投资学债券资产组合管理
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? Duration rule is a good approximation for only small changes in bond yields
16-14
Figure 16.3 Bond Price Convexity: 30Year Maturity, 8% Coupon; Initial Yield to
16-4
Table 16.1 Prices of 8% Coupon Bond (Coupons Paid Semiannually)
16-5
Table 16.2 Prices of Zero-Coupon Bond (Semiannually Compounding)
16-6
Duration
? Duration is shorter than maturity for all bonds except zero coupon bonds
? Duration is equal to maturity for zero coupon bonds
16-7
Duration: Calculation
16-11
Figure 16.2 Bond Duration versus Bond Maturity
16-12
Table 16.3 Bond Durations (Yield to Maturity = 8% APR; Semiannual Coupons)
16-13
Convexity
? The relationship between bond prices and yields is not linear
Maturity = 8%
16-15
Correction for Convexity
? Convexity?
1 P ? (1?
y)2
t
n ?1
? A measure of the effective maturity of a bond
? The weighted average of the times until each payment is received, with the weights proportional to the present value of the payment
CHAPTER 16
Managing Bond Portfolios
McGraw-Hill/Irwin
Investments, 8 th edition
Bodie, Kane and Marcus
Slides by Susan Hine
Copyright ? 2009 by The McGraw-Hill Companies, Inc. All rights reserved.
Price change is proportional to duration and not to maturity
?P P
?
?
Dx
?? ??
(1? y) 1? y
? ??
D* = modified duration
?P ? ?D*?y P
16-10
Leabharlann Baidu
Rules for Duration
Rule 1 The duration of a zero-coupon bond equals its time to maturity
16-2
Figure 16.1 Change in Bond Price as a Function of Change in Yield to Maturity
16-3
Bond Pricing Relationships Continued
? As maturity increases, price sensitivity increases at a decreasing rate
wt ? CF t (1 ? y)t Pr ice
T
? D ? t ? w t t?1
CF t ? Cash Flow for period t
16-8
Spreadsheet 16.1 Calculating the Duration of Two Bonds
16-9
Duration/Price Relationship
Rule 2 Holding maturity constant, a bond's duration is higher when the coupon rate is lower
Rule 3 Holding the coupon rate constant, a bond's duration generally increases with its time to maturity
? Price sensitivity is inversely related to a bond's coupon rate
? Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Rule 4 Holding other factors constant, the duration of a coupon bond is higher when the bond's yield to maturity is lower
Rules 5 The duration of a level perpetuity is equal to: (1+y) / y
Bond Pricing Relationships
? Inverse relationship between price and yield ? An increase in a bond's yield to maturity
results in a smaller price decline than the gain associated with a decrease in yield ? Long-term bonds tend to be more price sensitive than short-term bonds
16-14
Figure 16.3 Bond Price Convexity: 30Year Maturity, 8% Coupon; Initial Yield to
16-4
Table 16.1 Prices of 8% Coupon Bond (Coupons Paid Semiannually)
16-5
Table 16.2 Prices of Zero-Coupon Bond (Semiannually Compounding)
16-6
Duration
? Duration is shorter than maturity for all bonds except zero coupon bonds
? Duration is equal to maturity for zero coupon bonds
16-7
Duration: Calculation
16-11
Figure 16.2 Bond Duration versus Bond Maturity
16-12
Table 16.3 Bond Durations (Yield to Maturity = 8% APR; Semiannual Coupons)
16-13
Convexity
? The relationship between bond prices and yields is not linear
Maturity = 8%
16-15
Correction for Convexity
? Convexity?
1 P ? (1?
y)2
t
n ?1
? A measure of the effective maturity of a bond
? The weighted average of the times until each payment is received, with the weights proportional to the present value of the payment
CHAPTER 16
Managing Bond Portfolios
McGraw-Hill/Irwin
Investments, 8 th edition
Bodie, Kane and Marcus
Slides by Susan Hine
Copyright ? 2009 by The McGraw-Hill Companies, Inc. All rights reserved.
Price change is proportional to duration and not to maturity
?P P
?
?
Dx
?? ??
(1? y) 1? y
? ??
D* = modified duration
?P ? ?D*?y P
16-10
Leabharlann Baidu
Rules for Duration
Rule 1 The duration of a zero-coupon bond equals its time to maturity
16-2
Figure 16.1 Change in Bond Price as a Function of Change in Yield to Maturity
16-3
Bond Pricing Relationships Continued
? As maturity increases, price sensitivity increases at a decreasing rate
wt ? CF t (1 ? y)t Pr ice
T
? D ? t ? w t t?1
CF t ? Cash Flow for period t
16-8
Spreadsheet 16.1 Calculating the Duration of Two Bonds
16-9
Duration/Price Relationship
Rule 2 Holding maturity constant, a bond's duration is higher when the coupon rate is lower
Rule 3 Holding the coupon rate constant, a bond's duration generally increases with its time to maturity
? Price sensitivity is inversely related to a bond's coupon rate
? Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Rule 4 Holding other factors constant, the duration of a coupon bond is higher when the bond's yield to maturity is lower
Rules 5 The duration of a level perpetuity is equal to: (1+y) / y
Bond Pricing Relationships
? Inverse relationship between price and yield ? An increase in a bond's yield to maturity
results in a smaller price decline than the gain associated with a decrease in yield ? Long-term bonds tend to be more price sensitive than short-term bonds