A bond’s indenture contains the obligations, rights, and any options available to the issuer or buyer of a bond.

Covenants are the specific conditions of the obligation:

• Affirmative covenants specify actions that the borrower/issuer must perform.
• Negative covenants prohibit certain actions by the borrower/issuer.

Bonds have the following features:

• Maturity—the term of the loan agreement.
• Par value (face value)—the principal amount of the fixed income security that the bond issuer promises to pay the bondholders over the life of the bond.
• Coupon rate—the rate used to determine the periodic interest to be paid on the principal amount. Interest can be paid annually or semiannually, depending on the terms. Coupon rates may be fixed or variable.

Types of coupon rate structures:

• Option-free (straight) bonds pay periodic interest and repay the par value at maturity.
• Zero-coupon bonds pay no explicit periodic interest and are sold at a discount to par value.
• Step-up notes have a coupon rate that increases over time according to a specified schedule.
• Deferred-coupon bonds initially make no coupon payments (they are deferred for a period of time). At the end of the deferral period, the accrued (compound) interest is paid, and the bonds then make regular coupon payments until maturity.
• A floating (variable) rate bond has a coupon formula that is based on a reference rate (usually LIBOR) and a quoted margin. A cap is a maximum coupon rate the issuer must pay, and a floor is a minimum coupon rate the bondholder will receive on any coupon date.

Accrued interest is the interest earned since the last coupon payment date and is paid by a bond buyer to a bond seller.

Clean price is the quoted price of the bond without accrued interest.

Full price refers to the quoted price plus any accrued interest.

Bond retirement (payoff) provisions:

• Amortizing securities make periodic payments that include both interest and principal payments so that the entire principal is paid off with the last payment unless prepayment occurs.
• A prepayment option is contained in some amortizing debt and allows the borrower to pay off principal at any time prior to maturity, in whole or in part.
• Sinking fund provisions require that a part of a bond issue be retired at specified dates, typically annually.
• Call provisions enable the borrower (issuer) to buy back the bonds from the investors (redeem them) at a call price(s) specified in the bond indenture.
• Callable but nonrefundable bonds can be called prior to maturity, but their redemption cannot be funded by the issuance of bonds with a lower coupon rate.

Embedded options that benefit the issuer reduce the bond’s value (increase the yield) to a bond purchaser. Examples are:

• Call provisions.
• Accelerated sinking fund provisions.
• Caps (maximum interest rates) on floating-rate bonds.

Embedded options that benefit bondholders increase the bond’s value (decrease the yield) to a bond purchaser. Examples are:

• Conversion options (the option of bondholders to convert their bonds into shares of the bond issuer’s common stock).
• Put options (the option of bondholders to return their bonds to the issuer at a predetermined price).
• Floors (minimum interest rates) on floating-rate bonds.

There are many types of risk associated with fixed income securities:

• Interest rate risk—uncertainty about bond prices due to changes in market interest rates.
• Call risk—the risk that a bond will be called (redeemed) prior to maturity under the terms of the call provision and that the funds must then be reinvested at the then-current (lower) yield.
• Prepayment risk—the uncertainty about the amount of bond principal that will be repaid prior to maturity.
• Yield curve risk—the risk that changes in the shape of the yield curve will reduce bond values.
• Credit risk—includes the risk of default, the risk of a decrease in bond value due to a ratings downgrade, and the risk that the credit spread for a particular rating will increase.
• Liquidity risk—the risk that an immediate sale will result in a price below fair value (the prevailing market price).
• Exchange rate risk—the risk that the domestic currency value of bond payments in a foreign currency will decrease due to exchange rate changes.
• Volatility risk—the risk that changes in expected interest rate volatility will affect the values of bonds with embedded options.
• Inflation risk—the risk that inflation will be higher than expected, eroding the purchasing power of the cash flows from a fixed income security.
• Event risk—the risk of decreases in a security’s value from disasters, corporate restructurings, or regulatory changes that negatively affect the firm.
• Sovereign risk—the risk that governments may repudiate debt or not be able to make debt payments in the future.

When a bond’s coupon rate is less than its market yield, the bond will trade at a discount to its par value.

When a bond’s coupon rate is greater than its market yield, the bond will trade at a premium to its par value.

The level of a bond’s interest rate risk (duration) is:

• Positively related to its maturity.
• Negatively related to its coupon rate.
• Negatively related to its market YTM.
• Less over some ranges for bonds with embedded options.

The duration of a bond is the approximate percentage price change for a 1% change in yield.

The dollar duration of a bond is the approximate dollar price change for a 1% change in yield.

Yield curve risk of a bond portfolio is the risk (in addition to interest rate risk) that the portfolio’s value may decrease due to a non-parallel shift in the yield curve (change in its shape).

When yield curve shifts are not parallel, the duration of a bond portfolio does not capture the true price effects because yields on the various bonds in the portfolio may change by different amounts.

Disadvantages to an investor of a callable or prepayable security:

• Timing of cash flows is uncertain.
• Principal is most likely to be returned early when interest rates available for reinvestment are low.
• Potential price appreciation is less than that of option-free bonds.

A security has more reinvestment risk when it has a higher coupon, is callable, is an amortizing security, or has a prepayment option.

A prepayable amortizing security has greater reinvestment risk because of the probability of accelerated principal payments when interest rates, including reinvestment rates, fall.

Credit risk includes:

• Default risk—the probability of default.
• Downgrade risk—the probability of a reduction in the bond rating.
• Credit spread risk—uncertainty about the bond's yield spread to Treasuries based on its bond rating.

Credit ratings are designed to indicate to investors a bond’s relative probability of default. Bonds with the lowest probability of default receive ratings of AAA. Bonds rated AA, A, and BBB are also considered investment grade bonds. Speculative or high yield bonds are rated BB or lower.

Event risk encompasses non-financial events that can hurt the value of a bond, including disasters that reduce the issuer’s earnings or diminish asset values; takeovers or restructurings that can have negative effects on the priority of bondholders’ claims; and changes in regulation that can decrease the issuer’s earnings or narrow the market for a particular class of bonds.

Sovereign risk is the possibility that a foreign government will refuse to pay or become unable to repay its debts due to poor economic conditions and government deficit spending.

Sovereign debt refers to the debt obligations of governments. U.S. Treasury securities are sovereign debt of the U.S. government and are considered free of credit risk. Sovereign debt of other countries has varying degrees of credit risk.

Sovereign debt is typically issued using one of four methods:

• Regular auction cycle with the entire issue sold at a single price.
• Regular auction cycle with bonds issued at multiple prices.
• Ad hoc auction system with no regular cycle.
• Tap system, auctioning new bonds identical to previously issued bonds.

Securities issued by the U.S. Treasury include:

• Bills—pure-discount securities maturing in four weeks, three months, or six months.
• Notes—coupon securities maturing in two, five, and ten years.
• Bonds—coupon securities maturing in 20 or 30 years.

Treasury Inflation Protected Securities (TIPS) are U.S. Treasury issues in which the coupon rate is fixed but the par value is adjusted periodically for inflation, based on changes in the CPI.

U.S. Treasuries from the most recent auction are referred to as on-the-run issues, while Treasuries from previous auctions are referred to as off-the-run issues.

Stripped Treasury securities are created by bond dealers who buy Treasury securities, separate each of their scheduled coupon and principal payments, and resell these as zero-coupon securities.

Treasury strips are traded in two forms—coupon strips and principal strips—and are taxed by the IRS on the basis of accrued interest, like other zero-coupon securities.

A mortgage passthrough security is backed by a pool of amortizing mortgage loans (the collateral) and has monthly cash flows that include interest payments, scheduled principal payments, and prepayments of principal.

Prepayment risk is significant for investors in passthrough securities because most mortgage loans contain a prepayment option, which allows the issuer (borrower) to make additional principal payments at any time.

Collateralized mortgage obligations (CMOs) are customized claims to the principal and/or interest payments of mortgage passthrough securities and redistribute the prepayment risk and/or maturity risk of the securities.

Interest payments on state and local government securities (municipal securities, or munis) are usually exempt from U.S. federal taxes, and from state taxes in the state of issuance.

Municipal bonds include:

• Tax-backed (general obligation) bonds backed by the taxing authority of the governmental unit issuing the securities.
• Revenue bonds, backed only by the revenues from the project specifically financed by the bond issue.

Corporate debt securities include bonds, medium-term notes, and commercial paper. Bond rating agencies rate corporate bonds on capacity to repay (liquid assets and cash flow), management quality, industry prospects, corporate strategy, financial policies, credit history, overall debt levels, the collateral for the issue, and the nature of the covenants.

Corporate bonds may be secured or unsecured (called debentures). Security can be in the form of real property, financial assets, or personal property/equipment.

Medium-term notes (MTN) are issued periodically by corporations under a shelf registration, sold by agents on a best-efforts basis, and have maturities ranging from 9 months to more than 30 years.

Structured notes combine a bond with a derivative to create a security that fills a need for particular institutional investors.

Commercial paper is a short-term corporate financing vehicle and does not require registration with the SEC if its maturity is less than 270 days. CP comes in two forms:

• Directly-placed paper sold directly by the issuer.
• Dealer-placed paper sold to investors through agents/brokers.

Negotiable CDs are issued in a wide range of maturities by banks, trade in a secondary market, are backed by bank assets, and are termed Eurodollar CDs when denominated in U.S. dollars and issued outside the United States.

Bankers’ acceptances are issued by banks to guarantee a future payment for goods shipped, sold at a discount to the future payment they promise, short-term, and have limited liquidity.

Asset-backed securities (ABS) are debt that is supported by the cash flows from an underlying pool of mortgages, auto loans, credit card receivables, commercial loans, or other financial assets.

A special purpose vehicle is an entity to which the assets that back an ABS are legally transferred. If the corporation transferring these assets goes bankrupt, the assets are not subject to claims from its creditors. As a result, the ABS can receive a higher credit rating than the corporation and reduce the corporation’s funding costs.

External credit enhancement for an ABS can include corporate guarantees, letters of credit, or third-party bond insurance.

The primary market in bonds includes underwritten and best-efforts public offerings, as well as private placements.

The secondary market in bonds includes some trading on exchanges, a much larger volume of trading in a dealer market, and electronic trading networks which are an increasingly important part of the secondary market for bonds.

Yield curves represent the plot of yield against maturity.

The general yield curve shapes are upward or downward sloping, flat, or humped.

Theories of the yield curve and their implications for the shape of the yield curve are:

• The pure expectations theoryargues that rates at longer maturities depend only on expectations of future short-term rates and is consistent with any yield curve shape.
• The liquidity preference theoryof the term structure states that longer-term rates reflect investors’ expectations about future short-term rates and an increasing liquidity premium to compensate investors for exposure to greater amounts of interest rate risk at longer maturities. The liquidity preference theory can be consistent with a downward sloping curve if an expected decrease in short-term rates outweighs the liquidity premium.
• The market segmentation theory argues that lenders and borrowers have preferred maturity ranges and that the shape of the yield curve is determined by the supply and demand for securities within each maturity range, independent of the yield in other maturity ranges. It is consistent with any yield curve shape and in a somewhat weaker form is known as the preferred habitat theory.

Types of yield spreads:

• The absolute yield spreadis the difference between the yield on a particular security or sector and the yield of a reference (benchmark) security or sector, which is often on-the-run Treasury securities of like maturity.
• The relative yield spreadis the absolute yield spread expressed as a percentage of the benchmark yield. This is arguably a superior measure to the absolute spread, since it will reflect changes in the level of interest rates even when the absolute spread remains constant.
• The yield ratio is the ratio of the yield on a security or sector to the yield on a benchmark security or sector; it is simply one plus the relative yield spread.

A credit spread is the yield difference between two bond issues due to differences in their credit ratings.

Credit spreads narrow when the economy is healthy and expanding, while they increase during contractions/recessions reflecting a flight to (higher) quality by investors.

Call options and prepayment options increase yields and yield spreads compared to option-free bonds.

Put options and conversion options decrease yields and yield spreads compared to comparable option-free bonds.

To compare a tax-exempt bond with a taxable issue, use either of the following:

• After-tax yield = taxable yield × (1 − marginal tax rate), and compare it to tax-exempt yield.
• Taxable-equivalent yield = [image], and compare it to a taxable yield.

To value a bond, one must:

• Estimate the amount and timing of the bond’s future payments of interest and principal.
• Determine the appropriate discount rate(s).
• Calculate the sum of the present values of the bond’s cash flows.

To compute the value of an option-free coupon bond, value the coupon payments as an annuity and add the present value of the principal repayment at maturity.

The value of a zero-coupon bond calculated using a semiannual discount rate, i (one-half its annual yield to maturity), is:

[image]

When interest rates (yields) do not change, a bond’s price will move toward its par value as time passes and the maturity date approaches.

To compute the change in value that is attributable to the passage of time, revalue the bond with a smaller number of periods to maturity.

A Treasury spot yield curve is considered “arbitrage-free” if the present values of Treasury securities calculated using these rates are equal to equilibrium market prices.

If bond prices are not equal to their arbitrage-free values, dealers can generate arbitrage profits by buying the lower-priced alternative (either the bond or the individual cash flows) and selling the higher-priced alternative (either the individual cash flows or a package of the individual cash flows equivalent to the bond).

Three sources of return to a coupon bond:

• Coupon interest payments.
• Reinvestment income on the coupon cash flows.
• Capital gain or loss on the principal value.

Yield to maturity (YTM) for a semiannual-pay coupon bond is calculated as two times the semiannual discount rate that makes the present value of the bond’s promised cash flows equal to its market price plus accrued interest.

For an annual-pay coupon bond, the YTM is simply the annual discount rate that makes the present value of the bond’s promised cash flows equal to its market price plus accrued interest.

The current yield for a bond is its annual interest payment divided by its market price.

Yield to call (put) is calculated as a YTM but with the number of periods until the call (put) and the call (put) price substituted for the number of periods to maturity and the maturity value.

The cash flow yield is a monthly internal rate of return based on a presumed prepayment rate and the current market price of a mortgage-backed or asset-backed security.

These yield measures are limited by their common assumptions that: (1) all cash flows can be discounted at the same rate; (2) the bond will be held to maturity, with all coupons reinvested to maturity at a rate of return that equals the bond’s YTM; and (3) all coupon payments will be made as scheduled.

YTM is not the realized yield on an investment unless the reinvestment rate is equal to the YTM.

The amount of reinvestment income required to generate the YTM over a bond’s life is the difference between the purchase price of the bond, compounded at the YTM until maturity, and the sum of the bond’s interest and principal cash flows.

Reinvestment risk is higher when the coupon rate is greater (maturity held constant) and when the bond has longer maturity (coupon rate held constant).

The bond-equivalent yield of an annual-pay bond is:

[image]

The annual-pay yield can be calculated from the YTM of a semiannual-pay bond as:

[image]

The theoretical Treasury spot rate curve is derived by calculating the spot rate for each successive period N based on the spot rate for period N – 1 and the market price of a bond with N coupon payments.

To compute the value of a bond using spot rates, discount each separate cash flow using the spot rate corresponding to the number of periods until the cash flow is to be received.

Three commonly used yield spread measures:

• Nominal spread: bond YTM – Treasury YTM.
• Zero-volatility spread(Z-spread or static spread): the equal amount of additional yield that must be added to each Treasury spot rate to get spot rates that will produce a present value for a bond equal to its market price.
• Option-adjusted spread (OAS): spread to the spot yield curve after adjusting for the effects of embedded options. OAS reflects the spread for credit risk and liquidity risk primarily.

There is no difference between the nominal and Z-spread when the yield curve is flat. The steeper the spot yield curve and the earlier bond principal is paid (amortizing securities), the greater the difference in the two spread measures.

The option cost for a bond with an embedded option is Z-spread – OAS.

For callable bonds, Z-spread > OAS and option cost > 0.

For putable bonds, Z-spread < OAS and option cost < 0.

Forward rates are current lending/borrowing rates for short-term loans to be made in future periods.

A spot rate for a maturity of N periods is the geometric mean of forward rates over the N periods. The same relation can be used to solve for a forward rate given spot rates for two different periods.

To value a bond using forward rates, discount the cash flows at times 1 through N by the product of one plus each forward rate for periods 1 to N, and sum them.

The full valuation approach to measuring interest rate risk involves using a pricing model to value individual bonds and can be used to find the price impact of any scenario of interest rate/yield curve changes. Its advantages are its flexibility and precision.

The duration/convexity approach is based on summary measures of interest rate risk and, while simpler to use for a portfolio of bonds than the full valuation approach, is theoretically correct only for parallel shifts in the yield curve.

Callable bonds and prepayable securities will have less price volatility (lower duration) at low yields, compared to option-free bonds.

Putable bonds will have less price volatility at high yields, compared to option-free bonds.

Option-free bonds have a price-yield relationship that is curved (convex toward the origin) and are said to exhibit positive convexity. In this case, bond prices fall less in response to an increase in yield than they rise in response to an equal-sized decrease in yield.

Callable bonds exhibit negative convexity at low yield levels. In this case, bond prices rise less in response to a decrease in yield than they fall in response to an equal-sized increase in yield.

Effective duration is calculated as the ratio of the average percentage price change for an equal-sized increase and decrease in yield, to the change in yield.

[image]

The most intuitive interpretation of duration is as the percentage change in a bond’s price for a 1% change in yield to maturity.

Macaulay duration and modified duration are based on a bond’s promised cash flows.

Effective duration is appropriate for estimating price changes in bonds with embedded options because it takes into account the effect of embedded options on a bond’s cash flows.

The duration of a bond portfolio is equal to a weighted average of the individual bond durations, where the weights are the proportions of total portfolio value in each bond position.

Portfolio duration is limited because it gives the sensitivity of portfolio value only to yield changes that are equal for all bonds in the portfolio, an unlikely scenario for most portfolios.

Because of convexity, the duration measure is a poor approximation of price sensitivity for yield changes that are not absolutely small. The convexity adjustment accounts for the curvature of the price-yield relationship.

Incorporating both duration and convexity, we can estimate the percentage change in price in response to a change in yield of (Δy) as:

[image]

Price value of a basis point (PVBP) is an estimate of the change in a bond’s or a bond portfolio’s value for a one basis point change in yield.

PVBP = duration × 0.0001 × bond (or portfolio) value

Credit risk refers to the possibility that a borrower fails to make the scheduled interest payments or return of principal. Credit risk is composed of default risk, which is the probability of default, and loss severity, which is the portion of the value of a bond or loan a lender or investor will lose if the borrower defaults. The expected loss is the probability of default multiplied by the loss severity.

Spread risk is the possibility that a bond loses value because its credit spread widens relative to its benchmark. Spread risk includes credit migration or downgrade risk and market liquidity risk.

Corporate debt is ranked by seniority or priority of claims. Secured debt is a direct claim on specific firm assets and has priority over unsecured debt. Secured or unsecured debt may be further ranked as senior or subordinated. Priority of claims may be summarized as follows:

• First mortgage or first lien.
• Second or subsequent lien.
• Senior secured debt.
• Senior subordinated debt.
• Senior unsecured debt.
• Subordinated debt.
• Junior subordinated debt.

Issuer credit ratings, or corporate family ratings, reflect a debt issuer's overall creditworthiness and typically apply to a firm's senior unsecured debt.

Issue credit ratings, or corporate credit ratings, reflect the credit risk of a specific debt issue. Notching refers to the practice of adjusting an issue credit rating upward or downward from the issuer credit rating to reflect the seniority and other provisions of a debt issue.

Lenders and bond investors should not rely exclusively on credit ratings from rating agencies for the following reasons:

• Credit ratings can change during the life of a debt issue.
• Rating agencies cannot always judge credit risk accurately.
• Firms are subject to risk of unforeseen events that credit ratings do not reflect.
• Market prices of bonds often adjust more rapidly than credit ratings.

Components of traditional credit analysis are known as the four Cs:

• Capacity: The borrower's ability to make timely payments on its debt.
• Collateral: The value of assets pledged against a debt issue or available to creditors if the issuer defaults.
• Covenants: Provisions of a bond issue that protect creditors by requiring or prohibiting actions by an issuer's management.
• Character: Assessment of an issuer's management, strategy, quality of earnings, and past treatment of bondholders.

Credit analysts use profitability, cash flow, and leverage and coverage ratios to assess debt issuers’ capacity.

• Profitability refers to operating income and operating profit margin, with operating income typically defined as earnings before interest and taxes (EBIT).
• Cash flow may be measured as earnings before interest, taxes, depreciation, and amortization (EBITDA); funds from operations (FFO); free cash flow before dividends; or free cash flow after dividends.
• Leverage ratios include debt-to-capital, debt-to-EBITDA, and FFO-to-debt.
• Coverage ratios include EBIT-to-interest expense and EBITDA-to-interest expense.

Lower leverage, higher interest coverage, and greater free cash flow imply lower credit risk and a higher credit rating for a firm. When calculating leverage ratios, analysts should include in a firm's total debt its obligations such as underfunded pensions and off-balance-sheet financing.

For a specific debt issue, secured collateral implies lower credit risk compared to unsecured debt, and higher seniority implies lower credit risk compared to lower seniority.

Corporate bond yields comprise the real risk-free rate, expected inflation rate, credit spread, maturity premium, and liquidity premium. An issue’s yield spread to its benchmark includes its credit spread and liquidity premium.

The level and volatility of yield spreads are affected by the credit and business cycles, the performance of financial markets as a whole, availability of capital from broker-dealers, and supply and demand for debt issues. Yield spreads tend to narrow when the credit cycle is improving, the economy is expanding, and financial markets and investor demand for new debt issues are strong. Yield spreads tend to widen when the credit cycle, the economy, and financial markets are weakening, and in periods when the supply of new debt issues is heavy or broker-dealer capital is insufficient for market making.

Analysts can use duration and convexity to estimate the impact on return (the percentage change in bond price) of a change in credit spread.

For small spread changes:

return impact ≈ −duration × Δspread

For larger spread changes:

return impact ≈ −duration × Δspread + [image]convexity × (Δspread)²

High yield bonds are more likely to default than investment grade bonds, which increases the importance of estimating loss severity. Analysis of high yield debt should focus on liquidity, projected financial performance, the issuer’s corporate and debt structures, and debt covenants.

Credit risk of sovereign debt includes the issuing country’s ability and willingness to pay. Ability to pay is greater for debt issued in the country’s own currency than for debt issued in a foreign currency. Willingness refers to the possibility that a country refuses to repay its debts.

Analysis of general obligation municipal debt is similar to analysis of sovereign debt, focusing on the strength of the local economy and its effect on tax revenues. Analysis of municipal revenue bonds is similar to analysis of corporate debt, focusing on the ability of a project to generate sufficient revenue to service the bonds.