Question Bank 2 - SEP2019

Fixed Income Problem Set #2
1. Explain whether you agree or disagree with the following statements?

a) The duration of a coupon bond maturing at date T is always less than the duration
of a zero-coupon bond maturing on the same date.
b) When investing in bonds, we should invest in bonds with higher yields to maturity
(YTM) because they give higher expected returns.
c) The phrase ”On the run” refers to illiquid corporate bonds issued in secondary markets.
a) Investors expect higher returns on long-term bonds than short-term bonds because
they are riskier. Thus the term structure of interest rates is always upward sloping.
b) Bonds whose coupon rates fall when the general level of interest rates rise are
called reverse floaters. Everything else the same, these bonds have a lower modified
duration than their straight bond counterparts.
a) Term structure of interest rates must be always upward sloping because longer
maturity bonds are riskier.
b) Bonds with higher coupon rates have more interest rate risk.
4. Explain whether you agree or disagree with the following statement:
a) The term structure of interest rates is always upward sloping because bonds with longer
maturities are riskier and earn higher returns.
b) A flat term structure (identical spot rates for all maturities) indicates that investors do not
expect interest rates to change in the future.
5. Given the following spot rates and assuming that spot rates and YTMs are with
annual compounding, coupon payments are annual, and par values are 100
Calculate the prices and YTMs of the following bonds:
a) A zero-coupon bond with 3 years to maturity.

b) A bond with coupon rate 5% and 2 years to maturity.
c) A bond with coupon rate 6% and 4 years to maturity.
6. You are given the following spot rates:
a) Compute the forward rate between years 1 and 2.

b) Compute the forward rate between years 1 and 3.
7. You are given the following prices for US Treasury STRIPS. These are zero-coupon
bond issued with a principal of 100:
a) Determine the 1-, 2- and 3-year spot interest rates from the given prices.
b) Compute the annual forward rate from year two to year three, i.e., f3 (or f2,3).
c) Compute the yield to maturity of a 2-year coupon bond with a principal of 100 and a
coupon rate of 4.25%. Assume annual coupon payments.
8. The following is a list of prices for zero-coupon bonds of various maturities.

Calculate 1) the YTM of each bond and 2) the implied sequence of forward rates.
9. Refer to the table below showing Treasury prices and yields
a) What were the 1, 2, 3, 4, 6 and 10-year spot interest rates?

b) What was the forward interest rate from August 2007 to August 2008? From August
2009 to August 2010?
10. Consider a 10 year bond with a face value of $100 that pays an annual coupon of 8%.
Spot rates are flat at 5%.
(a) Calculate the bond’s price
(b) Calculate the bond’s Macaulay duration.
(c) Calculate the bond’s Modified duration
(d) If 10yr yields increase by 10bps – Calculate the approximate change and new price of the
bond.
(e) If 10yr yields increase by 200bps (from the original price). Calculate the approximate
change and new price of the bond.
11. Use the information in the table below
Assume that the par value is $100 and coupons are paid annually, with the first coupon payment
coming in exactly one year from now. The yield to maturity is also quoted as an annual rate.
a) What should be the price of a bond with a maturity of 3 years and coupon rate of 5%,
given the above information?
b) What should be the 1-year forward rate between years 2 and 3?
c) What is the modified duration of a bond portfolio with 30% invested in bond 1
and 70% invested in bond 3?
12. Explain whether you agree or disagree with the following statement. A corporate bond
has a stated duration of 8.53 years and a convexity of 124.77. This suggests that, if market
yields decrease significantly (e.g. by 250 basis points), the price of the bond will increase by
less than the amount indicated by the convexity measure alone.
13. Given the following information, compute the approximate duration.
14. Explain whether you agree or disagree with the following statements. Duration is a
linear estimate of a bond’s price change given an expected change in market interest rates and
underestimates a bond’s price increase and decrease given an expected change in market
interest rates.
15. An annual modified duration of a fixed rate bond is 5.75. Although there is no change in
benchmark yields but due to improved financial reporting quality and a ratings upgrade, the
flat price of the bond has increased from 98.10 to 101.65 per 100 of par value. Calculate the
estimated change in the credit spread of the bond.
16. Given the below table of spot rates, calculate the YTM of a 2-year 5% semi-annual coupon
paying bond.
17. A South African based company has a position in a European bond for a par value of
€50million. For a 1 basis point increase in yield the market value of the investment changes
to €49.85 million and for a 1 basis point decrease in yield investment value changes to €51.23
million. What is the price value of basis point for the investment?
18. Why is the procedure for valuing a bond with an embedded option called ‘‘backward
induction’’?
19. Why is the value produced by a binomial model and any similar models referred to as an
‘‘arbitrage-free value’’?
20. Use the information below to answer the following questions
a) Using the spot rates given below, what is the arbitrage-free value of a 3-year 8.5%
coupon issue of “Over-the-Top” Company?
b) Using the binomial tree above, determine the value of an 8.5% 3-year option-free bond.
c) Suppose that the 3-year 8.5% coupon issue is callable starting in Year 1 at par (100)
(that is, the call price is 100). What is the value of this 3-year 8.5% coupon callable issue?
d) What is the value of the embedded call option for the 3-year 8.5% coupon callable
issue?
21. Consider the following interest-rate tree (four 1-year periods)
a) Calculate the value at each node of the tree of a 5-year pure discount bond with face
value 100. What is the YTM on that bond?
b) Calculate the price of an identical bond that would be callable at $75. Calculate the YTM
on that bond and the spread over the straight bond.
c) What is the value of the embedded call option according to the model?
22. There are two forms of the ‘‘biased’’ expectations theory. Why are these two forms referred
to as ‘‘biased’’ expectations? Explain how these differ from pure expectations theory.
23. Given the following rates, calculate the value of a 4-year, 10% annual coupon paying bond
with a par value of R1000.
• 1-year fwd rate = 5.5%
• 1-year fwd rate one year from today = 7.63%
• 1-year fwd rate two years from today = 12.18%
• 1-year fwd rate two three years from today = 15.5%

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What are some of the concepts discussed regarding bonds?

What factors influence the price of a bond?

Fixed Income Problem Set #2

1. Explain whether you agree or disagree with the following statements?

2. Explain whether you agree or disagree with the following statements?

3. Explain whether you agree or disagree with the following statements?

4. Explain whether you agree or disagree with the following statement:

Calculate the prices and YTMs of the following bonds:

a) A zero-coupon bond with 3 years to maturity.

a) Compute the forward rate between years 1 and 2.

8. The following is a list of prices for zero-coupon bonds of various maturities.

9. Refer to the table below showing Treasury prices and yields

a) What were the 1, 2, 3, 4, 6 and 10-year spot interest rates?

11. Use the information in the table below

13. Given the following information, compute the approximate duration.

21. Consider the following interest-rate tree (four 1-year periods)

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