投资学第16章债券资产组合管理
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• 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
Figure 16.2 Bond Duration versus Bond Maturity
Table 16.3 Bond Durations (Yield to Maturity = 8% APR; Semiannual Coupons)
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Convexity
• The relationship between bond prices and yields is not linear
• Subject to negative convexity • Often sell for more than their principal
• The weighted average of the times until each payment is received, with the weights proportional to the present value of the payment
• Duration is shorter than maturity for all bonds except zero coupon bonds
Price change is proportional to duration and not to maturity
D* = modified duration
Rules for Duration
Rule 1 The duration of a zero-coupon bond equals its time to maturity
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
• Negative convexity • Use effective duration:
Figure 16.5 Price –Yield Curve for a Callable Bond
Mortgage-Backed Securities
• Among the most successful examples of financial engineering
Maturity = 8%
Correction for Convexity
Correction for Convexity:
Figure 16.4 Convexity of Two Bonds
Callable Bonds
• As rates fall, there is a ceiling on possible prices – The bond cannot be worth more than its call price
Table 16.1 Prices of 8% Coupon Bond (Coupons Paid Semiannually)
Table 16.2 Prices of Zero-Coupon Bond (Semiannually Compounding)
Duration
• A measure of the effective maturity of a bond
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
• Duration rule is a good approximation for only small changes in bond yields
Figure 16.3 Bond Price Convexity: 30Year Maturity, 8% Coupon; Initial Yield to
• Duration is equal to maturity for zero coupon bonds
Duration: Calculation
Spreadsheet 16.1 Calculating the Duration of Two Bonds
Duration/Price Relationship
投资学第16章债券资产 组合管理
2020/7/31
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
Figure 16.1 Change in Bond Price as a Function of Change in Yield to Maturity
Bond Pricing Relationships Continued
• As maturity increases, price sensitivity increases at a decreasing rate
• Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Figure 16.2 Bond Duration versus Bond Maturity
Table 16.3 Bond Durations (Yield to Maturity = 8% APR; Semiannual Coupons)
ห้องสมุดไป่ตู้
Convexity
• The relationship between bond prices and yields is not linear
• Subject to negative convexity • Often sell for more than their principal
• The weighted average of the times until each payment is received, with the weights proportional to the present value of the payment
• Duration is shorter than maturity for all bonds except zero coupon bonds
Price change is proportional to duration and not to maturity
D* = modified duration
Rules for Duration
Rule 1 The duration of a zero-coupon bond equals its time to maturity
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
• Negative convexity • Use effective duration:
Figure 16.5 Price –Yield Curve for a Callable Bond
Mortgage-Backed Securities
• Among the most successful examples of financial engineering
Maturity = 8%
Correction for Convexity
Correction for Convexity:
Figure 16.4 Convexity of Two Bonds
Callable Bonds
• As rates fall, there is a ceiling on possible prices – The bond cannot be worth more than its call price
Table 16.1 Prices of 8% Coupon Bond (Coupons Paid Semiannually)
Table 16.2 Prices of Zero-Coupon Bond (Semiannually Compounding)
Duration
• A measure of the effective maturity of a bond
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
• Duration rule is a good approximation for only small changes in bond yields
Figure 16.3 Bond Price Convexity: 30Year Maturity, 8% Coupon; Initial Yield to
• Duration is equal to maturity for zero coupon bonds
Duration: Calculation
Spreadsheet 16.1 Calculating the Duration of Two Bonds
Duration/Price Relationship
投资学第16章债券资产 组合管理
2020/7/31
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
Figure 16.1 Change in Bond Price as a Function of Change in Yield to Maturity
Bond Pricing Relationships Continued
• As maturity increases, price sensitivity increases at a decreasing rate