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Exam 6: Interest Rates

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Question 21

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The "yield curve" shows the relationship between bonds' maturities and their yields.

A) True
B) False

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Question 22

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The real risk-free rate of interest is expected to remain constant at 3% for the foreseeable future.However,inflation is expected to increase steadily over the next 30 years,so the Treasury yield curve has an upward slope.Assume that the pure expectations theory holds.You are also considering two corporate bonds,one with a 5-year maturity and one with a 10-year maturity.Both have the same default and liquidity risks.Given these assumptions,which of these statements is CORRECT?

A) Since the pure expectations theory holds,the 10-year corporate bond must have the same yield as the 5-year corporate bond.
B) Since the pure expectations theory holds,all 5-year Treasury bonds must have higher yields than all 10-year Treasury bonds.
C) Since the pure expectations theory holds,all 10-year corporate bonds must have the same yield as 10-year Treasury bonds.
D) The 10-year Treasury bond must have a higher yield than the 5-year corporate bond.
E) The 10-year corporate bond must have a higher yield than the 5-year corporate bond.

F) All of the above
G) B) and E)

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Question 23

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Kay Corporation's 5-year bonds yield 5.90% and 5-year T-bonds yield 4.40%.The real risk-free rate is r* = 2.5%,the inflation premium for 5-year bonds is IP = 1.50%,the default risk premium for Kay's bonds is DRP = 1.30% versus zero for T-bonds,and the maturity risk premium for all bonds is found with the formula MRP = (t - 1) $\times$ 0) 1%,where t = number of years to maturity.What is the liquidity premium (LP) on Kay's bonds?

The risk that interest rates will increase,and that increase will lead to a decline in the prices of outstanding bonds,is called "interest rate risk," or "price risk."

The four most fundamental factors that affect the cost of money are (1)production opportunities, (2)time preferences for consumption, (3)risk,and (4)weather conditions.

Which of the following statements is CORRECT,other things held constant?

Assume that inflation is expected to decline steadily in the future,but that the real risk-free rate,r*,will remain constant.Which of the following statements is CORRECT,other things held constant?

Suppose the real risk-free rate is 3.25%,the average future inflation rate is 4.35%,and a maturity risk premium of 0.07% per year to maturity applies to both corporate and T-bonds,i.e. ,MRP = 0.07%(t) ,where t is the number of years to maturity.Suppose also that a liquidity premium of 0.50% and a default risk premium of 2.40% apply to A-rated corporate bonds but not to T-bonds.How much higher would the rate of return be on a 10-year A-rated corporate bond than on a 5-year Treasury bond? Here we assume that the pure expectations theory is NOT valid.Disregard cross-product terms,i.e. ,if averaging is required,use the arithmetic average.

Suppose the federal deficit increased sharply from one year to the next,and the Federal Reserve kept the money supply constant.Other things held constant,we would expect to see interest rates decline.

Kop Corporation's 5-year bonds yield 6.50%,and T-bonds with the same maturity yield 5.90%.The default risk premium for Kop's bonds is DRP = 0.40%,the liquidity premium on Kop's bonds is LP = 0.20% versus zero on T-bonds,the inflation premium (IP) is 1.50%,and the maturity risk premium (MRP) on 5-year bonds is 0.40%.What is the real risk-free rate,r*?

If the Treasury yield curve were downward sloping,the yield to maturity on a 10-year Treasury coupon bond would be higher than that on a 1-year T-bill.

The risk that interest rates will decline,and that decline will lead to a decline in the income provided by a bond portfolio as interest and maturity payments are reinvested,is called "reinvestment rate risk."

If the pure expectations theory is correct,a downward sloping yield curve indicates that interest rates are expected to decline in the future.

Which of the following would be most likely to lead to a higher level of interest rates in the economy?

Interest rates are important in finance, and it is important for all students to understand the basics of how they are determined. However, the chapter really has two aspects that become clear when we try to write test questions and problems for the chapter. First, the material on the fundamental determinants of interest rates - the real risk-free rate plus a set of premiums - is logical and intuitive, and easy in a testing sense. However, the second set of material, that dealing with the yield curve and the relationship between 1-year rates and longer-term rates, is more mathematical and less intuitive, and test questions dealing with it tend to be more difficult, especially for students who are not good at math. As a result, problems on the chapter tend to be either relatively easy or relatively difficult, with the difficult ones being as much exercises in algebra as in finance. In the test bank for prior editions, we tended to use primarily difficult problems that addressed the problem of forecasting forward rates based on yield curve data. In this edition, we leaned more toward easy problems that address intuitive aspects of interest rate theory. We should note one issue that can be confusing if it is not handled carefully - the use of arithmetic versus geometric averages when bringing inflation into interest rate determination in yield curve related problems. It is easy to explain why a 2-year rate is an average of two 1-year rates, and it is logical to use a compounding process that is essentially a geometric average that includes the effects of cross-product terms. It is also easy to explain that average inflation rates should be calculated as geometric averages. However, when we combine inflation with interest rates, rather than using the formulation rRF = [(1 + r*) (1 + IP) ] – 1, almost everyone, from Federal Reserve officials down to textbook authors, uses the approximation rRF = r* + IP. Understandably, this can confuse students when they start working problems. In both the text and test bank problems we make it clear to students which procedure to use. Quite a few of the problems are based on this basic equation: r = r* + IP + MRP + DRP + LP. We tell our students to keep this equation in mind, and that they will have to do some transposing of terms to solve some of the problems. The other key equation used in the problems is the one for finding the 1-year forward rate, given the current 1-year and 2-year rates: (1 + 2-year rate) 2 = (1 + 1-year rate) (1 + X) , which converts to X = (1 + 2yr) 2/(1 + 1yr) – 1, where X is the 1-year forward rate. This equation, which is used in a number of problems, assumes that the pure expectations theory is correct and thus the maturity risk premium is zero. -Suppose the real risk-free rate is 4.20%,the average expected future inflation rate is 2.50%,and a maturity risk premium of 0.10% per year to maturity applies,i.e. ,MRP = 0.10%(t) ,where t is the number of years to maturity,hence the pure expectations theory is NOT valid.What rate of return would you expect on a 4-year Treasury security? Disregard cross-product terms,i.e. ,if averaging is required,use the arithmetic average.

Which of the following statements is CORRECT?

During periods when inflation is increasing,interest rates tend to increase,while interest rates tend to fall when inflation is declining.

Suppose the real risk-free rate is 3.50%,the average future inflation rate is 2.50%,a maturity premium of 0.20% per year to maturity applies,i.e. ,MRP = 0.20%(t) ,where t is the number of years to maturity.Suppose also that a liquidity premium of 0.50% and a default risk premium of 2.70% applies to A-rated corporate bonds.What is the difference in the yields on a 5-year A-rated corporate bond and on a 10-year Treasury bond? Here we assume that the pure expectations theory is NOT valid,and disregard any cross-product terms,i.e. ,if averaging is required,use the arithmetic average.

5-year Treasury bonds yield 4.4%.The inflation premium (IP) is 1.9%,and the maturity risk premium (MRP) on 5-year T-bonds is 0.4%.There is no liquidity premium on these bonds.What is the real risk-free rate,r*?

Kern Corporation's 5-year bonds yield 7.50% and 5-year T-bonds yield 4.30%.The real risk-free rate is r* = 2.5%,the default risk premium for Kern's bonds is DRP = 1.90% versus zero for T-bonds,the liquidity premium on Kern's bonds is LP = 1.3%,and the maturity risk premium for all bonds is found with the formula MRP = (t - 1) $\times$ 0) 1%,where t = number of years to maturity.What is the inflation premium (IP) on all 5-year bonds?