Chapter 5
How Do Risk and Term Structure
Affect Interest Rates?
Risk Structure of Interest Rates
Default Risk
Liquidity
Case: The Global Financial Crisis and the Baa-Treasury Spread
Income Tax Considerations
Summary
Case: Effects of the Bush Tax Cut and the Obama Tax Increase on Bond Interest Rates
Term Structure of Interest Rates
Following the Financial News: Yield Curves
Expectations Theory
Market Segmentation Theory
Liquidity Premium Theory
Evidence on the Term Structure
Summary
Mini-Case Box: The Yield Curve as a Forecasting Tool for Inflation and the Business Cycle
Case: Interpreting Yield Curves, 1980–2013
The Practicing Manager: Using the Term Structure to Forecast Interest Rates
◼ Overview and Teaching Tips
Chapter 5 applies the tools the student learned in Chapter 4 to understanding why and how various interest
rates differ. In courses that emphasize financial markets, this chapter is important because students are
curious about the risk and term structure of interest rates. On the other hand, professors who focus on public
policy issues might want to skip this chapter. The book has been designed so that skipping this chapter will
not hinder the student’s understanding of later chapters.
A particularly attractive feature of this chapter is that it gives students a feel for the interaction of data and
theory. As becomes clear in the discussion of the term structure, theories are modified because they cannot
explain the data. On the other hand, theories do help to explain the data, as the case on interpreting yield
curves in the 1980–2013 period demonstrates.
This chapter also has two cases that will pique students’ interest because they are so current. First is the
effect of the Bush tax cut and the Obama tax increase on bond interest rates. Since the topic of repeal of
the Bush tax cut and the Obama tax increase are such a hot political issue, evaluating what impact the
24 Mishkin/Eakins • Financial Markets and Institutions, Eighth Edition
repeal might have on interest rates is sure to be of interest to students. Also students are particularly
interested right now in how the recent financial crisis affected the economy, and this chapter has a case
that looks at this topic. The case on the global financial crisis and the Baa-Treasury spread applies the
analysis in the chapter to show how the recent financial crisis led to a dramatic increase in the spread
between interest rates on Baa securities with credit risk relative to U.S. Treasury securities that do not.
The Practicing Manager application at the end of the chapter shows how forecasts of interest rates from the
term structure using the theories outlined here can be used by financial institutions managers to set interest
rates on their financial instruments.
◼ Answers to End-of-Chapter Questions
2. U.S. Treasury bills have lower default risk and more liquidity than negotiable CDs. Consequently,
the demand for Treasury bills is higher, and they have a lower interest rate.
3. During business cycle booms, fewer corporations go bankrupt and there is less default risk on
4. True. When bonds of different maturities are close substitutes, a rise in interest rates for one bond
5. If yield curves on average were flat, this would suggest that the risk premium on long-term relative to
6. The flat yield curve at shorter maturities suggests that short-term interest rates are expected to fall
moderately in the near future, while the steep upward slope of the yield curve at longer maturities
7. The steep upward-sloping yield curve at shorter maturities suggests that short-term interest rates are
expected to rise moderately in the near future because the initial, steep upward slope indicates that
the average of expected short-term interest rates in the near future is above the current short-term
8. The reduction in income tax rates would make the tax-exempt privilege for municipal bonds less
Chapter 5: How Do Risk and Term Structure Affect Interest Rates? 25
9. The government guarantee will reduce the default risk on corporate bonds, making them more
11. Abolishing the tax-exempt feature of municipal bonds would make them less desirable relative to
◼ Quantitative Problems
1. a. The yield to maturity would be 5% for a one-year bond, 6% for a two-year bond, 6.33% for a
three-year bond, 6.5% for a four-year bond, and 6.6% for a five-year bond.
b. The yield to maturity would be 5% for a one-year bond, 4.5% for a two-year bond, 4.33% for a
2. Government economists have forecasted one-year T-bill rates for the following five years as follows:
Year
1-year rate
1
4.25%
2
5.15%
3
5.50%
4
6.25%
5
7.10%
You have liquidity premium 0.25% for the next two years and 0.50% thereafter. Would you be
willing to purchase a 4-year T-bond at a 5.75% interest rate?
Solution: Your required interest rate on a 4-year bond = Average interest on four 1-year bonds +
Liquidity Premium
3. What is the yield on a $1,000,000 municipal bond with a coupon rate of 8%, paying interest annually,
26 Mishkin/Eakins • Financial Markets and Institutions, Eighth Edition
Solution: Municipal bond coupon payments equal $80,000 per year. No taxes are deducted;
4. Consider the decision to purchase either a 5-year corporate bond or a 5-year municipal bond. The
corporate bond is a 12% annual coupon bond with a par value of $1,000. It is currently yielding 11.5%.
The municipal bond has an 8.5% annual coupon and a par value of $1,000. It is currently yielding 7%.
Which of the two bonds would be more beneficial to you? Assume that your marginal tax rate is 35%.
Solution: Municipal Bond
5. Debt issued by Southeastern Corporation currently yields 12%. A municipal bond of equal risk
currently yields 8%. At what marginal tax rate would an investor be indifferent between these two
bonds?
6. 1-year T-bill rates are expected to steadily increase by 150 basis points per year over the next 6 years.
Determine the required interest rate on a 3-year T-bond and a 6-year T-bond if the current 1-year
interest rate is 7.5%. Assume that the Pure Expectations Hypothesis for interest rates holds.
Solution: 3 year bond:
year 1 interest rate = 7.5%
Chapter 5: How Do Risk and Term Structure Affect Interest Rates? 27
7. The one-year interest rate over the next 10 years will be 3%, 4.5%, 6%, 7.5%, 9%, 10.5%, 13%,
14.5%, 16%, 17.5%. Using the pure expectations theory, what will be the interest rates on a 3-year
bond, 6-year bond, and 9-year bond?
8. Using the information from the previous question, now assume that the investor prefers holding
short-term bonds. A liquidity premium of 10 basis points is required for each year of a bond’s
maturity. What will be the interest rates on a 3-year bond, 6-year bond, and 9-year bond?
Solution: To solve this problem, you will need to use the following equation:
1 2 1
e e e
t t t t n
nt nt
i i i i
il
n
+ + + −
+ + + +
=+
3-year bond = (0.30) + [(3 + 4.5 + 6)]/(3) = 4.8%
6-year bond = (0.60) + [(3 + 4.5 + 6 + 7.5 + 9 + 10.5)]/(6) = 7.35%
9-year bond = (0.90) + [(3 + 4.5 + 6 + 7.5 + 9 + 10.5 + 13 + 14.5 + 16)]/(9) = 10.233%
9. Which bond would produce a greater return if the pure expectations theory was to hold true, a 2-year bond
with an interest rate of 15% or two 1-year bonds with sequential interest payment of 13% and 17%?
Solution: Both of the bonds would produce the same return.
10. Little Monsters Inc. borrowed $1,000,000 for two years from NorthernBank Inc. at an 11.5% interest
rate. The current risk-free rate is 2% and Little Monsters’s financial condition warrants a default risk
premium of 3% and a liquidity risk premium of 2%. The maturity risk premium for a two-year loan is
1%, and inflation is expected to be 3% next year. What does this information imply about the rate of
inflation in the second year?
Solution: If inflation were expected to remain constant at 3% over the life of the loan, the interest
11. One-year T-bill rates are 2% currently. If interest rates are expected to go up after 3 years by 2%
every year, what should be the required interest rate on a 10-year bond issued today?
27
2 2 2 2(1.02) 2(1.02) 2(1.02)
21.165 /10 2.1165%
==
28 Mishkin/Eakins • Financial Markets and Institutions, Eighth Edition
12. One-year T-bill rates over the next 4 years are expected to be 3%, 4%, 5%, & 5.5%. If 4-year T-
bonds are yielding 4.5%, what is the liquidity premium on this bond?
Solution:
13. At your favorite bond store, Bonds-R-Us, you see the following prices:
a. 1-year $100 zero selling for $90.19
b. 3-year 10% coupon $1000 par bond selling for $1000
c. 2-year 10% coupon $1000 par bond selling for $1000
Assume that the pure expectations theory for the term structure of interest rates holds, no liquidity or
maturity premium exists, and the bonds are equally risky. What is the implied 1-year rate two years
from now?
Solution: From (a), you know that the 1-year rate today is 10.877%.
Using this information, (c) tells you that:
14. You observe the following market interest rates, for both borrowing and lending:
one-year rate = 5%
two-year rate = 6%
one-year rate one year from now = 7.25%
How can you take advantage of these rates to earn a riskless profit? Assume that the Pure Expectation
Theory for interest rates holds.
Solution: Borrow $100 today at the two-year rate. You will be required to payback $100 (1.06)2,
or $112.36 in two years.
15. The expected one-year interest rate two years from now is
e