兹维博迪金融学第二版课件Chapter08.pptx

Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall1Chapter 8:Valuation of Known Cash Flows:BondsObjectiveValuation of fixed income securitiesExplain why bond prices changeCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall2Chapter 8 Contents8.1 Using Present Value Formulas to Value Known Flows8.2 The Basic Building Blocks:Pure Discount Bonds8.3 Coupon Bonds,Current Yield,and Yield-to-Maturity8.4 Reading Bond Listings8.5 Why Yields for the same Maturity Differ8.6 The Behavior of Bond Prices Over TimeCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall38.1 Using Present Value Formulas to Value Known FlowsYou have been offered the opportunity to purchase a mortgage.It was originally part of a creative financing package where the original owner financed the buyerThe remaining life of the mortgage is 60 months,with payment of$400.Your required rate of return is 1.5%/monthCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall4CalculationUsing the present value of an annuity formula discussed in chapter 4,you will pay no more thanCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall5Financial CalculatorAlternatively,using your financial calculator(remember to set the correct defaults)you obtainCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall6Change in Required RateIf your required rate of return increased to 1.6%/monthCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall7Using Present Value Formulas to Value Known FlowsObserve that the maximum you would pay for the bond has decreasedAn increase in the required rate of return always leads to a decrease in the value of a fixed income securityThe proof is very easyCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall8Bond Prices Rise as the Interest Rates FallWrite the PV of the fixed income security as the sum termsCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall9Bond Prices Rise as the Interest Rates FallIf i goes up,1+i goes up,1/(1+i)goes down for i -1,(1/(1+i)j goes down for i 0.So if the payments are positive,then the sum must also go down Similarly,i down-PV upCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall10Bond Prices Rise as the Interest Rates FallBasic principle in evaluating known flows A change in market interest rates causes a A change in market interest rates causes a change in the change in the oppositeopposite direction in the direction in the market values of all existing contracts market values of all existing contracts promising fixed payments in the futurepromising fixed payments in the futureCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall11NoteVolatile market rates imply volatile market valuesCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall12Finding the Correct Discount RateBond analysis is not as easy as this analysis appears to imply We need an interest rate to use in the We need an interest rate to use in the formulaformula We saw in Chapter 2 that interest rates are a We saw in Chapter 2 that interest rates are a function of time-to-maturityfunction of time-to-maturity Two default-free bonds with identical Two default-free bonds with identical maturities may have different YTMsmaturities may have different YTMsCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall13Yield CurveA typical yield curve:Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall148.2 The Basics Building Blocks:Pure Discount BondsWe can always analyze any fixed income contract into a sum of pure discount bondsA pure discount bond is a security that promises to pay a specified single cash payment(face value or par value)at a specified date called its maturity dateCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall15Pure Discount BondsNote There is no cash flow associated with There is no cash flow associated with interest interest Pure discount bonds are purchased at a Pure discount bonds are purchased at a discount from their face or par valuediscount from their face or par valueCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall16Pure Discount BondsThe pure discount bond is an example of the present value of a lump sum equation we analyzed in Chapter 4Solving this,the yield-to-maturity on a pure discount bond is given by the relationship:Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall17Pure Discount BondsIn this equation,P is the present value or price of the bondP is the present value or price of the bond F is the face or future value F is the face or future value n is the investment periodn is the investment period i is the yield-to-maturityi is the yield-to-maturityCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall18Pure Discount BondsExample You can purchase a pure discount bond for You can purchase a pure discount bond for$9,000,and it matures in two years with a$9,000,and it matures in two years with a face value of$10,000face value of$10,000 What is the ytm?What is the ytm?Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall19Pure Discount BondsCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall208.3 Coupon Bonds,Current Yield,and Yield to MaturityA coupon bond obligates the issuer to make periodic payments of interest(called make periodic payments of interest(called coupon paymentscoupon payments)to the bond holder until)to the bond holder until the bond matures the bond matures at which time the face value of the bond is at which time the face value of the bond is also paid to the bond holderalso paid to the bond holder and the contract is satisfiedand the contract is satisfiedCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall21Coupon RateThe coupon rate is the interest rate applied to the face value to compute the coupon payment A bond with a face value of$1,000 and a A bond with a face value of$1,000 and a coupon rate of 10%pays an annual coupon coupon rate of 10%pays an annual coupon of$100of$100 At maturity,the payment is$1,000+$100At maturity,the payment is$1,000+$100Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall22Cash Flows for 10%$1,000 Coupon BondCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall23Par,premium,and Discount BondsA coupon bond with its current price equal to its par value is a par bondIf it is trading below par it is a discount bondIf it is trading above par it is a premium bond(not to be confused with the U.K.lottery bond of the(not to be confused with the U.K.lottery bond of the same name!)same name!)Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall24Bonds Trading at Par Bond Pricing Principle#1:(Par Bonds)If a bonds price equals its face value,then If a bonds price equals its face value,then its yield-to-maturity=current yield=its yield-to-maturity=current yield=coupon rate.coupon rate.Proof:Proof:Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall25Coupon Bonds,Current Yield,and Yield-to-MaturityThe yield-to-maturity is the discount rate that makes the present value of the cash flows from the bond equal to the current price of the bondAn excellent way to compute the ytm is given in Chapter 4Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall26Using Pure Discount Bonds to Value other BondsValue a bond that pays its$100 coupon at the end of each year for 3-years,and its par value of$1,000 in 3-years You have discovered three pure discount You have discovered three pure discount bonds(each with a$1,000 par value)that bonds(each with a$1,000 par value)that mature in 1,2,and 3 years,and that are mature in 1,2,and 3 years,and that are trading at$960,$890,and$810 respectivelytrading at$960,$890,and$810 respectivelyCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall27First Solution MethodCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall28Second Solution MethodCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall29ConclusionThe first method uses the fact that a coupon bond is the sum of pure discount bonds it is fast and directit is fast and directThe second method first determines the yields-to-maturity of each discount bond cash flows are then evaluated using themcash flows are then evaluated using themCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall30The YTM of the Coupon BondWe have the price of the coupon bond,and the timing and magnitude of its future cash flows,so we can determine its YTMWe use the financial calculator,but a numerical method was provided in chapter 4 for this class of problemsCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall31The YTM of the Coupon BondCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall32ObservationThe yield to maturity on the 3-year pure discount bond was 7.28%and the yield-to-maturity on the 3-year coupon bond was 7.10%The yield-curve for default-free bonds is not a unique valueCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall33Bond Pricing Principle#2&3Bond Principle#2:Premium Bondsbond price face value bond price face value ytm current ytm current yield coupon rateyield coupon rateBond Principle#3:Discount Bondsbond price face value bond price current ytm current yield coupon rateyield coupon rateCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall34Proof of Relationship between YTM and Current YieldFor coupon bonds,we have the following relationships Note the(sensible)restrictions on the Note the(sensible)restrictions on the variable rangesvariable ranges Note that 1/(1+i)n-1)is always positiveNote that 1/(1+i)n-1)is always positiveCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall35Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall36Proof of Relationship between Current and Coupon Yields For coupon bonds,we have the following relationship derived from the bond formula Note that the differences between the Note that the differences between the reciprocals have the same sign,so the actual reciprocals have the same sign,so the actual differences also have the same signdifferences also have the same sign Note that size relationship is determined by Note that size relationship is determined by the discount factor which is always 1the discount factor which is always 1Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall37Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall38How to Remember PrinciplesImagine that the bond was issued at par the yield-to-maturity moves from the coupon the yield-to-maturity moves from the coupon yield in the opposite direction to priceyield in the opposite direction to price the coupon rate is unchangingthe coupon rate is unchangingThis diagram may help:Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall39Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall40High Yield T-Bond FundsYield curves with large positive slopes make longer-term T-bonds tempting because,like T-bills,they are default-free The above diagram was based on:par=The above diagram was based on:par=$1000,coupon=$100,n=10-years,flat$1000,coupon=$100,n=10-years,flat Observe the large effect of modest changes Observe the large effect of modest changes in interest on capitalin interest on capital A close up is given belowA close up is given belowCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall41Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall42ClarificationThe last example used a flat yield curveLet us look at an example with short-term rates remaining fixedshort-term rates remaining fixed longer-term rates rising on increased longer-term rates rising on increased expectation of a general rise in interest ratesexpectation of a general rise in interest ratesCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall43Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall44Investment ImplicationsAssume a 20-year bond with a coupon rate of 6%Purchase for$1016.54 when the lower curve Purchase for$1016.54 when the lower curve prevailsprevails When yield curve rises,the bond is worth When yield curve rises,the bond is worth only$814.05only$814.05 This is a massive capital risk This is a massive capital risk Additionally,long-term rates are more volatile Additionally,long-term rates are more volatile than short-term ratesthan short-term ratesCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall458.4 Reading Bond ListingsThere are traditions for reporting yields and computing earned interest that need to be understood before trading Coupon bonds are often quoted in terms of Coupon bonds are often quoted in terms of the annual rate compounded semi-annuallythe annual rate compounded semi-annually T-bills are often quoted on a discount basisT-bills are often quoted on a discount basis e.g.,a 1 year T-bill has 364 days outstanding,e.g.,a 1 year T-bill has 364 days outstanding,but a year has only 360 days(it gets nasty)but a year has only 360 days(it gets nasty)Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall46Reading Bond ListingsTake care that the fractional part of a number is understood Is it 16ths,32nds,64ths,100ths or some Is it 16ths,32nds,64ths,100ths or some other convention?other convention?Ask price:dealers selling priceBid price:dealers buying priceCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall478.5 Why Yields for the same Maturity Differ The fundamental building block of bonds is The fundamental building block of bonds is the pure discount bond:Coupon bonds may the pure discount bond:Coupon bonds may be viewed as a portfolio of discount bondsbe viewed as a portfolio of discount bonds The rule of one price applies to bonds The rule of one price applies to bonds through pure discount bondsthrough pure discount bonds It is a mistake to assume that coupon bonds It is a mistake to assume that coupon bonds with the same life have the same yield-their with the same life have the same yield-their coupon rates differ,leading to a different%coupon rates differ,leading to a different%mix of discount bondsmix of discount bondsCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall48Movement of a Pure Discount Bonds Price over TimeCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall498.6 The Behavior of Bond Prices Over TimeThe expected price of pure discount bonds rises exponentially to the face value with time,and the actual price never exceeds parCoupon bonds are more complex,and their price may exceed their par value,but at maturity they reach their par valueCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall50Bond Prices at Alternative YieldsCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall51Bond Price Sensitivity to Yield ChangesCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall52Bond Price TrajectoryThe following diagram shows the dynamic nat