investment in usa

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


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


3/17


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


4/17


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?


5/17


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


6/17


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

($)


7/172002 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%



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%



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



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



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



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



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



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



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



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


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

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