Chapter 2 Securities Markets and Transactions 15
11.21 Expected Yield
N = 3
11.22
a. Yield to Maturity b. Yield to Maturity c. Yield to Maturity
a. Yield to Call b. Yield to Call c. Yield to Call
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16 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
Of course it is worth noting here that because bonds A and C are trading well below their
11.23 Modified duration Macaulay duration/(1 Yield) 9.5/1.075 8.84
11.24 Percent change in bond price 1 Modified duration
Change in interest rates
Modified duration Macaulay duration/(1 Yield)
11.25 The prices of the bond at yields of 6.5%, 7.0% and 7.5% compounded semiannually are:
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Chapter 2 Securities Markets and Transactions 17
938.62 831.74 12.11 years
2 882.72 0.005
ED –
= =
´ ´
The effective duration is 12.11 years.
11.26 To calculate the duration of the bond, first calculate the bond’s current market price:
Bond terms: 10% coupon, 20 years, 8% YTM
Price
N = 20
I = 8
PMT = 100
FV = 1000
CPT
PV= –1,196.36
In the table below, start by listing the times when cash flow is paid. IN the next column, write down
the cash flow paid at each time. Next, calculate the present value of each cash payment by
PV of CF as Column 1
Time Cash Flow PV of CF % of bond price × Column 4
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18 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
PV of CF as Column 1
Time Cash Flow PV of CF % of bond price × Column 4
Modified duration
Duration in years
1 Yield-to-maturity+
% change in bond price 1 Modified duration Change in interest rates
1 9.42 1% 9.42%
If market yields rise 1%, the modified duration calculation predicts that the price of the bond will
Assuming that the bond’s yield does rise to 9%,we can use a calculator or Excel to calculate the
bond’s price. In Excel we would use =pv(.09,20,100,1000) to find the price of $1,091.29. This
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Chapter 2 Securities Markets and Transactions 19
11.27 This question is about bond price volatility. We need to measure the responsiveness of a bond’s
Modified duration
Duration in years
1 Yield-to-maturity+
a. Bond with duration of 8.46 years with YTM of 7.5%:
Modified duration
8.46 7.87%
1 .075 =
+
b. Bond with duration of 9.30 years with YTM of 10%:
Modified duration
9.30 8.45%
1 .10 =
+
c. Bond with duration of 8.75 years with YTM of 5.75%:
Modified duration
8.75 8.27%
1 .0575 =
+
Bond (b) offers the potential for maximum capital appreciation. To maximize gains, this bond
should be selected over the others.
Note: This question can be answered directly by looking at the modified duration. For a given
11.28 Current price of the bonds at 9% market interest:
Zero-coupon bond:
Bond 1 Bond 2
Capital gains:
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20 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
To maximize the dollar value of capital gains per bond, buy the 7.5%, 20-year bond, but this doesn’t
HPR
Interest Capital gains
Purchase price
+
Based on holding period return, Stacy should purchase the zero-coupon bond.
We know from Chapter 10 that prices of bonds with lower coupons and/or longer maturities will
The duration of a zero-coupon bond is equal to its actual maturity, while the duration of a
11.29 There is an error in this problem in one printing of the textbook. The prices and yields given for
each bond are not consistent with each other. A solution may be developed by taking the yield as
given and recalculating the price (this is the approach taken below) or by taking the price as given
and recalculating the yield. The bonds we are comparing have these characteristics:
a. 8.5%, 13-year, ytm = 7.47%, price = $1,083.84, duration = 8.54, modified duration = 7.94
b. 7.875%, 15-year, ytm = 7.6%, price = $1,024.12, duration = 9.37, mod. duration = 8.71
c. 0%, 20-year, ytm = 8.22%, price = $205.99, duration = 20, modified duration = 18.48
d. 7.5%, 24-year, ytm = 7.9%, price = $957.53, duration = 11.56, modified duration = 10.72
The tables below show the calculations for the price and duration for each bond. To find modified
duration, simply divide the duration by 1+ytm.
a.
Time CF PV of CF % of Price (1) × (4)
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Chapter 2 Securities Markets and Transactions 21
b.
Time CF PV of CF % of Price (1) × (4)
d.
Time CF PV of CF % of Price (1) (4)
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22 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
Time CF PV of CF % of Price (1) (4)
b. When Elliot invests $250,000 in each of the four bonds, the weighted average duration of the
portfolio is:
(1) (2)
Bond
Particulars
(3)
Amount
Invested
(4)
Weight
(5)
Bond
Duration
(6)
Weighted
Duration
(4) (5)
c. When Elliot invests $360,000 each into Bonds 1 and 3, and $140,000 each into Bonds 2 and 4,
the weighted average duration of the bond portfolio is:
(1) (2)
Bond
Particulars
(3)
Amount
Invested
(4)
Weight
(5)
Bond
Duration
(6)
Weighted
Duration
(4) (5)
d. Portfolio (c) has a higher duration than portfolio (b). If rates are about to rise, then it is safer to
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