978-1259285295 Chapter 7 Solution Manual

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Chapter 07 – The Risk and Term Structure of Interest Rates

Chapter 7

The Risk and Term Structure of Interest Rates

Conceptual and Analytical Problems

1. Consider a firm that issued a large quantity of commercial paper in the period leading

to a financial crisis. (LO1)

a. How would you expect the credit rating of the commercial paper to evolve as

the crisis unfolds?

b. Would you alter your prediction if, rather than commercial paper, the firm was

instead issuing asset-backed commercial paper?

Answer:

a. Commercial paper is generally issued without collateral, so that its rating will

2. Suppose that a major foreign government defaults on its debt. What, if anything, will

happen to the position and slope of the U.S. yield curve? (LO2)

Answer: If Treasury debt is a substitute for the foreign government debt, then U.S.

yield curve would shift downward, reflecting a flight to quality. If the holders of the

3. What was the connection between house price movements, the growth in subprime

mortgages, and securities backed by these mortgages—on the one hand—and on the

other hand—the difficulties encountered by some financial institutions during the

2007-2009 financial crisis? (LO1)

Answer: The viability of many subprime mortgages – and in particular ARMs –

depended on being able to refinance the loan before the interest rate reset to a higher

level. When house prices began to fall in 2006, pushing home values below the loan

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Chapter 07 – The Risk and Term Structure of Interest Rates

4. Suppose that the interest rate on one-year bonds is currently 4 percent and is expected

to be 5 percent in one year and 6 percent in two years. Using the Expectations

Hypothesis, compute the yield curve for the next three years. (LO2)

Answer:

Yield for one-year bond = 4%

5. *According to the liquidity premium theory, if the yield on both one-and two-year

bonds are the same, would you expect the one-year yield in one-year’s time to be

higher, lower or the same? Explain your answer. (LO2)

Answer: According to the liquidity premium theory, the two-year yield (i2,t) is an

As we can see from the formula, if the current one-and two-year yields are the same

6. You have $1,000 to invest over an investment horizon of three years. The bond

market offers various options. You can buy (i) a sequence of three one-year bonds;

(ii) a three-year bond; or (iii) a two-year bond followed by a one-year bond. The

current yield curve tells you that the one-year, two-year, and three-year yields to

maturity are 3.5 percent, 4.0 percent, and 4.5 percent respectively. You expect that

one-year interest rates will be 4 percent next year and 5 percent the year after that.

Assuming annual compounding, compute the return on each of the three investments,

and discuss which one you would choose. (LO2)

Answer:

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Chapter 07 – The Risk and Term Structure of Interest Rates

Expected return for (i) = (1.035)*(1.04)*(1.05) – 1 = 13.02%

The second and third options have higher expected returns than the first, but both

options involve investing in longer-term bonds (3-year and 2-year bonds,

respectively). Long-term bonds have higher inflation risk and interest-rate risk;

7. Suppose that the yield curve shows that the one-year bond yield is 3 percent, the

two-year yield is 4 percent, and the three-year yield is 5 percent. Assume that the risk

premium on the one-year bond is zero, the risk premium on the two-year bond is 1

percent, and the risk premium on the three-year bond is 2 percent. (LO2)

a. What are the expected one-year interest rates next year and the following

year?

b. If the risk premiums were all zero, as in the Expectations Hypothesis, what

would the slope of the yield curve be?

Answer:

which implies that the one-year interest rate next year will be 0.03. Using this

result, with a risk premium on the three-year bond of 0.02, we have:

8. *If inflation and interest rates become more volatile, what would you expect to see

happen to the slope of the yield curve? (LO2)

Answer: Investors are likely to demand a higher risk premium in the face of increased

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Chapter 07 – The Risk and Term Structure of Interest Rates

9. As economic conditions improve in countries with emerging markets, the cost of

borrowing funds there tends to fall. Explain why. (LO3)

Answer: As economic conditions improve, the chance that businesses will default on

10. Suppose your local government, threatened with bankruptcy, decided to tax the

interest income on its own bonds as part of an effort to rectify serious budgetary

woes. What would you expect to see happen to the yields on these bonds? (LO1)

Answer: You would expect the yields to rise to compensate investors for the loss of

11. *If, before the change in tax status, the yields on the bonds described in question 10

were below the Treasury yield of the same maturity, would you expect this spread to

narrow, to disappear, or to change sign after the policy change? Explain your answer.

(LO1)

Answer: We can attribute the lower yields on the local government bonds versus

Treasury issues to their tax-exempt status, as investors would view the federal

12. Suppose the risk premium on U.S. corporate bonds increases. How would the change

affect your forecast of future economic activity, and why? (LO3)

Answer: An increasing risk premium can be a sign of an impending recession, so you

13. If regulations restricting institutional investors to investment grade bonds were lifted,

what do you think would happen to the spreads between yields on investment grade

and speculative grade bonds? (LO1)

Answer: If institutional investors were willing to hold speculative-grade bonds in the

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Chapter 07 – The Risk and Term Structure of Interest Rates

14. Suppose a country with a struggling economy suddenly discovered vast quantities of

valuable minerals under government-owned land. How might the government’s bond

rating be affected? Using the model of demand and supply for bonds, what would

you expect to happen to the bond yields of that country’s government bonds? (LO3)

Answer: The ratings of the bonds would likely be upgraded, as the economic outlook

for the economy would improve and the reduction in the perceived riskiness of the

15. The misrating of mortgage-backed securities by rating agencies contributed to the

financial crisis of 2007-2009. List some recommendations you would make to avoid

such mistakes in the future. (LO1)

Answer: In the run-up to the 2007-2009 crisis, the absence of data capturing a period

of falling house prices at a national level caused models to underestimate the default

risk of the mortgages underlying the mortgage-backed securities. Running tests to

16. How do you think the abolition of investor protection laws would affect the risk

spread between corporate and government bonds? (LO1)

Answer: These laws were likely to be much more important in protecting purchasers

17. You and a friend are reading The Wall Street Journal and notice that the Treasury

yield curve is slightly upward sloping. Your friend comments that all looks well for

the economy but you are concerned that the economy is heading for trouble.

Assuming you are both believers in the liquidity premium theory, what might account

for your difference of opinion? (LO3)

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Chapter 07 – The Risk and Term Structure of Interest Rates

Answer: The difference in opinion could reflect different views on the size of the risk

premium. If the risk premium is large enough, a slightly upward-sloping yield curve

18. Do you think the term spread was an effective predictor of the recession that started in

December 2007? Why or why not? (LO3)

Answer: An inverted yield curve (negative term spread) is often a sign that the

economy is about to go into recession. Looking at the term spread (10-year yield

19. *Given the data in the accompanying table, would you say that this economy is

heading for a boom or for a recession? Explain your choice. (LO3)

3-month

Treasury-bill

10-year

Treasury bond

Baa corporate

10-year bond

January 1.00% 3.0% 7.0%

Answer: The information in both the term structure and the risk structure point to a

healthy economy. The term spread (the gap between the 10-year Treasury bond yield

The risk spread (the gap between the Treasury and corporate 10 year bonds) is

Data Exploration

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1. Did the financial crisis of 2007-2009 affect financial and nonfinancial firms to the

same extent? For the period beginning in 2006, plot the spread between the interest

rates on three-month non-financial commercial paper (FRED code: CPN3M) and

three-month Treasury bills (FRED code: TB3MS). Plot a similar spread using the

interest rates on three-month financial commercial paper (FRED code: CPF3M) and

Treasury bills (FRED code: TB3MS). Compare the evolution of these two spreads.

(LO1) (Hints: At the FRED Web site, select “Data Tools” and then “Create Your

Own Graph.” Type in the code for the non-financial commercial paper (FRED code:

CPN3M) and then set the “Observation Date Range” to begin in January 2006. Go

to “Add Data Series,” select the “Line 1” button, and then type in the code for the

Treasury bill rate (FRED code: TB3MS). At the formula box type in “a – b” (without

the quotes) and then select “Redraw Graph.” Repeat this process for financial

commercial paper (FRED code: CPF3M), but use the “Line 2” button when you

enter TB3MS again.)

Answer: The spreads between commercial paper (CP) rates and the Treasury bill rate

rose significantly in the second half of 2007 as the financial crisis began to unfold and

spiked even higher in the latter part of 2008 in the wake of the collapse of Lehman

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Chapter 07 – The Risk and Term Structure of Interest Rates

2. The Federal Reserve Bank of St. Louis publishes a weekly index of financial stress

(FRED code: STLFSI) that summarizes strains in financial markets, including

liquidity problems. For the period beginning in 1994, plot this index and, as a second

line, the difference between the Baa bond yield (FRED code: WBAA) and the

10-year U.S. Treasury bond yield (FRED code: WGS10YR). Does the index STLFSI

provide an early warning of stress? (LO3) (Hints: At the FRED Web site, select

“Data Tools” and then “Create Your Own Graph.” Type in the code for the Baa

bonds (FRED code: WBAA). Select “Add Data Series” and the “Line 1” button and

insert the code for the Treasury bond yield (FRED code: WGS10YR). At the formula

box, type in “a – b” (without the quotes) and then select “Redraw Graph.” Go again

to “Add Data Series” and type in the code for the financial stress index (FRED code:

STLFSI). Click “Copy to All Lines” next to the Observation Date Range for this

index. Finally, select “Redraw Graph.”)

Answer: The stress index deteriorated in 2007 before the bond yield spread widened.

It also improved in 2009 before the bond yield spread narrowed. Movements in this

3. How did the Great Depression (1930-33) and the Great Recession of 2007-2009

affect expectations of corporate default? To investigate, construct for each of those

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Chapter 07 – The Risk and Term Structure of Interest Rates

periods a separate plot of the corporate bond yield spread. For the depression period,

plot from 1930 to1933 to the difference between the Baa corporate bond yield (FRED

code: BAA) and a long-term Treasury bond yield (FRED code: LTGOVTBD). For the

Great Recession, plot from 2007 to 2009 the difference between the Baa yield (FRED

code: Baa) and the 10-year Treasury bond yield (FRED code: GS10). Compare the

plots. (LO1) (Hints: For the first plot, at the FRED website, select “Data Tools,”

then “Create Your Own Graphs.” At the “Graph” settings, turn off the recession

bars. In the “Add Data Series” box, type in the Baa bond yield code (FRED code:

BAA). Select “Add Data Series” again, select the “Line 1” button, and type in the

Treasury bond yield code (FRED code: LTGOVTBD). In the formula box, type in “a

– b” (without the quotes) and then select “Redraw Graph.” Finally, set the

observation range from January, 1930 to December, 1933 and then “Redraw

Graph.” For the second graph, start afresh by typing the Baa bond yield code (FRED

code: BAA) in the search box under “Add Data Series.” Choose “Add Data Series”

again, select the “Line 1” button, and type in the 10-year Treasury bond yield code

(FRED code: GS10). In the formula box, type in “a – b” (without the quotes) and

select “Redraw Graph.” Finally, select the Observation Date Range from January,

2007 to December, 2009, and choose “Redraw Graph.”)

Answer: The two data plots are below. The patterns are quite similar, though the risk

spread was modestly larger in the Great Depression than in the Great Recession. If

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Chapter 07 – The Risk and Term Structure of Interest Rates

4. How reliably does an inverted yield curve anticipate a recession? How far in

advance? Plot from 1970 (as in Figure 7.9A) the difference between the 10-year

Treasury yield (FRED code: GS10) and the three-month Treasury bill rate (FRED

code: TB3MS). Discuss the variability of the time between an inversion of the yield

curve and the subsequent recession. (LO3) (Hints: At the FRED Web site, select

“Data Tools” and then “Create Your Own Graph.” Type in the code for the 10-year

Treasury yield (FRED code: GS10). Go to “Add Data Series,” select the “Line 1”

button, and insert the code for the Treasury bill rate (FRED code: TB3MS). At the

formula box type in “a – b” (without the quotes), set the start date of 1970 in the

Observation Date Range box, and select “Redraw Graph .”)

Answer: The data plot is below. The yield curve inverts when the term spread

becomes negative, so we examine the spread for values around zero. Prior to the

downturn in 1973 the yield curve appears to have inverted several months in advance

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Chapter 07 – The Risk and Term Structure of Interest Rates

5. Download the data used in Data Exploration Problem 4 and (a) find the most recent

period for which the yield curve was (approximately) flat and (b) the longest time

period for which yield curve was inverted. (LO2) (Hint: Above the graph produced in

Data Exploration Problem 4, click on “Download Data in Graph” and examine the

resulting spreadsheet.)

Answer: The most recent period when the yield curve was approximately flat was in

* indicates more difficult problems

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