Exam 6: Interest Rates

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 rate of return on a 10-year T-bond is 6.55%,the expected average rate of inflation over the next 10 years is 2.0%,the MRP on a 10-year T-bond is 0.9%,no MRP is required on a TIPS,and no liquidity premium is required on any Treasury security.Given this information,what should the yield be on a 10-year TIPS? Disregard cross-product terms,i.e.,if averaging is required,use the arithmetic average.

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?

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?

One of the four most fundamental factors that affect the cost of money as discussed in the text is the time preference for consumption.The higher the time preference,the lower the cost of money,other things held constant.

An upward-sloping yield curve is often call a "normal" yield curve,while a downward-sloping yield curve is called "abnormal."

One of the four most fundamental factors that affect the cost of money as discussed in the text is the availability of production opportunities and their expected rates of return.If production opportunities are relatively good,then interest rates will tend to be relatively high,other things held constant.

If the pure expectations theory is correct (that is,the maturity risk premium is zero),which of the following is CORRECT?

If investors expect the rate of inflation to increase sharply in the future,then we should not be surprised to see an upward-sloping yield curve.

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

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

Assume that the current corporate bond yield curve is upward sloping.Under this condition,then we could be sure that

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*? The cross-product term should be considered,i.e.,if averaging is required,use the geometric average.

Kelly Inc's 5-year bonds yield 7.50% and 5-year T-bonds yield 4.90%.The real risk-free rate is r* = 2.5%,the default risk premium for Kelly's bonds is DRP = 0.40%,the liquidity premium on Kelly's bonds is LP = 2.2% versus zero on T-bonds,and the inflation premium (IP)is 1.5%.What is the maturity risk premium (MRP)on all 5-year bonds?

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

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 10-year T-bonds have a yield of 5.30% and 10-year corporate bonds yield 6.75%.Also,corporate bonds have a 0.25% liquidity premium versus a zero liquidity premium for T-bonds,and the maturity risk premium on both Treasury and corporate 10-year bonds is 1.15%.What is the default risk premium on corporate bonds?

Which of the following statements is CORRECT?

If the pure expectations theory holds,which of the following statements is CORRECT?

One of the four most fundamental factors that affect the cost of money as discussed in the text is the expected rate of inflation.If inflation is expected to be relatively high,then interest rates will tend to be relatively low,other things held constant.

If the demand curve for funds increased but the supply curve remained constant,we would expect to see the total amount of funds supplied and demanded increase and interest rates in general also increase.

The real risk-free rate is expected to remain constant at 3% in the future,a 2% rate of inflation is expected for the next 2 years,after which inflation is expected to increase to 4%,and there is a positive maturity risk premium that increases with years to maturity.Given these conditions,which of the following statements is CORRECT?