Tutorial: Debt / Fixed Income

What is a Bond? Floating-rate security? Treasury? Repo? Corporate Bond? MBS? CMO? and more.

A fixed income security is an obligation of the issuer who promises to pay a specified sum of money at a fixed future date in exchange for money now. As an example, "6.0 of 1/1/2010 trading at 98" means a bond with a 6.5 coupon rate, matures at 1/1/2010 and sells for 98% of its par value.

  • Indenture: written agreement between the issuer and holders regarding promises (of the issuer) and rights (of the bondholders)
    • made out to a third-party trustee as bondholders may have difficulty in ascertaining whether the issuer has been fulfilling its obligations.
    • two types of covenants: Affirmative covenants set forth certain actions that the borrowers must take, such as paying interest and principal on a timely basis, submitting periodic reports to a trustee for evaluation of the issuer's compliance with the indenture. Negative covenants - certain limitations and restrictions on the borrower's activities, such as the borrower's ability to incur additional debt unless certain tests are met, sale of assets.
  • par value: aka principal, face value, redemption value, maturity value. The amount that the issuer agrees to repay the bondholder by the maturity date.
    • Typically $1,000.
    • Quoted as a percentage of its par value. ie. a price of 95 means 95% of the par value.
    • may trade at a premium (above par) or at a discount.
  • Maturity: defines the remaining life of the bond.
    • the longer the maturity, the greater the price volatility (resulted from changes in IR)
    • defines 4 categories: Money market instruments (<= 1yr), Short-term notes ( 1yr< Mat <= 5yr), Intermediate-term bonds (5yr < Mat <= 12 years), and Long-term bonds (> 12yr)
  • coupon rate: the interest rate that the issuer agrees to pay each year. typically pay semiannually. The amount of interest that will be received by the buyer if an investor sells a bond between coupon payments (as interest is paid not daily) is known as accrued interest. The agreed upon bond price without accrued interest is referred to as the price (clean price). Full price or dirty price otherwise. Common coupon rate strucutures are
    • Zero-coupon bonds: pay the face amount at a future maturity date, without any interim interest payments. ie. a zero-coupon bond with $1,000 par is quoted at 80. The interest is $300. A type of accrual bonds that do not make any coupon payments until the maturity date.
    • Step-up bonds: have low initial and gradually increasing coupon rates, (ie. rates "step up" over time)
    • Deferred coupon bonds: no coupon payments for an initial period of typically 3 - 7 years. Then a lump-sum coupon is paid, and regular coupon payments begin.
    • Floating-rate securities: coupon rate = reference rate + quoted margin. Typical reference rates include LIBOR and US Treasury yields. Quoted margin often quoted in basis points. Coupon rate is determined at the coupon reset date but paid at the next coupon date.
  • Currency: A dollar-denominated issue makes payments to bondholders in US dollars. A dual-currency issue has coupon payments in one currency and principal payments in another.

Floating-rate securities

  • Bonds with limited coupon rates: cap (max coupon rate), floor (min coupon rate), collar (cap + floor)
  • Bonds with constant quoted margin
    • Inverse floater: coupon rate = fixed rate - multiplier * reference rate. For example, an inverse floater's coupon rate = 11% - 2 x 3-month LIBOR. If the 3-month LIBOR is 2.1%, then the coupon rate for the next interest payment period is: 11% - 2.1 x 2%. coupon rate moves in the opposite direction from the change in the reference rate. aka reserve floater.
    • Dual-indexed floater: coupon rate = Reference rate 1 - Reference rate 2 + Quoted margin.
    • Range note: coupon rate = the reference rate as long as the reference rate is within a certain range at the reset date. zero for the period otherwise.
    • Ratched bond: coupon rate is adjusted periodically at a fixed margin over a reference rate. However, it can only adjust downward, and once it is adjusted down, it cannot be readjusted up if the reference rate subsequently increases.
    • Deleveraged floater: coupon rate = fraction * referece rate + quoted margin, where 0 < fraction <1. For example, the coupon rate is reset every April 30 to 80% of the 5-year T-bond plus 2%. Suppose that the 5-year Treasury yield is 5% on April 30, then the coupon rate for the next interest payment period is: 0.8 x 5% + 2%.
  • Bonds with adjustable quoted margin
    • Stepped spread floater: quoted margin can step to either a higher or a lower level over the security's life. For example, a 5-year floating-rate note's coupon rate may be 6-month LIBOR + 1% for the first 2 years, and 3-month LIBOR + 3% for the remaining years.
    • Extendible reset bond: reset the coupon rate so that the issue will trade at a predetermined price (typically above par).
    • Drop-lock bond: coupon rate is automatically changed into a fixed coupon rate under certain circumstances.
    • Non-interest rate indexes: coupon can be indexed to movements in foreign exchange rates, the price of a commodity, the return on an equity index, etc. For example, the Treasury Inflation Protection Securities (TIPS)'s coupon is based on inflation rate.


  • Risk: Prices fluctuate significantly with shifts in interest rates (and therefore by inflation). They are also sensitive to changes in the political and economic scenarios.
  • Return: free of credit risk. interest income is exempt from state and city taxes.

  • T-Bills are Treasury securities with a maturity of <= 1yr. Do not pay any coupons.
    • Quoted on a bank discount basis: (Par-Price)/Par x 360/t. the convention for # of days in a year is 360.
    • Pure discount bond (ie. sell at a discount from par)
    • Highly liquid (low transaction cost and with not much price risk)
  • T-Note: 1yr < maturity < 10 yrs. Pay coupons.
  • T-Bond: 10yrs <= maturity < 30yr. Pay coupons. May be callable during a given period (usually the last 5 years).
  • On/Off/OffOff the Run: On-the-run issues are the newly issued securities that are being auctioned by the Treasury. More liquid (smaller bid offer spreads) than off-the-run issues, which are issued in previous auctions (more seasoned). (why important) For institutional investors who value liquidity (buy and sell large amounts of securities at short notice, without an adverse price reaction), on-the-run issues are clearly the more attractive investments. For investors to whom liquidity is less important, off-the-run issues may be more attractive since they tend to offer higher yields.
  • bid-offer spreads: very small (1/2 bps in the T-bill market and 1/64 - 4/32 in the T-note and T-bond markets) because the securities are very liquid and virtually riskless. Exists to compensate the price risk of the large inventory positions that the dealers take in the market.

Repo/Reverse Repo

transactions in which one party sells securities to another while agreeing to repurchase those securities at a later date. to borrow money by placing government securities as collaterals. Especially attractive to dealers with limited capital who wish to take positions in securities worth billions of dollars. on an overnight basis or for a very short term (not exceeding a few weeks). The owner will retain the right to any cash flows from the collateral. hair cut
  • General collateral repo rates/Special repo rates: the rate applied to most Treasury securities for overnight collateralized lending and borrowing. Dealers generally permit substitution of collaterals in such general collateral agreements. The special rates apply to collateralized transactions where no such substitutions are permitted. the special rates lower than the general collateral rates.

Fed Funds rates

All depository institutions must maintain a certain amount of reserves at the Fed to meet the reserve requirements. An institution that is short of reserves will often borrow from another that has surplus funds in the Fed funds market. Higher than repo rates due to the collateralized nature of the repo loans. If, however, the supply of Treasury securities increases and the need to refinance the inventory position becomes critical, the repo rates can climb over the Fed funds rate.


structured so that the investor receives a compensation for any increases in future inflation rates. The coupon rate, which is set at auction, remains fixed throughout the term of the security. The par (face or principal) amount of the security is adjusted for inflation, but the inflation-adjusted principal will be paid only at maturity. use Consumer Price Index (a specific one) for measuring the inflation rate. yield less than similar nominal Treasury securities.
  • Risks: the effectiveness of the underlying index to serve as a true proxy of the actual inflation rate; pays taxes well ahead of the maturity date when the inflation adjustments are actually realized (the inflation adjustments to the principal are taxable in the year in which such adjustments occur even though the inflation adjustments will not be paid until maturity); inflation risk due to the lag in the indexing process (the lag in the indexation scheme)


consists of the federally sponsored agency market which issues securities in the market and federal agencies which do not directly issue securities in the market-they tend to borrow from the Federal Financing Bank. The agencies were created to promote the availability of credit to certain critical sectors of the economy such as agriculture and housing. ie. Freddie Mac, Fannie Mae, Ginnie Mae.
  • small Treasury yield spread: widely assumed that the government would step in with assistance if an agency neared default.
  • Callable (most): Agencies such as the FNMA and the FHLMC buy mortgage loan portfolios. Prepayment risks can be handled by issuing liabilities that can be called (ie. the prepayment cash flows can be used to call away the liabilities.


  • Risk: illiquid (requires a portion of the principal to be retired at prespecified times)
  • Return: interest income exempt from federal and state taxes (local taxes are exempt in the issuing state as well). Capital gains taxes must be paid on "munis", when the bonds mature or if they are sold for more than the investor's purchase price.
  • revenue bonds/general obligation bonds: Revenue bonds are municipal issues that derive their cash flows from specific project revenues (ie. ridges, turnpikes, and airports). GOB issued on the basis of the taxing power of the municipality.
  • insurance: increases the credit reputation. Rating agencies tend to rate insured municipal bonds at the highest category (Aaa or AAA).


Categorized by the credit quality of the issuer, maturity, components of the indenture (sinking fund or call feature); or type of security offered by the issuer.
  • Risk: The presence of credit risk, the relative lack of liquidity, and the call features cause the investors to demand a yield premium (~2%) over comparable Treasury securities.
  • Return:
  • Commercial paper/Medium term notes/Bonds: Commercial paper is corporate short term debt with maturity ranging from 30 to 270 days. Trade above or below comparable LIBOR rates depending on credit rating. Medium term 1yr <= maturities <= 7yr. CP: corporations do not have to register with SEC in order to issue CPs. This represents savings in time commitment and resources. Also corporations are able to directly access the capital market for short-term capital without having to rely on intermediaries such as commercial banks for their financing needs. For highly rated corporations, this is a real advantage because they are able to borrow at rates below the London interbank offered rates (LIBOR) or at "sub-LIBOR" rates.
  • Callable: potential conflicts between managers and creditors, and the potential changes in credit reputation. (If the management believes that the credit standing of the issuer will improve but the market does not share this belief in pricing the issue - given the levels of interest rate have not risen. Also bondholders can block certain mergers, acquisitions or major investments. ). protection against falling interest rate.
  • Sinking fund: for an orderly retirement of debt in scheduled installments. In the event of bankruptcy, senior debt holders have a prior claim to the assets of the firm. commit issuers to make periodic payments to retire the balloon payment in installments. By which creditors can assess the cash-flow-generating capacity or the solvency of the firm.
  • Convertible bonds
  • Floater/InverseFloater: issue Floaters if expect interest rates to decline in the long term and hope to pay a rate that is only marginally higher than the market rate (do not want to tie themselves to the prevailing higher rate. ) Inverse Floaters are securities whose coupon rates are inversely related to an index of interest rate such as LIBOR and T-bills. If the rates go up, inverse floaters pay less and vice versa. These are issued by firms whose cash flows from assets are inversely related to the interest rates.
  • Zero coupon bonds: securities that do not pay any coupons but pay only the balloon payment at maturity. Issued by firms that have growth prospects but are currently cash-constrained. For investor, no reinvestment risk.
  • Yankee bonds: issued by foreign companies in the U.S. bond markets. Their domestic market may be "saturated" with their securities. Any imperfections across the domestic and U.S. markets will be exploited in the issue of Yankee bonds.
  • Pay-in-kind (PIK) bonds: a form of high yield debt. Issuers with poor credit rating seek to raise capital from sources other than banks.
  • Investment-grade bonds/Junk bonds: Investment grade bonds enjoy a high credit reputation from rating agencies. Typically, investment grade debt is rated Baa3 or better by Moody's or BBB- or better by Standard and Poor. Junk or noninvestment grade debt is rated below Baa3 or BBB-. Many of the junk issues tend to pay high coupons and are usually callable.junk issues tend to pay high coupons and are usually callable.


  • Risk: prepayment. very liquid
  • Return:
  • Negative Convexity (aka compression to par): The existence of the prepayment feature implies that the value of the mortgage-backed securities behaves differently at low interest rates. As interest rates fall, bullet fixed-income securities appreciate in value, but a mortgage-backed security is compressed to par due to the risk of prepayments. When interest rates are close to the coupon of the mortgage-backed security and the volatility of the rates increases, the probability that the call will be exercised increases as well. This may produce a reduction in the price of the mortgage-backed securities.


a 4-step process by which illiquid assets are transformed into very liquid financial instruments
  • Originating: A private institution such as an S&L or a federal agency creates individual mortgages.
  • Pooling and Standardizing: The assets of several such originators are then pooled so that they may interest large investors. The various features of the loan (interest rates, maturity, the geographic location, and so forth) are then standardized to allow for ease in predicting cash flows.
  • Guaranteeing: The portfolio is now guaranteed (for a fee) against default by a federal agency or a creditable private agency. Defaults may occur at the level of the individual mortgage holder or of the issuer. However, the guaranteeing entity will make the payments. This insurance makes the security attractive in the marketplace.
  • Creating the SPV: issues securities after it has set up the pool and monitors its functioning to maintain a high credit rating. Put some distance between the originators and the pool of assets. For instance, the SPV is structured such that the bankruptcy of the originator(s) does not affect the pool of financial assets held by the SPV. This separation is critical in obtaining the necessary credit enhancements that usually lead to a high credit rating for the asset-backed securities.

Prepayments Factors

  • Refinancing Incentive: accelerate in periods of falling interest rates, especially when the belief in the market is that the rates have bottomed out.
  • Seasonality (school year) Factor: families typically do not move during the school year. Movings accelerate during 6 - 9.
  • Age of the Mortgage: The rate of prepayments appears to slow down for loans in the 10- to 25-year range.
    • <10 years old: During the early part of the mortgage loan, interest payments far exceed the principal component. This, in part, implies that the interest savings associated with refinancing are greater during the earlier part of the mortgage loan.
    • >25 years old: When the mortgage is more than 25 years old, there may be an incentive to pay it off to secure the property's title.
  • Family Circumstances: A number of family circumstances dictate the prepayment decision of a household: marital status, job switching/loss, and so on.
  • Housing Prices: The housing price affects the LTV ratio, which in turn affects the ability of the household to qualify for refinancing. If the house price increases, then the LTV decreases, enhancing the homeowner's ability to refinance.
  • Mortgage Status (Premium Burnout): the relationship between the contractual interest rate in a mortgage loan (r) and the going mortgage interest rates (R).
    • Premium mortgages: r > R. A prime candidate for prepayment.
    • Discount mortgage: r < R.

Collateralized Mortgage Obligation (CMO)

A mortgage-backed security (MBS) that comprises several classes or tranches of bonds all backed by the same mortgage collateral. The bonds or tranches are structured to each have their own risk characteristics and maturity range, and offer varying levels of protection against prepayments. Most rated AAA.

Backed by pools of residential mortgages or mortgage-backed securities such as GNMAs. Cash flows from the collateral are divided and allocated to several classes or tranches of bonds.

  • Sequential Structure: tends to have four tranches
    • The first tranche is typically allotted a stated coupon. also be allotted any prepayments that are made.
    • Until the first tranche is fully retired, no payments are made to other tranches, except that the second and third tranches will receive the predetermined coupon amounts. The prepayments are passed through to the second tranche only after the first is fully retired.
    • In this sense, each tranche successively receives prepayments as soon as its immediate predecessor is retired.
    • The last (fourth) tranche: called the Z bond, which receives no cash flows until all earlier tranches are fully retired. The face amount, however, accrues at the stated coupon. After all tranches are retired, the Z bond receives the coupon on its current face amount plus all the prepayments.
  • Planned Amortization Class (PAC) structure: The collateral's principal is divided into two categories
    • Designated PAC bonds: The amortization schedule remains fixed over a range of prepayment rates measured by a range of PSAs (ie. a metric for projecting prepayments over the life of a pool). Allows for more stable average lives (at the expense of the companion group). Tend to be priced tightly to respective Treasuries.
    • The companion group: priced at much wider spreads relative to Treasuries.
  • Targeted Amortization Class (TAC) structure: Protection from prepayments are provided only for certain PSA rates (ie. do not protect against low prepayment rates.) Less stability from prepayment risk is provided to certain tranches. Offer higher yields than comparable PAC bonds.

Must be over collateralized: to create an insurance cushion that helps to offset any cash flow shortages that may result due to a fall in reinvestment income from the underlying monthly cash flows. (reinvestment due to the fact CMOs pay semiannual/quarterly, but the underlying monthly)


Emerging market/Brady bonds

  • Collateral: Principal and certain interest is collateralized by U.S. Treasury zero- coupon bonds and other high-grade instruments. Enhanced credit reputation and the liquidity.
  • Spreads between emerging-market bonds and Treasury securities: influenced by default risk, liquidity risk, contractual differences, foreign currency risk, sovereign /political risk.

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