Sample Problems—Interest rates
1.
Assume that k* = 2.0%; the maturity risk premium is found as MRP = 0.1%(t – 1) where t = years to
maturity; the default risk premium for corporate bonds is DRP = 0.05%(t – 1); the liquidity premium is
1.0 % for corporate bonds, 0 for Treasury bonds; and inflation is expected to be 3 percent, 4 percent,
and 5 percent during the next three years and 6 percent thereafter. What is the difference in interest
rates between 10-year corporate and Treasury bonds?
2.
Due to the recession, the rate of inflation expected for the coming year is only 3.5 percent. However,
the rate of inflation in Year 2 and thereafter is expected to be constant at some level above 3.5 percent.
Assume that the real risk-free rate is k*=2% for all maturities and there are no maturity premiums. If
3-year Treasury bonds yield 3 percentage points more than 1-year bonds, what rate of inflation is
expected after Year 1?
3.
Assume that k*=2.0%; the maturity risk premium is MRP=0.1%(t-1) where t=years to maturity; the
default risk premium for corporate bonds is DRP=0.05%(t-1); the liquidity premium is 1.0 percent for
corporate bonds; and inflation is expected to be 3%, 4%, and 5% during the next three years and then
6% thereafter. What is the difference in interest rates between 10-year corporate and Treasury bonds?
4.
Assume that the real risk-free rate is 2 percent, that the expected inflation rate during Year 2 is 3
percent, and that 2-year T-bonds yield 5.5 percent. If the maturity risk premium is zero, what is the
inflation rate during Year 1?
5.
If a 1-year Treasury bond has a yield of 5 percent, if the expected rate of inflation during the coming
year is 3 percent, and if the maturity risk and liquidity premiums on a 1-year bond are zero, then What
is the real risk-free rate, k*?
6.
Assume that a 3-year Treasury bond has no maturity risk nor liquidity risk and that the real risk-free
rate of interest is 2 percent. A 3-year T-bond carries a yield of 12 percent. If the expected inflation
rate is 12 percent for the coming year and 10 percent the year after, what is the implied expectation
inflation rate for the third year?
7.
Assume that k*=1.0%; the maturity risk premium is found as MRP=0.2%(t-1) where t=years to
maturity; the default risk premium for AT&T bonds is found as DRP=0.07%(t-1); the liquidity
premium is 0.50 percent for AT&T bonds but zero for Treasury bonds; and inflation is expected to be
7 percent, 6 percent, and 5 percent during the next three years and then 4 percent thereafter. What is
the difference in interest rates between 10-year AT&T bonds and 10-year Treasury bonds?
8.
Interest rates on 1-year Treasury securities are currently 5.6 percent, while 2-year Treasury securities
are yielding 6 percent. What is the 1-year interest rate expected in year 2?
9.
One-year government bonds yield 6.9 percent and two-year government bonds yield 7.2 percent.
Assume that the expectations theory holds. What does the market believe the rate on one-year
government bonds will be one year from today?
10. The real risk-free rate of interest is 2 percent. Inflation is expected to be 3 percent the next 2 years and
5 percent during the next 3 years after that. Assume that the maturity risk premium is zero. What is
the yield on 3-year Treasury securities?
11. Assume k*=3.0%; the maturity risk premium is MRP=0.1%(t-1) where t=years to maturity; the default
risk premium for corporate bonds is DRP=0.05%(t-1); the liquidity premium is 1.5% for corporate
bonds; and inflation is expected to be 4%, 5%, and 6% during the next three years and then 7%
thereafter. What is the difference in interest rates between 10-year corporate and Treasury bonds?
12. Three-year Treasury bonds currently yield 6 percent. Four-year Treasury bonds currently yield 6.5
percent. Assume that the expectations theory holds. What does the market believe the rate will be on
one-year Treasury bonds three years from now?
13. Using the following data, calculate the rate of return on a long-term Treasury bond.
k*
4%
Inflation premium
7%
Maturity risk premium
1%
Default risk premium
3%
Liquidity premium
2%
14. Three-year Treasury bonds currently yield 6 percent. Four-year Treasury bonds currently yield 6.5
percent. Assume that the expectations theory holds. What does the market believe the rate will be on
one-year Treasury securities three years from now?
15. The real risk-free rate, k*, is 2.5 percent. Inflation is expected to average 2.8 percent a year for the
next 4 years, after which time inflation is expected to average 3.75 percent per year. Assume that there
is no maturity risk premium. An 8-year corporate bond has a yield of 8.3 percent. Assume that the
liquidity premium on the corporate bond is 0.75%. What is the default risk premium on the corporate
bond?
16. One-year Treasury securities yield 5 percent, 2-year Treasury securities yield 5.5 percent, and 3-year
Treasury securities yield 6 percent. Assume that the expectations theory holds. What does the market
expect will be the yield on 1-year Treasury securities two years from now?