第四章债券及其估价chapter4Bondsandtheirvaluation

1、4-1CHAPTER 4Bonds and Their ValuationnKey features of bondsnBond valuationnMeasuring yieldnAssessing risk4-22021-10-16Ch4 Bonds and Their Valuation4.1 Key Features of Bond4-32021-10-16Ch4 Bonds and Their ValuationWhat is a bond?nA long-term debt instrument in which a borrower agrees to make payments

2、 of principal and interest, on specific dates, to the holders of the bond.4-42021-10-16Ch4 Bonds and Their ValuationFour types of bonds (according to bond issuer) p.140nTreasury bondsnCorporate bondsnMuniciple bondsnForeign bonds4-52021-10-16Ch4 Bonds and Their ValuationKey Elements of a BondnPar va

3、lue face amount of the bond, which is paid at maturity (assume $1,000).nCoupon interest rate stated interest rate (generally fixed) paid by the issuer. Multiply by par to get dollar payment of interest.nMaturity years until the bond must be repaid.nIssue date when the bond was issued.nYield to matur

4、ity - rate of return earned on a bond held until maturity (also called the “promised yield”).4-62021-10-16Ch4 Bonds and Their ValuationSome special bonds：Bonds with a call provision p.143nAllows issuer to refund the bond issue if rates decline (helps the issuer, but hurts the investor).nBorrowers ar

5、e willing to pay more, and lenders require more, for callable bonds.nMost bonds have a deferred call and a declining call premium.4-72021-10-16Ch4 Bonds and Their ValuationBonds with sinking fund provision p.143nProvision to pay off a loan over its life rather than all at maturity.nReduces risk to i

6、nvestor, shortens average maturity.nBut not good for investors if rates decline after issuance.4-82021-10-16Ch4 Bonds and Their ValuationConvertible bond may be exchanged for common stock of the firm, at the holders option.Bonds issued with Warrant long-term option to buy a stated number of shares o

7、f common stock at a specified price.Putable bond allows holder to sell the bond back to the company prior to maturity.Income bond pays interest only when interest is earned by the firm.Indexed bond interest rate paid is based upon the rate of inflation.4-92021-10-16Ch4 Bonds and Their ValuationBond

8、markets p.163nCorporate bonds primarily traded in the over-the-counter (OTC) market.nMost bonds are owned by and traded among large financial institutions.nFull information on bond trades in the OTC market is not published, but a representative group of bonds is listed and traded on the bond divisio

9、n of the NYSE.4-102021-10-16Ch4 Bonds and Their ValuationHow about China?Types of bondsn国债n企业债券n政策性金融债券n公司债券n可转换公司债n商业银行次级债券等等4-112021-10-16Ch4 Bonds and Their ValuationScale of bondsn发行规模： 1.1981年国债发行额48.66亿元，1994年即突破l000亿元，2007、2008年分别达到23483亿元,8615亿元。2.2008年，银行间债券市场累计发行人民币债券25625.8亿元4-122021-10-1

10、6Ch4 Bonds and Their Valuationn交易规模：2008年-银行间债券市场现券交易规模达到37万亿元，银行间债券品种多达200个-沪深两市债券交易规模仅仅2200亿元4-132021-10-16Ch4 Bonds and Their ValuationMarket structuren沪、深证券交易所债券市场(为债券场内交易市场)n全国银行间债券交易市场(债券场外交易市场)n银行柜台市场(债券场外交易市场) (2001年以后，中国人民银行、中国证监会和财政部等主管部门加强了交易所债券市场和银行间债券市场的连通工作，例如2004年财政部通过银行间债券市场发行了l4期共44

11、13.9亿元记账式国债，其中跨市场国债有8期共3398.7亿元，占整个发行量的76.69%)4-142021-10-16Ch4 Bonds and Their Valuation4.2 Bond ValuationnThe value of any financial asset(as well as physical assets) is The present value of the cash flows the asset is expected to produce.4-152021-10-16Ch4 Bonds and Their ValuationThe value of fin

12、ancial assetsnn2211k)(1CF . k)(1CF k)(1CF Value012nkCF1CFnCF2Value.4-162021-10-16Ch4 Bonds and Their Valuation4.2.1 Valuation of annual coupon bond4-172021-10-16Ch4 Bonds and Their ValuationThe value of annual coupon bondsndndn2d21d1b)k(1M )k(1INT . )k(1INT )k(1INT V012nkdINT1INTnMINT2Vb.NOTE: kd is

13、 the bonds market interest rate; it is not the coupon interest rate.4-182021-10-16Ch4 Bonds and Their ValuationWhat is the value of a 10-year, 10% annual coupon bond(par value:$1000), if kd = 10%?$1,000 10) PVIF(10%,*1000 10) PVIFA(10%,*100 V(1.10)$1,000 (1.10)$100 . (1.10)$100 VB10101B01210kd100100

14、 + 1,000100VB = ?.4-192021-10-16Ch4 Bonds and Their ValuationnAttention1： Kd influences bond value!4-202021-10-16Ch4 Bonds and Their Valuation Kd and Bond Value 1.When kd increases:nSuppose inflation rises by 2%, causing kd = 12%. Now, kd rises above the coupon rate, the bonds value falls below par,

15、 and sells at a discount.$887.02 10) PVIF(12%,*1000 10) PVIFA(12%,*100 VB4-212021-10-16Ch4 Bonds and Their Valuation2.When kd decreases:nSuppose inflation falls by 2%, causing kd = 8%. Now, kd falls below the coupon rate, the bonds value rises above par, and sells at a premium.$1134.21 10) PVIF(8%,*

16、1000 10) PVIFA(8%,*100 VB4-222021-10-16Ch4 Bonds and Their ValuationnAttention2： Years to maturity also influences bond value!4-232021-10-16Ch4 Bonds and Their ValuationBond values over timenAt maturity, the value of any bond must equal its par value.nIf kd remains constant:nThe value of a premium b

17、ond would decrease over time, until it reached $1,000.nThe value of a discount bond would increase over time, until it reached $1,000.nA value of a par bond stays at $1,000.4-242021-10-16Ch4 Bonds and Their ValuationThe price path of a bondnWhen buying dates vary, what would happen to the value of t

18、his bond if its required rate of return remained at 10%, or at 12%, or at 8% until maturity?Years to Maturity1,225.161,134.211,000887.02838.93025 20 15 10 5 0kd = 8%.kd = 12%.kd = 10%.VB4-252021-10-16Ch4 Bonds and Their Valuation4.2.2 Valuation of semiannual coupon bonds4-262021-10-16Ch4 Bonds and T

19、heir ValuationWhat is the value of a 10-year, 10% semiannual coupon bond, if kd = 10%?$1,000 20) PVIF(5%,*1000 20) PVIFA(5%,*50 VB0122*10=20Kd/2=5%5050 + 1,00050VB = ?.4-272021-10-16Ch4 Bonds and Their Valuation When kd=12%nSuppose kd = 12%. What is the value of a 10-year, 10% semiannual coupon bond

20、?$885.30 20) PVIF(6%,*1000 20) PVIFA(6%,*50 VB0122*10=20Kd/2=6%5050 + 1,00050VB = ?.4-282021-10-16Ch4 Bonds and Their Valuation When kd=8%nSuppose kd = 8%. What is the value of a 10-year, 10% semiannual coupon bond?$1135.92 20) PVIF(4%,*1000 20) PVIFA(4%,*50 VB0122*10=20Kd/2=4%5050 + 1,00050VB = ?.4

21、-292021-10-16Ch4 Bonds and Their Valuation2Nd2N1ttdB/2)k(1/2)k(1INT/2 VMValuation of semiannual coupon bonds: p.1511.Decide no. of periods; (2N)2.Decide periodic rate; (kd/2)3.Decide interest paid per period. (par value*coupon interest rate/2)4.Calculate.4-302021-10-16Ch4 Bonds and Their Valuation4.

22、3 Measuring YieldsYield to maturity(YTM) p.148Yield to call(YTC) p.1494-312021-10-16Ch4 Bonds and Their Valuation4.3.1 Yield to MaturitynYield to Maturity: the annual rate of return of a bond held to maturity.n It is the rate “kd” that makes : Vb=bond price 4-322021-10-16Ch4 Bonds and Their Valuatio

23、nHow to solve for YTM?nMake clear the cash flow in (interests and principal)and cash flow out (buying price);nUse the bond valuation formula but substitute Vb with bond price;nSolve for “Kd” 4-332021-10-16Ch4 Bonds and Their ValuationEg.1 What is the YTM on a 10-year, 9% annual coupon, $1,000 par va

24、lue bond, selling for $887?nMust find the kd that solves this model.)10,(*1000)10,(*90887$)k(11,000 )k(190 . )k(190 $887)k(1M )k(1INT . )k(1INT V10d10d1dNdNd1dBddKPVIFKPVIFA4-342021-10-16Ch4 Bonds and Their ValuationUsing trial-and error methodnSuppose kd=10%, VB=938.51887.00nSuppose kd=11%, VB=882.

25、01887.00nSo, %91.10%10 10%)-(11%*938.51)-(882.01938.51)-(887 Kd4-352021-10-16Ch4 Bonds and Their ValuationEg. 2 Find YTM, if the bond price was $1,134.20.nThis bond sells at a premium, so YTM coupon rate.)10,(*1000)10,(*902 .1134$)k(11,000 )k(190 . )k(190 $1134.210d10d1dddKPVIFKPVIFA4-362021-10-16Ch

26、4 Bonds and Their ValuationUsing trial-and error methodnSuppose kd=8%, VB=1067.111134.2nSo, %08. 7%7 7%)-(8%*1140.42)-(1067.111140.42)-(1134.2 Kd4-372021-10-16Ch4 Bonds and Their Valuation4.3.2 Yield to CallnYield to Call: the annual rate of return of a bond called before its maturity date.nIt is al

27、so the rate “kd” that makes : Vb=bond price 4-382021-10-16Ch4 Bonds and Their ValuationHow to solve for YTC?Solving for the YTC is identical to solving for YTM, except the time to call is used for N and the call price substitute for M.4-392021-10-16Ch4 Bonds and Their Valuation Eg:A 10-year, 10% ann

28、ual coupon, $1,000 par value bond selling for $1,135.90 can be called in 4 years for $1,050, what is its yield to call (YTC)?1135.9100 *(, 4)1050 *(, 4)8% ,1102.991135.9;7% ,1139.761135.9(1139.761135.9) * (8%7% )7%7.10%1139.761102.99dbdbPVIFA YTCPVIF YTCIf KVIf KVYTC4-402021-10-16Ch4 Bonds and Their

29、 ValuationIf the bond will not be called:0)PVIF(YTM,1*100010)PVIFA(YTM,*1001135.9YTM=8.02%4-412021-10-16Ch4 Bonds and Their ValuationHow about YTM or YTC of bonds with semiannual coupon?Eg: P.168 4-2(1)Solve for YTM1100=40*PVIFA(KPER,20)+1000*PVIF(KPER,20)KPER=3.33%YTM=2* KPER =6.66%0122*10=20Kper=Y

30、TM/24040 + 1,00040-1100.4-422021-10-16Ch4 Bonds and Their Valuation(2)Solve for YTC1100=40*PVIFA(KPER,10)+1050*PVIF(KPER,10)KPER=3.25%YTC=2* KPER =6.50%0122*5=10KPER=YTC/24040 + 1,05040-1100.4-432021-10-16Ch4 Bonds and Their Valuation4.4 Assessing RisksInterest rate riskReinvestment riskDefault risk

31、4-442021-10-16Ch4 Bonds and Their ValuationWhat is interest rate (or price) risk?nInterest rate risk is the concern that rising kd will cause the value of a bond to fall.% change 1 yr kd 10yr % change+4.7%$1,047 5% $1,386 +38.6%$1,00010% $1,000-4.3% $957 15% $749 -25.1%The 10-year bond is more sensi

32、tive to interest rate changes, and hence has more interest rate risk.4-452021-10-16Ch4 Bonds and Their ValuationWhat is reinvestment rate risk?nReinvestment rate risk is the concern that kd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income.EXAMPLE: Suppose yo

33、u just won$500,000 playing the lottery. You intend to invest the money and live off the interest.4-462021-10-16Ch4 Bonds and Their ValuationReinvestment rate risk examplenYou may invest in either a 10-year bond or a series of ten 1-year bonds. Both 10-year and 1-year bonds currently yield 10%.nIf yo

34、u choose the 1-year bond strategy:nAfter Year 1, you receive $50,000 in income and have $500,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to $15,000.nIf you choose the 10-year bond strategy:nYou can lock in a 10% interest rate, and $50,000 annual income.4-472021-10

35、-16Ch4 Bonds and Their ValuationInterest rate risk and reinvestment rate risk: a comparisonnCONCLUSION: Nothing is riskless!Short-term AND/OR High coupon bondsLong-term AND/OR Low coupon bondsInterest rate riskLowHighReinvestment rate riskHighLow4-482021-10-16Ch4 Bonds and Their ValuationDefault risknIf an issuer defaults, investors receive less than the promised return. nInfluenced by the issuers financial strength and the terms of the bond contract.4