Interest Rates Are Important in Finance, and It Is Important

question 9

Multiple Choice

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.
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-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%

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Definitions:

Ohms

The unit of electrical resistance, representing the resistance between two points of a conductor when a voltage of one volt produces a current of one ampere.

Circuit Protection

Devices such as fuses, fuse links, and circuit breakers in an electrical circuit that stop the flow of electricity in the event that a fault occurs in the circuit. These help to protect people from injury and prevent damage to the vehicle’s electrical system.

Fuse Links

Safety devices in electrical systems that melt and break the circuit when current exceeds a certain level, preventing overheating.

Relays

Electrically operated switches that open or close circuits when activated, used in various applications to control high power or high voltage devices with low power signals.