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Exam 6: Interest Rates

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Question 1

True/False

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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.

A) True
B) False

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Question 2

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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 r_RF = [(1 + r*) (1 + IP) ]^0.5 - 1, almost everyone, from Federal Reserve officials down to textbook authors, uses the approximation r_RF = 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 yield on a 10-year T-bond is currently 5.05% and that on a 10-year Treasury Inflation Protected Security (TIPS) is 2.15%.Suppose further that the MRP on a 10-year T-bond is 0.90%,that no MRP is required on a TIPS,and that no liquidity premium is required on any T-bond.Given this information,what is the expected rate of inflation over the next 10 years? Disregard cross-product terms,i.e.,if averaging is required,use the arithmetic average.

A) 1.81%
B) 1.90%
C) 2.00%
D) 2.10%
E) 2.21%

F) A) and E)
G) C) and E)

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Question 3

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Suppose the interest rate on a 1-year T-bond is 5.00% and that on a 2-year T-bond is 6.00%.Assume that the pure expectations theory is NOT valid,and the MRP is zero for a 1-year T-bond but 0.40% for a 2-year bond.What is the yield on a 1-year T-bond expected to be one year from now?

Assume the following: The real risk-free rate,r*,is expected to remain constant at 3%.Inflation is expected to be 3% next year and then to be constant at 2% a year thereafter.The maturity risk premium is zero.Given this information,which of the following statements is CORRECT?

If investors expect a zero rate of inflation,then the nominal rate of return on a very short-term U.S.Treasury bond should be equal to the real risk-free rate,r*.

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 r_RF = [(1 + r*) (1 + IP) ]^0.5 - 1, almost everyone, from Federal Reserve officials down to textbook authors, uses the approximation r_RF = 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 3.10%,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.

If the pure expectations theory of the term structure is correct,which of the following statements would be CORRECT?

Assuming that the term structure of interest rates is determined as posited by the pure expectations theory,which of the following statements is CORRECT?

Because the maturity risk premium is normally positive,the yield curve is normally upward sloping.

Which of the following statements is CORRECT?

The Federal Reserve tends to take actions to increase interest rates when the economy is very strong and to decrease rates when the economy is weak.

Keys Corporation's 5-year bonds yield 6.20% 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 liquidity premium for Keys' bonds is LP = 0.5% versus zero for T-bonds,and the maturity risk premium for all bonds is found with the formula MRP = (t − 1) × 0.1%,where t = number of years to maturity.What is the default risk premium (DRP) on Keys' bonds?

Koy Corporation's 5-year bonds yield 7.00%,and 5-year T-bonds yield 5.15%.The real risk-free rate is r* = 3.0%,the inflation premium for 5-year bonds is IP = 1.75%,the liquidity premium for Koy's bonds is LP = 0.75% versus zero for T-bonds,and the maturity risk premium for all bonds is found with the formula MRP = (t − 1) × 0.1%,where t = number of years to maturity.What is the default risk premium (DRP) on Koy's bonds?

Suppose 1-year Treasury bonds yield 4.00% while 2-year T-bonds yield 5.10%.Assuming the pure expectations theory is correct,and thus the maturity risk premium for T-bonds is zero,what is the yield on a 1-year T-bond expected to be one year from now?

The four most fundamental factors that affect the cost of money are (1)production opportunities,(2)time preferences for consumption,(3)risk,and (4)the skill level of the economy's labor force.

Which of the following factors would be most likely to lead to an increase in nominal interest rates?

One of the four most fundamental factors that affect the cost of money as discussed in the text is the current state of the weather.If the weather is dark and stormy,the cost of money will be higher than if it is bright and sunny,other things held constant.

Which of the following statements is CORRECT?

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 r_RF = [(1 + r*) (1 + IP) ]^0.5 - 1, almost everyone, from Federal Reserve officials down to textbook authors, uses the approximation r_RF = 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. ​ ​ -The real risk-free rate is 3.55%,inflation is expected to be 3.15% this year,and the maturity risk premium is zero.Taking account of the cross-product term,i.e.,not ignoring it,what is the equilibrium rate of return on a 1-year Treasury bond?

One of the four most fundamental factors that affect the cost of money as discussed in the text is the risk inherent in a given security.The higher the risk,the higher the security's required return,other things held constant.