FI1: Bond valuation and YTM (2024)

Basics of a bond

Interest rate increases, bond value decreases.
Bonds are rated based on their relative probability of default (failure to make promised payments). Higher risk, worse credit quality, higher yields. From 1950 to 2020 stock returns an average of 8% per annum, whereas bond returns for IG bonds have been 4-5%.
Bond's rating decreases, bond price decreases, and thus yield increases
Key features: Issuer, maturity date, par value (principal value to be paid), coupon rate and frequency, currency in which payments will be made

Bond maturity/term to maturity:

the date on which the principal is to be repaid.
Once a bond has been issued, the time remaining until maturity is referred to as the term to maturity or tenor of a bond (1 day to 30 years).
Bonds with no maturity = perpetual bonds, making periodic interest payments but do not promise to repay the principal amount. Redeemable/irredeemable bonds.
Bonds with original maturities of one year or less are referred to as money market securities.

Examples include U.S. Treasury bills, commercial paper (issued by corporations), and negotiable certificates of deposit, or CDs (issued by banks).

Bonds with original maturities of more than one year are referred to as capital market securities.

Par value/nominal/face value

principal amount that will be repaid at maturity, also called the face value,maturity value,redemption value,or principal value of a bond. Bonds can have a par value of any amount, and their prices are quoted as a percentage of par. A bond with a par value of $1,000 quoted at 98 is selling for $980. Hong Kong, HKD 50k, Europe, 100.
premium, > par; at par, = par; discount, < par

Coupon payments (nominal rate = coupon rate); effective rate is essentially yield

Coupon usually annually or semi-annually

The coupon rate on a bond is the annual percentage of its par value that will be paid to bondholders
A $1,000 par value semiannual-pay bond with a 5% coupon would pay 2.5% of $1,000, or $25, every six months.
A bond with a fixed coupon rate is called a plain vanilla bond or a conventional bond.
Some bonds pay no interest prior to maturity and are called zero-coupon bonds/ pure discount bond (sold at a discount to par, and interest paid all at maturity tgt with par). A 10-year,$1,000, zero-coupon bond yielding 7% would sell at about $500 initially and pay $1,000 at maturity

A zero-coupon, or pure discount, bond pays no interest; instead, it is issued at a discount to par value and redeemed at par. As a result, the interest earned is implied and equal to the difference between the par value and the purchase price.

Redemption proceeds
Amount paid at maturity

Currency

A dual-currency bond makes coupon interest payments in one currency and the principal repayment at maturity in another currency.
A currency option bond gives bondholders a choice of which of two currencies they would like to receive their payments in.

！Bond indenture债务合约， or trust deed

The legal contract between the bond issuer (borrower) and bondholders (lenders)
债务合约(bondindenture)债务合约是一项法律合同 (us and canada)，它对债券发行者和持有者的权利和义务进行了规定，其中的条款叫convenants, 包括negative covenants (prohibitions on the borrower) and affirmative covenants (actions the borrower promises to perform)

Negative covenants serve to protect the interests of bondholders and prevent the issuing firm from taking actions that would increase the risk of default.at - the same time,the covenants must not be so restrictive that they prevent the firm from taking advantage of opportunities that arise or responding appropriately to changing business circ*mstances.

Affirmative covenants typically do not impose additional costs to the issuer, while negative covenants are frequently costly.

Affirmative covenants do not typically restrict the operating decisions of the issuer. Common affirmative covenants are to make timely interest and principal payments to bondholders, to insure and maintain assets, and to comply with applicable laws and regulations.

Two examples of affirmative covenants are cross-default and pari passu provisions.
A cross-default clause states that if the issuer defaults on any other debt obligation, they will also be considered in default on this bond.
A pari passu clause states that this bond will have the same priority of claims as the issuer's other senior debt issues.

The indenture defines the obligations of and restrictions on the borrower and forms the basis for all future transactions between the bondholder and the issuer.
Legal, regulatory, and tax considerations

Domestic or foreign? Mainly depends on where this is issued, all trade in national markets, denominated in national currency (panda bonds/yankee bonds)
Eurobond. 1. issued outside the jurisdiction of any one country; 2. denominated in a currency different from the currency of the countries in which they are sold. （look at denomination currency & the most strange)

They are subject to less regulation than domestic bonds in most jurisdictions and were initially introduced to avoid U.S. regulations. A bond issued by a Chinese firm that is denominated in yen and traded in markets outside Japan would fit the definition of a eurobond
A is incorrect because Eurobonds are bonds issued outside the jurisdiction of any single country.
Eurobonds are referred to by the currency they are denominated in. Eurodollar bonds are denominated in U.S. dollars, and euroyen bonds are denominated in yen.

Global bond. Eurobonds that trade in the national bond market of a country other than the country that issues the currency the bond is denominated in, and in the eurobond market, are referred to as global bonds. （as long you don't trade in the currency market).

Bearer bonds may be more attractive than registered bonds to those seeking to avoid taxes.
B is incorrect because global bonds are bonds issued in the Eurobond market and at least one domestic country simultaneously.

Foreign bonds. Bonds sold in a country and denominated in that country’s currency by an entity from another country are referred to as foreign bonds.(issuer is foreign)
Eurobonds are typically issued as bearer bonds (i.e., bonds for which the trustee does not keep records of ownership). In contrast, domestic and foreign bonds are typically registered bonds for which ownership is recorded by either name or serial number.

Other info
Sovereign nations also issue bonds denominated in currencies different from their own. Credit ratings are often higher for a sovereign’s local currency bonds than for example, its euro or U.S. dollar-denominated bonds. This is because the national government cannot print the developed market currency and the developed market currency value of local currency tax collections is dependent on the exchange rate between the two currencies
Trading is most active and prices most informative for the most recently issued government securities of a particular maturity. These issues are referred to as on-the-run bonds and also as benchmark bonds because the yields of other bonds are determined relative to the “benchmark” yields of sovereign bonds of similar maturities. Sovereign governments issue fixed-rate, floating-rate, and inflation-indexed bonds.

Securitized bonds, SPE(entity) in US, SPV in Europe
Collateral

Equipment trust certificates are debt securities backed by equipment such as railroad cars and oil drilling rigs.
Collateral trust bonds are backed by financial assets, such as stocks and (other) bonds. Be aware that while the term debentures refers to unsecured debt in the United States and elsewhere, in Great Britain and some other countries the term refers to bonds collateralized by specific assets
MBS. The underlying assets are a pool of mortgages, and the interest and principal payments from the mortgages are used to pay the interest and principal on the MBS.
Covered bonds, often issued in European countries by financial companies. Similar to ABS, but the underlying assets (the cover pool), although segregated, remain on the balance sheet of the issuing corporation (i.e., no SPE is created). -> Which of the following type of debt obligation most likely protects bondholders when the assets serving as collateral are non-performing?

A covered bond is a debt obligation backed by a segregated pool of assets called a “cover pool.” When the assets that are included in the cover pool become non-performing (i.e., the assets are not generating the promised cash flows), the issuer must replace them with performing assets.

Credit enhancement. Can be either internal or external

(internal e.g., overcollateralization, in which the collateral pledged has a value greater than the par value of the debt issued. One limitation of this method of credit enhancement is that the additional collateral is also the underlying assets, so when asset defaults are high, the value of the excess collateral declines in value.

cashreserve fund. A cash reserve fund is cash set aside to make up for credit losses on the underlying assets
an excess spread account. the yield promised on the bonds issued is less than the promised yield on the assets supporting the ABS. This gives some protection if the yield on the financial assets is less than anticipated. If the assets perform as anticipated, the excess cash flow from the collateral can be used to retire (pay off the principal on) some of the outsta nding bonds
divide a bond issue into tranches (French for slices) with different seniority of claims. The most senior tranches in this structure can receive very high credit ratings because the probability is very low that losses will be so large that they cannot be absorbed by the subordinated tranches. The subordinated tranches must have higher yields to compensate investors for the additional risk of default. This is sometimes referred to as waterfall structure because available funds first go to the most senior tranche of bonds, then to the next-highest priority bonds, and so forth.

External credit enhancement

surety bonds/bank guarantees: issued by insurance companies and are a promise to make up any shortfall in the cash available to service the debt
letters of credit from financial institutions. a promise to lend money to the issuing entity if it does not have enough cash to make the promised payments on the covered debt
While all three of these external credit enhancements increase the credit quality of debt issues and decrease their yields, deterioration of the credit quality of the guarantor will also reduce the credit quality of the covered issue.

Taxation of bond income

Income tax. Most often, the interest income paid to bondholders is taxed as ordinary income at the same rate as wage and salary income. The interest income from bonds issued by municipal governments in the United States, however, is most often exempt from national income tax and often from any state income tax in the state of issue.
Capital tax. When a bondholder sells a coupon bond prior to maturity, it may be at a gain or a loss relative to its purchase price. Such gains and losses are considered capital gains income (rather than ordinary taxable income). Capital gains are often taxed at a lower rate than ordinary income. Capital gains on the sale of an asset that has been owned for more than some minimum amount of time may be classified as long-term capital gains and taxed at an even lower rate
Pure-discount bonds and other bonds sold at significant discounts to par when issued are termed original issue discount (OID) bonds. Because the gains over an OID bond’s tenor as the price moves towards par value are really interest income, these bonds can generate a tax liability even when no cash interest payment has been made. Meaning, the original issue discount tax provision requires the investor to include a prorated portion of the original issue discount in his taxable income every tax year until maturity. The original issue discount is equal to the differ- ence between the bond’s par value and its original issue price.

Pure discount bond does not reduce tax, but annualises them

Sales of newly issued bonds are referred to as primary market transactions. Newly issued bonds can be registered with securities regulators for sale to the public, a public offering, or sold only to qualified investors, a private placement.

A public offering of bonds in the primary market is typically done with the help of an investment bank. The investment bank has expertise in the various steps of a public offering, including:

Determining funding needs.
Structuring the debt security.
Creating the bond indenture.
Naming a bond trustee (a trust company or bank trust department).
Registering the issue with securities regulators.
Assessing demand and pricing the bonds given market conditions.
Selling the bonds.

Bonds can be sold through an underwritten offering or a best efforts offering. In an underwritten offering, the entire bond issue is purchased from the issuing firm by the investment bank, termed the underwriter in this case. While smaller bond issues may be sold by a single investment bank, for larger issues, the lead underwriter heads a syndicate of investment banks who collectively establish the pricing of the issue and are responsible for selling the bonds to dealers, who in turn sell them to investors. The syndicate takes the risk that the bonds will not all be sold.

A new bond issue is publicized and dealers indicate their interest in buying the bonds, which provides information about appropriate pricing. Some bonds are traded on a when-issued basis in what is called the grey market. Such trading prior to the offering date of the bonds provides additional information about the demand for and market clearing price (yield) for the new bond issue.

In a best efforts offering, the investment banks sell the bonds on a commission basis. Unlike an underwritten offering, the investment banks do not commit to purchase the whole issue (i.e., underwrite the issue). Some bonds, especially government bonds, are sold through an auction.

US Treasuries

Securities are sold through single price auctions with the majority of purchases made by primary dealers that participate in purchases and sales of bonds with the Federal Reserve Bank of New York to facilitate the open market operations of the Fed.
Individuals can purchase U.S. Treasury securities through periodic auctions as well, but are a small part of the total.
In a shelf registration, a bond issue is registered with securities regulators in its aggregate value with a master prospectus. Bonds can then be issued over time when the issuer needs to raise funds. Because individual offerings under a shelf registration require less disclosure than a separate registration of a bond issue, only financially sound companies are granted this option. In some countries, bonds registered under a shelf registration can be sold only to qualified investors.

Secondary bond markets

the trading of previously issued bonds. While some government bonds and corporate bonds are traded on exchanges, the great majority of bond trading in the secondary market is made in the dealer, or over-the-counter, market. Dealers post bid (purchase) prices and ask or offer (selling) prices for various bond issues. The difference between the bid and ask prices is the dealer's spread. The average spread is often between 10 and 12 basis points but varies across individual bonds according to their liquidity and may be more than 50 basis points for an illiquid issue
Bond trades are cleared through a clearing system, just as equities trades are. Settlement (the exchange of bonds for cash) for government bonds is either the day of the trade (cash settlement) or the next business day (T + 1). Corporate bonds typically settle on T + 2 or T + 3, although in some markets it is longer
One example of a secondary market transaction in bonds is a tender offer, in which an issuer offers to repurchase some of its outstanding bonds at a specified price. Typically, a tender offer involves bonds that are trading at a discount. For example, if a corporate bond is trading for 90% of par value, the company might offer to repurchase part of the issue for a higher price (say 93% of par value). This has advantages for both the issuer and the bondholders. The bondholders can receive a higher price for their bonds than they can currently obtain in the market, and the issuer can pay less than face value to retire the bonds.

Returns of a bond

three sources of returns from investing in a fixed-rate bond

1. Coupon and principal payments.

2. Interest earned on coupon payments that are reinvested over the investor’s holding period for the bond (usually assumed as the same as YTMon the bond)

3.Any capital gain or loss if the bond is sold prior to maturity.

Bond cash flows and contingencies

Bullet structure is the norm. Periodic interest payments (coupon payments) are made over the life of the bond, and the principal value is paid with the final interest payment (tgt called ballon payment) at maturity

Amortizing loan, A loan structure in which the periodic payments include both interest and some repayment of principal (the amount borrowed). If fully amortizing, principal is fully paid off when last payment is made. E.g., automobile loans and home loans; if partially amortizing, the final payment includes just the remaining unamortized principal amount

A bond that is fully amortized is characterized by a fixed periodic payment schedule that reduces the bond’s outstanding principal amount to zero by the maturity date.

Sinking fund provisions provide for the repayment of principal through a series of payments over the life of the issue rather than the full principal amount. For example, a 20-year issue with a face amount of $300 million may require that the issuer retire $20 million of the principal every year beginning in the sixth year. The price at which bonds are redeemed under a sinking fund provision is typically par but can be different from par. If the market price is less than the sinking fund redemption price, the issuer can satisfy the sinking fund provision by buying bonds in the open market with a par value equal to the amount of bonds that must be redeemed. This would be the case if interest rates had risen since issuance so that the bonds were trading below the sinking fund redemption price.

Pros: bonds with a sinking fund provision have less credit risk because the periodic redemptions reduce the total amount of principal to be repaid at maturity
Cons: can be a disadvantage to bondholders when interest rates fall.

A bondholder would suffer a loss if her bonds were selected to be redeemed at a price below the current market price. This means the bonds have more reinvestment risk because bondholders who have their bonds redeemed can only reinvest the funds at the new, lower yield (assuming they buy bonds of similar risk)
Reinvestment risk: the uncertainty about the interest to be earned on cash flows from a bond that are reinvested in other debt securities. In the case of a bond with a sinking fund, the greater probability of receiving the principal repayment prior to maturity increases the expected cash flows during the bond’s life and, therefore, the uncertainty about interest income on reinvested funds.

Coupon structures besides a fixed-coupon structure

!!Floating-rate notes (FRN)/floaters 加息神器; the market rate of interest is called the market reference rate (MRR). PMT = MRR+Margin. E.G., Libor +75 bps annually. Typically paid quarterly and are based on quarterly (90-day) reference date. May have a cap, which protects the issuer; and a floor, which benefits the bondholder. The new 1-year rate at that time will determine the rate of interest paid at the end of the next year. 一定用的是前一个时间的mrr+margin
!!An inverse floater: has a coupon rate that increases when the reference rate decreases and decreases when the reference rate increases.

when interest rates rise, the coupon rate on an inverse floater decreases. Thus, inverse floaters are favored by investors who believe that interest rates will decline, not rise.
Purchasing floating-rate debt is attractive to some institutions that have variable-rate sources of funds (liabilities), such as banks.
This allows these institutions to avoid the balance sheet effects of interest rate increases that would increase the cost of funds but leave the interest income at a fixed rate.
Investors who want exposure to private sector debt in these markets can obtain it indirectly by investing in financial institutions that lend to private-sector borrowers.

Libor London Interbank Offered Rate. The fact that LIBOR is not based on actual transactions, and has been subject to manipulation by bankers reporting their expected interbank lending rates, has led to an effort to replace LIBOR with market-determined rates
Thus, alternatives to LIBOR must be found for each of the various currencies involved. In the United States, the new rate will likely be the structured overnight financing rate (SOFR), which is based on the actual rates of repurchase (repo) transactions and reported daily by the Federal Reserve.
For floating-rate bonds, the market reference rate must match the frequency with which the coupon rate on the bond is reset. For example, a bond with a coupon rate that is reset twice each year would use a six-month MRR.

! Step-up coupon bonds. The coupon rate increases according to a predetermined schedule.

Typically, step-up coupon bonds have a call feature that allows the firm to redeem the bond issue at a set price at each step-up date. If the new higher coupon rate is greater than what the market yield would be at the call price, the firm will call the bonds and retire them.
This means if market yields rise, a bondholder may, in turn, get a higher coupon rate because the bonds are less likely to be called on the step-up date, which can be viewed as having some protection against interest rate rise
A is incorrect because a bond with a step-up coupon is one in which the coupon, which may be fixed or floating, increases by specified margins at specified dates. This feature benefits the bondholders, not the issuer, in a rising interest rate environment because it allows bondholders to receive a higher coupon in line with the higher market interest rates.

A credit-linked coupon bond. Coupon rate is linked to rise and fall of credit rating. A higher coupon would actually make the financial situation of the issuer worse.

Because credit ratings tend to decline the most during recessions, credit-linked coupon bonds may thus provide some general protection against a poor economy by offering increased coupon payments when credit ratings decline.

A payment-in-kind (PIK) bond. Allows to increase principal amount of the outstanding bonds, or to pay bond interest with more bonds. Firms do so expect less cash flow., oft because of high levels of debt financing (leverage). These typically ahve higher yields because of a lower perceived credit quality
Deferred coupon bond/split coupon bond. Coupon pmt only begins after some time, this correlates with the timing of coupon interest pmt. Might be appropriate for financing a large project that will only be completed later.
An index-linked bond. Commodity/equity/inflation index-linked (linker). Some are principal protected bonds, not paying less even as index has decreased

Indexed-annuity bonds. Fully amortizing bonds with the periodic payments directly adjusted for inflation or deflation.
Indexed zero-coupon bonds. The payment at maturity is adjusted for inflation.
Interest-indexed bonds. The coupon rate is adjusted for inflation while the principal value remains unchanged.
!! Capital-indexed bonds (or principal-indexed). This is the most common structure. An example is U.S. Treasury Inflation Protected Securities(TIPS). The coupon rate remains constant, and the principal value of the bonds is increased by the rate of inflation (or decreased by deflation).

Contingency provision (call benefits issuer, put benefits bondholder)

A contingency provision in a contract describes an action that may be taken if an event (the contingency) actually occurs. Contingency provisions in bond indentures are referred to as embedded options, embedded in the sense that they are an integral part of the bond contract and are not a separate security. Some embedded options are exercisable at the option of the issuer of the bond and, therefore, are valuable to the issuer; others are exercisable at the option of the purchaser of the bond and, thus, have value to the bondholder.

A call option gives the issuer the right to redeem all or part of a bond issue at a specific price (call price) if they choose to; often to provide refinancing choice to issuers in case of lower interest rate or increasing quality, and sold with higher yield to compensate for reinvestment risk

Bond without these are called straight or option-free bonds
When it is not callable, it is called call protection. This 5-year period is also referred to as a lockout period, a cushion, or a deferment period.

2017 first call date. Amount by which the call price is above par = call premium. 2022, fist par call date.

A call option has value to the issuer because it gives the issuer the right to redeem the bond and issue a new bond(borrow) if the market yield on the bond declines.
This could occur either because interest rates in general have decreased or because the credit quality of the bond has increased(default risk has decreased). So that they can issue new bond at lower yield thus less cost

This is analogous to refinancing a home mortgage when mortgage rates fall in order to reduce the monthly payments. A callable bond must offer a higher yield because reinvestment risk is disadvantageous to them.

Three styles of exercise for callable bonds:

1. American style-the bonds can be called anytime after the first call date.
2. European style-the bonds can only be called on the call date specified.
3. Bermuda style-the bonds can be called on specified dates after the first call date, often on coupon payment dates.

To avoid the higher interest rates required on callable bonds but still preserve the option to redeem bonds early when corporate or operating events require it, issuers introduced bonds with make-whole call provisions.

Make-whole call provisions.

A make-whole call provision requires the issuer to make a lump sum payment to the bondholders based on the present value of the future coupon payments and principal repayments not paid because of the bond being redeemed early by the issuer.
The call price is not fixed but includes a lump-sum payment based on the present value of the future coupons the bondholder will not receive if the bond is called early.
With a make-whole call provision, the calculated call price is unlikely to be lower than the market value of the bond. Therefore the issuer is unlikely to call the bond except when corporate circ*mstances, such as an acquisition or restructuring, require it. The make-whole provision does not put an upper limit on bond values when interest rates fall as does a regular call provision. The make-whole provision actually penalizes the issuer for calling the bond. The net effect is that the bond can be called if necessary, but it can also be issued at a lower yield than a bond with a traditional call provision.

Putable bonds. A put option gives the bondholder the right to sell the bond back to the issuing company at a prespecified price, typically par. to protect downside and sold at a premium

Bondholders are likely to exercise such a put option when the fair value of the bond is less than the put price because interest rates have risen or the credit quality of the issuer has fallen. Usu. sold at a premium as it benefits holders.
Relative to a one-time put bond that incorporates a single sellback opportunity, a multiple put bond offers more frequent sellback opportunities, thus providing the most benefit to bondholders.

Convertible bonds

Convertible bonds, typically issued with maturities of 5–10 years, give bondholders the option to exchange the bond for a specific number of shares of the issuing corporation's common stock. Usu. issued with lower yields compared to straight bonds.
For holder: Downside protection of a bond, but at a reduced yield, and the upside opportunity of equity shares. What is beneficial to the bondholder is trader at a higher price
For issuer: a lower yield (interest cost) compared to straight bonds.

a conversion provision (convertible bond) is beneficial to the bondholders. If the issuing company’s share price increases, the bondholders have the right to exchange the bond for a specified number of common shares in the issuing company.
Some terms related to convertible bonds:

Conversion price
Conversion ratio. Equal to the par value of the bond divided by the conversion price. If a bond with a $1,000 par value has a conversion price of $40, its conversion ratio is 1,000 / 40 = 25 shares per bond

Conversion value. This is the market value of the shares that would be received upon conversion. A bond with a conversion ratio of 25 shares when the current market price of a common share is $50 would have a conversion value of 25 × 50 = $1,250. Some issuers might enforce a call option in order to prevent the case where the holder does not want to convert as coupon is still higher than dividend yield.

Warrants

An alternative way to give bondholders an opportunity for additional returns when the firm's common shares increase in value is to include warrants with straight bonds when they are issued. Warrants give their holders the right to buy the firm’s common shares at a given price over a given period of time.
As an example, warrants that give their holders the right to buy shares for $40 will provide profits if the common shares increase in value above $40 prior to expiration of the warrants. For a young firm, issuing debt can be difficult because the downside (probability of firm failure) is significant, and the upside is limited to the promised debt payments. Including warrants, which are sometimes referred to as a “sweetener,” makes the debt more attractive to investors because it adds potential upside profits if the common shares increase in value

Contingent Convertible Bonds （Cocos）

bonds that convert from debt to common equity automatically if a specific event occurs. Some European banks have issued them.
Banks must maintain specific levels of equity financing. If a bank’s equity falls below the required level, they must somehow raise more equity financing to comply with regulations. CoCos are often structured so that if the bank’s equity capital falls below a given level, they are automatically converted to common stock.
This has the effect of decreasing the bank’s debt liabilities and increasing its equity capital at the same time, which helps the bank to meet its minimum equity requirement.

Value of a coupon bond = sum of PV of all the bond's promised cash flows

YTM=market Discount rate/ price you pay for the money you lend: Interest rate, or market discount rate, is Yield to Maturity (YTM)

Difference with Coupon rate

YTM (also known as redemption yield): % return for a bond assuming held to maturity. It is the sum of all remaining coupon payments; changes depending on its market value & how many payments remain to be made . It is an estimated rate of return, assuming each interest pmt is reinvested at the same ist rate; thus, it includes the coupon rate. YTM is caculated as if the discount rate for every bond cash flow is the same, which actually rather depend on the time period in which the bond payment will be made, namely spot rates. Spot rates are the actual market discount rates for a single payment to be received future. Discount rates for zero-coupon bons are spot rates and we refer to as zero-coupon rates. Market interest rates are spot rates;when interest rate rises, bond value decreasesbecause the present value of a bond’s promised cash flows decreases when a higher discount rate is used

To obtain the spot yield curve, a bond analyst would prefer to use the most recently issued and actively traded government bonds. Such bonds will have similar liquidity as well as fewer tax effects because they will be priced closer to par value. Corporate bond has worse liquidity as investors buy and hold

Price calculated with spot rates is also called no-arbitrage price, as if it's priced differently, there will be a profit opportunity from arbitrage from bonds

Bond prices:

Matrix pricing

Coupon rate: Annual amount of interest receivable from bond; it is yearly
YTM matters more to a bond trader, and coupon rate matters more to an investor. At the time of purchase, the two are the same. For a bond trader, there is potential P/L generated by market price change.

If bond is purchased at par/face value, YTM = coupon rate
If purchased at a discount, YTM > Coupon rate
If purchased at a premium, YTM < Coupon rate
YTM is the average return % over its remaining lifetime.

It is the effective rate of return based on the actual market value of the bond. As interest rate rise or fall, the coupon rate offered by gov or corp might be higher or lower, and the market value of the bond might change depending on how attractive investors find the bond under new interest rate conditions
yield and price are inversely proportional and move in opposite

Value and YTM, if we know one, we can calculate another:

This is kind of why, market value/YTM does not matter to a bond investor, as individual investor usually rely on coupon as a source of profit, and they can not trade as bond trader, and to watch the bond market value as frequently.

If market discount rate is 8%, lower than 10%. it would sell at a preimum of 134.2, why? above it's par value. When bond yields decreases, the present value of its payments, its market value, increases. (lower discount rate means lower risk and safer investment; so HY almost always has cheaper market value than IG)

Valuing semis

If calculating a semi-annual bond, we change the PMT to 50, rather than 100 for the annual payment. Remember to also divide YTM by 2, and increase N from 10 t0 20.

Conversely, need to double YTM to get full year YTM

Valuing zero-coupon bonds

The value of a zero-coupon bond is simply the present value of the maturity payment.

With a discount rate of 3% per period, a 5-period zero-coupon bond with a par value of $1,000 has a value of:

Relationships

We can summarize the relationships between price and yield as follows:

1. At a point in time,a decrease(increase) in a bond's YTM will increase(decrease) its price.

2. If a bond's coupon rate is greater than its YTM, its price will be at a premium to par value. If a bond's coupon rate is less than its YTM, its price will be at a discount to par value.

3. The percentage decrease in value when the YTM increases by a given amount is smaller than the increase in value when the YTM decreases by the same amount (the price-yield relationship is convex).

4. Other things equal, the price of a bond with a lower coupon rate is more sensitive to a change in yield than is the price of a bond with a higher coupon rate.

5. Other things equal, the price of a bond with a longer maturity is more sensitive to a change in yield than is the price of a bond with a shorter maturity.

Relationship Price V.S. Maturity - constant-yield price trajectory

Prior to maturity,a bond can be selling at a significant discount or premium to par value. However, regardless of its required yield, the price will converge to par value as maturity approaches.

Financial statement impact of issuing bond

Leases

Pension plans

Yield measures

The number of bond coupon payments per year is referred to as the periodicity of a bond.A bond with a periodicity of 2 will have its yield to maturity quoted on a semiannual bond basis. For a given coupon rate, the greater the periodicity, the more compounding periods, and the greater the annual yield.

Adjusting periodicity for comparability

It may be necessary to adjust the quoted yield on a bond to make it comparable with the yield on a bond with a different periodicity.This is illustrated in the following example.

4% on a semiannual bond basis is an effective yield of 2% per 6-month period.