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28.
Interest rates You are considering an investment in 30-year bonds issued by a
corporation. The bonds have no special covenants.
The Wall Street Journal
reports that
one-year T-bills are currently earning 3.50 percent. Your broker has determined the
following information about economic activity and the corporation bonds:
Real interest rate = 2.50 percent
Default risk premium = 1.75 percent
Liquidity risk premium = 0.70 percent
Maturity risk premium = 1.50 percent
What is the inflation premium? What is the fair interest rate on the corporation's 30-year
bonds?
29.
Interest rates A corporation's 10-year bonds have an equilibrium rate of return of 7
percent. For all securities, the inflation risk premium is 1.50 percent and the real interest
rate is 3.0 percent. The security's liquidity risk premium is 0.15 percent and maturity risk
premium is 0.70 percent. The security has no special covenants. What is the bond's
default risk premium?
30.
Interest rates A two-year Treasury security currently earns 5.25 percent. Over the next
two years, the real interest rate is expected to be 3.00 percent per year and the inflation
premium is expected to be 2.00 percent per year. What is the maturity risk premium on the
two-year Treasury security?
31.
Unbiased Expectations Theory Suppose that the current one-year rate (one-year spot
rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and
4, respectively) are as follows:
Using the unbiased expectations theory, what is the current (long-term) rate for four-year-
maturity Treasury securities?
32.
Unbiased Expectations Theory One-year Treasury bills currently earn 5.50 percent. You
expect that one year from now, one-year Treasury bill rates will increase to 5.75 percent. If
the unbiased expectations theory is correct, what should the current rate be on two-year
Treasury securities?
33.
Liquidity Premium Hypothesis One-year Treasury bills currently earn 5.50 percent. You
expect that one year from now, one-year Treasury bill rates will increase to 5.75 percent.
The liquidity premium on two-year securities is 0.075 percent. If the liquidity theory is
correct, what should the current rate be on two-year Treasury securities?
34.
Liquidity Premium Hypothesis Based on economists' forecasts and analysis, one-year
Treasury bill rates and liquidity premiums for the next four years are expected to be as
follows:
Using the liquidity premium hypothesis, what is the current rate on a four-year Treasury
security?
35.
Unbiased Expectations Theory One-year Treasury bills currently earn 3.15 percent. You
expected that one year from now, 1-year Treasury bill rates will increase to 3.65 percent
and that two years from now, one-year Treasury bill rates will increase to 4.05 percent. If
the unbiased expectations theory is correct, what should the current rate be on three-year
Treasury securities?
36.
Unbiased Expectations Theory One-year Treasury bills currently earn 2.55 percent. You
expected that one year from now, one-year Treasury bill rates will increase to 2.85 percent
and that two years from now, one-year Treasury bill rates will increase to 3.15 percent. If
the unbiased expectations theory is correct, what should the current rate be on 3-year
Treasury securities?
37.
Interest rates
The Wall Street Journal
reports that the rate on three-year Treasury
securities is 7.00 percent, and the six-year Treasury rate is 7.25 percent. From discussions
with your broker, you have determined that expected inflation premium is 1.75 percent
next year, 2.25 percent in Year 2, and 2.40 percent in Year 3 and beyond. Further, you
expect that real interest rates will be 3.75 percent annually for the foreseeable future.
What is the maturity risk premium on the six-year Treasury security?
38.
Interest rates A corporation's 10-year bonds are currently yielding a return of 7.75
percent. The expected inflation premium is 3.0 percent annually and the real interest rate
is expected to be 3.00 percent annually over the next 10 years. The liquidity risk premium
on the corporation's bonds is 0.50 percent. The maturity risk premium is 0.25 percent on
two-year securities and increases by 0.10 percent for each additional year to maturity.
What is the default risk premium on the corporation's 10-year bonds?
39.
Unbiased Expectations Theory Suppose we observe the following rates: 1
R
1 = 6 percent,
1
R
2 = 7.5 percent. If the unbiased expectations theory of the term structure of interest
rates holds, what is the one-year interest rate expected one year from now,
E
(2
r
1)?
40.
Unbiased Expectations Theory
The Wall Street Journal
reports that the rate on four-year
Treasury securities is 4.75 percent and the rate on five-year Treasury securities is 5.95
percent. According to the unbiased expectations hypotheses, what does the market expect
the one-year Treasury rate to be four years from today,
E
(5
r
1)?
41.
Liquidity Premium Hypothesis
The Wall Street Journal
reports that the rate on three-year
Treasury securities is 4.75 percent and the rate on four-year Treasury securities is 5.00
percent. The one-year interest rate expected in three years is
E
(4
r
1), 5.25 percent.
According to the liquidity premium hypotheses, what is the liquidity premium on the four-
year Treasury security,
L
4?
42.
Liquidity Premium Hypothesis Suppose we observe the following rates: 1
R
1 = 8 percent,
1
R
2 = 10 percent, and
E
(2
r
1) = 8 percent. If the liquidity premium theory of the term
structure of interest rates holds, what is the liquidity premium for year 2,
L
2?
43.
Forecasting Interest Rates You note the following yield curve in
The Wall Street Journal.
According to the unbiased expectations hypothesis, what is the one-year forward rate for
the period beginning one year from today, 2
f
1?
44.
Forecasting Interest Rates On May 23, 20XX, the existing or current (spot) one-year,
two-year, three-year, and four-year zero-coupon Treasury security rates were as follows:
Using the unbiased expectations theory, what is the one-year forward rate on zero-coupon
Treasury bonds for year 4 as of May 23, 20XX?
45.
Interest rates
The Wall Street Journal
reports that the current rate on 10-year Treasury
bonds is 6.75 percent, on 20-year Treasury bonds is 7.25 percent, and on a 20-year
corporate bond is 8.50 percent. Assume that the maturity risk premium is zero. If the
default risk premium and liquidity risk premium on a 10-year corporate bond is the same
as that on the 20-year corporate bond, what is the current rate on a 10-year corporate
bond.
46.
Interest rates
The Wall Street Journal
reports that the current rate on 5-year Treasury
bonds is 6.50 percent and on 10-year Treasury bonds is 6.75 percent. Assume that the
maturity risk premium is zero. Calculate the expected rate on a 5-year Treasury bond
purchased five years from today, E(5
r
1).
47.
Unbiased Expectations Theory Suppose we observe the three-year Treasury security
rate (1
R
3) to be 6 percent, the expected one-year rate next year
E
(2
r
1) to be 3 percent, and
the expected one-year rate the following year
E
(3
r
1) to be 5 percent. If the unbiased
expectations theory of the term structure of interest rates holds, what is the one-year
Treasury security rate, 1
R
1?
48.
Unbiased Expectations Theory
The Wall Street Journal
reports that the rate on three-
year Treasury securities is 6.25 percent and the rate on five-year Treasury securities is
6.45 percent. According to the unbiased expectations hypotheses, what does the market
expect the two-year Treasury rate to be three years from today,
E
(4r2)?
