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1、Lecture Presentation Software to accompanyInvestment Analysis and Portfolio ManagementSeventh Editionby Frank K. Reilly & Keith C. BrownChapter 19Chapter 19 - The Analysis and Valuation of BondsQuestions to be answered: How do you determine the value of a bond based on the present value formula? Wha
2、t are the alternative bond yields that are important to investors?Chapter 19 - The Analysis and Valuation of Bonds How do you compute the following major yields on bonds: current yield, yield to maturity, yield to call, and compound realized (horizon) yield? What are spot rates and forward rates and
3、 how do you calculate these rates from a yield to maturity curve? What is the spot rate yield curve and forward rate curve?Chapter 19 - The Analysis and Valuation of Bonds How and why do you use the spot rate curve to determine the value of a bond? What are the alternative theories that attempt to e
4、xplain the shape of the term structure of interest rates? What factors affect the level of bond yields at a point in time? What economic forces cause changes in bond yields over time?Chapter 19 - The Analysis and Valuation of Bonds When yields change, what characteristics of a bond cause differentia
5、l price changes for individual bonds? What is meant by the duration of a bond, how do you compute it, and what factors affect it? What is modified duration and what is the relationship between a bonds modified duration and its volatility?Chapter 19 - The Analysis and Valuation of Bonds What is effec
6、tive duration and when is it useful? What is the convexity for a bond, how do you compute it, and what factors affect it? Under what conditions is it necessary to consider both modified duration and convexity when estimating a bonds price volatility?Chapter 19 - The Analysis and Valuation of Bonds W
7、hat happens to the duration and convexity of bonds that have embedded call options?Chapter 19 - The Analysis and Valuation of Bonds What are effective duration and effective convexity and when are they useful? What is empirical duration and how is it used with common stocks and other assets? What ar
8、e the static yield spread and the option-adjusted spread?The Fundamentals of Bond ValuationThe present-value modelntnpttmiPiCP212)21 ()21 (2Where:Pm=the current market price of the bondn = the number of years to maturityCi = the annual coupon payment for bond ii = the prevailing yield to maturity fo
9、r this bond issuePp=the par value of the bondThe Fundamentals of Bond Valuation If yield coupon rate, bond will be priced at a discount to its par value Price-yield relationship is convex (not a straight line) The Yield ModelThe expected yield on the bond may be computed from the market priceWhere:i
10、 = the discount rate that will discount the cash flows to equal the current market price of the bondntnptimiPiCP212)21 ()21 (2Computing Bond YieldsYield Measure PurposeNominal YieldMeasures the coupon rateCurrent yieldMeasures current income ratePromised yield to maturityMeasures expected rate of re
11、turn for bond held to maturityPromised yield to callMeasures expected rate of return for bond held to first call dateRealized (horizon) yieldMeasures expected rate of return for a bond likely to be sold prior to maturity. It considers specified reinvestment assumptions and an estimated sales price.
12、It can also measure the actual rate of return on a bond during some past period of time.Nominal YieldMeasures the coupon rate that a bond investor receives as a percent of the bonds par valueCurrent YieldSimilar to dividend yield for stocksImportant to income oriented investorsCY = Ci/Pm where: CY =
13、 the current yield on a bondCi = the annual coupon payment of bond iPm = the current market price of the bondPromised Yield to Maturity Widely used bond yield figure Assumes Investor holds bond to maturity All the bonds cash flow is reinvested at the computed yield to maturitySolve for i that will e
14、quate the current price to all cash flows from the bond to maturity, similar to IRRntnptimiPiCP212)21 ()21 (2Computing the Promised Yield to MaturityTwo methods Approximate promised yield Easy, less accurate Present-value model More involved, more accurateApproximate Promised YieldCoupon + Annual St
15、raight-Line Amortization of Capital Gain or LossAverage Investment2 APYmpmpiPPnPPC=Present-Value ModelntnptimiPiCP212)21 ()21 (2Promised Yield to CallApproximation May be less than yield to maturity Reflects return to investor if bond is called and cannot be held to maturity2mcmctPPncPPCAYCWhere:AYC
16、 = approximate yield to call (YTC)Pc = call price of the bondPm = market price of the bondCt = annual coupon paymentnc = the number of years to first call datePromised Yield to CallPresent-Value MethodWhere:Pm = market price of the bondCi = annual coupon paymentnc = number of years to first callPc =
17、 call price of the bondnccncttimiPiCP221)1 ()1 (2/Realized Yield Approximation2PPhpPPCARYffiWhere:ARY = approximate realized yield to call (YTC)Pf = estimated future selling price of the bondCi = annual coupon paymenthp = the number of years in holding period of the bondRealized YieldPresent-Value M
18、ethodhpfhptttmiPiCP221)21 ()21 (2/Calculating Future Bond PricesWhere:Pf = estimated future price of the bondCi = annual coupon paymentn = number of years to maturityhp = holding period of the bond in yearsi = expected semiannual rate at the end of the holding periodhpnphpnttifiPiCP22221)21 ()21 (2/
19、Yield Adjustments for Tax-Exempt BondsWhere:T = amount and type of tax exemptionT-1return annualETY What Determines Interest Rates Inverse relationship with bond prices Forecasting interest rates Fundamental determinants of interest ratesi = RFR + I + RP where: RFR = real risk-free rate of interest
20、I = expected rate of inflation RP = risk premiumWhat Determines Interest Rates Effect of economic factors real growth rate tightness or ease of capital market expected inflation or supply and demand of loanable funds Impact of bond characteristics credit quality term to maturity indenture provisions
21、 foreign bond risk including exchange rate risk and country riskWhat Determines Interest Rates Term structure of interest rates Expectations hypothesis Liquidity preference hypothesis Segmented market hypothesis Trading implications of the term structureExpectations Hypothesis Any long-term interest
22、 rate simply represents the geometric mean of current and future one-year interest rates expected to prevail over the maturity of the issueLiquidity Preference Theory Long-term securities should provide higher returns than short-term obligations because investors are willing to sacrifice some yields
23、 to invest in short-maturity obligations to avoid the higher price volatility of long-maturity bonds Segmented-Market Hypothesis Different institutional investors have different maturity needs that lead them to confine their security selections to specific maturity segments Trading Implications of t
24、he Term Structure Information on maturities can help you formulate yield expectations by simply observing the shape of the yield curve Yield Spreads Segments: government bonds, agency bonds, and corporate bonds Sectors: prime-grade municipal bonds versus good-grade municipal bonds, AA utilities vers
25、us BBB utilities Coupons or seasoning within a segment or sector Maturities within a given market segment or sectorYield SpreadsMagnitudes and direction of yield spreads can change over timeWhat Determines the Price Volatility for BondsBond price change is measured as the percentage change in the pr
26、ice of the bond1BPBEPBWhere:EPB = the ending price of the bondBPB = the beginning price of the bondWhat Determines the Price Volatility for BondsFour Factors1. Par value2. Coupon3. Years to maturity4. Prevailing market interest rateWhat Determines the Price Volatility for BondsFive observed behavior
27、s1. Bond prices move inversely to bond yields (interest rates)2. For a given change in yields, longer maturity bonds post larger price changes, thus bond price volatility is directly related to maturity3. Price volatility increases at a diminishing rate as term to maturity increases4. Price movement
28、s resulting from equal absolute increases or decreases in yield are not symmetrical5. Higher coupon issues show smaller percentage price fluctuation for a given change in yield, thus bond price volatility is inversely related to couponWhat Determines the Price Volatility for Bonds The maturity effec
29、t The coupon effect The yield level effect Some trading strategiesThe Duration Measure Since price volatility of a bond varies inversely with its coupon and directly with its term to maturity, it is necessary to determine the best combination of these two variables to achieve your objective A compos
30、ite measure considering both coupon and maturity would be beneficialThe Duration MeasureDeveloped by Frederick R. Macaulay, 1938Where: t = time period in which the coupon or principal payment occursCt = interest or principal payment that occurs in period t i = yield to maturity on the bondprice)()1
31、()1 ()(111nttntttntttCPVtiCitCDCharacteristics of Duration Duration of a bond with coupons is always less than its term to maturity because duration gives weight to these interim payments A zero-coupon bonds duration equals its maturity There is an inverse relation between duration and coupon There
32、is a positive relation between term to maturity and duration, but duration increases at a decreasing rate with maturity There is an inverse relation between YTM and duration Sinking funds and call provisions can have a dramatic effect on a bonds durationModified Duration and Bond Price VolatilityAn
33、adjusted measure of duration can be used to approximate the price volatility of a bondmYTM1durationMacaulay duration modifiedWhere:m = number of payments a yearYTM = nominal YTMDuration and Bond Price Volatility Bond price movements will vary proportionally with modified duration for small changes i
34、n yields An estimate of the percentage change in bond prices equals the change in yield time modified durationiDPPmod100Where:P = change in price for the bondP = beginning price for the bondDmod = the modified duration of the bondi = yield change in basis points divided by 100Trading Strategies Usin
35、g Duration Longest-duration security provides the maximum price variation If you expect a decline in interest rates, increase the average duration of your bond portfolio to experience maximum price volatility If you expect an increase in interest rates, reduce the average duration to minimize your p
36、rice decline Note that the duration of your portfolio is the market-value-weighted average of the duration of the individual bonds in the portfolioBond Duration in Years for Bonds Yielding 6 Percent Under Different TermsCOUPON RATESYears toMaturity0.020.040.060.0810.9950.9900.9850.98154.7564.5584.39
37、34.254108.8918.1697.6627.2862014.98112.98011.90411.2325019.45217.12916.27315.82910017.56717.23217.12017.064817.16717.16717.16717.167Source: L. Fisher and R. L. Weil, Coping with the Risk of Interest Rate Fluctuations:Returns to Bondholders from Nave and Optimal Strategies, Journal of Business 44, no
38、. 4 (October 1971): 418. Copyright 1971, University of Chicago Press.Bond Convexity Equation 19.6 is a linear approximation of bond price change for small changes in market yieldsYTM100modDPPBond Convexity Modified duration is a linear approximation of bond price change for small changes in market y
39、ields Price changes are not linear, but a curvilinear (convex) functioniDPPmod100Price-Yield Relationship for Bonds The graph of prices relative to yields is not a straight line, but a curvilinear relationship This can be applied to a single bond, a portfolio of bonds, or any stream of future cash f
40、lows The convex price-yield relationship will differ among bonds or other cash flow streams depending on the coupon and maturity The convexity of the price-yield relationship declines slower as the yield increases Modified duration is the percentage change in price for a nominal change in yieldModif
41、ied DurationFor small changes this will give a good estimate, but this is a linear estimate on the tangent linePdidPDmodDeterminants of ConvexityThe convexity is the measure of the curvature and is the second derivative of price with resect to yield (d2P/di2) divided by priceConvexity is the percent
42、age change in dP/di for a given change in yieldPdiPd22Convexity Determinants of Convexity Inverse relationship between coupon and convexity Direct relationship between maturity and convexity Inverse relationship between yield and convexityModified Duration-Convexity Effects Changes in a bonds price
43、resulting from a change in yield are due to: Bonds modified duration Bonds convexity Relative effect of these two factors depends on the characteristics of the bond (its convexity) and the size of the yield change Convexity is desirableDuration and Convexity for Callable Bonds Issuer has option to c
44、all bond and pay off with proceeds from a new issue sold at a lower yield Embedded option Difference in duration to maturity and duration to first call Combination of a noncallable bond plus a call option that was sold to the issuer Any increase in value of the call option reduces the value of the c
45、allable bondOption Adjusted Duration Based on the probability that the issuing firm will exercise its call option Duration of the non-callable bond Duration of the call optionConvexity of Callable Bonds Noncallable bond has positive convexity Callable bond has negative convexityLimitations of Macaul
46、ay and Modified Duration Percentage change estimates using modified duration only are good for small-yield changes Difficult to determine the interest-rate sensitivity of a portfolio of bonds when there is a change in interest rates and the yield curve experiences a nonparallel shift Initial assumpt
47、ion that cash flows from the bond are not affected by yield changes Effective Duration Measure of the interest rate sensitivity of an asset Use a pricing model to estimate the market prices surrounding a change in interest ratesEffective DurationEffective Convexity PSPP2 22PSPPPP- = the estimated pr
48、ice after a downward shift in interest ratesP+ = the estimated price after a upward shift in interest ratesP = the current priceS = the assumed shift in the term structureEffective Duration Effective duration greater than maturity Negative effective duration Empirical durationEmpirical Duration Actu
49、al percent change for an asset in response to a change in yield during a specified time periodYield Spreads With Embedded Options Static Yield Spreads Consider the total term structure Option-Adjusted Spreads Consider changes in the term structure and alternative estimates of the volatility of interest ratesThe InternetInvestments OnlineEnd of Chapter 19The Analysis and Valuation of BondsFuture topicsChapter 20 Bond Portfolio Management Strategies