14-1
第 14章债券的价格和收益
Bond Prices and Yields
14-2
债券的价格和收益
Bond Prices and Yields
14.1 债券的特点
14.2 债券定价
14.3 债券收益率
14.4 债券的时间价格
14.5 违约风险与债券价格
14-3
债券的特征
Bond Characteristics
面值 Face or par value
息票利率 Coupon rate
– 零息债券 Zero coupon bond
复利和支付 Compounding and payments
– 应计利息 Accrued Interest
契约 Indenture
14-4
债券的发行者
Different Issuers of Bonds
财政部 U.S,Treasury
– 票据和债券 Notes and Bonds
公司 Corporations
市政府 Municipalities
外国政府和公司 International Governments and
Corporations
14-5
债券的条款
Provisions of Bonds
安全的或非安全的 Secured or unsecured
提前赎回条款 Call provision
可转换条款 Convertible provision
卖回条款 Put provision (putable bonds)
浮动利率债券 Floating rate bonds
偿债基金 Sinking funds
14-6
债券市场上的创新
Innovations in the Bond Market
反向浮动债券 Reverse floaters
资产支撑债券 Asset-backed bonds
支付选择权债券 (以同类证券作支付的证券 )
Pay-in-kind bonds
灾难债券 Catastrophe bonds
指数债券 Indexed bonds
– TIPS (通货膨胀保护 债券 Treasury Inflation
Protected Securities)
14-7
债券定价
Bond Pricing
P C
r
P a r V a l u e
r
B t
T
t
T
T
T
( ) ( )1 11
PB = 债券价格 Price of the bond
Ct = 利息或息票 interest or coupon payments
T = 周期数 number of periods to maturity
r = 半年期利息或息票 semi-annual discount rate or
the semi-annual yield to maturity
Par Value,面值
14-8
票息利率为 8%，面值为本 1000
元的 10年期债券，分 20次支付利息，每次利息支付额为 40元，假定年利率为 6%，该债券的价格为：
14-9
Price of 8%,10-yr,with yield at 6%
77.148,1
)03.1(
1
1000
)03.1(
1
40
20
20
1
P
P
B
t
tB
票息 Coupon = 4%*1,000 = 40 (Semiannual)
利率 Discount Rate = 3% (Semiannual)
期限 Maturity = 10 years or 20 periods
面值 Par Value = 1,000
14-10
价格与望期收益率具有反向相关关系。
Prices and Yields (required rates of return) have an
inverse relationship
在期望收益率接近 0时，债券的价值正好等于它的所有现金流的和。
When yields approach zero,the value of the bond
approaches the sum of the cash flows.
当期望收益率走高时，债券的价值将会降低。
When yields get very high the value of the bond will be
very low.
债券价格与收益率
Bond Prices and Yields
14-11
价格和期望收益率关系
Relationship between Prices and Yields
价格
Price
收益 Yield
14-12
例如，假定息票利率为 8%，债券期限为 30年，债券售价为 1276.76 美元。投资者在这个价格购入债券，平均回报率是多少？为了回答这个问题，我们要找出让债券支付本息的现值与债券价格相等时的利率，这是与被考察的债券价格保持一致的利率。为此，我们要利用下面方程求出
$1,276.76=∑ $40/(1+r)t + $1,000 /(1+r) 60
t =1 to 60
或者
1276.76＝ 40× 年金因素 (r,60) ＋ 1000 × 现值因素 (r,60)
你可以用财务计算器求得半年期利率 r＝ 0.03或 3%。这就被认为是债券的到期收益率。
14-13
For example,suppose an 8% coupon,30-year bond is selling at $1,276.76,
What aver- age rate of return would be earned by an investor purchasing the
bond at this price? To answer this question,we find the interest rate at which
the present value of the remaining bond payments equals the bond price,This
is the rate that is consistent with the observed price of the bond,Therefore,
we solve for r in the following equation:
$1,276.76=∑ $40/(1+r)t + $1,000 /(1+r) 60
t =1 to 60
These equations have only one unknown variable,the interest rate,r,You
can use a financial calculator to confirm that the solution to the equation is r
=.03,or 3% per half year,This is considered the bond’s yield to maturity,
as the bond would be fairly priced at $1,276.76 if the fair market rate of
return on the bond over its entire life were 3% per half year.
14-14
债券收益率的多种量值
Alternative Measures of Yield
当前收益率 Current Yield
回购收益率 Yield to Call
– 回购价格替换面值 Call price replaces par
– 回购日期替换到期日 Call date replaces maturity
持有期收益率 Holding Period Yield
– 考虑实际票息的重投资
Considers actual reinvestment of coupons
– 考虑任何在债券到期前的价格变化
Considers any change in price if the bond is held less than
its maturity
14-15
债券收益率的多种量值
Alternative Measures of Yield
例如，如果一种 30年期、年息票收入为 80美元的债券以 1 000 美元购入，它的到 期收益率为 8%。如果债券价格到年底升为 1 050 美元，它的到期收益率将下降到 8%以 下（现在债券的售价高于面值，所以到期收益率一定低于
8%的息票利率），但本年持 有期回报率将高于 8%。
持有期回报率＝ [80美元＋ (1 050 美元 -1 000美元 )]/1 000美元＝ 0.13 或 13%
Consider as example a 30-year bond paying an annual coupon
of $80 and selling at par value of $1,000,The bond’s initial yield
to maturity is 8%,If the yield remains at 8% over the year,the
bond price will remain at par,so the holding period return also
will be 8%,But if the yield falls below 8%,the bond price will
increase,Suppose the price increases to $1,050,Then the
holding period return is greater than 8%:
Holding period return = [80+1050-1000)/1000]=0.13 (13%)
14-16
溢价和帖现债券
Premium and Discount Bonds
溢价债券 Premium Bond
– 在到期日息票利率超过收益利率
Coupon rate exceeds yield to maturity
– 债券价格在到期日将降到面值
Bond price will decline to par over its maturity
帖现债券 Discount Bond
– 在到期日收益利率超过息票利率
Yield to maturity exceeds coupon rate
– 债券价格在到期日将升到面值
Bond price will increase to par over its maturity
14-17
坐标上的溢价和 折扣 债券
Premium and Discount Bonds over Time
溢价债券
Premium Bond
面值债券
Par Bond
折扣债券
Discount Bond
期限 Maturity
价格 Price
14-18
违约风险和量化
Default Risk and Ratings
量化公司 Rating companies
– 穆迪投资者服务公司 Moody’s Investor Service
– 标准普尔 Standard & Poor’s
– 费奇 Fitch
量化类别 Rating Categories
– 投资等级 Investment grade
– 投机等级 Speculative grade
14-19
用来量化公司的因素
Factors Used by Rating Companies
债务保障比例 Coverage ratios
杠杆系数 Leverage ratios
流动性比例 Liquidity ratios
盈利比例 Profitability ratios
现金流对债务比例 Cash flow to debt
14-20
防错保护
Protection Against Default
偿债基金 Sinking funds
未来债务的次级合约 Subordination of future debt
（次级债务）
股利限制 Dividend restrictions
担保品 Collateral
14-21
Summary
固定收益证券向投资者承诺支付一固定收入或一特定的收入流。息票债券为其典型形式。
Fixed-income securities are distinguished by
their promise to pay a fixed or specified
stream of income to their holders,The
coupon bond is a typical fixed-income
security.
14-22
Summary
中长期国债的期限大于一年。它们按照或接近于面值发行，其价格考虑了应计净利息。长期国债在整个生命期的最后五年内可能被赎回。
Treasury notes and bonds have original
maturities greater than one year,They are
issued at or near par value,with their prices
quoted net of accrued interest,T-bonds may
be callable during their last five years of life.
14-23
Summary
赎回债券应提供更高的到期收益率，以补偿投资者在利率下降和发生债券以赎 回价被赎回时所遭受的资本利得损失。债券发行时，经常制定一赎回保护期。除此以 外，折扣债券以远低于赎回价的价格销售，这实质上体现了赎回保护。
Callable bonds should offer higher promised yields to maturity
to compensate investors for the fact that they will not realize
full capital gains should the interest rate fall and the bonds be
called away from them at the stipulated call price,Bonds
often are issued with a period of call protection,In addition,
discount bonds selling significantly below their call price offer
implicit call protection.
14-24
Summary
可卖回债券赋予债券的持有人而不是发行人以终止或延长债券寿命期的权利。
Put bonds give the bondholder rather than
the issuer the option to terminate or extend
the life of the bond.
14-25
Summary
可转换债券的持有人可自行决定是否要将手中的债券换成一定数量的股票，可转换债券持有人获得这一期权的代价是接受较低的息票利率。
Convertible bonds may be exchanged,at
the bondholder’s discretion,for a specified
number of shares of stock,Convertible
bondholders,pay” for this option by
accepting a lower coupon rate on the
security.
14-26
Summary
浮动利率债券支付一个超过短期参照利率的固定溢价。风险是有限的，因为支付的利率与当前市场条件紧密相连。
Floating-rate bonds pay a coupon rate at a
fixed premium over a reference short-term
interest rate,Risk is limited because the
rate is tied to current market conditions.
14-27
Summary
到期收益率是一个与到期价格现金流的现值相等的单一利率。债券价格与收益率是负相关的。对于溢价债券来说，息票利率高于现行收益率，现行收益率高于到期收益率。对于折扣债券来说，这一顺序是相反的。
The yield to maturity is the single interest rate that
equates the present value of a security’s cash flows
to its price,Bond prices and yields are inversely
related,For premium bonds,the coupon rate is
greater than the current yield,which is greater than
the yield to maturity,The order of these inequalities
is reversed for discount bonds.
14-28
Summary
到期收益率常常被解释为投资者购买并持有一种债券到期的平均回报率的估计，但这个解释是错误的。与此相关的测度是赎回收益率、已实现的复利收益率和预期（相对于承诺）的到期收益率。
The yield to maturity is often interpreted as an
estimate of the average rate of return to an
investor who purchases a bond and holds it until
maturity,This interpretation is subject to error,
however,Related measures are yield to call,
realized compound yield,and expected (versus
promised) yield to maturity.
14-29
Summary
零息债券的价格随时间变化呈指数型上升，它提供了一个与利率相等的增值率。国内税务署将这一价格升值作为对投资者按利息收入估算的税收基础。
Prices of zero - coupon bonds rise
exponentially over time,providing a rate of
appreciation equal to the interest rate,The
IRS treats this price appreciation as imputed
taxable interest income to the investor,
14-30
Summary
当债券有可能违约时，到期拟定收益率就是债券持有人有可能得到的到期收益率的最大值。不管什么原因，只要发生了违约，承诺的收益就会落空。为了补偿投资者的这一违约风险，债券必须提供违约溢价。也就是承诺付给比无违约的政府证券更高的收益。
如果公司经营业绩良好，公司债券就可提供高于政府债券的回报。
否则，公司债券的回报就低于政府债券。
When bonds are subject to potential default,the stated yield to
maturity is the maximum possible yield to maturity that can be
realized by the bondholder,In the event of default,however,
that promised yield will not be realized,To compensate bond
investors for default risk,bonds must offer default premiums,
that is,promised yields in excess of those offered by default -
free government securities,If the firm remains healthy,its
bonds will provide higher returns than government bonds,
Otherwise the returns may be lower.
第 14章债券的价格和收益
Bond Prices and Yields
14-2
债券的价格和收益
Bond Prices and Yields
14.1 债券的特点
14.2 债券定价
14.3 债券收益率
14.4 债券的时间价格
14.5 违约风险与债券价格
14-3
债券的特征
Bond Characteristics
面值 Face or par value
息票利率 Coupon rate
– 零息债券 Zero coupon bond
复利和支付 Compounding and payments
– 应计利息 Accrued Interest
契约 Indenture
14-4
债券的发行者
Different Issuers of Bonds
财政部 U.S,Treasury
– 票据和债券 Notes and Bonds
公司 Corporations
市政府 Municipalities
外国政府和公司 International Governments and
Corporations
14-5
债券的条款
Provisions of Bonds
安全的或非安全的 Secured or unsecured
提前赎回条款 Call provision
可转换条款 Convertible provision
卖回条款 Put provision (putable bonds)
浮动利率债券 Floating rate bonds
偿债基金 Sinking funds
14-6
债券市场上的创新
Innovations in the Bond Market
反向浮动债券 Reverse floaters
资产支撑债券 Asset-backed bonds
支付选择权债券 (以同类证券作支付的证券 )
Pay-in-kind bonds
灾难债券 Catastrophe bonds
指数债券 Indexed bonds
– TIPS (通货膨胀保护 债券 Treasury Inflation
Protected Securities)
14-7
债券定价
Bond Pricing
P C
r
P a r V a l u e
r
B t
T
t
T
T
T
( ) ( )1 11
PB = 债券价格 Price of the bond
Ct = 利息或息票 interest or coupon payments
T = 周期数 number of periods to maturity
r = 半年期利息或息票 semi-annual discount rate or
the semi-annual yield to maturity
Par Value,面值
14-8
票息利率为 8%，面值为本 1000
元的 10年期债券，分 20次支付利息，每次利息支付额为 40元，假定年利率为 6%，该债券的价格为：
14-9
Price of 8%,10-yr,with yield at 6%
77.148,1
)03.1(
1
1000
)03.1(
1
40
20
20
1
P
P
B
t
tB
票息 Coupon = 4%*1,000 = 40 (Semiannual)
利率 Discount Rate = 3% (Semiannual)
期限 Maturity = 10 years or 20 periods
面值 Par Value = 1,000
14-10
价格与望期收益率具有反向相关关系。
Prices and Yields (required rates of return) have an
inverse relationship
在期望收益率接近 0时，债券的价值正好等于它的所有现金流的和。
When yields approach zero,the value of the bond
approaches the sum of the cash flows.
当期望收益率走高时，债券的价值将会降低。
When yields get very high the value of the bond will be
very low.
债券价格与收益率
Bond Prices and Yields
14-11
价格和期望收益率关系
Relationship between Prices and Yields
价格
Price
收益 Yield
14-12
例如，假定息票利率为 8%，债券期限为 30年，债券售价为 1276.76 美元。投资者在这个价格购入债券，平均回报率是多少？为了回答这个问题，我们要找出让债券支付本息的现值与债券价格相等时的利率，这是与被考察的债券价格保持一致的利率。为此，我们要利用下面方程求出
$1,276.76=∑ $40/(1+r)t + $1,000 /(1+r) 60
t =1 to 60
或者
1276.76＝ 40× 年金因素 (r,60) ＋ 1000 × 现值因素 (r,60)
你可以用财务计算器求得半年期利率 r＝ 0.03或 3%。这就被认为是债券的到期收益率。
14-13
For example,suppose an 8% coupon,30-year bond is selling at $1,276.76,
What aver- age rate of return would be earned by an investor purchasing the
bond at this price? To answer this question,we find the interest rate at which
the present value of the remaining bond payments equals the bond price,This
is the rate that is consistent with the observed price of the bond,Therefore,
we solve for r in the following equation:
$1,276.76=∑ $40/(1+r)t + $1,000 /(1+r) 60
t =1 to 60
These equations have only one unknown variable,the interest rate,r,You
can use a financial calculator to confirm that the solution to the equation is r
=.03,or 3% per half year,This is considered the bond’s yield to maturity,
as the bond would be fairly priced at $1,276.76 if the fair market rate of
return on the bond over its entire life were 3% per half year.
14-14
债券收益率的多种量值
Alternative Measures of Yield
当前收益率 Current Yield
回购收益率 Yield to Call
– 回购价格替换面值 Call price replaces par
– 回购日期替换到期日 Call date replaces maturity
持有期收益率 Holding Period Yield
– 考虑实际票息的重投资
Considers actual reinvestment of coupons
– 考虑任何在债券到期前的价格变化
Considers any change in price if the bond is held less than
its maturity
14-15
债券收益率的多种量值
Alternative Measures of Yield
例如，如果一种 30年期、年息票收入为 80美元的债券以 1 000 美元购入，它的到 期收益率为 8%。如果债券价格到年底升为 1 050 美元，它的到期收益率将下降到 8%以 下（现在债券的售价高于面值，所以到期收益率一定低于
8%的息票利率），但本年持 有期回报率将高于 8%。
持有期回报率＝ [80美元＋ (1 050 美元 -1 000美元 )]/1 000美元＝ 0.13 或 13%
Consider as example a 30-year bond paying an annual coupon
of $80 and selling at par value of $1,000,The bond’s initial yield
to maturity is 8%,If the yield remains at 8% over the year,the
bond price will remain at par,so the holding period return also
will be 8%,But if the yield falls below 8%,the bond price will
increase,Suppose the price increases to $1,050,Then the
holding period return is greater than 8%:
Holding period return = [80+1050-1000)/1000]=0.13 (13%)
14-16
溢价和帖现债券
Premium and Discount Bonds
溢价债券 Premium Bond
– 在到期日息票利率超过收益利率
Coupon rate exceeds yield to maturity
– 债券价格在到期日将降到面值
Bond price will decline to par over its maturity
帖现债券 Discount Bond
– 在到期日收益利率超过息票利率
Yield to maturity exceeds coupon rate
– 债券价格在到期日将升到面值
Bond price will increase to par over its maturity
14-17
坐标上的溢价和 折扣 债券
Premium and Discount Bonds over Time
溢价债券
Premium Bond
面值债券
Par Bond
折扣债券
Discount Bond
期限 Maturity
价格 Price
14-18
违约风险和量化
Default Risk and Ratings
量化公司 Rating companies
– 穆迪投资者服务公司 Moody’s Investor Service
– 标准普尔 Standard & Poor’s
– 费奇 Fitch
量化类别 Rating Categories
– 投资等级 Investment grade
– 投机等级 Speculative grade
14-19
用来量化公司的因素
Factors Used by Rating Companies
债务保障比例 Coverage ratios
杠杆系数 Leverage ratios
流动性比例 Liquidity ratios
盈利比例 Profitability ratios
现金流对债务比例 Cash flow to debt
14-20
防错保护
Protection Against Default
偿债基金 Sinking funds
未来债务的次级合约 Subordination of future debt
（次级债务）
股利限制 Dividend restrictions
担保品 Collateral
14-21
Summary
固定收益证券向投资者承诺支付一固定收入或一特定的收入流。息票债券为其典型形式。
Fixed-income securities are distinguished by
their promise to pay a fixed or specified
stream of income to their holders,The
coupon bond is a typical fixed-income
security.
14-22
Summary
中长期国债的期限大于一年。它们按照或接近于面值发行，其价格考虑了应计净利息。长期国债在整个生命期的最后五年内可能被赎回。
Treasury notes and bonds have original
maturities greater than one year,They are
issued at or near par value,with their prices
quoted net of accrued interest,T-bonds may
be callable during their last five years of life.
14-23
Summary
赎回债券应提供更高的到期收益率，以补偿投资者在利率下降和发生债券以赎 回价被赎回时所遭受的资本利得损失。债券发行时，经常制定一赎回保护期。除此以 外，折扣债券以远低于赎回价的价格销售，这实质上体现了赎回保护。
Callable bonds should offer higher promised yields to maturity
to compensate investors for the fact that they will not realize
full capital gains should the interest rate fall and the bonds be
called away from them at the stipulated call price,Bonds
often are issued with a period of call protection,In addition,
discount bonds selling significantly below their call price offer
implicit call protection.
14-24
Summary
可卖回债券赋予债券的持有人而不是发行人以终止或延长债券寿命期的权利。
Put bonds give the bondholder rather than
the issuer the option to terminate or extend
the life of the bond.
14-25
Summary
可转换债券的持有人可自行决定是否要将手中的债券换成一定数量的股票，可转换债券持有人获得这一期权的代价是接受较低的息票利率。
Convertible bonds may be exchanged,at
the bondholder’s discretion,for a specified
number of shares of stock,Convertible
bondholders,pay” for this option by
accepting a lower coupon rate on the
security.
14-26
Summary
浮动利率债券支付一个超过短期参照利率的固定溢价。风险是有限的，因为支付的利率与当前市场条件紧密相连。
Floating-rate bonds pay a coupon rate at a
fixed premium over a reference short-term
interest rate,Risk is limited because the
rate is tied to current market conditions.
14-27
Summary
到期收益率是一个与到期价格现金流的现值相等的单一利率。债券价格与收益率是负相关的。对于溢价债券来说，息票利率高于现行收益率，现行收益率高于到期收益率。对于折扣债券来说，这一顺序是相反的。
The yield to maturity is the single interest rate that
equates the present value of a security’s cash flows
to its price,Bond prices and yields are inversely
related,For premium bonds,the coupon rate is
greater than the current yield,which is greater than
the yield to maturity,The order of these inequalities
is reversed for discount bonds.
14-28
Summary
到期收益率常常被解释为投资者购买并持有一种债券到期的平均回报率的估计，但这个解释是错误的。与此相关的测度是赎回收益率、已实现的复利收益率和预期（相对于承诺）的到期收益率。
The yield to maturity is often interpreted as an
estimate of the average rate of return to an
investor who purchases a bond and holds it until
maturity,This interpretation is subject to error,
however,Related measures are yield to call,
realized compound yield,and expected (versus
promised) yield to maturity.
14-29
Summary
零息债券的价格随时间变化呈指数型上升，它提供了一个与利率相等的增值率。国内税务署将这一价格升值作为对投资者按利息收入估算的税收基础。
Prices of zero - coupon bonds rise
exponentially over time,providing a rate of
appreciation equal to the interest rate,The
IRS treats this price appreciation as imputed
taxable interest income to the investor,
14-30
Summary
当债券有可能违约时，到期拟定收益率就是债券持有人有可能得到的到期收益率的最大值。不管什么原因，只要发生了违约，承诺的收益就会落空。为了补偿投资者的这一违约风险，债券必须提供违约溢价。也就是承诺付给比无违约的政府证券更高的收益。
如果公司经营业绩良好，公司债券就可提供高于政府债券的回报。
否则，公司债券的回报就低于政府债券。
When bonds are subject to potential default,the stated yield to
maturity is the maximum possible yield to maturity that can be
realized by the bondholder,In the event of default,however,
that promised yield will not be realized,To compensate bond
investors for default risk,bonds must offer default premiums,
that is,promised yields in excess of those offered by default -
free government securities,If the firm remains healthy,its
bonds will provide higher returns than government bonds,
Otherwise the returns may be lower.
