions is by short selling anon-the-run Treasury security with a similar maturity. The price of such an on-the-run security willtend to move up and down with the old security;consequently, if the price of the old security falls,generating a loss, the price of the on-the-run security will also fall, generating an offsetting gain.Assuming the dealer does in fact sell the on-the-runsecurity short, the dealer now has an additionalshort position that generates cash (from the buyer)but requires delivery of the security. The dealeruses the cash (from the short sale) to acquire thesecurity as collateral in a reverse repurchase agreement, which is then delivered on the short sale (seeChart 4).Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W Second Quarter 2002
CHART 4Making a Market IIOutright Customerbid pricefundsOutright sA dealer purchases an old Treasury from a seller but has no immediate buyer.CHART 5Making a Market IIINew repoToldRefinancing:Rehedging:Unwind old repoToldCustomerDealerCustomerfundsfundsNew reverseTnewUnwind old reverseTnewCustomerDealerfundsCustomerfundsIf no purchaser arrives (the next day), the dealer refinances and rehedges.CHART 6Making a Market IVOutright saleToldUnwind old repoToldPurchaserDealerCustomerask pricefundsNew reverseTnewUnwind old reverseTnewCustomerDealerfundsCustomerfundsWhen a purchaser arrives, the dealer sells the old Treasury (to the purchaser) and buys the on-the-run Treasury to close the short position.If a purchaser for the original security does notarrive the next day, the dealer will repo the securityout again and, using the funds obtained from therepo, reverse in the on-the-run Treasury again (seeChart 5). When a purchaser arrives, the dealer sellsthe original security, uses the funds to unwind therepo on the old Treasury, and purchases the on-therun Treasury outright and delivers it to unwind thereverse, using the funds to pay for the purchase(see Chart 6). If all goes well, the dealer earns a bidask spread that compensates for the cost of holdingand hedging the inventory.43. This greater liquidity is reflected in smaller bid-ask spreads for the on-the-run security.4. Implicitly, it is assumed that dealers can borrow the full value of a Treasury security. For interdealer transactions, thisassumption is not unrealistic. In other transactions, dealers and/or customers face haircuts, which amount to margin requirements. A more accurate accounting of haircuts (larger haircuts for customers than for dealers) would complicate the storywithout changing the central results significantly.Federal Reserve Bank of Atlanta E C O N O M I C R E V I E W Second Quarter 200231
Recall that the hedge is a short position in anon-the-run Treasury security. In the example, thehedged asset is another (older, less liquid) Treasurysecurity. Dealers hedge a variety of fixed-incomesecurities by taking short positions in on-the-runTreasuries. For example, dealers hedge mortgagebacked securities by selling short the on-the-runten-year Treasury note. As noted above, on-the-runTreasuries are more liquid than older Treasuries;indeed, on-the-run Treasuries are perhaps the mostliquid securities in the world. Liquidity is especiallyimportant for short sellers because of the possibilityof being caught in a short squeeze. In a short squeeze,Dealers’ hedging activities create a linkbetween the repo market and the auctioncycle for newly issued (on-the-run)Treasury securities.it is costly to acquire the collateral for delivery onthe short positions. Because the probability of beingsqueezed is high for large short positions, such positions are not typically established in illiquid securities; consequently, squeezes are rarely seen in illiquidsecurities, which is to say the unconditional probability is low. The equilibrium result is that squeezesarise most often in very liquid securities (unconditionally), because the (conditional) probability ofbeing squeezed is low.Repo Rates and the Repo Dividends noted above, repurchase agreement transactions can be thought of as collateralized loans.The loan is said to finance the collateral. For mostpublicly traded U.S. Treasury securities the financing rate in the repo market is the general collateralrate (which can be thought of as the risk-free interestrate). In contrast, for some Treasury securities—typically recently issued securities—the financingrate is lower than the general collateral rate. Thesesecurities are said to be on special, and their financing rates are referred to as specific collateral rates,also known as special repo rates. The differencebetween the general collateral rate and the specificcollateral rate is the repo spread.Let r denote the current one-period general collateral rate (also referred to as the risk-free rate),and let R denote the current one-period specificA32collateral rate, where R r.5 The repo spread isgiven by s r – R. If R r, then the repo spread ispositive and the collateral is on special. Let p denotethe value of the specific collateral.The repo spread allows the holder of the collateralto earn a repo dividend.6 Let δ denote the repo dividend, which equals the repo spread times the value ofthe bond: δ (r – R)p sp. A dealer holding somecollateral on special (that is, for which R r) can capture the repo dividend as follows (see Chart 7). Thedealer repos out the specific collateral (borrows p atrate R) and simultaneously reverses in general collateral of the same value (lends p at rate r). The netcash flow is zero and the net change in risk is (effectively) zero. Next period the dealer unwinds bothtransactions, receiving the specific collateral back inexchange for paying (1 R)p and receiving (1 r)pin exchange for return
Finally, the article presents an analysis of a repo squeeze, in which a repo trader with market power chooses the optimal mix of funding via a triparty repo and funding directly in the repo market. Two appen-dixes provide additional analysis on the term struc-ture of repo spreads and on how repo rates affect the
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Regulatory Arbitrage in Repo Markets . Benjamin Munyan . . contribute to an understanding of repo markets and their potential for systemic risk and to the literature on seasonality. Section 2 provides an overview of the repo markets and . liquidity risk in the quantity and type of collateral they pledge, increasing their exposure
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