FIN 684 Fixed-Income Analysis From Repos to Monetary Policy. Funding Positions

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1 FIN 684 Fixed-Income Analysis From Repos to Monetary Policy Professor Robert B.H. Hauswald Kogod School of Business, AU Funding Positions Short-term funding: repos and money markets funding trading positions liquidity management monetary policy conduct Revisiting the yield curve borrowing cost and forward rates yield-curve shapes and explanations Forwards: locking-in future borrowing cost 2/18/2014 Short-Term Credit Robert B.H. Hauswald 2

2 Money Markets The term money market is a misnomer. they do not actually trade money (currency); instead, MM securities are short term with high liquidity; therefore, they are close to being money. 1. Money market securities are usually sold in large denominations ($1,000,000 or more) 2. They have low default risk 3. They mature in one year or less from their issue date: what about interest-rate risk? 2/18/2014 Short-Term Credit Robert B.H. Hauswald 3 Money Markets: Overview Short-term debt instruments Maturity of < 1 year Services immediate cash needs: liquidity Borrowers need short-term working capital Lenders need an interest-earning parking space for excess funds Instruments trade in an active secondary market Liquid market provides easy entry & exit for participants Speed and efficiency of transactions allows cash to active even for very short periods of time (over night). Market size in 2004: $5.3 Trillion 2/18/2014 Short-Term Credit Robert B.H. Hauswald 4

3 Money Market Securities Treasury Bills Federal Funds Repurchase agreements Commercial paper Negotiable Certificates of Deposit (CDs) Bankers acceptances All of these instruments are what comprise YOUR money market investment account at your local bank 2/18/2014 Short-Term Credit Robert B.H. Hauswald 5 Money Market Participants (excluding brokers/dealers) Security Borrower (issuer) Lender (investor) Treasury bills Federal Funds & Repurchase agreements Commercial paper U.S. Treasury (Federal Government) Commercial banks, other FIs Corporations, Commercial banks FED, Commercial banks, Mutual Funds, Corporations, etc. Commercial banks, other FIs Corporations, Mutual funds, other FIs Negotiable CDs Commercial banks Corporations, Mutual funds, other FIs Bankers acceptances Commercial banks Corporations, Community banks 2/18/2014 Short-Term Credit Robert B.H. Hauswald 6

4 Repurchase Agreement Definition: selling an asset with an explicit agreement to repurchase the asset after a set period of time Example: A bank has deficient reserves and needs to borrow overnight. 1. Bank A sells a treasury security to Bank B at P 0 2. Bank A agrees to buy the treasury back at a higher price P f > P 0 3. Bank B earns a rate of return implied by the difference in prices i RA = P f P x P 0 days 4. Since the loan is backed by collateral, the rate is usually lower than the rate available in the Federal Funds market 5. Fed conducts open market transactions through RAs, using transactions that are generally less than 15 days. 2/18/2014 Short-Term Credit Robert B.H. Hauswald 7 Repos and Reverse-Repos Repurchase agreements are widely used by corporate treasurers and other institutional investors peculiar form of overnight borrowing Repos and reverses may be overnight or term repos for time periods up to several months For some (like Orange County), reverse repos were a way of leveraging a portfolio 2/18/2014 Short-Term Credit Robert B.H. Hauswald 8

5 Transaction Structure A repurchase agreement, or repo, is a single transaction consisting of 1) A spot portion in which a security is sold for cash and 2) A forward portion in which the security is repurchased for later settlement Dealers often use repos to finance inventories of securities: long positions Repo can be for overnight, term or open 2/18/2014 Short-Term Credit Robert B.H. Hauswald 9 Forward Rates 2 ( 1+ y ) = ( 1+ r )( + f ) Lock in future loan rate simple arbitrage argument implies formula Example: making a 1-year loan in a year s time, the bank/lender/investor could buy a two years bond; or buy a one year bond and then use the money to buy another bond (the price can be fixed today). 2/18/2014 Short-Term Credit Robert B.H. Hauswald f 12 = 2 ( 1+ y2 ) ( 1+ y ) 1

6 Forward-Rate Principle t t s ( ) ( 1+ yt ) 1+ fst =, s < t s ( 1+ y ) To replicate a t - s year loan in s years time buy a t-year bond, which must be equivalent to buying an s-year bond and then use the money to buy another t s year bond forward To find a forward interest rate one needs today s date forward s/loan s start and end dates zero (yield) curve spot rates y t : Bloomberg 2/18/2014 Short-Term Credit Robert B.H. Hauswald 11 s Repo: Spot Portion Securities Dealer Collateral Date 1 Cash (Principal) Investor At settlement, the collateral is sold for cash ( good funds) to an investor. 2/18/2014 Short-Term Credit Robert B.H. Hauswald 12

7 Repo: Forward Portion Securities Dealer Collateral Date 2 Cash (Principal + Interest) Investor At maturity, the dealer repurchases the collateral for cash. The extra cash paid at maturity is interest and is determined by the repo rate. 2/18/2014 Short-Term Credit Robert B.H. Hauswald 13 Repo Securities Dealer Collateral Date 1 Cash (Principal) Investor Securities Dealer Collateral Date 2 Cash (Principal + Interest) Investor 2/18/2014 Short-Term Credit Robert B.H. Hauswald 14

8 Balance-Sheet Perspective Federal Reserve Commercial Bank Securities Dealer Assets Liabilities Assets Liabilities Assets Liabilities U.S. Notes Reserves Reserves Deposits U.S.Notes Cash U.S.Notes Cash Repo Repurchase agreements are a way for dealers to finance their inventories of securities Collateralized borrowing but what are the risks? Market is also open to corporations with excess cash through Fed wire Repo 2/18/2014 Short-Term Credit Robert B.H. Hauswald 15 Modern Repos Traders X and Y agree today that Y pays $F to X X delivers security S to Y n days from now: X pays the $F back to Y X also pays n days of interest on $F, at annual rate r to Y Interest is F(n/360)(r/100) Y delivers security S back to X 2/18/2014 Short-Term Credit Robert B.H. Hauswald 16

9 Example 7-day Repo Term repo rate 5.00% Day 1 Collateral value (market) $ 1,000,000 Margin 0% Repo principal $1,000,000 Day 7 Collateral value $1,000,000 Repurchase price $1,000, ( ) P repurchase = P initial 1+ y t sm 360 2/18/2014 Short-Term Credit Robert B.H. Hauswald 17 Repo Mechanics The party who sells collateral in the first leg and repurchases collateral in the second leg is called the repo seller: dealers who finance securities with repo are repo sellers. the other party is the repo buyer: investors who invest in repo are repo buyers. Margin: collateral in excess of the principal amount of the transaction Demanded to limit credit exposure Typically 1% to 3% (5% to 10% for riskier collateral) Example: If margin were 2%, a dealer would deliver $10.2 million (market value) of collateral against a principal amount of $10 million. 2/18/2014 Short-Term Credit Robert B.H. Hauswald 18

10 Example: T-bill Margin T-bill Financing Settlement day 2/18/2005 Bill maturity 8/18/2005 Days to maturity 181 Bid 4.45% Margin rate ("haircut") 0.10% Market price (at bid) Margin value Repo principal $10,000,000 Face amount of collateral required: with margin $10,234, without margin $10,228, margin amount $5, Percent of face value 0.051% market value of margin $5, /18/2014 Short-Term Credit Robert B.H. Hauswald 19 Collateral Collateral may be marked to market and the trade adjusted Margin call: If collateral value declines, additional collateral may be required to restore the original margin. (Dealer delivers more collateral to investor.) Repricing: If collateral value declines, the principal amount of the transaction can be reduced to restore the original margin. (Dealer wires cash back to investor.) Collateral Substitution Dealer may request the investor to return the original collateral in exchange for different collateral having the same market value If collateral cannot be substituted, it is special 2/18/2014 Short-Term Credit Robert B.H. Hauswald 20

11 Delivery Cash flows The repo seller is entitled to receive any interest or principal payments off the collateral Delivery Outright: Seller delivers the collateral to the buyer. Buyer returns the collateral at maturity. Safekeeping: Seller holds the collateral for the buyer. Also known as letter repo or held in custody repo. Third party: Seller delivers collateral to purchaser s custodial account at seller s clearing bank. 2/18/2014 Short-Term Credit Robert B.H. Hauswald 21 Reverse Repo A reverse is a repo viewed from the perspective of the counterparty lending cash There are two reasons for doing reverses: Investors seeking short-term relatively safe investments may invest in repo. Traders seeking to cover a short position in a security may borrow the needed securities by doing a reverse for specific collateral 2/18/2014 Short-Term Credit Robert B.H. Hauswald 22

12 Repos and Reverse Repos 2/18/2014 Short-Term Credit Robert B.H. Hauswald 23 Repo Books and Trading Dealers often work both sides of the market, doing repo with one group of investors and reverses with another. In a matched book, a dealer reverses in securities from one party, repos them out to another party, and earns the spread. Example A Brazilian bank finances some of its Brazilian Brady holdings by doing a repo with a dealer in New York for LIBOR + 1% The repo dealer in New York uses the collateral to do a repo with an American investor for LIBOR The dealer pockets the spread (1%) 2/18/2014 Short-Term Credit Robert B.H. Hauswald 24

13 Repo Rates General collateral rates Relation to the Fed funds rate Specials Rates can go special when there is strong demand for specific collateral Example: Traders as a group build up a sizeable short position in a particular issue. Market squeezes: futures, forwards reason Fed keeps inventory to avoid adverse movements 2/18/2014 Short-Term Credit Robert B.H. Hauswald 25 Repo Rates 2/18/2014 Short-Term Credit Robert B.H. Hauswald 26

14 Application: Bond Repo Trading /08+ Same-Day Settlement Assumed (a) Accrued Interest is (53/182)(4.25/2) = (b) Invoice bid price is (8/32) = (c) Yield to bid price = 3.85% (d) 2/18/2014 Short-Term Credit Robert B.H. Hauswald 27 10Y UST Bond Repo Bloomberg calculates a repo of this note, assuming $1M face value (e) Next business-day termination (f) 4.05% interest rate (g) from the previous screen Sale/Repurchase amount = 1/1.02 of Security value at the bid (h) Current market conditions then imply Sale/Repurchase amount (per $100 face)= /1.02= (i) So for $1M face value it is $1,018, (j) Interest = ($1,018,321.75)(1/360)(4.05/100) = $ (k) Margin analysis If the market bid price drops from 103:08 to , i.e. about 101:07, then the margin is wiped out (security value = loan amount) Yield corresponding to 101:07 is 4.10 (l) If the bid yield rises from its current 3.85 up to 4.10, then the bond value is just enough to make the money lender whole in case of default 2/18/2014 Short-Term Credit Robert B.H. Hauswald 28

15 Financing and Leverage How to finance an investment in $1M of the current 10Y? Purchase price, at the ask of 103:08+, is / = per $100 face value, so $1M face value costs $1,038,844. Where to get it? Repoing out the bond, as we just illustrated, brings in $1,018,322 You only need $1,038,844 1,018,322 = $20,522 in cash Remember all that talk about hedge funds engaging in 50:1 leverage? LTCM? repos and other margin plays allow to turn $5bn into trillions Daily cost of the loan is the $ interest on the borrowed money, plus any capital charge on the $20K you re paying in: 2% margin 2/18/2014 Short-Term Credit Robert B.H. Hauswald 29 Application: Tailing Buy a 3M T-bill and hold it for 30 days = 2M bill. Buy a T-bill with t 1 days to maturity Finance it for t 2 days with term repo Inherit a T-bill with t 1 - t 2 days to maturity when the financing comes off. Dealers use this strategy to buy T-bills forward; why? 30 days 60 days Buy 90- day bill Finance for 30 days Own 60- day bill Bill matures 2/18/2014 Short-Term Credit Robert B.H. Hauswald 30

16 Tailing Example Settlement date 1/7/2008 Bill maturity date 4/6/2008 Days to maturity day bill rate 4.42% Amount (face) $ 1,000,000 Market value $ 988,950 Repo rate 4.100% Margin (in bp) 10 Repo amount $ 988,700 Dealer equity ($ margin) $ 250 Unwinding date 1/14/2008 Days financed 7 Financing cost $ 788 Days until the bill matures 83 Implied 83-day bill cost $ 989,738 Implied 83-day bill rate 4.45% A dealer creates an 83-day bill tail from Bloomberg: 1W In effect, the dealer purchases the 83-day bill for a rate of 4.45% 2/18/2014 Short-Term Credit Robert B.H. Hauswald 31? The Federal Reserve: Buys and Sells T-bills through repos from commercial banks as a means of changing the level of bank reserves and hence changing the money supply. The US Treasury: Finances the Deficit by issuing T-bills. A T-bill is an I.O.U. Congress: Spends and Collects Taxes Runs as Deficit: Deficit = G - T 2/18/2014 Short-Term Credit Robert B.H. Hauswald 32

17 Federal Funds Short term transactions between financial institutions: 1. Term is generally over night/week-end 2. Not backed by collateral - unsecured loans 3. Highly liquid market 4. Depository institutions use this market to buy/sell excess deposits in order to manage their liabilities. 5. For banks, this is sometimes referred to as hot money Federal Fund Yields: 1. No coupon payment - sold at a discount 2. Quoted rates assume a 360 day year, conversion i bond = i ff (365/360) Federal Funds Market: 1. Trades take place between banks that buy/sell excess reserves held at their federal reserve bank 2. Banks or FIs that are not FRB members can use a correspondent bank (that is a member) to conduct the transaction 3. Transactions take place over the Fedwire 2/18/2014 Short-Term Credit Robert B.H. Hauswald % 2/18/2014 Short-Term Credit Robert B.H. Hauswald 34

18 Summary Cash flow engineering: replication the importance of STRIPS: arbitrage Grand tour of money markets repurchase agreements (repos) interest-rate forwards (related to FRAs) yield-curve explanations Monetary policy and borrowing costs the importance of federal policy 2/18/2014 Short-Term Credit Robert B.H. Hauswald 35 Forward Rates Suppose you will need a loan in two years from now for one year. locking in borrowing costs for future date How one can create such a loan today? borrow for three years and lend for two Transaction mechanics: Go short a three-year zero coupon bond. Go long a two-year zero coupon bond. 2/18/2014 Short-Term Credit Robert B.H. Hauswald 36

19 Term Structure of IR r 1 = 8% r 1 = 10% r 3 = 11% r 4 = 11% If we knew the future one-year spot rates the spot rate is the YTM a on a one-year zero (bill/bond) 0(Today) 8% 1 10% 2 11% 3 11% we could easily price a zero (do we know them?) $1,000 P = ( )( )( )( ) 2/18/2014 Short-Term Credit Robert B.H. Hauswald 37 From Future to Spot Rates r 1 = 8% r 1 = 10% r 3 = 11% r 4 = 11% y 1 = 8% ( ) = y 2 = 8.995% 3 ( ) 1 1 =? y 3 = 9.66% y 4 = 9.993% 2/18/2014 Short-Term Credit Robert B.H. Hauswald 38

20 1 Future Loan = 2 Transactions Cash flows Go short a three-year zero coupon bond. Go long a two-year zero coupon bond /18/2014 Short-Term Credit Robert B.H. Hauswald 39 Forward Rates f n The condition: (1 + y n ) n = (1 + y n-1 ) n-1 (1 + f n ) follows from Borrow for n periods Lend for n - 1 (1 + y n-1 ) n-1 (1 + y n ) n f n 2/18/2014 Short-Term Credit Robert B.H. Hauswald 40

21 Term Structure of Forward Rates 3 2 ( 1+ y ) = ( 1+ r )( 1+ f ) = ( 1+ r )( 1+ f )( + f ) /18/2014 Short-Term Credit Robert B.H. Hauswald 41 History of Money Market Rates 2/18/2014 Short-Term Credit Robert B.H. Hauswald 42

22 1 2 Money Market Rates since 1990 M o n e y M a r k e t R a t e s s i n c e C D 3 0 D A Y E U R O $ 3 0 D A Y F F C P 3 0 D A Y F F E D P R I M E T B I L L 3 0 D A Y 2/18/2014 Short-Term Credit Robert B.H. Hauswald % The federal funds rate is a target rate. MONTHLY WEEKLY DAILY 2/18/2014 Short-Term Credit Robert B.H. Hauswald 44

23 The federal funds rate is a target rate. 3.00% MONTHLY WEEKLY DAILY 2/18/2014 Short-Term Credit Robert B.H. Hauswald April 2006 (200) 200 August 23 years 2006 (203.9) Doubling of CPI 2/18/2014 Short-Term Credit Robert B.H. Hauswald 46

24 203.5 April 2006 (200) August 2006 (203.9) 2/18/2014 Short-Term Credit Robert B.H. Hauswald % The federal funds rate is a target rate. 2/18/2014 Short-Term Credit Robert B.H. Hauswald 48

25 5.25% The federal funds rate is a target rate. 2/18/2014 Short-Term Credit Robert B.H. Hauswald 49 Term Structure of Interest Rates r zero Yield curve Time to maturity 0 3m 6m 1yr 3yr 5yr 10yr 30yr 2/18/2014 Short-Term Credit Robert B.H. Hauswald 50

26 Determinants of the Yield Curve Factors affecting Bond yields and term structure Base interest rate - benchmark interest rate Risk Premium - spread Expected liquidity Market forces - Demand and supply FRB sets a target level for the Fed-funds rate the rate at which depository institutions make uncollaterized overnight loans to one another Long-term rates reflect expectations of future rates can be influenced by the outlook for monetary policy. 2/18/2014 Short-Term Credit Robert B.H. Hauswald 51 Liquidity Bid-offer spread 1-2 cents per $100 face Corporate bonds for example 13 cents High yield bonds 19 cents On-the-run - recently issued in a particular maturity class. With time becomes off-the-run. Flight to Quality price and bid-ask effects corporate bid-ask: cents who is the market maker in UST securities? 2/18/2014 Short-Term Credit Robert B.H. Hauswald 52

27 Yield-Curve Explanation 1 The Expectations Hypothesis suggested by Lutz. Forward interest rates = expected future spot rates Cox-Ingersoll-Ross have investigated this hypothesis they find that it is not consistent with an economic equilibrium. However it gives often a right direction for expectations. 2/18/2014 Short-Term Credit Robert B.H. Hauswald 53 Yield-Curve Explanation 2 Liquidity Preference Hicks (1939) suggested that lenders demand a premium for locking up their money for long period of time. This implies that the term structure will be always upward sloping. The theory ignores the borrowing side of the market. what type of premium: risk, liquidity, inflation? 2/18/2014 Short-Term Credit Robert B.H. Hauswald 54

28 Yield-Curve Explanation 3 Market Segmentation and Preferred Habitat Theories Modigliani and Sutch The market is segmented, investors absolutely prefer one maturity over another. This means that there is no connection between interest rates for different maturities. not supported but clientele effects do exist 2/18/2014 Short-Term Credit Robert B.H. Hauswald 55 Constructing the Term Structure There are too many data plus some noise. We are missing certain maturities The easiest way to measure the TS is with liquid zero coupon bonds. We obtain a series of points. 2/18/2014 Short-Term Credit Robert B.H. Hauswald 56

29 Measuring the Term Structure r zero Time to maturity 0 3m 6m 1yr 3yr 5yr 10yr 30yr 2/18/2014 Short-Term Credit Robert B.H. Hauswald 57 r zero First Order Spline Time to maturity 0 3m 6m 1yr 3yr 5yr 10yr 30yr 2/18/2014 Short-Term Credit Robert B.H. Hauswald 58

30 Second Order Spline r zero Time to maturity 0 3m 6m 1yr 3yr 5yr 10yr 30yr 2/18/2014 Short-Term Credit Robert B.H. Hauswald 59 Measuring the Term Structure There are too many data plus some noise. The easiest way to measure the TS is with liquid zero coupon bonds. We obtain a series of points. One can connect them with a spline. First order is good for pricing simple bonds. For swaps one need a very high precision. 2/18/2014 Short-Term Credit Robert B.H. Hauswald 60

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