投资学第16章债券资产组合管理.ppt
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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
• 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
16-4
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
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
• 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
Price change is proportional to duration and not to maturity
P P
ቤተ መጻሕፍቲ ባይዱ
Dx
(1 y) 1 y
D* = modified duration
P D * y P
16-10
Rules for Duration
Rule 1 The duration of a zero-coupon bond equals its time to maturity
Maturity = 8%
16-15
Correction for Convexity
Convexity
1 P (1 y)2
n CFt
t 1
(1
y)t
(t 2 t)
Correction for Convexity:
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
wt CFt (1 y)t Price
T
D t wt t 1
CFt Cash Flow for period t
16-8
Spreadsheet 16.1 Calculating the Duration of Two Bonds
16-9
Duration/Price Relationship
CHAPTER 16
Managing Bond Portfolios
McGraw-Hill/Irwin
Investments, 8th edition
Bodie, Kane and Marcus
Slides by Susan Hine
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved.
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
• 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 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
16-14
Figure 16.3 Bond Price Convexity: 30Year Maturity, 8% Coupon; Initial Yield to
• 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
16-4
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
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
• 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
Price change is proportional to duration and not to maturity
P P
ቤተ መጻሕፍቲ ባይዱ
Dx
(1 y) 1 y
D* = modified duration
P D * y P
16-10
Rules for Duration
Rule 1 The duration of a zero-coupon bond equals its time to maturity
Maturity = 8%
16-15
Correction for Convexity
Convexity
1 P (1 y)2
n CFt
t 1
(1
y)t
(t 2 t)
Correction for Convexity:
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
wt CFt (1 y)t Price
T
D t wt t 1
CFt Cash Flow for period t
16-8
Spreadsheet 16.1 Calculating the Duration of Two Bonds
16-9
Duration/Price Relationship
CHAPTER 16
Managing Bond Portfolios
McGraw-Hill/Irwin
Investments, 8th edition
Bodie, Kane and Marcus
Slides by Susan Hine
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved.
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
• 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 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