Post on 14-Apr-2018
7/29/2019 investment in usa
1/17
10C h a p t e r
Bond Prices and YieldsExtra
second edition
Fundamentals
ofInvestmentsValuation & Management
CharlesJ.Corrado BradfordD.Jordan
McGraw Hill / Irwin Slides by Yee-Tien (Ted) Fu
7/29/2019 investment in usa
2/17
2002 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw Hill / Irwin
10 - 2
Bond PricesStraight bond prices:
2M2M
2
YTM1
FV
2
YTM1
11
YTM
CpriceBond
C = annual coupon
FV = face valueM = maturity (years)
YTM = Yield to maturity
Assume a bond has 15 years to maturity, a 9% coupon,and the YTM is 8%. What is the price?
$1,086.46
2
.081
1000
2
.081
11
.08
90priceBond
3030
7/29/2019 investment in usa
3/17
2002 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw Hill / Irwin
10 - 3
More on Bond Prices
2M2M2
YTM1FV
2YTM1
11YTM
CpriceBond
$1,107.412
.081
1000
2.081
11
.08
90priceBond
5050
Now assume a bond has 25 years to maturity, a 9% coupon,and the YTM is 8%. What is the price? Is the bond selling atpremium or discount?
Now assume the same bond has a YTM of 10%. (9% coupon &
25 years to maturity) What is the price? Is the bond selling atpremium or discount?
$908.722
.101
1000
2.101
11
.10
90priceBond
5050
7/29/2019 investment in usa
4/17
2002 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw Hill / Irwin
10 - 4
More on Bond Prices (contd)
$1,040.552
.081
1000
2.081
11.08
90priceBond 1010
Now assume the same bond has a YTM of 10%. (9% coupon &5 years to maturity) What is the price? Is the bond selling at
premium or discount?
$961.392
.101
1000
2.101
11
.10
90priceBond
1010
Now assume the same bond has 5 years to maturity (9% coupon& YTM of 8%) What is the price? Is the bond selling atpremium or discount?
7/29/2019 investment in usa
5/17
2002 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw Hill / Irwin
10 - 5
More on Bond Prices (contd)
Where does this leave us? We found:Coupon Years YTM Price
9% 25 8% $1,1079% 25 10% $ 9089% 5 8% $1,0409% 5 10% $ 961
$900
$950
$1,000
$1,050
$1,100
$1,150
8% 9% 10% 11%
25 years
5 years
7/29/2019 investment in usa
6/17
2002 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw Hill / Irwin
10 - 6
Figure 10.2: Bond prices and yields
0
500
1000
1500
2000
2500
3000
0 2 4 6 8 10 12 14 16 18 20
Bond yields (%)
Bond
prices
($)
7/29/2019 investment in usa
7/172002 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw Hill / Irwin
10 - 7
Bond YTM
2M2M2
YTM1
FV
2YTM1
11YTM
CpriceBond
Assume a bond has 15 years to maturity,a 9% coupon, and the bond is selling for is $1,080.What is the YTM?
3030 2YTM11000
2YTM1
11
YTM
90$1,080
YTM = 4.0354% x 2 = 8.07%
7/29/2019 investment in usa
8/172002 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw Hill / Irwin
10 - 8
Bond Yield to Call
2T2T2
YTC1
CP
2YTC1
11YTC
CpricebondCallable
Assume the previous bond has 5 years until it can be
called with a $90 call premium. (9% coupon & sellingfor $1,080.) What is the YTM?
1010 2YTC11090
2YTC1
11
YTC
90$1,080
YTC = 4.243% x 2 = 8.49%
7/29/2019 investment in usa
9/172002 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw Hill / Irwin
10 - 9
Malkiels Theorems
Bond Prices and Yields (8% bond)
Time to Maturity
Yields 5 years 10 years 20 years
7 percent $1,041.58 $1,071.06 $1,106.78
9 percent 960.44 934.96 907.99
Price Difference $81.14 $136.10 $198.79
7/29/2019 investment in usa
10/172002 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw Hill / Irwin
10 - 10
Malkiels Theorems (contd)
20-Year Bond Prices and YieldsCoupon Rates
Yields 6 percent 8 percent 10 percent
6 percent $1,000.00 $1,231.15 $1,462.30
8 percent 802.07 1,000.00 1,197.93
10 percent 656.82 828.41 1,000.00
7/29/2019 investment in usa
11/172002 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw Hill / Irwin
10 - 11
Malkiels Theorems (contd)8% coupon, 20 year bond
Yield Price Falls 2% Rises 2% Increase Decrease6% $1,231 $1,547 $1,000 25.70% 18.80%
8% $1,000 $1,231 $828 23.10% 17.20%
10% $828 $1,000 $699 20.80% 15.60%
Price when yieldPercentage price
change
7/29/2019 investment in usa
12/172002 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw Hill / Irwin
10 - 12
Duration Example
years8.512.091
11
.09
2.091
durationMac.30
Assume you have a par value bond with 9% coupon, 9% YTM,and 15 years to maturity. Calculate Macaulays Duration.
years8.7812
.081.09.08
.08.09152.08
1.08
2.08
1Dur.Mac.30
Assume you have a bond with 9% coupon, 8% YTM,and 15 years to maturity. Calculate Macaulays Duration.
10 13
7/29/2019 investment in usa
13/172002 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw Hill / Irwin
10 - 13
Price Change & Duration
2
YTM1
YTMinChangeMDpricebondin%
To compute the percentage change in a bonds priceusing Macaulay Duration:
To compute the Modified Duration:
2
YTM1
durationMacaulaydurationModified
To compute the percentage change in a bonds priceusing Modified Duration:
YTMinChangeDurationModifiedpricebondin%
10 14
7/29/2019 investment in usa
14/172002 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw Hill / Irwin
10 - 14
Calculating Price Change
16.27%
2
.091
.11.09
8.5pricebondin%
Assume a bond with Macaulays duration of 8.5 years,with the YTM at 9%, but estimated the YTM will go to 11%,calculate the percentage change in bond price and thenew bond price.
Change in bond price, assuming bond was originally at par:
Approx. new price = $1,000 + (-16.27% x $1,000) = $837.30
10 15
7/29/2019 investment in usa
15/172002 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw Hill / Irwin
10 - 15
Price Change & Duration
Assume you have a bond with Macaulays duration of8.5 years and YTM of 9%, calculate the modified duration.
years8.134
2
.091
8.5durationModified
Using the bond above with modified duration of 8.134years and a change in yields from 9% to 11%, calculatethe percentage change in bond price.
16.27%.11.098.134pricebondin% Note this is the same percentage change as computed previously.
10 16
7/29/2019 investment in usa
16/172002 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw Hill / Irwin
10 - 16
Example of Target Date Hedging
Assume you are setting up a target portfolio. You need $1,470 in
five years. You can choose a 7.9% coupon bond with 5 years to
maturity or a 7.9% coupon bond with 6 years to maturity and a5-year duration. The YTM is now 7.9%. Which do you choose?
10 17
7/29/2019 investment in usa
17/172002 by The McGraw-Hill Companies Inc All rights reservedMcGraw Hill / Irwin
10 - 17
Solution:
To compare, calculate the total wealth in five years:
If interest rates do not change the total wealth of the 5-yearbond in 5 years is $1,473.14 (in five years you receive $1,000
plus 5 coupon payments of $79 each, which earn interest at7.9%)
If interest rates change to 6%:
The 5-year bond will earn total wealth of $1,452.82 ($1,000plus 5 coupon payments of $79, which earn interest at 6%)
The 6-year bond (MD = 5 years) will earn total wealth of$1,471.00 (5 coupon payments of $79 compounded at 6%,
plus a bond with 1-year to maturity worth $1,018.18)
The duration matched bond protected your portfolio.
Example of Target Date Hedging