Topic 6: Bond Fundamentals and Valuation - Larry Schrenk
FIN 377: Investments Topic 6: Bond Fundamentals and Valuation Larry Schrenk, Instructor 06:26 AM 1 of 88 Overview 12.1 Basic Features of a Bond 12.2 The Global Bond Market Structure 12.3 Survey of Bond Issues 12.4 Bond Yield Curves 12.5 Bond Valuation and Yields 13.1 Bond Analysis Tools 06:26 AM
2 of 88 Learning Objectives 1. What are some of the basic features of bonds that affect their risk, return, and value? 2. What is the current country structure of the world bond market, and how has the makeup of the global bond market changed in recent years? 3. What are the major components of the world bond market? 4. What are bond ratings, and what is their purpose? What is the difference between investment-grade bonds and high-yield (junk) bonds? 5. What are the characteristics of bonds in the major bond categories, such as governments, agencies, municipalities, and corporates, and how are their prices quoted? 6. What are the important characteristics of corporate bond issues developed in the United States over the past decades, such as mortgage-backed securities, other asset-backed securities, zero-coupon bonds, and high-yield bonds? 7. What is a yield curve, and how is its shape determined? 8. What is the difference between the par and spot yield curves? 9. How do you determine the value of a bond based on the discounted cash flow formula?
10. How does bond valuation change when you are between two coupon dates? 11. How do you compute the following yields on bonds: current yield, yield to maturity, yield to call, and compound realized (horizon) yield? 12. What are implied forward rates, and how do you calculate these rates from a spot yield curve? 13. What is meant by the duration of a bond, how do you compute it, and what factors affect it? 14. What is modified duration, and what is the relationship between a bonds modified duration and its price volatility? 06:26 AM 3 of 88 Readings Reilley, et al., Investment Analysis and Portfolio Management, Chap. 12 and 13.1
06:26 AM 4 of 88 12.1 Basic Features of a Bond 06:26 AM 5 of 88 12.1 Basic Features of a Bond Public bonds Long-term, fixed-obligation debt securities Periodic fixed amount of interest
Fixed principal at the date of maturity Interest is paid every six months Principal is due at maturity Par (or face) value 06:26 AM 6 of 88 12.1 Basic Features of a Bond Segments are based on maturity: 1. Short-term Maturities of one year or less
Money market 2. Intermediate-term Maturities 1 to 10 years These instruments are known as notes 3. Long-term 06:26 AM Maturities in excess of 10 years
Callable bonds 7 of 88 12.1.1 Bond Characteristics Intrinsic Features Coupon Term to maturity Principal or par (face) value Types of ownership Bearer vs. registered bond 06:26 AM 8 of 88 12.1.1 Bond Characteristics
Types of Issues Secured bonds (mortgages) Backed by legal claim on some specified property E.g. mortgage bonds, equipment trust certificates Unsecured bonds (debentures) General claim on firm assets Senior vs junior (subordinate) debentures 06:26 AM 9 of 88 12.1.1 Bond Characteristics Indenture provisions
The indenture is the contract between the issuer and the bondholder specifying the issuers legal requirements 06:26 AM 10 of 88 12.1.1 Bond Characteristics Features affecting a bonds maturity Call option Deferred call Call premium Amount above par value for prematurely retiring the bond
Nonrefunding provision Prohibits call Sinking fund Bond paid off systematically over its life 06:26 AM 11 of 88 Features of a May Department Stores Bond Terms Explanations
Amount of issue $125 million The company will issue $125 million worth of bonds. Date of issue 2/28/86 The bonds were sold on 2/28/86. Maturity 3/1/16 The principal will be paid in 30 years. Annual coupon 9.25The denomination of the bonds is $1,000. Each bondholder will receive $92.50 per bond per year (9.25% of the face value). Offer price 100 The offer price will be 100% of the $1,000 face value per bond.
06:26 AM 12 of 88 Features of a May Department Stores Bond (concluded) Terms Explanations Coupon payment dates 3/1, 9/31 Coupons of $92.50/2 = $46.25 will be paid on these dates. Security None The bonds are debentures.
Sinking fund Annual, toward beginning 3/1/97 Call Provision Not callable The firm will make annual payments The bonds have a deferred call the sinking fund. before 2/28/93 Call price 106.48 initially, After 2/28/93, the company can buy
declining to 100 back the bonds for $1,064.80 per bond, declining to $1,000 on 2/28/05. Rating Moodys A2 have a low probability of default. 06:26 AM This is one of Moodys higher ratings. The bonds 13 of 88
12.2 The Global Bond Market Structure 06:26 AM 14 of 88 12.2 The Global Bond Market Structure Fixed-income securities market substantially larger than equity exchanges Equity less than 10 percent of all new security issues (US 2010)
06:26 AM 15 of 88 12.2 The Global Bond Market Structure 06:26 AM 16 of 88 12.2.1 Participating Issuers Sovereign bonds Quasi and foreign governments (including agency bonds)
Securitized and collateralized bonds from governments or corporations Directly issued corporate bonds High-yield and/or emerging market bonds 06:26 AM 17 of 88 12.2.1 Participating Issuers 06:26 AM 18 of 88 12.2.2 Participating Investors
Individual investors Institutional investors Life Insurance Companies Commercial Banks Property and Liability Insurance Companies Pension Funds Mutual Funds Two factors
Applicable tax code Institutions liability structure 06:26 AM 19 of 88 12.2.3 Bond Ratings Primary risk: Default The three major rating agencies Moodys Standard and Poors Fitch Investors Service Description of bond ratings
06:26 AM Investment-grade securities Speculative bonds Income obligations or revenue bonds Default High yield or junk bonds 20 of 88 12.2.3 Bond Ratings
06:26 AM 21 of 88 12.3 Survey of Bond Issues 06:26 AM 22 of 88 12.3.1 Domestic Government Bonds United States T-bills, notes, bonds
Japan Second-largest single country government bond market United Kingdom Gilts Eurozone Combined value larger than the Japanese market All denominated in euros 06:26 AM 23 of 88 12.3.2 Government Agency Issues
Government obligations issued through specific agency Not direct Treasury issues, but carry the full faith and credit of U.S. government Some subject to state and local income tax 06:26 AM 24 of 88 12.3.2 Government Agency Issues 06:26 AM 25 of 88
12.3.3 Municipal Bonds Types: General obligation (GO) bonds Revenue bonds Interest payments are exempt from federal income tax Convert the tax-free yield of a municipal to an equivalent taxable yield (ETY) as follows: Where ETY = equivalent taxable yield i = yield of the municipal obligations t = marginal tax rate of the investor 06:26 AM
i ETY = 1-t 26 of 88 12.3.4 Corporate Bonds U.S. Corporate Bond Market Includes utilities, industrials, rail and transportation, and financial issues Debentures First-mortgage issues Debentures Convertible obligations Bonds with warrants
Subordinated debentures Income bonds (similar to municipal revenue bonds) Collateral trust bonds backed by financial assets 06:27 AM
Equipment trust certificates Asset-backed securities (ABS) including mortgage-backed securities (MBS) Collateralized mortgage obligations (CMOs) Certificates for automobile receivables (CARs) Credit cardbacked securities Collateralized debt obligations (CDOs) 27 of 88 12.3.4 Corporate Bonds 06:26 AM
28 of 88 12.3.5 Nontraditional Bond Coupon Structures Variable-rate notes Popular during periods of high interest rates, Typically two unique features Coupon rate allowed to adjust (float) After the first year or two, the notes are redeemable at par, at the holders option, usually at six-month intervals 06:26 AM
29 of 88 12.3.5 Nontraditional Bond Coupon Structures Zero-coupon (or pure discount) bond: No interim interest payments Price is present value of principal Return is difference between cost and principal 06:26 AM 30 of 88
12.3.6 High-Yield Bonds Also speculative or junk bonds Rated below BBB, that is, non-investment grade bonds Market exploded in the early 1980s Major owners are mutual funds, insurance companies, and pension funds 06:26 AM 31 of 88 12.3.7 International Bonds Foreign bonds are sold in one country and currency by a borrower of a different nationality
Yankee bonds are U.S. dollar-denominated bonds sold in the U.S. but issued by a foreign firm Eurobonds underwritten by international bond syndicates and sold in several national markets 06:26 AM 32 of 88 12.3.7 International Bonds United States Yankee bonds register with SEC Eurodollar bond market affected by changes in value of U.S. dollar
Japan Samurai bonds: Yen denominated issued by nonJapanese firms in Japan Euroyen bonds: Yen denominated, sold outside Japan 06:26 AM 33 of 88 12.4 Bond Yield Curves (Chapter 12 and 13.1.1) 06:26 AM 34 of 88
12.4 Bond Yield Curves Bonds yield to maturity (YTM) is perhaps the most important statistic Yield to maturity is expected return to the bond 06:26 AM 35 of 88 12.4.1 The Determinants of Bond Yields Factors causing interest rates (i) to
change: i = RRFR + I + RP Where: RRFR = real risk-free rate of interest I = expected rate of inflation RP = risk premium 06:26 AM 36 of 88 12.4.1 The Determinants of Bond Yields Effect of Economic Factors RRFR is economic cost of moneythe opportunity cost necessary to forgo consumption
Determined by real growth rate of te economy with short-run effects due to easing or tightening in the capital market The expected rate of inflation is the other economic influence on interest rates Add expected level of inflation (I ) to real risk-free rate (RRFR) to specify nominal rf, which is an observable rate like the current yield on government T-bills 06:26 AM 37 of 88 12.4.1 The Determinants of Bond Yields The Impact of Bond Characteristics
Characteristics unique to individual securities, market sectors, or countries influence risk premium (RP) Risk premium has four components: 1. Quality of the issue, i.e., risk of default 2. Term to maturity 3. Indenture provisions 4. Foreign bond risk, including exchange rate and country risk 06:26 AM 38 of 88 12.4.2 Yield Curves and the Term Structure of Interest Rates Term structure of interest rates (or yield
curve) relates maturity to the yield of bonds at a given point in time Cross section of comparable bonds Quality should be constant with similar coupons and call features 06:26 AM 39 of 88 12.4.2 Yield Curves and the Term Structure of Interest Rates 06:26 AM 40 of 88
12.4.2 Types of Yield Curves 06:26 AM 41 of 88 Implied Future Interest Rates If I know the average return of A one year bond (x), and A two year bond (y) I should be able to calculate The interest rate in year 2 (f2) One Year Average (x)
Two Year Average (y) Interest Rate in Year 2 (f2) 06:26 AM 42 of 88 Implied Future Interest Rates Think of it this way What would the year 2 interest rate (f2) need to be, to change the one year average (x) to the two year average (y)?
One Year Average (x) Two Year Average (y) Interest Rate in Year 2 (f2) 06:26 AM NOTE: f = implied future interest rate in year n n 43 of 88 Example: Future Interest Rates Maturit y Rate
1 2 3 4 5.4 5.6 6.1
5.8 5.4% 5.6% 6.1% 5.8% 06:26 AM 44 of 88 Implied Future Interest Rates ??? 5.4%
5.6% HPR one two-year bond (1.056)2 - 1 HPR two one-year bonds 1.054(1+ f2) - 1 These must be equal 1.054(1+ f2) - 1 = (1.056)2- 1 Solve for f2 f2 = (1.056)2 /1.054 1 = 5.8% 06:26 AM 45 of 88 Implied Future Interest Rates General Formula t
ft 1 rt 1 t1 1 rt 1 ft = Implied Future Rate at t rt = Average Annual Return to t t = Time 06:26 AM
46 of 88 Implied Future Interest Rates Maturit y 06:26 AM 1 2 3 4
Rate 5.4 5.6 6.1 5.8 fn 5.4
5.8 2 7.1 4.9 1.056 f2 1 5.8% 1.054 3 1.061
f3 1 7.1% 2 1.056 4 1.058 f4 1 4.9% 3 1.061 47 of 88 12.4.4 Yield Curves for Credit-Risky
Bonds Credit spread Yield differential representing the risk premium associated with the possibility that the corporate issuer will be unable to pay back what it has promised to the investor 06:26 AM 48 of 88 12.4.4 Yield Curves for Credit-Risky Bonds 06:26 AM
49 of 88 12.4.5 Determining the Shape of the Term Structure Expectations Hypothesis Long-term interest rate is geometric mean of oneyear interest rates over the life of the issue Expectations short-term rates rising rising yield curve Expectations short-term rates falling declining yield curve Similarly for flat and humped yield curves 06:26 AM 50 of 88
12.4.5 Determining the Shape of the Term Structure Liquidity Preference Theory Long-term securities provide higher returns because investors sacrifice some yields to avoid price volatility of long-maturity bonds Yield curve should slope upward and any other shape viewed as a temporary aberration 06:26 AM 51 of 88 12.4.5 Determining the Shape of the
Term Structure Segmented-Market Hypothesis Different institutional investors have different maturity needs depending on the supply and demand within that maturity segment Shape of the yield curve function of investment policies of major financial institutions 06:26 AM 52 of 88 12.5 Bond Valuation and Yields
06:26 AM 53 of 88 12.5 Bond Valuation and Yields with Coupons Bond value: P= n t=1
C 1 + i t + F 1 + i n
Where: C = period coupon rate i = yield to maturity, stated on a period basis n = maturity date of the bond, stated in periods 06:26 AM 54 of 88 Bond Pricing Example I Price of a semi-annual 30 year, 8% coupon bond. Market rate of interest is 10%. 60
Price = t=1 $40 1.05 t + $1000 1.05
60 Pric e =$810.71 06:26 AM 55 of 88 Bond Pricing Example II Price of a semi-annual 30 year, 8% coupon bond. Market rate of interest is 10%. P/Y = 2; N = 60; I = 10; PV = $810.71; PMT = -40; FV = -1000 NOTE: Negatives
06:26 AM 56 of 88 12.5 Bond Valuation and Yields with Semiannual Coupons The Yield (to Maturity YTM) Model Price bonds in terms of their yieldsexpected rates of return Use the observed current market price (MP ) and the expected cash flows to compute the expected yield on the bond 0
Equivalent to IRR 06:26 AM 57 of 88 Yield to Maturity Example I Suppose an 8% coupon, semi-annual 30 year bond is selling for $1276.76. What is its average rate of return? $40 1000 + 60 = $1276.76 t (1+r)
t =1 (1+r) 60 r = 3% per half year YTM = 6% 06:26 AM 58 of 88 Yield to Maturity Example II Suppose an 8% coupon, semi-annual 30 year bond is selling for $1276.76. What is its average rate of return? P/Y = 2; N = 60; I = 6.00%; PV = 1276.76; PMT = -40; FV = -1000
06:26 AM 59 of 88 12.5 Relationship between Bond Yields, Coupon Rates, and Prices Price moves in the opposite direction to YTM 1. YTM < cr premium bond 2. YTM > cr discount bond 3. YTM = cr par value bond 4. The price-yield relationship is convex 06:26 AM
As yields decline, the price increases at an increasing rate; As yields increase, the price declines at a declining rate 60 of 88 12.5 Relationship between Bond Yields, Coupon Rates, and Prices Bond and Price Change Magnitude Bond value inversely related to YTM Magnitude of change depends on other characteristics, such as the coupon rate and time to maturity Two additional facts: 1. Lower coupon rate greater percentage price change for a given shift in yields 2. Same coupon rate, longer maturity greater percentage price
change for a given shift in yields 06:26 AM 61 of 88 12.5 Relationship between Bond Yields, Coupon Rates, and Prices 06:26 AM 62 of 88 12.5 Computing Other Bond Yield Measures Current Yield
How much return comes from annual payments Ratio of annual coupon to current price C CY = MP0 Where C is the fixed annual coupon MP0 is the bonds current market price 06:26 AM 63 of 88 Current Yield Example
Current Yield Bonds annual coupon payment divided by the bond price Suppose an 8% coupon, semi-annual 30 year bond is selling for $1276.76. What is its current yield? 80.00 6.27% 1276.76 06:26 AM 64 of 88 12.5 Computing Other Bond Yield
Measures Yield to Call (YTC) Expected return is bond called at first opportunity Adjust present value equation: MP0 = ncall t=1 C 1 + i
t + Pcall 1 + i ncall Where: ncall = number of periods to first call date Pcall = call price of the bond 06:26 AM
65 of 88 Yield to Call Example Suppose an 8% coupon, 30 year semiannual bond is selling for $1100.55. If it can be called in 2 years with a call price is $1,100 what is its yield to call? P/Y = 2; N = 4; I = 7.25%; PV = 1100.55; PMT = -40; FV = -1100 06:26 AM 66 of 88 12.5 Computing Other Bond Yield Measures
Realized (Horizon) Yield Expected rate of return for some time horizon Assumes holding period (hp, expressed in periods) less than n Adjust discounted cash flow valuation: hp MP0 = t=1 C 1 + i
t + Php 1 + i hp where: Php = anticipated selling price of the bond at the end of the investment horizon 06:26 AM
67 of 88 13.1 Bond Analysis Tools (Chapter 13.1.2-3) 06:26 AM 68 of 88 Bond Duration and Convexity Convexity Duration 06:26 AM
69 of 88 13.1.2 Bond Duration Calculating Bond Duration Bond duration can be interpreted as a measure of the bonds price volatility (interest rate sensitivity) Duration is bonds price elasticity coefficient with respect to yield changes 06:26 AM 70 of 88
13.1.2 Bond Duration Macaulay versus Modified Duration Macaulay duration: How many years to be repaid bonds price by the its total cash flows Modified duration: Price change in a bond given a 1% change in interest rates 06:26 AM 71 of 88 13.1.2 Bond Duration Macaulay duration: Weighted average of the payment dates associated with an N-period bond:
where: CFt = cash flow (that is, coupon or principal) paid on Date t t = date on which payment is made i = yield to maturity of the bond, stated on a periodic basis 06:26 AM 72 of 88 13.1.2 Bond Duration Example: Consider the following two bonds: Assume YTM for both bonds is 8 percent and pay annual coupons
06:26 AM 73 of 88 13.1.2 Bond Duration 06:26 AM 74 of 88 13.1.2 Bond Duration Duration is measured in units of time, not dollars Weights are the PV of cash flow scaled by the PV (P0) of the bond
Higher coupon lower duration More of the total cash flow is paid sooner Zero-coupon bond duration = maturity 06:26 AM 75 of 88 13.1.2 Bond Duration 06:26 AM 76 of 88 13.1.2 Bond Duration
Measuring Bond Price Volatility Duration is bonds price elasticity coefficient with respect to yield changes: Where: 06:26 AM 77 of 88 13.1.2 Bond Duration Equation rewritten to predict change in a price for a small change in YTM: 06:26 AM
78 of 88 13.1.2 Bond Duration Bond price change inputs: Macaulay duration of the bond, D Prevailing bond yield, i Forecasted change in the bond yield, i Modified durations combines the first two components: 06:26 AM 79 of 88 13.1.2 Bond Duration
The equation can be simplified to: The basis point value (BPV) measures the dollar price change for a one basis point change in yields: 06:26 AM 80 of 88 13.1.2 Bond Duration Duration of a Portfolio Duration of a portfolio is the weighted average of the payment dates for all of the cash flows across the collection of bonds Estimated by a weighted average of the durations for each of the bonds using the investment weight of each position:
06:26 AM 81 of 88 13.1.3 Bond Convexity Trade-off between price and YTM is curved (convex) function Mod D misses convexity property Mod D estimates a curved line with a straight (tangent) line 06:26 AM 82 of 88
13.1.3 Bond Convexity 06:26 AM 83 of 88 13.1.3 Bond Convexity Duration approximation of the price-yield relationship is conservative Overestimates price decline following yield increase Underestimates price increase induced by yield decrease Modified duration: Approximates bond price change as interest rates
changes Convexity approximates how modified duration will change with yield curve shifts 06:26 AM 84 of 88 13.1.3 Bond Convexity Convexity formula: 06:26 AM 85 of 88 13.1.3 Bond Convexity
06:26 AM 86 of 88 13.1.3 Bond Convexity For annual bond, the formula modified by adding a second term involving the convexity statistic: 06:26 AM 87 of 88 13.1.3 Bond Convexity
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