andValuationofBonds(投资分析与投资组合管理)ppt课件

1、Lecture Presentation Software to accompanyInvestment Analysis and Portfolio ManagementSeventh Editionby Frank K. Reilly & Keith C. BrownChapter 19.Chapter 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?What

2、 are the alternative bond yields that are important to investors?.Chapter 19 - The Analysis and Valuation of BondsHow 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 h

3、ow 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 BondsHow and why do you use the spot rate curve to determine the value of a bond?What are the alternative theories that attempt to expla

4、in 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 BondsWhen yields change, what characteristics of a bond cause differential pric

5、e 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 BondsWhat is effective dur

6、ation 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 BondsWhat happen

7、s to the duration and convexity of bonds that have embedded call options?.Chapter 19 - The Analysis and Valuation of BondsWhat 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 are the static

8、 yield spread and the option-adjusted spread?.The Fundamentals of Bond ValuationThe present-value modelWhere: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 for this bond issuePp=the par value of

9、the bond.The Fundamentals of Bond ValuationIf yield coupon rate, bond will be priced at a discount to its par valuePrice-yield relationship is convex (not a straight line) .The Yield ModelThe expected yield on the bond may be computed from the market priceWhere:i = the discount rate that will discou

10、nt the cash flows to equal the current market price of the bond.Computing Bond YieldsYield Measure PurposeNominal YieldMeasures the coupon rateCurrent yieldMeasures current income ratePromised yield to maturityMeasures expected rate of return for bond held to maturityPromised yield to callMeasures e

11、xpected 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. It can also measure the actual rate of return on a bond during

12、 some past period of time.Nominal YieldMeasures the coupon rate that a bond investor receives as a percent of the bonds par value.Current YieldSimilar to dividend yield for stocksImportant to income oriented investorsCY = Ci/Pm where: CY = the current yield on a bondCi = the annual coupon payment of

13、 bond iPm = the current market price of the bond.Promised Yield to MaturityWidely used bond yield figureAssumesInvestor holds bond to maturityAll the bonds cash flow is reinvested at the computed yield to maturitySolve for i that will equate the current price to all cash flows from the bond to matur

14、ity, similar to IRR.Computing the Promised Yield to MaturityTwo methodsApproximate promised yieldEasy, less accuratePresent-value modelMore involved, more accurate.Approximate Promised YieldCoupon + Annual Straight-Line Amortization of Capital Gain or LossAverage Investment=.Present-Value Model.Prom

15、ised Yield to CallApproximationMay be less than yield to maturityReflects return to investor if bond is called and cannot be held to maturityWhere:AYC = 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

16、call date.Promised Yield to CallPresent-Value MethodWhere:Pm = market price of the bondCi = annual coupon paymentnc = number of years to first callPc = call price of the bond.Realized Yield ApproximationWhere:ARY = approximate realized yield to call (YTC)Pf = estimated future selling price of the bo

17、ndCi = annual coupon paymenthp = the number of years in holding period of the bond.Realized YieldPresent-Value Method.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 = expect

18、ed semiannual rate at the end of the holding period.Yield Adjustments for Tax-Exempt BondsWhere:T = amount and type of tax exemption.What Determines Interest RatesInverse relationship with bond pricesForecasting interest ratesFundamental determinants of interest ratesi = RFR + I + RP where:RFR = rea

19、l risk-free rate of interest I = expected rate of inflation RP = risk premium.What Determines Interest RatesEffect of economic factorsreal growth ratetightness or ease of capital marketexpected inflationor supply and demand of loanable fundsImpact of bond characteristicscredit qualityterm to maturit

20、yindenture provisionsforeign bond risk including exchange rate risk and country risk.What Determines Interest RatesTerm structure of interest ratesExpectations hypothesisLiquidity preference hypothesisSegmented market hypothesisTrading implications of the term structure.Expectations HypothesisAny lo

21、ng-term interest rate simply represents the geometric mean of current and future one-year interest rates expected to prevail over the maturity of the issue.Liquidity Preference TheoryLong-term securities should provide higher returns than short-term obligations because investors are willing to sacri

22、fice some yields to invest in short-maturity obligations to avoid the higher price volatility of long-maturity bonds .Segmented-Market HypothesisDifferent institutional investors have different maturity needs that lead them to confine their security selections to specific maturity segments .Trading

23、Implications of the Term StructureInformation on maturities can help you formulate yield expectations by simply observing the shape of the yield curve .Yield SpreadsSegments: government bonds, agency bonds, and corporate bondsSectors: prime-grade municipal bonds versus good-grade municipal bonds, AA

24、 utilities versus BBB utilitiesCoupons or seasoning within a segment or sectorMaturities within a given market segment or sector.Yield SpreadsMagnitudes and direction of yield spreads can change over time.What Determines the Price Volatility for BondsBond price change is measured as the percentage c

25、hange in the price of the bondWhere:EPB = the ending price of the bondBPB = the beginning price of the bond.What Determines the Price Volatility for BondsFour Factors1. Par value2. Coupon3. Years to maturity4. Prevailing market interest rate.What Determines the Price Volatility for BondsFive observe

26、d behaviors1. 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. Pric

27、e movements 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 coupon.What Determines the Price Volatility for BondsThe matu

28、rity effectThe coupon effectThe yield level effectSome trading strategies.The Duration MeasureSince 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 objectiveA

29、composite measure considering both coupon and maturity would be beneficial.The 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 bond.Ch

30、aracteristics of DurationDuration of a bond with coupons is always less than its term to maturity because duration gives weight to these interim paymentsA zero-coupon bonds duration equals its maturityThere is an inverse relation between duration and couponThere is a positive relation between term t

31、o maturity and duration, but duration increases at a decreasing rate with maturityThere is an inverse relation between YTM and durationSinking funds and call provisions can have a dramatic effect on a bonds duration.Modified Duration and Bond Price VolatilityAn adjusted measure of duration can be us

32、ed to approximate the price volatility of a bondWhere:m = number of payments a yearYTM = nominal YTM.Duration and Bond Price VolatilityBond price movements will vary proportionally with modified duration for small changes in yieldsAn estimate of the percentage change in bond prices equals the change

33、 in yield time modified durationWhere: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 100.Trading Strategies Using DurationLongest-duration security provides the maximum price variationIf you expect a

34、 decline in interest rates, increase the average duration of your bond portfolio to experience maximum price volatilityIf you expect an increase in interest rates, reduce the average duration to minimize your price declineNote that the duration of your portfolio is the market-value-weighted average

35、of the duration of the individual bonds in the portfolio.Bond Duration in Years for Bonds Yielding 6 Percent Under Different Terms.Bond ConvexityEquation 19.6 is a linear approximation of bond price change for small changes in market yields.Bond ConvexityModified duration is a linear approximation o

36、f bond price change for small changes in market yieldsPrice changes are not linear, but a curvilinear (convex) function.Price-Yield Relationship for BondsThe graph of prices relative to yields is not a straight line, but a curvilinear relationshipThis can be applied to a single bond, a portfolio of

37、bonds, or any stream of future cash flowsThe convex price-yield relationship will differ among bonds or other cash flow streams depending on the coupon and maturityThe convexity of the price-yield relationship declines slower as the yield increasesModified duration is the percentage change in price

38、for a nominal change in yield.Modified DurationFor small changes this will give a good estimate, but this is a linear estimate on the tangent line.Determinants of ConvexityThe convexity is the measure of the curvature and is the second derivative of price with resect to yield (d2P/di2) divided by pr

39、iceConvexity is the percentage change in dP/di for a given change in yield.Determinants of ConvexityInverse relationship between coupon and convexityDirect relationship between maturity and convexityInverse relationship between yield and convexity.Modified Duration-Convexity EffectsChanges in a bond

40、s price resulting from a change in yield are due to:Bonds modified durationBonds convexityRelative effect of these two factors depends on the characteristics of the bond (its convexity) and the size of the yield changeConvexity is desirable.Duration and Convexity for Callable BondsIssuer has option

41、to call bond and pay off with proceeds from a new issue sold at a lower yieldEmbedded optionDifference in duration to maturity and duration to first callCombination of a noncallable bond plus a call option that was sold to the issuerAny increase in value of the call option reduces the value of the callable bond.Option Adjusted DurationBased on the probability that the issuing firm will exercise its call optionDuration of the non-callable bondDuration of the call option.Convexity of Callable BondsNoncallable bond has positive convexityCallable bond has negative co