16-1
第 16章债券资产组合的管理
Managing Bond Portfolios
16-2
债券资产组合的管理
Managing Bond Portfolios
16.1 利率风险
16.2 凸性
16.3 消极的债券管理
16.4 积极的债券管理
16.5 利率互换
16.6 金融工程与衍生利率
16-3
积极策略 Active strategy
– 根据利率预测来交易
Trade on interest rate predictions
– 根据市场价格失衡信息来交易
Trade on market inefficiencies
消极策略 Passive strategy
– 控制风险 Control risk
– 平衡风险和收益 Balance risk and return
Managing Fixed Income
Securities,Basic Strategies
16-4
价格和收益是反向关系
Inverse relationship between price and yield.
债券到期收益率的增长会导致价格下降的幅度低于与收益的等规模减少相联系的价格上升的幅度
An increase in a bond’s yield to maturity results in a
smaller price decline than the gain associated with a
decrease in yield.
长期债券比短期债券更具价格敏感性
Long-term bonds tend to be more price sensitive
than short-term bonds.
债券价格关系
Bond Pricing Relationships
16-5
当到期收益率增长时，价格对收益变化的敏感性以一下降的比率增加，
As maturity increases,price sensitivity increases at
a decreasing rate.
价格对收益变化的敏感性与债券的息票率有一反向关系。
Price sensitivity is inversely related to a bond’s
coupon rate.
债券价格对收益变化的敏感性与该债券销售的到期收益率承负相关关系,
Price sensitivity is inversely related to the yield to
maturity at which the bond is selling.
债券价格关系
Bond Pricing Relationships (cont’d)
16-6
久期
Duration
一种测量债券有效期限的方法
A measure of the effective maturity of a bond
每次利息或本金的支付时间的加权平均，权重应与每次支付的现值相联系
The weighted average of the times until each
payment is received,with the weights proportional
to the present value of the payment
除了零息债券，久期短于债券的到期日
Duration is shorter than maturity for all bonds
except zero coupon bonds
久期等于零息债券的到期日
Duration is equal to maturity for zero coupon
bonds
16-7
t t
tw CF y i c e( )1 Pr
twtD
T
t
1
CF C a s h F l o w f o r p e r i o d tt?
久期：计算
Duration,Calculation
Y=债券的到期收益 W t = 权重
D=久期 CF t = t 时的现金流
t=时间
16-8
久期：计算
Duration Calculation,
16-9
久期：计算
Duration Calculation,
16-10
久期 /价格关系
Duration/Price Relationship
价格变化与久期成比例而与到期日无关
Price change is proportional to duration and not to
maturity
DP/P = -D x [D(1+y) / (1+y)
D* = 修正久期 modified duration
D* = D / (1+y)
DP/P = - D* x Dy
16-11
久期 /价格关系
Duration/Price Relationship
为了确定久期和债券价格对利率变化的敏感性之间的关系，让我们将表 16 一 3 中久期为 1.8853 年的 2 年期息票债券的价格敏感性和久期与期限同为 1.8853 年的零息票债券的价格敏感性相比较。如果久期真是测度利率风险暴露程度的有用尺度的话，
两者应当具有相同的价格敏感性。
初始半年利率为 5 ％的息票债券售价为 964.54 美元。如果债券的半年收益率上升一个基点（ 1 ％的 1 / 100 ）至 5.01 %,那么它的价格将会跌至 964.19美元，下降了 0.0359 ％。零息票债券的期限为 1.8853x2 =3.7706 个半年期（由于我们用的是 5 ％的半年利率，我们也需要以半年为单位来定义久期以保证单位的一致性）。半年利率最初为 5 %,它将以 831.9623 美元（ l 000
美元／ l0537706）的价格出售。当利率上涨一个基点时，它的价格将跌至 831.6636 美元，资本同样损失了 0.0359 ％。由此我们可以得出结论，久期相等的资产对利率波动的敏感性实际是一样的。
16-12
久期 /价格关系
Duration/Price Relationship
To confirm the relationship between duration and the sensitivity of bond
price to interest rate changes,let’s compare the price sensitivity of the two-
year coupon bond in Table 16.3,which has a duration of 1.8852 years,to
the sensitivity of a zero-coupon bond with maturity and duration of 1.8852
years,Both should have equal price sensitivity if duration is a useful
measure of interest rate exposure.
The coupon bond sells for $964.5405 at the initial semiannual interest rate
of 5%,If the bond’s semiannual yield increases by 1 basis point (i.e.,.01%)
to 5.01%,its price will fall to $964.1942,a percentage decline of,0359%,
The zero-coupon bond has a maturity of 1.8852* 2= 3.7704 half-year
periods,(Because we use a half-year interest rate of 5%,we also need to
define duration in terms of a number of half-year periods to maintain
consistency of units.) At the initial half-year interest rate of 5%,it sells at a
price of $831.9704 ($1,000/1.053.7704),When the interest rate
increases,its price falls to $831.6717 ($1,000/1.05013.7704),for an
identical,0359% capital loss,We conclude,therefore,that equal-duration
assets are in fact equally sensitive to interest rate movements.
16-13
久期 /价格关系
Duration/Price Relationship
不同债券价格对市场利率变动的敏感性不一样。债券久期是衡量这种敏感性最重要和最主要的标准。久期等于利率变动一个单位所引起的价格变动。如市场利率变动 1％，债券的价格变动 3，则久期是 3。
16-14
久期法则
Rules for Duration
久期法则 1：零息票债券的久期等于它的到期时间。
Rule 1 The duration of a zero-coupon bond equals
its time to maturity.
久期法则 2,到期日不变时，债券的久期随着息票利率的降低而延长。
Rule 2 Holding maturity constant,a bond’s duration
is higher when the coupon rate is lower.
16-15
久期法则
Rules for Duration
久期法则 3：当息票利率不变时，债券的久期通常随着债券到期时间的增长而增长。
Rule 3 Holding the coupon rate constant,a bond’s
duration generally increases with its time to maturity.
久期法则 4,在其他因素都不变，债券的到期收益率较低时，息票债券的久期较长。
Rule 4 Holding other factors constant,the duration
of a coupon bond is higher when the bond’s yield to
maturity is lower.
16-16
久期法则
Rules for Duration (cont’d)
久期法则 5：无限期限债券的久期为
Rules 5 The duration of a level perpetuity is
equal to:
久期法则 6,稳定年金的久期由以下等式给出：
Rule 6 The duration of a level annuity is equal
to:
1)1(
1
Ty
T
y
y
y
y )1(?
16-17
久期法则
Rules for Duration (cont’d)
久期法则 7：公司息票债券的久期等于
Rule 7 The duration for a corporate bond is equal to:
c,为每个支付期的息票利率
coupon rate
yyc
ycTy
y
y
T
]1)1[(
)()1(1
16-18
久期法则
Rules for Duration (cont’d)
久期法则 8,由于息票债券是以面值出售的，计算久期的法则 7 可以简化成如下形式
Rule 8 For coupon bonds selling at par value,
rule 7 simplifies to the following formula for
duration,
16-19
曲线的形状，譬如价格 -收益关系的形状是凸的，价格 -收益曲线的曲率就称作债券的凸性。凸性一般被认为是债券的理想特征：
当债券收益下降时，债券价格以更大的曲率增长；当债券收益增长时，债券价格则以较低的曲率降低。
Curves with shapes such as that of the price-yield relationship
are said to be convex,and the curvature of the price-yield curve
is called the convexity of the bond,We can quantify convexity
as the rate of change of the slope of the price-yield curve,
expressed as a fraction of the bond price,As a practical rule,you
can view bonds with higher convexity as exhibiting higher
curvature in the price-yield relationship,
久期和凸性
Duration and Convexity
16-20
久期和凸性
Duration and Convexity
16-21
久期和凸性
Duration and Convexity
16-22
收益 Yield
价格 Price
久期
Duration
来自凸性的价格差
Pricing Error from
convexity
久期和凸性
Duration and Convexity
16-23
凸性的修正
Correction for Convexity
n
t
t
t tt
y
CF
yP
C o n v e x i t y
1
2
2 )()1()1(
1
修正凸性 Correction for Convexity:
])([21 2yC o n v e i x i t yyDP P DDD
16-24
债券指数基金 Bond-Index Funds
利率风险的免疫 Immunization of interest rate risk:
– 净值免疫 Net worth immunization
资产久期＝负债久期
Duration of assets = Duration of liabilities
– 目的数据免疫 Target date immunization
持有期匹配久期 Holding Period matches Duration
现金流匹配和贡献
Cash flow matching and dedication
消极债券管理
Passive Management
16-25
积极的债券管理：互换策略
Active Bond Management,Swapping Strategies
替代互换 Substitution swap
市场价差互换 Intermarket swap
利率预测互换 Rate anticipation swap
纯收益率转高互换 Pure yield pickup
税收互换 Tax swap
16-26
利率互换
Interest Rate Swaps
利率互换基本特征
Interest rate swap basic characteristics
– 一方支付固定和收到变动
One party pays fixed and receives variable
– 另一方一方支付变动而收到固定
Other party pays variable and receives fixed
16-27
利率互换
Interest Rate Swaps
利率互换又称“利率掉期”，是指银行与客户在约定的期限内，将相同外汇币种不同利率形式的资产或债务相互交换。如：固定利率和浮动利率间的相互转换，或浮动利率与浮动利率间的相互转换。浮动利率的计息基础一般选用 LIBOR（伦敦同业拆放利率），
利率设定日为每一利息计算期前两个工作日，利息交换方式为差额交割。利率互换不涉及本金的交换。
利率可以有多种形式，任何两种不同的形式都可以通过利率互换进行相互转换，其中最常用的利率互换是在固定利率与浮动利率之间进行转换。
16-28
利率互换
Interest Rate Swaps
An agreement between two parties (known as
counterparties) where one stream of future interest
payments is exchanged for another based on a
specified principal amount,Interest rate swaps often
exchange a fixed payment for a floating payment that
is linked to an interest rate (most often the LIBOR),A
company will typically use interest rate swaps to limit,
or manage,its exposure to fluctuations in interest
rates,or to obtain a marginally lower interest rate
than it would have been able to get without the swap.
16-29
利率互换
Interest Rate Swaps
市场的发展 Growth in market
– 1980年开始 Started in 1980
– 估计日交易量超过 600亿美元
Estimated over $60 trillion today
套期保值的应用 Hedging applications
16-30
或有免疫
Contingent Immunization
积极和消极管理的混合
A combination of active and passive management.
策略含有低限收益率的积极管理
The strategy involves active management with a floor
rate of return.
只要收益率高与低限收益率，组合就是积极管理
As long as the rate earned exceeds the floor,the
portfolio is actively managed.
只要达到低限收益率或 trigger rate,则组合就被免疫
Once the floor rate or trigger rate is reached,the
portfolio is immunized.
16-31
summary
甚至那些没有违约风险的债券，譬如财政部发行的债券仍然有利率风险。长期债券一般比短期债券对利率变动更敏感。债券平均生命期是用麦考利久期测度的，它被定义为债券每次支付时间的加权平均，其权重与支付的现值成比例。
Even default-free bonds such as Treasury issues
are subject to interest rate risk,Longer-term
bonds generally are more sensitive to interest rate
shifts than are short- term bonds,A measure of the
average life of a bond is Macaulay’s duration,defined
as the weighted average of the times until each
payment made by the security,with weights
proportional to the present value of the payment.
16-32
summary
久期是债券价格对其收益敏感程度的一个直接测度，债券价格成比例的变化等于负的久期乘以
（ 1＋ y）的成比例变化。
Duration is a direct measure of the sensitivity of
a bond’s price to a change in its yield,The
proportional change in a bond’s price equals
the negative of duration multiplied by the
proportional change in 1+y.
16-33
summary
免疫策略是消极管理固定收入资产组合的特征，
这一策略试图让个人或公司免除利率波动的风险。
免疫采取的形式或者是对资产组合净值或者是对资产组合的未来累计值进行利率风险免疫。
Convexity refers to the curvature of a bond’s
price-yield relationship,Accounting for
convexity can substantially improve on the
accuracy of the duration approximation for bond
price sensitivity to changes in yields.
16-34
summary
计划对全部资金的免疫是通过匹配资产与负债的久期来完成的。
随着时间的流失和利率的变化，为了保持免疫的头寸必须对资产组合按期进行再平衡。传统的免疫也取决于平缓的收益曲线的平行移动。但是这个假定不是现实的，因此，免疫通常不能做到完全彻底。为了减轻问题的严重程度，可以运用多因素久期模型，
它允许收益曲线的形状有所变化。
Immunization strategies are characteristic of passive
fixed-income portfolio management,Such strategies
attempt to render the individual or firm immune from
movements in interest rates,This may take the form of
immunizing net worth or,instead,immunizing the future
accumulated value of a fixed-income portfolio.
16-35
summary
免疫的更直接的形式是贡献或现金流匹配。如果资产组合的现金流与相关的负债的现金流是完全匹配的，再平衡就不再必要。
Immunization of a fully funded plan is accomplished by
matching the durations of assets and liabilities,To
maintain an immunized position as time passes and
interest rates change,the portfolio must be periodically
rebalanced,Classic immunization also depends on parallel
shifts in a flat yield curve,Given that this assumption is
unrealistic,immunization generally will be less than
complete,To mitigate the problem,multifactor duration
models can be used to allow for variation in the shape of
the yield curve.
16-36
summary
债券价格 -收益关系的曲率称作凸性，考虑到凸性可以大幅度改进久期近似值的准确性，而久期近似值反映了债券价格对债券收益变化的敏感程度。
A more direct form of immunization is
dedication,or cash flow matching,If a
portfolio is perfectly matched in cash
flow with projected liabilities,rebalancing
will be unnecessary.
16-37
summary
积极的债券管理包括利率预测技术和市场之间的利差分析。一种通常的分类方法把积极管理策略分为替换掉期、
市场间价差掉期、利率预期掉期或净收益增长掉期。
Active bond management consists of interest rate
forecasting techniques and intermarket spread
analysis,One popular taxonomy classifies active
strategies as substitution swaps,intermarket
spread swaps,rate anticipation swaps,or pure
yield pickup swaps.
16-38
summary
水平分析是一种利率预测技术。在这个过程中，分析人员预测收益曲线在一些持有期结束时的位置，再根据收益曲线预测有关债券的价格。因此，可以根据整个持有期的预期总收益（息票利息加资本利得）对债券排序。
Horizon analysis is a type of interest rate forecasting,
In this procedure the analyst forecasts the position of
the yield curve at the end of some holding period,and
from that yield curve predicts corresponding bond
prices,Bonds then can be ranked according to
expected total returns (coupon plus capital gain) over
the holding period.
16-39
summary
在固定收入市场中主要最新的发展是利率掉期。在这些安排中，掉期的双方交换不同证券的现金流，但是并不实际直接交换任何证券。这对于管理资产组合的久期是十分有用的工具，这对于那些在国外信用市场可以获得优惠利率贷款的公司来说也是有用的，这些公司在国外获得了比国内信用市场更友好的对待。
Interest rate swaps are major recent developments in
the fixed-income market,In these arrangements
parties trade the cash flows of different securities
without actually ex- changing any securities directly,
This is a useful tool to manage the duration of a
portfolio.
16-40
summary
金融工程已经创造了许多具有新奇的风险特征的固定收入衍生资产。
Financial engineering has created many new
fixed-income derivative assets with novel risk
characteristics.
第 16章债券资产组合的管理
Managing Bond Portfolios
16-2
债券资产组合的管理
Managing Bond Portfolios
16.1 利率风险
16.2 凸性
16.3 消极的债券管理
16.4 积极的债券管理
16.5 利率互换
16.6 金融工程与衍生利率
16-3
积极策略 Active strategy
– 根据利率预测来交易
Trade on interest rate predictions
– 根据市场价格失衡信息来交易
Trade on market inefficiencies
消极策略 Passive strategy
– 控制风险 Control risk
– 平衡风险和收益 Balance risk and return
Managing Fixed Income
Securities,Basic Strategies
16-4
价格和收益是反向关系
Inverse relationship between price and yield.
债券到期收益率的增长会导致价格下降的幅度低于与收益的等规模减少相联系的价格上升的幅度
An increase in a bond’s yield to maturity results in a
smaller price decline than the gain associated with a
decrease in yield.
长期债券比短期债券更具价格敏感性
Long-term bonds tend to be more price sensitive
than short-term bonds.
债券价格关系
Bond Pricing Relationships
16-5
当到期收益率增长时，价格对收益变化的敏感性以一下降的比率增加，
As maturity increases,price sensitivity increases at
a decreasing rate.
价格对收益变化的敏感性与债券的息票率有一反向关系。
Price sensitivity is inversely related to a bond’s
coupon rate.
债券价格对收益变化的敏感性与该债券销售的到期收益率承负相关关系,
Price sensitivity is inversely related to the yield to
maturity at which the bond is selling.
债券价格关系
Bond Pricing Relationships (cont’d)
16-6
久期
Duration
一种测量债券有效期限的方法
A measure of the effective maturity of a bond
每次利息或本金的支付时间的加权平均，权重应与每次支付的现值相联系
The weighted average of the times until each
payment is received,with the weights proportional
to the present value of the payment
除了零息债券，久期短于债券的到期日
Duration is shorter than maturity for all bonds
except zero coupon bonds
久期等于零息债券的到期日
Duration is equal to maturity for zero coupon
bonds
16-7
t t
tw CF y i c e( )1 Pr
twtD
T
t
1
CF C a s h F l o w f o r p e r i o d tt?
久期：计算
Duration,Calculation
Y=债券的到期收益 W t = 权重
D=久期 CF t = t 时的现金流
t=时间
16-8
久期：计算
Duration Calculation,
16-9
久期：计算
Duration Calculation,
16-10
久期 /价格关系
Duration/Price Relationship
价格变化与久期成比例而与到期日无关
Price change is proportional to duration and not to
maturity
DP/P = -D x [D(1+y) / (1+y)
D* = 修正久期 modified duration
D* = D / (1+y)
DP/P = - D* x Dy
16-11
久期 /价格关系
Duration/Price Relationship
为了确定久期和债券价格对利率变化的敏感性之间的关系，让我们将表 16 一 3 中久期为 1.8853 年的 2 年期息票债券的价格敏感性和久期与期限同为 1.8853 年的零息票债券的价格敏感性相比较。如果久期真是测度利率风险暴露程度的有用尺度的话，
两者应当具有相同的价格敏感性。
初始半年利率为 5 ％的息票债券售价为 964.54 美元。如果债券的半年收益率上升一个基点（ 1 ％的 1 / 100 ）至 5.01 %,那么它的价格将会跌至 964.19美元，下降了 0.0359 ％。零息票债券的期限为 1.8853x2 =3.7706 个半年期（由于我们用的是 5 ％的半年利率，我们也需要以半年为单位来定义久期以保证单位的一致性）。半年利率最初为 5 %,它将以 831.9623 美元（ l 000
美元／ l0537706）的价格出售。当利率上涨一个基点时，它的价格将跌至 831.6636 美元，资本同样损失了 0.0359 ％。由此我们可以得出结论，久期相等的资产对利率波动的敏感性实际是一样的。
16-12
久期 /价格关系
Duration/Price Relationship
To confirm the relationship between duration and the sensitivity of bond
price to interest rate changes,let’s compare the price sensitivity of the two-
year coupon bond in Table 16.3,which has a duration of 1.8852 years,to
the sensitivity of a zero-coupon bond with maturity and duration of 1.8852
years,Both should have equal price sensitivity if duration is a useful
measure of interest rate exposure.
The coupon bond sells for $964.5405 at the initial semiannual interest rate
of 5%,If the bond’s semiannual yield increases by 1 basis point (i.e.,.01%)
to 5.01%,its price will fall to $964.1942,a percentage decline of,0359%,
The zero-coupon bond has a maturity of 1.8852* 2= 3.7704 half-year
periods,(Because we use a half-year interest rate of 5%,we also need to
define duration in terms of a number of half-year periods to maintain
consistency of units.) At the initial half-year interest rate of 5%,it sells at a
price of $831.9704 ($1,000/1.053.7704),When the interest rate
increases,its price falls to $831.6717 ($1,000/1.05013.7704),for an
identical,0359% capital loss,We conclude,therefore,that equal-duration
assets are in fact equally sensitive to interest rate movements.
16-13
久期 /价格关系
Duration/Price Relationship
不同债券价格对市场利率变动的敏感性不一样。债券久期是衡量这种敏感性最重要和最主要的标准。久期等于利率变动一个单位所引起的价格变动。如市场利率变动 1％，债券的价格变动 3，则久期是 3。
16-14
久期法则
Rules for Duration
久期法则 1：零息票债券的久期等于它的到期时间。
Rule 1 The duration of a zero-coupon bond equals
its time to maturity.
久期法则 2,到期日不变时，债券的久期随着息票利率的降低而延长。
Rule 2 Holding maturity constant,a bond’s duration
is higher when the coupon rate is lower.
16-15
久期法则
Rules for Duration
久期法则 3：当息票利率不变时，债券的久期通常随着债券到期时间的增长而增长。
Rule 3 Holding the coupon rate constant,a bond’s
duration generally increases with its time to maturity.
久期法则 4,在其他因素都不变，债券的到期收益率较低时，息票债券的久期较长。
Rule 4 Holding other factors constant,the duration
of a coupon bond is higher when the bond’s yield to
maturity is lower.
16-16
久期法则
Rules for Duration (cont’d)
久期法则 5：无限期限债券的久期为
Rules 5 The duration of a level perpetuity is
equal to:
久期法则 6,稳定年金的久期由以下等式给出：
Rule 6 The duration of a level annuity is equal
to:
1)1(
1
Ty
T
y
y
y
y )1(?
16-17
久期法则
Rules for Duration (cont’d)
久期法则 7：公司息票债券的久期等于
Rule 7 The duration for a corporate bond is equal to:
c,为每个支付期的息票利率
coupon rate
yyc
ycTy
y
y
T
]1)1[(
)()1(1
16-18
久期法则
Rules for Duration (cont’d)
久期法则 8,由于息票债券是以面值出售的，计算久期的法则 7 可以简化成如下形式
Rule 8 For coupon bonds selling at par value,
rule 7 simplifies to the following formula for
duration,
16-19
曲线的形状，譬如价格 -收益关系的形状是凸的，价格 -收益曲线的曲率就称作债券的凸性。凸性一般被认为是债券的理想特征：
当债券收益下降时，债券价格以更大的曲率增长；当债券收益增长时，债券价格则以较低的曲率降低。
Curves with shapes such as that of the price-yield relationship
are said to be convex,and the curvature of the price-yield curve
is called the convexity of the bond,We can quantify convexity
as the rate of change of the slope of the price-yield curve,
expressed as a fraction of the bond price,As a practical rule,you
can view bonds with higher convexity as exhibiting higher
curvature in the price-yield relationship,
久期和凸性
Duration and Convexity
16-20
久期和凸性
Duration and Convexity
16-21
久期和凸性
Duration and Convexity
16-22
收益 Yield
价格 Price
久期
Duration
来自凸性的价格差
Pricing Error from
convexity
久期和凸性
Duration and Convexity
16-23
凸性的修正
Correction for Convexity
n
t
t
t tt
y
CF
yP
C o n v e x i t y
1
2
2 )()1()1(
1
修正凸性 Correction for Convexity:
])([21 2yC o n v e i x i t yyDP P DDD
16-24
债券指数基金 Bond-Index Funds
利率风险的免疫 Immunization of interest rate risk:
– 净值免疫 Net worth immunization
资产久期＝负债久期
Duration of assets = Duration of liabilities
– 目的数据免疫 Target date immunization
持有期匹配久期 Holding Period matches Duration
现金流匹配和贡献
Cash flow matching and dedication
消极债券管理
Passive Management
16-25
积极的债券管理：互换策略
Active Bond Management,Swapping Strategies
替代互换 Substitution swap
市场价差互换 Intermarket swap
利率预测互换 Rate anticipation swap
纯收益率转高互换 Pure yield pickup
税收互换 Tax swap
16-26
利率互换
Interest Rate Swaps
利率互换基本特征
Interest rate swap basic characteristics
– 一方支付固定和收到变动
One party pays fixed and receives variable
– 另一方一方支付变动而收到固定
Other party pays variable and receives fixed
16-27
利率互换
Interest Rate Swaps
利率互换又称“利率掉期”，是指银行与客户在约定的期限内，将相同外汇币种不同利率形式的资产或债务相互交换。如：固定利率和浮动利率间的相互转换，或浮动利率与浮动利率间的相互转换。浮动利率的计息基础一般选用 LIBOR（伦敦同业拆放利率），
利率设定日为每一利息计算期前两个工作日，利息交换方式为差额交割。利率互换不涉及本金的交换。
利率可以有多种形式，任何两种不同的形式都可以通过利率互换进行相互转换，其中最常用的利率互换是在固定利率与浮动利率之间进行转换。
16-28
利率互换
Interest Rate Swaps
An agreement between two parties (known as
counterparties) where one stream of future interest
payments is exchanged for another based on a
specified principal amount,Interest rate swaps often
exchange a fixed payment for a floating payment that
is linked to an interest rate (most often the LIBOR),A
company will typically use interest rate swaps to limit,
or manage,its exposure to fluctuations in interest
rates,or to obtain a marginally lower interest rate
than it would have been able to get without the swap.
16-29
利率互换
Interest Rate Swaps
市场的发展 Growth in market
– 1980年开始 Started in 1980
– 估计日交易量超过 600亿美元
Estimated over $60 trillion today
套期保值的应用 Hedging applications
16-30
或有免疫
Contingent Immunization
积极和消极管理的混合
A combination of active and passive management.
策略含有低限收益率的积极管理
The strategy involves active management with a floor
rate of return.
只要收益率高与低限收益率，组合就是积极管理
As long as the rate earned exceeds the floor,the
portfolio is actively managed.
只要达到低限收益率或 trigger rate,则组合就被免疫
Once the floor rate or trigger rate is reached,the
portfolio is immunized.
16-31
summary
甚至那些没有违约风险的债券，譬如财政部发行的债券仍然有利率风险。长期债券一般比短期债券对利率变动更敏感。债券平均生命期是用麦考利久期测度的，它被定义为债券每次支付时间的加权平均，其权重与支付的现值成比例。
Even default-free bonds such as Treasury issues
are subject to interest rate risk,Longer-term
bonds generally are more sensitive to interest rate
shifts than are short- term bonds,A measure of the
average life of a bond is Macaulay’s duration,defined
as the weighted average of the times until each
payment made by the security,with weights
proportional to the present value of the payment.
16-32
summary
久期是债券价格对其收益敏感程度的一个直接测度，债券价格成比例的变化等于负的久期乘以
（ 1＋ y）的成比例变化。
Duration is a direct measure of the sensitivity of
a bond’s price to a change in its yield,The
proportional change in a bond’s price equals
the negative of duration multiplied by the
proportional change in 1+y.
16-33
summary
免疫策略是消极管理固定收入资产组合的特征，
这一策略试图让个人或公司免除利率波动的风险。
免疫采取的形式或者是对资产组合净值或者是对资产组合的未来累计值进行利率风险免疫。
Convexity refers to the curvature of a bond’s
price-yield relationship,Accounting for
convexity can substantially improve on the
accuracy of the duration approximation for bond
price sensitivity to changes in yields.
16-34
summary
计划对全部资金的免疫是通过匹配资产与负债的久期来完成的。
随着时间的流失和利率的变化，为了保持免疫的头寸必须对资产组合按期进行再平衡。传统的免疫也取决于平缓的收益曲线的平行移动。但是这个假定不是现实的，因此，免疫通常不能做到完全彻底。为了减轻问题的严重程度，可以运用多因素久期模型，
它允许收益曲线的形状有所变化。
Immunization strategies are characteristic of passive
fixed-income portfolio management,Such strategies
attempt to render the individual or firm immune from
movements in interest rates,This may take the form of
immunizing net worth or,instead,immunizing the future
accumulated value of a fixed-income portfolio.
16-35
summary
免疫的更直接的形式是贡献或现金流匹配。如果资产组合的现金流与相关的负债的现金流是完全匹配的，再平衡就不再必要。
Immunization of a fully funded plan is accomplished by
matching the durations of assets and liabilities,To
maintain an immunized position as time passes and
interest rates change,the portfolio must be periodically
rebalanced,Classic immunization also depends on parallel
shifts in a flat yield curve,Given that this assumption is
unrealistic,immunization generally will be less than
complete,To mitigate the problem,multifactor duration
models can be used to allow for variation in the shape of
the yield curve.
16-36
summary
债券价格 -收益关系的曲率称作凸性，考虑到凸性可以大幅度改进久期近似值的准确性，而久期近似值反映了债券价格对债券收益变化的敏感程度。
A more direct form of immunization is
dedication,or cash flow matching,If a
portfolio is perfectly matched in cash
flow with projected liabilities,rebalancing
will be unnecessary.
16-37
summary
积极的债券管理包括利率预测技术和市场之间的利差分析。一种通常的分类方法把积极管理策略分为替换掉期、
市场间价差掉期、利率预期掉期或净收益增长掉期。
Active bond management consists of interest rate
forecasting techniques and intermarket spread
analysis,One popular taxonomy classifies active
strategies as substitution swaps,intermarket
spread swaps,rate anticipation swaps,or pure
yield pickup swaps.
16-38
summary
水平分析是一种利率预测技术。在这个过程中，分析人员预测收益曲线在一些持有期结束时的位置，再根据收益曲线预测有关债券的价格。因此，可以根据整个持有期的预期总收益（息票利息加资本利得）对债券排序。
Horizon analysis is a type of interest rate forecasting,
In this procedure the analyst forecasts the position of
the yield curve at the end of some holding period,and
from that yield curve predicts corresponding bond
prices,Bonds then can be ranked according to
expected total returns (coupon plus capital gain) over
the holding period.
16-39
summary
在固定收入市场中主要最新的发展是利率掉期。在这些安排中，掉期的双方交换不同证券的现金流，但是并不实际直接交换任何证券。这对于管理资产组合的久期是十分有用的工具，这对于那些在国外信用市场可以获得优惠利率贷款的公司来说也是有用的，这些公司在国外获得了比国内信用市场更友好的对待。
Interest rate swaps are major recent developments in
the fixed-income market,In these arrangements
parties trade the cash flows of different securities
without actually ex- changing any securities directly,
This is a useful tool to manage the duration of a
portfolio.
16-40
summary
金融工程已经创造了许多具有新奇的风险特征的固定收入衍生资产。
Financial engineering has created many new
fixed-income derivative assets with novel risk
characteristics.
