54.
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?
a.
If the yield curve for Treasury securities is flat, Short’s bond must under all conditions have the same yield
as
Long’s bonds.
b.
If the yield curve for Treasury securities is upward sloping, Long’s bonds must under all conditions have a
higher yield than Short’s bonds.
c.
If Long’s and Short’s bonds have the same default risk, their yields must under all conditions be equal.
d.
If the Treasury yield curve is upward sloping and Short has less default risk than Long, then Short’s bonds
must under all conditions have a lower yield than Long’s bonds.
e.
If the Treasury yield curve is downward sloping, Long’s bonds must under all conditions have the lower
yield.
Multiple Choice: Problems
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)]0.5 –
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.