固定收益证券第二章课件.ppt

Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,第,2,讲债券的收益率,1.,利差,2.,复利,3.,债券收益率的度量,1.,债券收益率利差,基准利率：,国债收益率,LIBOR,央行对基准利率的影响,影响,yield spread,的因素：,信用品质,经济景气,内含期权,Call or prepayment,Put or conversion option,流动性,发行规模,税收,其他,2.,复利,普通复利,计息频率或计息周期,利率,r,的时间单位和期数,N,的时间单位应该相同,已发行债券的剩余期限不是计息期的倍数,时计算要特别小心,连续复利,同一利率的不同表达,连续复利的优点,计息天数不整齐或是现金流时间间隔不规则,计算多期收益率：算术平均,符合正态分布假设,取值范围,多期收益率仍然符合正态分布,不存在汇率收益率悖论,缺点,横截面组合收益率单个资产收益率加权平均,普通复利（,R,m,）和连续复利（,R,c,）的转换,特别地，当,m=1,时，对数差分收益率,年百分比收益率,APR,与年有效收益率,AEY,债券等价收益率,BEY,3.,债券收益率的度量,就传统的固定收益债券而言，投资收益包括：,定期的利息支付,本金收回（资本利得）,再投资收益,3.1,息票率,3.2,当期收益率,current yield,=Annual Interest/Market Price,3.3,到期收益率,Yield to Maturity,使债券未来承诺现金流的现值与其当前价格相等的贴现率,与债券价格包含同样信息,内在收益率,解,下列,关于,y,的,方程,:,Yield to Maturity:Example,10,yrs MaturityCoupon Rate=7%,Price=$950,y,=3.8635%,YTM=3.86%x 2=7.72%,bond equivalent yield(BEY),对价格为面值的债券而言,息票率,=,当期收益率,=,到期收益率,对溢价债券而言,息票率,当期收益率,到期收益率,对折价债券而言,到期收益率,当期收益率,息票率,到期收益率的优缺点,综合反应债券投资的三种未来现金收益,与债券价格一一对应,仅仅是特定条件下的承诺到期收益率，非预期收益率的精确指标,到期收益率的隐含假设,没有违约风险,投资者持有到期,每一期现金流都按照,y,进行再投资（忽略再投资风险）,对复杂债券预期收益率的衡量精度尤其低,YTC=6.64%YTM=6.82%,3.4,赎回收益率,Yield to Call,call protection,yield to,call,for premium bonds,yield to,maturity,for discount bonds,3.5,3.6,注意：,YTC,、,YTP,、,CFY,与,YTM,同为内在收益率,存在同样局限,CFY,有提前偿付率的假定,3.7,实现复利收益率,Realized compound Yield,在,a,）的情况下，,实现复利收益率为,1000(1+,y,realized,),2,=1210,y,realized,=10%,在,b,）的情况下，,实现复利收益率,为,1000(1+y,realized,),2,=1208,y,realized,=9.91%,However,in an economy with future interest rate uncertainty,the rates at which interim coupons will be reinvested are not yet known.,This reduces much of the attraction of the realized yield measure.,3.8,持有期回报率,Holding-Period Return,HPR=I+(,P,n,-,P,0,),/,P,0,where,I,=interest payment,P,1,=price in n periods,P,0,=purchase price,Holding-Period Return,：,Example,CR=8%YTM=8%,N=10 years,Semiannual Compounding,P,0,=$1000,In six months the rate falls to 7%,P,1,=$1068.55,HPR=40+(1068.55-1000)/1000,HPR=10.85%(semiannual),When the yield to maturity is unchanged over the period,the rate of return on the bond will equal that yield.,An increase in the bond,s yield acts to reduce its price,which means that the holding period return will be less than the initial yield.,Conversely,a decline in yield will result in a holding period return greater than the initial yield.,Annualizing the holding period return,Over multiple years,From quarterly holding period returns,(1+,HPR,)=(1+HPR1)(1+HPR2)(1+HPR3)(1+HPR4),3.9 OID,债券的税后收益,有些债券以较低的息票率发行，按面值打折出售（,OID,，,original issue discount,）,极端的例子为零息债券，没有息票利息，而以价格升值的形式提供全部收益。

美国的国库券是短期零息债券,长期零息债券一般由中长期国债剥离而成（,separate trading of registered interest and principal of securities,STRIPS,）例如，一张,10,年期国债、可以剥离成,21,张独立的零息债券，期限从,6,个月到,10,年债券剥离,bond stripping,债券重构,bond reconstitution,Figure 14.7 The Price of a 30-Year Zero-Coupon Bond over Time at a Yield to,Maturity,of 10%,The tax authorities recognize that the,“,built-in,”,price appreciation on OID bonds such as zero-coupon bonds represents an implicit interest payment to the holder of the security.,基于市场利率不变的价格升值计为应税利息收入；而因市场利率变化而导致的额外价格变动则被看作是资本利得。

例,1,：如果当前市场利率为,10,，一个,30,年期零息票债券的发行价是,1000/(1.10),30,=57.31,元,第二年，如果利率仍为,10,，则债券价格应为,1000/(1.10),29,=63.04,元,应税利息收入为,63.04,57.31=5.73,元,如果利率发生变化，如跌到,9.9,，那么债券价格将是,1000/(1.099),29,=64.72,元,如果卖出债券，则,64.72,元与,63.04,元之差就是资本利得并要按资本利得税率纳税；如果不卖出，那么这个价差就是未实现的资本利得，在当年不纳税例,2,：,30-year maturity bond,，,issued with a coupon rate of 4%,（,annually,）,and a yield to maturity of 8%,P,0,=,$549.69,If the bond,s yield to maturity remains at 8%in one year,P,1,=,$,553.66,Taxable interest income,=,$553.66,$549.69=$3.97,Suppose that the YTM actually falls to 7%by the end of the first year,and that the investor sells the bond after the first year.If the investor,s tax rate on interest income is 36%and the tax rate on capital gains is 20%,what is the investor,s after-tax rate of return?,3.10,到期收益率与违约风险,违约溢价,default premium,:,公司债券的承诺收益率与类似期限的无违约风险政府债券收益率之差,.,违约风险越大的债券，提供的违约溢价越高，因而到期收益率也就越高。

这一关系被称为,“,利率的风险结构,”,.,违约溢价随经济周期变动,.,Figure 14.11 Yields on Long-Term Bonds,1954,2006,承诺到期收益率,promised,YTM,:,公司履行全部本息支付,期望到期收益率,expected,YTM,:,考虑公司违约可能,例 假设某公司,20,年前发行了一种息票利率为,9,的债券，到目前为止还有,10,年到期由于公司面临财务困境，投资者虽然相信公司有能力按期支付利息，但预期在债券到期日公司将被迫破产，届时债券持有人将只能收回面值的,70,债券当前的市场价格为,750,元该债券的期望到期收益率和承诺到期收益率分别是多少？,承诺到期收益率,=13.7,期望到期收益率,=11.6,1.,Bonds of Zello Corporation with a par value of$1,000 sell for$960,mature in five years,and have a 7%annual coupon rate paid semiannually.,a.,Calculate the:,i.Current yield.,ii.Yield to maturity(to the nearest whole percent,i.e.,3%,4%,5%,etc.).,iii.Realized compound yield for an investor with a three-year holding period and a reinvestment rate of 6%over the period.At the end of three years the 7%coupon bonds with two years remaining will sell to yield 7%.,b.,Cite one major shortcoming for each of the following fixed-income yield measures:,i.Current yield.,ii.Yield to maturity.,iii.Realized compound yield.,2.,A newly 。