Questions
1. Characteristics That Affect Security Yields. Identify the relevant characteristics of any security that
can affect the security’s yield.
ANSWER: The relevant characteristics are:
1. default risk
2. Impact of Credit Risk on Yield. What effect does a high credit risk have on securities?
3. Impact of Liquidity on Yield. Discuss the relationship between the yield and liquidity of securities.
4. Tax Effects on Yields. Do investors in high tax brackets or those in low tax brackets benefit more
from tax-exempt securities? Why? Do municipal bonds or corporate bonds offer a higher before-tax
yield at a given point in time? Why? Which has the higher after-tax yield? If taxes did not exist,
would Treasury bonds offer a higher or lower yield than municipal bonds with the same maturity?
Why?
ANSWER: High-tax bracket investors benefit more from tax-exempt securities because their tax
savings from avoiding taxes is greater.
If taxes did not exist, Treasury bonds would offer a lower yield than municipal bonds because they
5. Pure Expectations Theory. Explain how a yield curve would shift in response to a sudden
expectation of rising interest rates, according to the pure expectations theory.
ANSWER: The demand for short-term securities would increase, placing upward (downward)
pressure on their prices (yields). The demand for long-term securities would decrease, placing
6. Forward Rate. What is the meaning of the forward rate in the context of the term structure of interest
rates? Why might forward rates consistently overestimate future interest rates? How could such a bias
be avoided?
ANSWER: The forward rate is the expected interest rate at a future point in time.
If forward rates are estimated without considering the liquidity premium, it may overestimate the
7. Pure Expectations Theory. Assume there is a sudden expectation of lower interest rates in the
future. What would be the effect on the shape of the yield curve? Explain.
ANSWER: The demand for short-term securities would decrease, placing downward (upward)
8. Liquidity Premium Theory. Explain the liquidity premium theory.
ANSWER: If investors believe that securities with larger maturities are less liquid, they will require a
9. Impact of Liquidity Premium on Forward Rate. Explain how consideration of a liquidity premium
affects the estimate of a forward interest rate.
10. Segmented Markets Theory. If a downward-sloping yield curve is mainly attributed to segmented
markets theory, what does that suggest about the demand for and supply of funds in the short-term
and long-term maturity markets?
ANSWER: A downward-sloped yield curve suggests that the demand for short-term funds is high
11. Segmented Markets Theory. If the segmented markets theory causes an upward-sloping yield curve,
what does this imply? If markets are not completely segmented, should we dismiss the segmented
markets theory as even a partial explanation for the term structure of interest rates? Explain.
ANSWER: An upward-sloped yield curve caused by segmented markets implies that the demand for
Even if markets are not completely segmented, investors and borrowers may prefer a particular
12. Preferred Habitat Theory. Explain the preferred habitat theory.
ANSWER: The preferred habitat theory suggests that while investors and borrowers may prefer a
13. Yield Curve. What factors influence the shape of the yield curve? Describe how financial market
participants use the yield curve.
ANSWER: The yield curve’s shape is affected by the demand and supply conditions for securities in
The yield curve can be used to determine the market’s expectations of future interest rates. Market
Advanced Questions
14. Segmented Markets Theory. Suppose that the Treasury decided to finance its deficit with mostly
long-term funds. How could this decision affect the term structure of interest rates? If short-term and
long-term markets are segmented, would the Treasury’s decision have a more or less pronounced
impact on the term structure? Explain.
ANSWER: If the Treasury borrowed heavily in the long-term markets, it could place upward pressure
15. Yield Curve. If liquidity and interest rate expectations are both important for explaining the shape of
a yield curve, what does a flat yield curve indicate about the market’s perception of future interest
rates?
ANSWER: A flat yield curve without consideration of a liquidity premium would represent no
16. Global Interaction among Yield Curves. Assume that the yield curves in the United States, France,
and Japan are flat. If the U.S. yield curve suddenly becomes so positively sloped, do you think the
yield curves in France and Japan would be affected? If so, how?
ANSWER: The yield curves in other countries would also be affected if the event precipitating the
shift in the U.S. yield curve affects either actual or expected interest rates in other countries. If
17. Multiple Effects on the Yield Curve. Assume that (1) investors and borrowers expect that the
economy will weaken and that inflation will decline, (2) investors require a small liquidity premium,
and (3) markets are partially segmented and the Treasury currently has a preference for borrowing in
short-term markets. Explain how each of these forces would affect the term structure, holding other
factors constant. Then explain the effect on the term structure overall.
ANSWER: The weak economy creates the expectation of a decline in interest rates, so according to
The Treasury’s preference would result in a downward-sloping demand yield curve, when other
18. Effect of Crises on the Yield Curve. During some crises, investors shift their funds out of the stock
market and into money market securities for safety, even if they do not fear rising interest rates.
Explain how and why these actions by investors affect the yield curve. Is the shift due to the
expectations theory, liquidity premium theory, or segmented markets theory?
ANSWER: The movement into money market securities results in a larger supply of short-term funds,
19. How the Yield Curve May Respond to Prevailing Conditions. Consider how economic conditions
affect the default risk premium. Do you think the default risk premium will likely increase or decrease
during this semester? How do you think the yield curve will change during this semester? Offer some
logic to support your answers.
ANSWER: This question is open-ended. It requires students to apply the concepts that were presented
20. Assessing Interest Rate Differentials among Countries. In some countries where there is high
inflation, the annual interest rate is more than 50 percent, while in other countries such as the U.S.
and many European countries, the annual interest rates are typically less than 10 percent. Do you
think such a large interest rate differential is primarily attributed to the difference in the risk-free rates
or to the difference in the credit risk premiums between countries? Explain.
ANSWER: The risk-free foreign interest rates are determined by supply and demand for funds in their
local currency. Inflationary expectations affect the risk-free interest rate. Thus, the difference in
21. Applying the Yield Curve to Risky Debt Securities. Assume that the yield curve for Treasury bonds
has a slight upward slope, starting at 6% for a 10-year maturity and slowly rising to 8% for a 30-year
maturity. Create a yield curve that you believe would exist for A-rated bonds. Create a yield curve
that you believe would exist for B-rated bonds.
ANSWER: The yield curve for A-rated bonds would likely have a similar slope as the yield curve for
22. Changes to Credit Rating Process. Explain how credit raters have changed their process following
criticism of their ratings during the credit crisis.
ANSWER: In response to the criticism, credit rating agencies made some changes to improve their
rating process and their transparency. They now disclose more information about how they derived
Interpreting Financial News
Interpret the following comments made by Wall Street analysts and portfolio managers.
a. “An upward-sloping yield curve persists because many investors stand ready to jump into the
stock market.”
Investors are holding short-term Treasury securities, and are unwilling to hold long-term
Treasury securities, because they may liquidate these securities soon, and prefer liquid securities
that are less susceptible to interest rate risk.
b. “Low-rated bond yields rose as recession fears caused a flight to quality.”
As investors selected safer bonds, they sold low-rated bonds, which placed downward pressure
on prices of low-rated bonds and upward pressure on yields of low-rated bonds. Thus, the risk
premium of low-rated bonds increased.
c. “The shift from an upward-sloping yield curve to a downward-sloping yield curve is sending a
warning about a possible recession.”
If the shift is due to changes in interest rate expectations, it suggests that interest rates may now
be expected to decline. Such expectations can occur when the market expects that economic
growth is slowing or is negative.
Managing in Financial Markets
As an analyst at a bond rating agency, you have been asked to interpret the implications of the recent shift
in the yield curve. Six months ago, the yield curve exhibited a slight downward slope. Over the last six
months, the long-term yields declined, while short-term yields remained the same. Analysts stated that the
shift was due to revised expectations of interest rates.
a. Given the shift in the yield curve, does it appear that firms increased or decreased their demand
for long-term funds over the last six months?
b. Interpret what the shift in the yield curve suggests about the market’s changing expectations of
future interest rates.
c. Recently, an analyst argued that the underlying reason for the yield curve shift was that many of
the large U.S. firms anticipate a recession. Explain why an anticipated recession could force the
yield curve to shift as it has.
When the economic conditions are expected to deteriorate, the demand for loanable funds by
firms tends to decrease (because firms reduce their borrowing when they cut back on their
d. What could the specific shift in the yield curve signal about the ratings of existing corporate
bonds? What types of corporations would be most likely to experience a change in their bond
ratings as a result of the specific shift in the yield curve?
To the extent that the downward shift in the yield curve signals an anticipated recession (or at
Corporations that are more sensitive to economic downturns would be more susceptible to a bond
Problems
1. Forward Rate. a. Assume that as of today, the annualized two-year interest rate is 13 percent, while
the one-year interest rate is 12 percent. Use this information to estimate the one-year forward rate.
ANSWER:
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5. Deriving Current Interest Rates. Assume that interest rates for one-year securities are expected to
be 2 percent today, 4 percent one year from now and 6 percent two years from now. Using only the
pure expectations theory, what are the current interest rates on two-year and three-year securities?
ANSWER:
(1 + ti2 )2 = (1 + ti1)(1 + t+1r1)
(1 + ti3)3 = (1 + ti1)(1 + t+1r1)(1 + t+2r1)
6. Commercial Paper Yield.
a. A corporation is planning to sell its 90-day commercial paper to investors offering an 8.4 percent
yield. If the three-month T-bill’s annualized rate is 7 percent, the default risk premium is
estimated to be 0.6 percent and there is a 0.4 percent tax adjustment, what is the appropriate
liquidity premium?
ANSWER:
Ycp, n = Rf,n + DP + LP + TA
LP = Ycp,n – Rf,n – DP – TA
b. If due to unexpected changes in the economy the default risk premium increases to 0.8 percent,
what is the appropriate yield to be offered on the commercial paper (assuming no other changes
occur)?
ANSWER:
Ycp,n = Rf,n + DP + LP + TA
7. Forward Rate.
a. Determine the forward rate for various one-year interest rate scenarios if the two-year interest rate
is 8 percent, assuming no liquidity premium. Explain the relationship between the one-year
interest rate and the one-year forward rate, holding the two-year interest rate constant.
ANSWER: As the one-year interest rate rises, the forward rate declines. The one-year forward rate is
b. Determine the one-year forward rate for the same one-year interest rate scenarios in question (a),
assuming a liquidity premium of 0.4 percent. Does the relationship between the one-year interest
rate and the forward rate change when the liquidity premium is considered??
c. Determine how the one-year forward rate would be affected if the quoted two-year interest rate
rises, holding the quoted one-year interest rate constant. Also, hold the liquidity premium
constant. Explain the logic of this relationship.
ANSWER: The forward rate increases for higher levels of a two-year interest rate. The greater the
d. Determine how the one-year forward rate would be affected if the liquidity premium rises,
holding the quoted one-year interest rates constant. Also, hold the two-year interest rate constant.
Explain the logic of this relationship.
ANSWER: The forward rate is reduced for higher levels of the liquidity premium, holding the
8. After-tax Yield. Determine how the after-tax yield from investing in a corporate bond is affected by
higher tax rates, holding the before-tax yield constant. Explain the logic of this relationship.
ANSWER: The after-tax yield is reduced for higher levels of the tax rate, holding the before-tax yield
9. Debt Security Yield.
a. Determine how the appropriate yield to be offered on a security is affected by a higher risk-free
rate. Explain the logic of this relationship.
ANSWER: The appropriate yield to be offered on a security would need to be increased if the
b. Determine how the appropriate yield to be offered on a security is affected by a higher default
risk premium. Explain the logic of this relationship.
ANSWER: The appropriate yield to be offered on a security would need to be increased if the default
Flow of Funds Exercise
Influence of the Structure of Interest Rates
Recall that Carson Company has obtained substantial loans from finance companies and commercial
banks. The interest rate on the loans is tied to the six-month Treasury bill rate (and includes a risk
premium) and is adjusted every six months. Thus, Carson’s cost of obtaining funds is sensitive to interest
rate movements. Because of its expectations that the U.S. economy will strengthen, Carson plans to grow
in the future by expanding its business and through acquisitions. Carson expects that it will need
substantial long-term financing to finance its growth, and plans to borrow additional funds either through
loans or by issuing bonds. It is also considering the issuance of stock to raise funds in the next year.
a. Assume that the market’s expectations for the economy are similar to those of Carson. Also
assume that the yield curve is primarily influenced by interest rate expectations. Would the yield
curve be upward sloping or downward sloping? Why?
b. If Carson could obtain more debt financing for 10-year projects, would it prefer to obtain
credit at a long-term fixed interest rate, or at a floating rate. Why?
The prevailing interest rate would be lower on loans than on the bonds, but the interest rate on
c. If Carson attempts to obtain funds by issuing 10-year bonds, explain what information would
help to estimate the yield it would have to pay on 10-year bonds. That is, what are the key factors
that would influence the rate it would pay on the 10-year bonds?
The key factors are the risk-free rate on 10-year bonds, the risk premium, and any special
d. If Carson attempts to obtain funds by issuing loans with floating interest rates every six
months, explain what information would help to estimate the yield it would have to pay over the
next ten years. That is, what are the key factors that would influence the rate it would pay over the
10-year period?
e. An upward-sloping yield curve suggests that the initial rate that financial institutions could
charge on a long-term loan to Carson would be higher than the initial rate that they could charge
on a loan that floats in accordance with short-term interest rates. Does this imply that creditors
should prefer to provide a fixed-rate loan rather than a floating-rate loan to Carson? Explain why
Carson’s expectations of future interest rates are not necessarily the same as those of some
financial institutions.
Creditors may prefer to provide fixed-rate loans if they expect interest rates to decline (so that
they could lock in today’s rate on their loan) and floating-rate loans if they expect interest rates
Solution to Integrative Problem for Part I
Interest Rate Forecasts and Investment Decisions
1. The appropriate recommendation requires a rational forecast of U.S. interest rates based on the
information provided. A rational forecast can be created by recognizing what factors will or will not
influence future interest rates, and weighing the potential influence of any relevant factors. Each of
the nine pieces of information provided to the student is addressed below:
1. Movements in interest rates over the year surely affected bond prices, but this information does
not help forecast future interest rates.
2. Changes in economic conditions over the last year affected interest rates (and therefore bond
prices), but this information does not help forecast future interest rates.
5. A stronger U.S. economy should place upward pressure on U.S. interest rates, regardless of the
economy two years ago. What is important is the change in the future U.S. economy relative to
8. The expectation of a weaker dollar by investors around the world could cause foreign investors to
reduce their investing in the United States, causing a net decline in the supply of funds in the
interest rates.
9. The market’s expectations about future interest rates in the United States are implied by the U.S.
yield curve. Based on the downward slope, and an assumed small liquidity premium, the U.S.
Overall, Numbers 1, 2, 4, and 9 should have no influence on your forecast of U.S. interest rates.
Number 3 suggests a slight decline in U.S. interest rates, while Numbers 5, 6, 7, and 8 suggest an
increase in U.S. interest rates. The net effect is an expected increase in U.S. interest rates.
1 Following the same procedure as stated in Question 1, you can develop a rational forecast of
Canadian interest rates. The assessment of Canadian bonds must be separated from the assessment of
U.S. bonds since Canadian Treasury bond values will not always move in tandem with U.S. Treasury
bond values.
Most of the information is either irrelevant for forecasting future interest rates in Canada or suggests
no change. The only factors that influence Canadian interest rates and are expected to change are
Canadian inflation and the value of the Canadian dollar. The expected decline in Canadian inflation
2 The yield on newly issued U.S. corporate bonds should rise to a greater degree than newly issued U.S.
Treasury bonds, because the change in the yield of newly issued corporate bonds should reflect not
only the increase in the risk-free rate, but also the increase in the risk premium.