Bond Price Volatility
Joel R. Barber
Joel R. Barber ()
Chapter 4
1 / 29
Price-yield curve for noncallable bonds
1
example: CR
=
6%, T
=
20 years, M
=
$100
2
value: P
(
y
) =
3A
(
y /2, 40
) +
100
(
1
+
y /2
)
40
3
declining
4
convex
0.02
0.04
0.06
0.08
0.10
0.12
0.14
60
80
100
120
140
160
yield
P
Joel R. Barber ()
Chapter 4
2 / 29
Bond price properties
1
prices are inversely related to yield
2
for a small yield change (either or up or down) the price sensitivity
can be measured by the slope 3 for a large change in yield the price sensitivity is greater when yields
decrease 4 sensitivity is negatively related to the yield Joel R. Barber () Chapter 4 3 / 29 Characteristics of a bond that explain price volatility 1 positively related to maturity 2 price versus yield for coupon rate of 6% with 5, 15, and 30 year
maturities 0.02 0.04 0.06 0.08 0.10 0.12 0.14 50 100 150 200 yield P Joel R. Barber () Chapter 4 4 / 29 Characteristics of a bond that explain price volatility 1 negatively related to coupon rate 2 value per dollar invested (assuming yield initial yield of 6 percent)
versus yield for coupon rate of 0, 6, and 12 percent 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 yield P Joel R. Barber () Chapter 4 5 / 29 Duration analysis 1 modied duration MD 1 P dP dy y = y 0 %P y for small y 2 Macaully Duration: D 1 + y P dP dy 3 formula: D = 1 P C 1 ( 1 + y ) + 2C 2 ( 1 + y ) 2 + + NC N ( 1 + y ) N 4 for semi-annual bonds substitute y 2 for y and multiply D by 1
2 5 relationship D = ( 1 + y ) MD Joel R. Barber () Chapter 4 6 / 29 Duration as measure of a bonds e
can be measured by the slope 3 for a large change in yield the price sensitivity is greater when yields
decrease 4 sensitivity is negatively related to the yield Joel R. Barber () Chapter 4 3 / 29 Characteristics of a bond that explain price volatility 1 positively related to maturity 2 price versus yield for coupon rate of 6% with 5, 15, and 30 year
maturities 0.02 0.04 0.06 0.08 0.10 0.12 0.14 50 100 150 200 yield P Joel R. Barber () Chapter 4 4 / 29 Characteristics of a bond that explain price volatility 1 negatively related to coupon rate 2 value per dollar invested (assuming yield initial yield of 6 percent)
versus yield for coupon rate of 0, 6, and 12 percent 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 yield P Joel R. Barber () Chapter 4 5 / 29 Duration analysis 1 modied duration MD 1 P dP dy y = y 0 %P y for small y 2 Macaully Duration: D 1 + y P dP dy 3 formula: D = 1 P C 1 ( 1 + y ) + 2C 2 ( 1 + y ) 2 + + NC N ( 1 + y ) N 4 for semi-annual bonds substitute y 2 for y and multiply D by 1
2 5 relationship D = ( 1 + y ) MD Joel R. Barber () Chapter 4 6 / 29 Duration as measure of a bonds e
