CHAPTER 10

1. CHAPTER 10 Bond Prices and Yields

2. The Goals of Chapter 10 • Discuss different characteristics in bond contracts (some content was discussed in Ch 2) • Review the pricing of bonds • Analyze the price-yield relationship for bonds • Discuss the default risk of corporate bonds • Introduce the term structure of interest rates ※Why talking about bond markets first? • Bond markets is even more important than stock markets in terms of size and trading volume • By the end of 2010, the size of the global bond market is estimated as $158 trillion, of which the size of the outstanding U.S. bond market was $51 trillion • The size of the world stock market is estimated to be $54 trillion by the end of 2010

3. 10.1 BOND CHARACTERISTICS

4. Bond Characteristics • Bond: • A security that obligates the issuer (the borrower) to make specified payments to the holder (the lender) over a period of time • Bond indenture (債券契約) • Maturity date • Face or par value (the amount at which the issuer needs to pay the holder at maturity) • Coupon rate • Abond’s annual interest payment per dollar of the par value • Semiannual or annual interest payments • Zero-coupon bond (no coupon payments, sold at a discount)

5. Treasury Bonds • Maturities • For T-bills, the maturities are less than one year • T-note maturities range up to 10 years • T-bond maturities range from 10 to 30 years • Both T-bonds and T-notes are issued in denominations of $1,000 (typically) or more • Both with semiannual coupon payments • Bid and ask prices are quoted as a percent of the par value (see the next slide) • For T-bills (zero-coupon bonds) • Bid and asked prices are quoted in hundredths, which are annual discount rates of the face value • T-bills, T-notes, and T-Bonds are traded over the counter, i.e., in a dealer market

6. Prices and Yields of U.S. Treasuries ※ The quotation methods for T-bonds, T-notes, and T-bills are already introduced in Ch2 ※ The yield to maturity (as well as the yield to call) according to the asked price will be discussed in detail on Slide 10-30

7. Treasury Bonds • Quoted (clean or flat) price vs. Invoice (dirty) price • If a bond is purchased between coupon payment dates, the buyer must pay the invoice price, which equals the quoted price plus the accrued interest • Interests are paid in arrear, i.e., paid at the end of each period, and quoted price does not include interest accrued • So new bond holders should pay previous bond holders not only the quoted price but also the accrued interest • Suppose the semiannual coupon payments is $40, and the bond is quoted as $990. If 30 days have passed since the last coupon payment, and there are 182 days in this semiannual coupon period

8. Treasury Bonds • The dirty price is in essence the sum of the present values of future coupon and principal payments • In fact, the dirty prices are calculated first and next the accrued interest between coupon payment dates is deducted from the dirty price to derive the clean price • The reason to distinguish clean and dirty prices • Clean prices are more stable over time than dirty prices–when clean prices change, it usually reflects an economic reason, for instance, a change in interest rates or in the bond issuer's credit quality • Dirty prices, on the other hand, change day to day depending on where the current date is in relation to the coupon payment dates, in addition to any economic reasons

9. Corporate Bonds • Listing of corporate bonds (on the next slide) • Registered vs. non-registered • Bonds issued in the U.S. today are registered, meaning that the issuing firm keeps records of the owners (helpful to tax authorities for tax collection) • Bearer bonds (無記名債券) are bonds without any record of ownership. The physical possession of the bond certificate is the only evidence of ownership (common in Eurobond markets) • It is useful for investors who wish to retain anonymity • Recovery of the value of a bearer bond in the event of its loss, theft, or destruction is usually impossible • Call provisions(贖回權) (callable bonds) • Corporate bonds that may be redeemed by the issuer at a specified call price during the call period

10. Corporate Bonds • ※ The “rating” column is the estimation of the default risk (or called credit risk) associated with the bond offered by three major bond rating agencies (the default risk will be discussed in greater detail in Section 10.5) • ※ Investment grade bonds (rated BBB or above) vs. Speculative grade or junk bonds (rated BB or below)

11. Corporate Bonds • Triggered when bond market prices > call price (when interest rate decreases) • Refunding(借新償舊) strategy when the interest rate falls: Firms use funds from issuing new bonds (with lower interest costs) to buy back old bonds (with higher interest costs) • Advantage for firms: callable bonds should offer higher coupons (or be cheaper) than noncallable bonds • Put provision (賣回權)(puttable bonds) • The holder may choose to sell the bonds back to the issuer at a pre-specified put price on some date • This right is often exercised when the coupon rate is much lower than the prevailing interest rate (in this scenario, the bond is worth at a deep discount)

12. Corporate Bonds • It is a advantage for holders, so puttable bonds should offer lower coupons (or be more valuable) than nonputtable bonds • Convertible provision(轉換權) (convertible bonds) • An option to exchange the bond for a specified number of shares of common stock of the issuing firm • The market conversion value is the current value of the shares for which the bond may be exchanged • The conversion premium is the excess of the bond price over its market conversion value • Convertible bondholders could benefit from price appreciation, so convertible bonds usually offer lower coupon rates than nonconvertible bonds

13. Corporate Bonds • Floating rate bonds(浮動利率型債券) • The interest payments (coupon rate) are adjusted according to some measure of market rates, e.g., the prevailing T-bill rate plus 2% • The 2% is called the yield spread, which reflects the issuer’s credit condition. A lower credit rating implies a higher yield spread • The advantage is that the coupon rate can reflect the change of the market situation, and thus the bond price is relatively stable than that of the fixed rate bond

14. Other Domestic Issuers • State or local governments • Municipal Bonds (interest payment is tax-exempt) • Government agencies • Federal Home Loan Bank Board • Farm Credit Agencies • Ginnie Mae • Fannie Mae • Freddie Mac ※ These bond securities are already introduced in Ch2

15. International Bonds • Foreign bonds • Issued by a borrower from a nation other than the nation in which the bond is sold, e.g., a German firm sells a dollar-denominated bond in the U.S. • Dollar-denominated foreign bonds are called Yankee bonds • Yen-denominated foreign bonds are called Samurai bonds • Pound-denominated foreign bonds are called Bulldog bonds • Eurobonds • Issued in the currency of one nation but sold in other national markets • Eurodollar bonds are dollar-denominated bonds sold outside the U.S. (not only in Europe) • Euroyen bonds are yen-denominated bonds sold outside Japan • Eurosterling bonds are pound-denominated bonds sold outside the U.K.

16. Innovations in the Bond Market • Inverse floaters(反向浮動利率型債券) • Similar to floating rate bonds except that the coupon rate on these bond falls when the prevailing interest rate rises • Benefit (suffer) doubly when rates fall (rise) • Asset-backed securities (資產基礎證劵) • Serviced by the income from a specified group of assets, like mortgage, auto, or credit card loans • A singer can issue ABS to borrow money by linking the coupon rate with the selling amount of his albums • Pay-in-kind bonds(實物支付型債券) • Issuers of pay-in-kind bonds may choose to pay interest either in cash or in newly issued bonds if they are short of cash

17. Innovations in the Bond Market • Catastrophe bonds (巨災債券) • Catastrophe: earthquake, hurricane, flood, etc • Holders receive higher coupon rates, but in the event of a catastrophe, the holders will give up all or part of their principal • This bond provides a way to transfer the catastrophe risk from insurance companies to the capital market • Indexed bonds (追蹤指數型債券) • Indexed bonds make payments that are tied to a general price index or the price of a particular commodity • Mexico had issued bonds with payments depending on the price of oil • The U.S. started issuing TIPS (Treasury Inflation Protected Securities) since 1997

18. Innovations in the Bond Market • The par value of the TIPS is adjusted according to the growth rate of the consumer price index (CPI) • Interest incomes of TIPS thus increase in proportion to the CPI and bring holders the same level of purchasing power • RORs on TIPS are real risk-free RORs • A TIPSwith three-year maturity, $1,000 par value, and 4% coupon rate paid annually

19. 10.2 BOND PRICING

20. Bond Pricing ※If Ct’s are constant, the above summation term represents a geometric series (等比級數), which can be evaluated by the corresponding formula as follows PB = theoretical value of the bond Ct = interest or coupon payments at period t T = number of periods to maturity r = one-period discount rate or one-period yield to maturity ※Annuity factor(r, T) is the sum of the PVs of $1 for each of T periods ※PV factor(r, T) is the PV of $1 at the end of T periods

21. Price of 8%, 30-yr. with yield at 10% Coupon = 8%× ½ × 1,000 = 40 (semiannual or per period) Discount Rate = 10% × ½ = 5% (semiannual or per period) Maturity = 30 years = 60 periods Par Value = 1,000

22. Yield at 6% or 8% Discount Rate = 3% or 4% (semiannual or per period) ※

23. The Inverse Relationship Between Bond Prices and Yields ※ Bond prices and discount yields (or discount interest rates or required rates of return) have an inverse relationship ※ When yields become high, the value of the bond will be low ※ When yields approach zero, the value of the bond approaches the sum of all promised cash flows

24. Price of Perpetual Bond • Perpetual bond (永續債券) • A bond with no maturity date, which means it pays a steady stream of coupon interest forever • Set T to be infinity in the bond pricing formula, which implies a permanent series of constant cash flows and the par value will never be paid off • As a result, the price of a perpetual bond equals C / r, where C is the coupon payment per period and r is the one-period discount rate or one-period yield

25. Valuing Bonds using Excel ※ PRICE(settlement date, maturity date, annual coupon rate, yield to maturity, redemption value as percent of par value, number of coupon payments per year, different day count convention): return the quoted (or clean) price ※ COUPDAYBS(settlement date, maturity date, number of coupon payments per year, different day count convention): return the number of days from the beginning of the coupon period to the settlement date ※ COUPDAYS(settlement date, maturity date, number of coupon payments per year, different day count convention): return the number of days in the coupon period that contains the settlement date ※ Different day count convention: 0 is 30/360 in USA; 1 is actual/actual; 2 is actual/360; 3 is actual/365; 4 is 30/360 in Europe)

26. 10.3 BOND YIELDS

27. Yield to Maturity • Yield to maturity (YTM) is the discount rate that makes the present value of a bond’s payments equal to its market price • 8% coupon rate, 30-year bond sold at $1,276.76: • YTM can be interpreted as the average rate of return if the bond is purchased today and held until maturity • Note that the financial press reports yield on an annualized basis, and annualizes the bond’s semiannual yield using the simple interest approach, resulting an annual percentage rate (APR) • Yields annualized using the simple interest approach are also called bond equivalent yields

28. Use Excel to calculate YTM ※ YIELD(settlement date, maturity date, annual coupon rate, bond (clean) price, redemption value as percent of par value, number of coupon payments per year, different day count convention) ※ The accurate formula in the above example should be “=YIELD(B3, B4, B5, B6, B7, B8, 1)”

29. Alternative Measures of Yield • Current Yield • The ratio of the bond’s annual coupon payment over the bond price, e.g., $80/$1,276.76 = 6.27% in the previous example • For premium bonds, coupon rate > current yield > YTM • coupon rate > current yield: because the coupon payments are divided by the par value for the coupon rate and by the market value for the current yield • current yield > YTM: because the YTM reflects the “build-in” capital loss for premium bonds that the bond price will eventually fall to $1,000 at maturity, but the current yield does not account for this capital loss (see Slide 10-35) • For discount bonds, coupon rate < current yield < YTM

30. Alternative Measures of Yield • Yield to Call (YTC) • Similar to YTM except that call price replaces the par value and call date replaces the maturity date ※ Holders of premium bonds are often more interested in the bond’s YTC rather than YTM, because the bond price is high and it is with higher probability to be retired on the call date

31. Price-yield relationship for Callable and Straight Bonds ※ At high rates, the probability of calling back is negligible because the present value of the bond is less than the call price, which is $1,100 ※ At low rates, the present value of the bond exceeds the call price, so the bond is possible to be called back ※ If we assume the firm will redeem the bond as soon as it can do so, the bond price will never exceed the call price

32. The Improper Implication of YTM on the Growth of Invested Funds ※ The above example highlights the problem with the conventional YTM, in which all coupons are assumed to be reinvested at the bond’s yield to maturity ※ Realized compound return (RCR): compound rate of return on a bond with all coupons reinvested until maturity, i.e., bond price×(1+RCR)n = sum of all future values of coupon and principal payments after reinvestment

33. Alternative Measures of Yield • Horizon analysis (to calculate the RCR) • The forecast of total payoff depends on the forecasted YTM of the bond when you sell it and the rate at which you are able to reinvest coupon income

34. 10.4 BOND PRICES OVER TIME

35. Premium and Discount Bonds • Premium bond: coupon rate > discount rate • “Build-in” capital losses: bond price will decline to par over its life period • Discount bond: coupon rate < discount rate • “Build-in” capital gains: bond price will increase to par over its life period ※Because fewer of these above-market (below-market) payments remains for premium (discount) bonds

36. Premium and Discount Bonds • Expected holding-period return: • A 3-year bond, 7% (9%) coupon rate with annual payments, and the discount yield in the market is 8% • The expected HPR for discount and premium bonds ※”Build in” capital gains (losses) of a discount (premium) bond compensate (offset) its low (high) coupon rates ※Both premium and discount bonds offer the same expected HPR, which equals the yield to maturity ※The reason is that a bond must offer a yield competitive with other bonds with the same level of credit risk

37. OID Bonds and Treasury STRIPS • Original issue discount (OID) bonds are those bonds sold at a discount at issuance • The zero-coupon bond is the most extreme OID bond • T-bills are the most important short-term zero-coupon bonds • Longer-term zero-coupon bonds are commonly created from coupon-bearing notes and bonds • A broker can ask the U.S. Department of Treasury to break down a 10-year coupon bond into its 20 semiannual coupon payment and the final principal repayment, each of which can be viewed as a zero-coupon bond • The Treasury program for coupon stripping is called STRIPS (Separate Trading of Registered Interest and Principal of Securities), and these zero-coupon securities are called Treasury strips

38. Tax issues about the OID bonds • The tax authorities recognize that the “build-in” price appreciation on OID bonds represents an implicit interest payment to the holder of the security • The forecasted price appreciation, treated as interest income, is subject to personal or corporate taxes • Gains or losses deviated from the forecasted price appreciation are treated as capital gains or losses

39. Tax issues about the OID bonds • IRS (Internal Revenue Service) is the United States federal government agency that collects taxes and enforces the tax laws • The above taxation rule is not only for zero-coupon bonds but also for all OID bonds • IRS always applies the “constant yield method” to calculate the price appreciation schedule for OID bonds

40. 10.5 DEFAULT RISK AND BOND PRICING

41. Default Risk and Ratings • Default risk (DR): If issuers go bankrupt, bondholders will not receive all the payments they have been promised • The fix-income securities are not so safe as this name suggests • Credit rating agencies • Moody’s Investor Service, Standard & Poor’s, Fitch • Common factors used by rating agencies • Coverage ratio (earnings to fixed costs)↑ DR ↓ • Leverage ratio (debt-to-equity ratio) ↑ DR ↑ • Liquidity ratio (current ratio: current assets/current liabilities or quick ratio: (current assets – inventories)/current liabilities) ↑ DR ↓ • Profitability ratios (ROA and ROE) ↑ DR ↓ • Cash flow-to-debt ratio (total cash flow to outstanding debt) ↑ DR ↓

42. Default Risk and Ratings

43. Protection Against Default • Sinking funds (償債準備基金條款) • The payment of the par value at maturity generates the cash pressure for firms • Issuing firms may agree to establish a sinking fund to spread the payment burden over several years • The fund can be used to repurchase a fraction of outstanding bonds in the open market each year • Firms may repurchase a fraction of outstanding bonds, at the lower of the market price and the sinking fund call price (Hurts investors: firms choose to buy back discount bonds at their market price and premium bonds at the sinking fund call price) • Different from the call provision • Only a limited fraction of outstanding bonds are repurchased • Usually the sinking fund call price is set at par, whereas the call prices are above the par value in general

44. Protection Against Default • Serial bond issue: firms sell bonds with sequential maturity dates such that the principal repayment burden is spread over time just like the sinking fund scheme • Dividend restrictions(股利限制條款) • One common used dividend payment restriction is that the dividend distribution is allowed only when the firm makes profits (after the payments of interest expenses) and the maximum distributed dividend cannot exceed the profits • It protects bondholders because it forces the firm to retain assets rather than pay them out to stockholders

45. Protection Against Default • Subordination of future debt(後續借款次順位求償條款) • Bondholders do not like the issuing firm to raise additional debts because more outstanding debts implies higher default probability • Subordination clauses require additional debts to be subordinated in priority to existing debt (senior bonds) • Later bonds are called junior bonds • Subordination is sometimes called a “me-first rule,” meaning the senior (earlier) bondholders are to be paid first in the event of bankruptcy

46. Protection Against Default • Collateral(擔保條款) • Collateral is a specific asset pledged against possible default on a bond • If the issuer defaults, this specific asset is sold and the sale proceeds are used exclusively to liquidate the bond • A bond backed by collateral is called a secured bond, whereas the unsecured bond, also called debenture, by contrast do not provide specific collateral • If the collateral is a property, the bond is called the mortgage bond • If the collateral is other securities held by the firm, the bond is a collateral trust bond • In the case of equipments, the bond is known as an equipment obligation bond

47. YTM and Default Risk • Promised YTM vs. Expected YTM • The promised (or stated) YTM is calculated under the assumption that firms meet the obligations of bonds • The expected YTM is based on expected cash flows, which may be far less than the promised cash flows • To estimate expected cash flows, both the default probability (or the default time point) and the recovery rate (回復率)in the event of default should be considered

48. Yield Spreads (Default Premium) on Long-Term Bonds Subprime Crisis and Financial Tsunami ※ The default premiumis defined as the yield spread between the promised YTM of a corporate bond and that of a comparable Treasury bond ※ The above figure suggests that when a bond comes more subject to default risk, its default premium is higher to reflect the higher tendency to default ※ The default premium of bonds increases during the crises, especially for junk bonds because in the crises, investors lose confidence of the ability of the issuers of junk bonds to fulfill the obligation

49. Credit Default Swaps (CDS) • Credit Default Swaps (CDS) is an insurance policy on the default risk of a corporate bond or loan • Invented by JPMorgan in 1997, CDS was designed to shift the default risk from the protection buyerto the protection seller (see the next slide) • Price of CDS (or called CDS spread): If a BBB-rated bond + a CDS  a AAA-rated bond, the fair price of this CDS ought to approximately the yield spread between AAA-rated and BBB-rated bonds • Thus, during the subprime crisis and financial tsunami, the yield spreads of corporate bonds as well as the CDS spreads skyrocketed

50. Credit Default Swaps (CDS) ※ For the protection buyer, CDS provides insurance against the possibility that a borrower might not pay ※ For the protection seller, CDS provides a way to earn profits by bearing default risk without ever holding the credit instrument itself