Chapter 6: Bonds

Coupon Payment

(1) _____: CPN = (Coupon Rate X Face Value) / (Number of Coupon Payments per Year) -This name comes from coupon structure

Yield to Maturity of an n-Year Zero-Coupon Bond

(2) _____ = 1 + YTM_sub_n = (Face Value / Price)^(1 / n)

Interest + Principle, maturity, bondholder, creditor, issuer

*Bond Terminology*... As you can see from Figure 1, historically, on a payment date, the holder of the bond would clip off the next coupon for the next payment and present it for payment. It follows that the interest payments on the bond are called *coupon payments*. -A bond is a financial obligation of an entity (ISSUER) that promises to pay a specified sum of money (___1___) to a LENDER (CREDITOR) at a specified future dates (maturity). -Like a borrower and a lender. But instead of a lender, you have a ___2___ or a ___3___ (though ___2___ is more common), and instead of a borrower you have an ___4___.

Bills, Notes, Bonds

*Bond Types Based On the Maturity* -T-___1___- maturity is up to one year: 4, 13, 26, and 52 weeks -T-___2___- maturity is one to 10 years -T-___3___-maturity is more than 10 years =T stands for treasury (meaning government is borrowing) =Structure between these are identical

Clean Price, Accrued Interest

*Clean and Dirty Prices for Coupon Bonds*... ___1___ = Cash (Dirty) Price - Accrued Interest ___2___ = Coupon Amount X (Days Since Last Coupon Payment / Days in Current Coupon Period)

Higher yield, Lower yield

*Figure 2: Zero-Coupon Yield Curve Consistent with the Bond Prices in Example 1* -Longer maturity = ___1___ -Shorter maturity = ___2___

inversely related

*Why Bond Prices Change? Interest rates change!* -As Figure 2 shows, *interest rates are _____ to bond prices* --Bond prices increase when interest rates decrease --Bond prices decrease when interest rates increase

notation

*_____* -CPN = coupon payment on a bond -FV = face value of a bond -n = number of periods -P = initial price of a bond -PV = present value -y = yield to maturity -YTM = yield to maturity -YTM_sub_n = yield to maturity on a zero-coupon bond with n periods to maturity

Coupon Bond Cash Flows

*_____* While an investor's return on a zero-coupon bond comes from buying it at a discount to its principal value, the return on a coupon bond comes from two sources: (1) any difference between the purchase price and the principal, and (2) its periodic coupon payments.

Bond Prices and Interest Rate Risk

*_____* (Bond Prices and Interest Rate Risk) -Unpredictable changes in interest rates affect bond prices. This is called interest rate risk. -Bonds with different characteristics will respond differently to changes in interest rates --Investors view long-term bonds to be riskier than short-term bonds --Investors view lower coupon paying bonds to be riskier than higher coupon paying bonds

Bond Prices

*_____* (Bond Prices) -Zero-coupon bonds always trade for a discount -Coupon bonds may trade at a discount or at a premium -Most issuers of coupon bonds choose a coupon rate so that the bonds will initially trade at, or very close to, par -After the issue date, the market price of a bond changes over time

Bond Ratings

*_____* (Bond Ratings) -Investment-grade bonds -Speculative bonds --junk bonds --high-yield bonds -The rating depends on --the risk of bankruptcy --bondholders' claim to assets in the event of bankruptcy

Coupon Bond Price Quotes

*_____* (Coupon Bond Price Quotes) -Because bonds can have different par value, the general practice is to quote the price of a bond as % of its par value. -Example: Quoted dollar price=102 , par value=$5,000 therefore bond's trading price=5,000*1.02=$5,100

Price of Zero-Coupon Bonds

*_____* (Price of Zero-Coupon Bonds) -Example: Treasury bills are zero-coupon U.S. government bonds with maturity of up to one year Price for zero coupon bonds = Face Value / (1 + YTM)^n -The bond's price= the present value of its face amount @ the bond's yield to maturity. =Formula is just like PV = C / (1 +r)^n

Example 7

*_____*... *Evaluate* *If a bond's yield to maturity does not change, then the rate of return of an investment in the bond equals its yield to maturity even if you sell the bond early*.

Interest Rate Risk and Bond Prices

*_____*... Bonds with higher coupon rates - because they pay higher cash flows up-front - are less sensitive to interest rate changes than otherwise identical bonds with lower coupon rates^4. Table 4 summarizes this conclusion... ^4 The *duration* of a bond measures its sensitivity to interest rate changes. A full discussion of the concept of duration is beyond the scope of this text.

Corporate Bond Yields

*_____*... Due to credit risk, the cash flows that a purchaser of a corporate bond actually *expects* to receive may be less than that amount... Because the yield to maturity of GM's bonds is computed by comparing the price to the *promised* cash flows, the yield to maturity *increased* as the probability of being paid as promised decreased. This example highlights the following general truths: 1. Investors pay less for bonds with credit risk than they would for an otherwise identical default-free bond. 2. Because the yield of maturity for a bond is calculated using the promised cash flows instead of the *expected* cash flows, the yield of bonds with credit risk will be higher than that of otherwise identical default-free bonds. These two points lead us to an important conclusion: *the yield to maturity of a default-able bond is not equal to the expected return of investing in the bond*. The promised cash flows used to determine the yield to maturity are always higher than the expected cash flows investors use to calculate the expected return. As a result, the yield to maturity will always be higher than the expected return of investing in the bond. *Moreover, a higher yield to maturity does not necessarily imply that a bond's expected return is higher*.

Corporate Yield Curves

*_____*... Figure 6 shows the average yields of U.S. corporate coupon bonds with three different Standard & Poor's bond ratings: two curves are for investment-grade bonds (AAA and BBB) and one is for junk bonds (B). Figure 6 also includes the U.S. (coupon-paying) Treasury yield curve.

Interest Rate Changes and Bond Prices

*_____*... In our example, the price of the 8% bond will drop to below face value ($1000), so it will be trading at a discount (also called trading *below par*). If the bond trades at a discount, an investor who buys the bond will earn a return both from receiving the coupons *and* from receiving a face value that exceeds the price paid for the bond... A bond that pays a coupon can also trade at a premium to its face value (trading *above par*)... *a bond trades at a premium whenever its yield to maturity is less than its coupon rate*... *as interest rates and bond yields rise, bond prices will fall, and vice versa, so that interest rates and bond prices always move in the opposite direction*. Table 3 summarizes the relationship between interest rates and bond prices.

Why Bond Prices Change

*_____*... Most issuers of coupon bonds choose a coupon rate so that the bonds will *initially* trade at, or very close to, *par*...

Yield to Maturity of a Coupon Bond

*_____*... The yield to maturity of the bond is the *single* discount rate that equates the present value of the bond's remaining cash flows to its current price... (3) _____: P = CPN X 1 / y (1 - 1 / (1 + y)^N) + FV / (1 + Y)^N = Present Value of all of the periodic coupon payments + Present Value of the Face Value repayment using the YTM (y)... When we calculate a bond's yield to maturity by solving Eq. 3, the yield we compute will be a rate *per coupon interval*. However, yields are typically quoted as APRs, so we multiply by the number of coupons per year, thereby converting the answer into an APR quote with the same compounding interval as the coupon rate. -The relationship between the coupon rate and the bond's _____ determines if the bond will sell at a *premium*, a *discount*, or *at par*.

Risk-Free Interest Rate

*_____s*... we will often refer to the yield to maturity of the appropriate maturity, zero-coupon risk-free bond as *the* _____. Some financial professionals also use the term *spot interest rates* to refer to these... -The yield curve plots the _____s for different maturities. (See Figure 6.2 Zero-Coupon Yield Curve Consistent with the Bond Prices in Example 6.1)

fixed-coupon bonds

-Pay coupon semi-annually -Interest=f(Coupon payments + Bond Price-Par value) =_____ are known as "plain vanilla" bonds due to being straight-forward

zero-coupon bond

A bond that makes only one payment at maturity. -No coupon payments -Interest = *Bond price* - Par Value

dirty price or invoice price

A bond's actual cash price.

clean price

A bond's cash price less an adjustment for accrued interest, the amount of the next coupon payment that has already accrued.

zero-coupon yield curve

A plot of the yield of risk-free zero-coupon bonds (STRIPS) as a function of the bond's maturity date.

discount

A price at which bonds trade that is less than their face value. -Coupon Rate < YTM -We say the bond trades "below par" or "at a _____"

par

A price at which coupon bonds trade that is equal to their face value. -We say the bond trades At _____. -Coupon Rate = YTM

premium

A price at which coupon bonds trade that is greater than their face value. -We say the bond trades "above par" or "at a _____" -Coupon Rate > YTM

Treasury notes

A type of U.S. Treasury coupon security, currently traded in financial markets, with original maturities from one to ten years.

Treasury bonds

A type of U.S. Treasury coupon security, currently traded in financial markets, with original maturities of more than ten years -Issuer is the US government -(Default-free) Risk-free bonds!! -Treasury bills, T-notes and T-bonds

speculative bonds, junk bonds, or high-yield bonds

Bonds in one of the bottom five categories of creditworthiness (below investment grade) that have a high risk of default.

investment-grade bonds

Bonds in the top four categories of credit-worthiness with a low risk of default.

corporate bonds

Bonds issued by corporations. -Issuers are the corporations -Risky bonds!! -Risk is the creditor risk -Credit Risk is the risk of default, so that the bond's cash flows are not known with certainty. -Corporations with higher default risk will need to pay higher coupons to attract buyers to their bonds. -Corporate Bond Yields --Yield to maturity of a defaultable bond is higher than yield to maturity of Treasury bonds. --Yields on Treasury securities such as T-bills, T-notes, T-bonds are risk-free rates in the economy. -Yield = RF + Risk Premium

coupon bonds

Bonds that pay regular coupon interest payments up to maturity, when the face value is also paid. *_____*... As Table 2 indicates, two types of U.S. Treasury coupon securities are currently traded in financial markets: *Treasury notes*... and *Treasury bonds*...

present value

Price means _____! Calculate price -> calculate _____!

bond certificate

States the terms of a bond as well as the amounts and dates of all payments to be made.

default spread or credit spread

The difference between the risk-free interest rate on U.S. Treasury notes and the interest rates on all other loans. The magnitude of the credit spread will depend on investors' assessment of the likelihood that a particular firm will default -Credit spreads = yield on corporate bond - yield on T-securities

maturity date

The final repayment date of a bond. Payments continue until this date.

face value, par value, principal amount

The notional amount of a bond used to compute its interest payments. The face value of the bond is generally due at the bond's maturity. Usually standard increments, such as $1000.

coupons

The promised interest payments of a bond, paid periodically until the maturity date of the bond. (Coupon Rate X Face Value) / (Number of Coupon Payments per Year) -99% of bonds are semiannual

yield to maturity (YTM) ("or just the *yield*)

The rate of return of an investment in a bond that is held to its maturity date, or the discount rate that sets the present value of the promised bond payments equal to the current market price of the bond. =*This is NOT the same as coupon rate!*

credit risk

The risk of default by the issuer of any bond that is not default free; it is an indication that the bond's cash flows are not known with certainty.

term

The time remaining until the final repayment date of a bond.

Treasury bills

Zero-coupon bonds, issued by the US government, with a maturity of up to one year.

pure discount bonds

Zero-coupon bonds.

SUMMARY OF CHAPTER 6 BONDS

_____ (SUMMARY OF CHAPTER 6 BONDS) -Bond price= PV(YTM, MATURITY,COUPON PAYMENTS, FACE VALUE) -Bond's YTM=RATE(MATURITY, COUPON PAYMENTS, -PRICE,FACE VALUE) -YTM IS THE EXPECTED MARKET INTEREST RATE --IF ANNUAL COUPON BOND: USE YTM PER YEAR --IF SEMI-ANNUAL COUPON BOND: USE YTM/2 PER SEMI-ANNUAL --YTM OF COPRORATIONS=YTM OF TREASURY BOND(RISK-FREE (RF))+ RISK PREMIUM --RISK PREMIUM DEPENDS ON CREDIT RATINGS ---HIGH CREDIT RATING IS BETTER ---LOW CREDIT RATING MEANS BONDS ARE JUNK. -COUPON RATE IS THE ACTUAL INTEREST RATE ON THE BOND -COUPON PAYMENTS=(COUPON RATE*FACE VALUE)/# OF PAYMENTS IN A YEAR --ANNUAL COUPONS: COUPON PAYMENTS=(COUPON RATE*FACE VALUE)/1 --SEMI-ANNUAL COUPONS: COUPON PAYMENTS=(COUPON RATE*FACE VALUE)/2 -MATURITY --IF ANNUAL COUPON BOND: USE YEARS --IF SEMI-ANNUAL COUPON BOND: USE YEARS*2 -FACE VALUE --IF IT IS NOT GIVEN IN THE QUESTION, ASSUME IT IS $1000

Price

_____ means present value! Calculate _____ -> calculate present value!