Question

Suppose that the current 1-year rate (1-year spot rate) and expected 1-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows: 1R1 = 1%, E(2r1) = 4.25%, E(3r1) = 4.75%, E(4r1) = 6.25% Using the unbiased expectations theory, calculate the current (longterm) rates for 1-, 2-, 3-, and 4-year-maturity Treasury securities. Plot the resulting yield curve. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer #1

1 Year Rate = 1R1 i.e 1%

2 Years Rate = Square Root [ (1+1R1) * (1+E(2r1)) ] - 1

= Square root [ (1+0.01)* (1+0.0425) ] - 1

= Square Root [ (1.01)*(1.0425) ] - 1

= Square Root [ 1.0529 ] - 1

= 1.0261 - 1

= 0.0261 i.e 02.61%

**3 Years rate :**

3 Years Rate = [ (1+1R1) *(1+(E(3r1))^{2}
]^{1/3} - 1

= [ (1+0.01) *(1+0.0475)^{2} ]^{1/3} - 1

= [ (1.01) *(1.0475)^{2} ]^{1/3} - 1

= [ (1.01) *1.0973]^{1/3} - 1

= [ (1.01) *1.0973]^{1/3} - 1

= 1.1083^{1/3} - 1

= 1.0349 - 1

= 0.0349 i.e 3.49%

**4 Years rate :**

4 Years Rate = [ (1+1R1) *(1+(E(4r1))^{3}
]^{1/4} - 1

= [ (1+0.01) *(1+0.0625)^{3} ]^{1/4} - 1

= [ (1.01) *(1.0625)^{3} ]^{1/4} - 1

= [ (1.01) *1.1995 ]^{1/4} - 1

= [ 1.2115 ]^{1/4} - 1

= 1.0491 - 1

= 0.0491 i.e 04.91%

**Yield Curve:**

Suppose that the current 1-year rate (1-year spot rate) and
expected 1-year T-bill rates over the following three years (i.e.,
years 2, 3, and 4, respectively) are as follows:
1R1 = 6%,
E(2r1) = 7%,
E(3r1) = 7.60%,
E(4r1) = 7.95%
Using the unbiased expectations theory, calculate the current
(long-term) rates for 1-, 2-, 3-, and 4-year-maturity Treasury
securities. (Round your answers to 2 decimal
places.)

Question: Suppose that the current one-year rate (one-year spot
rate) and expected one-year T-bill rates over the following 3 years
(i.e., years 2, 3 and 4 respectively) are as follows:
1R1 = 0.4%, E(2r1) = 1.4%, E(3r1) = 8.8% E(4r1) = 9.15%
Using the unbiased expectations theory, calculate the current
(long-term) rates for three-year- and four-year-maturity Treasury
securities. Using the unbiased expectations theory, calculate the
long term rates for one, two, three, and four years maturity
Treasury securities. (Round answers...

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: 1R1=4.70%, E(2r1) =5.70%, E(3r1) =6.20%,
E(4r1)=6.55% Using the unbiased expectations theory, what is the
current (long-term) rate for four-year-maturity Treasury
securities?
Multiple Choice
6.5500%
5.7852%
5.7875%

Based on economists’ forecasts and analysis, one-year T-bill
rates and liquidity premiums for the next four years are expected
to be as follows:
1R1
=
.33%
E(2r1)
=
.70%
L2
=
0.06%
E(3r1)
=
.80%
L3
=
0.15%
E(4r1)
=
1.10%
L4
=
0.16%
Identify the four annual rates. (Round your answers to 2
decimal places. (e.g., 32.16))
Annual Rates
Year
1
%
Year
2
%
Year
3
%
Year
4
%

Based on economists’ forecasts and analysis, one-year T-bill
rates and liquidity premiums for the next four years are expected
to be as follows:
1R1
=
5.65
%
E(2r1)
=
6.75
%
L2
=
0.05
%
E(3r1)
=
6.85
%
L3
=
0.10
%
E(4r1)
=
7.15
%
L4
=
0.12
%
Calculate the four annual rates. (Round your answers to 2
decimal places. (e.g., 32.16))
Annual Rates
Year 1
%
Year 2
%
Year 3
%
Year 4
%

Based on economists’ forecasts and analysis, one-year T-bill
rates and liquidity premiums for the next four years are expected
to be as follows:
1R1
=
.50%
E(2r1)
=
.98%
L2
=
0.09%
E(3r1)
=
1.08%
L3
=
0.14%
E(4r1)
=
1.38%
L4
=
0.16%
Calculate the four annual rates. (Round your answers to 2
decimal places. (e.g., 32.16))
Year 1: 0.50%
Year 2: ____%
Year 3: _____%
Year 4: _____%

Based on economists’ forecasts and analysis, one-year T-bill
rates and liquidity premiums for the next four years are expected
to be as follows: 1R1 = .50% E(2r1) = .75% L2 = 0.07% E(3r1) = .85%
L3 = 0.16% E(4r1) = 1.15% L4 = 0.17% Identify the four annual
rates. (Round your answers to 2 decimal places. (e.g., 32.16))
Annual Rates Year 1 .5 % Year 2 % Year 3 % Year 4 %

Based on economists’ forecasts and analysis, 1-year Treasury
bill rates and liquidity premiums for the next four years are
expected to be as follows:
R1
=
2.10
%
E(2r1)
=
3.00
%
L2
=
0.07
%
E(3r1)
=
3.40
%
L3
=
0.09
%
E(4r1)
=
3.85
%
L4
=
0.14
%
Using the liquidity premium theory, determine the current
(long-term) rates. (Do not round intermediate calculations.
Round your answers to 2 decimal places.)
YEAR 1
YEAR 2
YEAR 3...

Problem 6-11 Liquidity Premium Theory (LG6-7)
Based on economists’ forecasts and analysis, 1-year Treasury
bill rates and liquidity premiums for the next four years are
expected to be as follows:
R1
=
0.55
%
E(2r1)
=
1.70
%
L2
=
0.08
%
E(3r1)
=
1.80
%
L3
=
0.12
%
E(4r1)
=
2.10
%
L4
=
0.14
%
Using the liquidity premium theory, determine the current
(long-term) rates. (Do not round intermediate calculations.
Round your answers to 2 decimal places.)

Suppose we observe the three-year Treasury security rate
(1R3) to be 4.3 percent, the
expected one-year rate next
year—E(2r1)—to be 4.8
percent, and the expected one-year rate the following
year—E(3r1)—to be 5.6
percent. If the unbiased expectations theory of the term structure
of interest rates holds, what is the one-year Treasury security
rate? (Do not round intermediate calculations. Round your
answer to 2 decimal places. (e.g., 32.16))
one-year Treasury security rate: _______%

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