FIN3702A: Investment Analysis and Portfolio Management
Homework #3
Emirhan İlhan
True/False Questions
Determine whether the following statements are true or false.
1.
True
ally.
2.
False The liquidity of bond markets globally is comparable to that of equity markets
globally.
3.
True A bond’s yield to maturity (YTM) assumes all coupon payments are reinvested
at the YTM rate.
The size of bond markets globally is comparable to that of equity markets glob-
4.
True
The price of a zero-coupon bond is at most equal to its face value.
5.
False
The price of a coupon bond is at at most equal to its face value.
6.
False
The duration of a bond is always lower than its time to maturity.
7.
True A bond trading at a premium must have a coupon rate higher than its yield to
maturity.
8.
True A descending yield curve implies that investors expect a deflationary interest
rate environment in the future.
9.
10.
False
All sovereign bonds have lower yields than all corporate bonds.
True Credit Default Swaps (CDS) can be used to hedge against changes in the value of
the underlying bonds.
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FIN3702A: Investment Analysis and Portfolio Management, Spring 2025
Multiple Choice Questions
Select the correct answer in the following questions.
11. When interest rates increase:
⃝ Bond prices increase and yields decrease
√
Bond prices decrease and yields increase
⃝ Both bond prices and yield increase
⃝ Both bond prices and yield decrease
⃝ How bond prices and yields change depends on the bond characteristics.
12. Immunization is primarily concerned with:
⃝ Maximizing portfolio returns.
⃝ Minimizing portfolio risk.
√
Matching the duration of assets and liabilities.
⃝ Minimizing transaction costs.
⃝ Diversifying across different bond maturities.
13. What does a normal yield curve typically indicate about investors’ expectations? Select all
that apply.
⃝ An upcoming recession in the near future.
√
Strong economic growth in the near future.
√
Interest rate hikes in the near future.
⃝ Interest rate cuts in the near future.
⃝ Economic growth and interest rates not particularly different than today in the
near future.
14. If the yield of short-term bonds are higher for U.S. than Germany, select all that apply
from below.
√
The default risk of short-term U.S. bonds are higher than that of German
bonds.
⃝ The default risk of long-term U.S. bonds are higher than that of German bonds.
√
The inflation rate in the U.S. is likely higher today than in Germany.
⃝ The inflation rate in the U.S. is likely lower today than in Germany.
⃝ Buying a house with a mortgage in the U.S. is likely cheaper than in Germany.
⃝ Economic growth is likely stronger in the U.S. today than in Germany.
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Copyright ©2025 by Emirhan İlhan
FIN3702A: Investment Analysis and Portfolio Management, Spring 2025
Numerical Questions
15. A portfolio manager needs to immunize a liability of $1,000,000 due in 4 years. They have
access to:
A. 2-year zero-coupon bond.
B. 6-year zero-coupon bond.
C. 8-year zero-coupon bond.
The portfolio manager wants to create an immunization strategy by investing non-zero
amounts into bonds A, B, and C for a total of $1,000,000. If the manager invests $100,000
in bond C, how much would be allocated to bonds A and B?
Solution: We have the following combination:
$100, 000
$900, 000
× X years +
× 8 years = 4 years
$1, 000, 000
$1, 000, 000
0.9 × X + 0.1 × 8 = 4 ⇒ X = 3.556 years
In other words, we have to find the amounts that combine bonds A and B such that the
combined bond portfolio has a duration of 3 years. Thus, we can write the following:
w × 2 years + (1 − w) × 6 years = 3.556 years
2w + 6 − 6w = 3.556 ⇒ w = 0.611
This means that we need to allocate 61.1% of the remaining $900,000 into bond A.
Thus, the portfolio manager has to have the following allocation:
A. 61.1% × $900, 000 = $549, 900
B. (1 − 61.1%) × $900, 000 = $350, 100
C. $100, 000
16. A 10-year zero-coupon bond with a face value of $1,000 and a yield-to-maturity of 4%
and a 4-year semi-annual coupon bond trade at the same price in the open market. If both
bonds have the same yield-to-maturity, but the coupon bond has half the face value as
the zero-coupon bond, what is the per period cash payment received by the holders of the
coupon bond? Round your answer to the closest integer value.
Solution: The prices of the bonds can be written as follows:
P=
F
$1, 000
=
= $675.56
4
(1 + y)
(1 + 4%)4
If we call C the per-period cash payment of the coupon bond, we need to solve the
following equation:
!
1
$500
C
1−
+
$675.56 =
2%
(1 + 2%)8
(1 + 2%)8
C = $33.966 ≈ $34
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Copyright ©2025 by Emirhan İlhan
FIN3702A: Investment Analysis and Portfolio Management, Spring 2025
17. A 10-year zero-coupon bond with a face value of $1,000 and a yield-to-maturity of 4%
and a 4-year semi-annual coupon bond trade at the same price in the open market. If the
coupon bond has a coupon rate of 14% and half the face value as the zero-coupon bond,
what is its yield-to-maturity? Answer in percentages and round your answer to the closest
two decimals.
Solution: The zero-coupon bond is identical to the zero-coupon bond from the previous question and thus, has the same price of $675.56. However, we now have to solve
the following equation:
!
$500 × 14%
$500
1
$675.56 =
+
1−
8
y/2
y
(1 + /2)
(1 + y/2)8
Analytically solving this equation isn’t really possible, so one can do a trial-and-error
or use a solver. A trial-and-error setup in Excel looks as follows:
You can also use the solver in Excel or tools like WolframAlpha to immediately solve
for y. For example, the WolframAlpha result would look something like the following:
All in all, the answer is y = 4.32% .
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Copyright ©2025 by Emirhan İlhan
FIN3702A: Investment Analysis and Portfolio Management, Spring 2025
18. Suppose you are given the following bonds, each with a face value of $1,000. All bonds
have annual payments. Given this information, what is the price of a 2-year zero-coupon
Time to Maturity (Years)
Bond
Coupon Rate
Yield-to-Maturity
1
2
3
4
A
B
C
D
0%
15%
10%
5%
2.0%
2.9%
3.2%
5.3%
bond with a face value of $1,000?
Solution: The cash flows of bond B are as follows:
0
1
2
$150
$1, 150
We can write the price of this bond B by using its yield-to-maturity (YTM) or 1-year
and 2-year spot rates as follows:
PB =
$150
$1, 150
$1, 150
$150
+
+
=
2
(1 + y2 ) (1 + y2 )
(1 + s1 ) (1 + s2 )2
We already know that s1 = 2% since bond A is a zero-coupon bond. We also know that
y2 = 2.9%. As a result, we can use the equation above to find the 2-year spot rate as
follows:
$150
$1, 150
+
= $1, 231.87
(1 + 2.9%) (1 + 2.9%)2
$150
$1, 150
+
= $1, 231.87 → s2 = 2.961%
(1 + 2%) (1 + s2 )2
PB =
Finally, we can find the price of a 2-year zero-coupon bond with a face value of $1,000
(P2 ) by using the 2-year spot rate:
P2 =
$1, 000
(1 + 2.961%)2
P2 = $943.31
19. Given the table of information above, what is the four-year spot rate?
Solution: To find the four-year spot rate, we can use the information about bond C
and bond D. Let’s start with the cash flows of each of these bonds:
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Copyright ©2025 by Emirhan İlhan
FIN3702A: Investment Analysis and Portfolio Management, Spring 2025
C:
D:
0
0
1
2
3
$100
$100
$1, 100
1
2
3
4
$50
$50
$50
$1, 050
First, use the YTM of bond C to calculate the price of bond C. The price of bond C can
also be calculated using the 1-year spot rate (3%) and 2-year spot rate (5%) and 3-year
spot rate (s3 ).
$100
$100
$1, 100
+
+
= $1, 191, 61
2
(1 + 3.2%) (1 + 3.2%)
(1 + 3.2%)3
$100
$100
$1, 100
+
+
= $1, 057.02 → s3 = 3.254%
(1 + 2%) (1 + 2.961%)2 (1 + s3 )3
PC =
We can follow the same procedure for bond D to find the 4-year spot rate:
$50
$1, 050
$50
$50
+
+
+
= $989.44
(1 + 5.3%) (1 + 5.3%)2 (1 + 5.3%)3 (1 + 5.3%)4
$50
$1, 050
$50
$50
+
+
+
= $989.44 → s4 = 5.492%
2
3
(1 + 2%) (1 + 2.961%)
(1 + 3.254)
(1 + s4 )4
PD =
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Copyright ©2025 by Emirhan İlhan