Exam 6: Interest Rates

Because the maturity risk premium is normally positive,the yield curve must have an upward slope.If you measure the yield curve and find a downward slope,you must have done something wrong.

Kop Corporation's 5-year bonds yield 6.50%,and T-bonds with the same maturity yield 4.40%.The default risk premium for Kop's bonds is DRP = 0.40%,the liquidity premium on Kop's bonds is LP = 1.70% 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*?

In the foreseeable future,the real risk-free rate of interest,r*,is expected to remain at 3%,inflation is expected to steadily increase,and the maturity risk premium is expected to be 0.1(t − 1)%,where t is the number of years until the bond matures.Given this information,which of the following statements is CORRECT?

If 10-year T-bonds have a yield of 6.2%,10-year corporate bonds yield 8.5%,the maturity risk premium on all 10-year bonds is 1.3%,and corporate bonds have a 0.4% liquidity premium versus a zero liquidity premium for T-bonds,what is the default risk premium on the corporate bond?

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 3.05%,inflation is expected to be 2.75% this year,and the maturity risk premium is zero.Ignoring any cross-product terms,what is the equilibrium rate of return on a 1-year Treasury bond?

5-year Treasury bonds yield 5.5%.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*?

Niendorf Corporation's 5-year bonds yield 8.00%,and 5-year T-bonds yield 4.80%.The real risk-free rate is r* = 2.75%,the inflation premium for 5-year bonds is IP = 1.65%,the default risk premium for Niendorf's bonds is DRP = 1.20% 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 liquidity premium (LP)on Niendorf's bonds?

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 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 1-year T-bills currently yield 7.00% and the future inflation rate is expected to be constant at 3.20% per year.What is the real risk-free rate of return,r*? Disregard any cross-product terms,i.e.,if averaging is required,use the arithmetic average.

Suppose the U.S.Treasury issued $50 billion of short-term securities and sold them to the public.Other things held constant,what would be the most likely effect on short-term securities' prices and interest rates?

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 1.35% 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.

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 0.90% 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.

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."

Assuming the pure expectations theory is correct,which of the following statements is CORRECT?

Which of the following statements is CORRECT?

Short Corp just issued bonds that will mature in 10 years,and Long Corp issued bonds that will mature in 20 years.Both bonds promise to pay a semiannual coupon,they are not callable or convertible,and they are equally liquid.Further assume that the Treasury yield curve is based only on the pure expectations theory.Under these conditions,which of the following statements is CORRECT?

Since yield curves are based on a real risk-free rate plus the expected rate of inflation,at any given time there can be only one yield curve,and it applies to both corporate and Treasury securities.

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.

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.

Crockett Corporation's 5-year bonds yield 6.35%,and 5-year T-bonds yield 4.75%.The real risk-free rate is r* = 3.60%,the default risk premium for Crockett's bonds is DRP = 1.00% versus zero for T-bonds,the liquidity premium on Crockett's bonds is LP = 0.90% 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 inflation premium (IP)is built into 5-year bond yields?