Question

Assume the pure expectations hypothesis (PEH) holds, and estimate the term structure for the next three years (i.e. calculate the spot rate for the first year, and the forward rates for the second, and third years).

Bond |
Coupon Rate |
Maturity |
Market Price |

A |
3% paid annually |
1 year |
$998.06 |

B |
4% paid annually |
2 years |
$1011.49 |

C |
7% paid annually |
3 years |
$1094.68 |

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answered by: anonymous

Suppose that the expectations hypothesis holds and that the
current term structure of interest rates is as follows:
• y1 = 5%
• y2 = 6%
• y3 = 7%
a. What is the expected value of the two-year spot rate
realizing at year one, E(1y3)?
b. What is the expected price of a two-year zero-coupon bond
with a face value of $100 trading at year one?

If the pure expectations theory of the term structure is
correct, which of the following statements is CORRECT?
A. An upward sloping yield curve would imply that interest rates
are expected to be lower in the future.
B. If a 1-year Treasury bill has a yield to maturity of 7% and a
2-year Treasury bill has a yield to maturity of 8%, this would
imply the market believes that 1-year rates will be 7.5% one year
from now.
C. The...

4. Assume that short-term rate, r1 = 6%, and that the
expected market rates,
E(r 12 ) = 7 % and E(r 23 ) = 9 % . Also assume that the
unbiased expectations theory holds such that the forward rates are
identical to expected spot rates.
a. What should be the current price of a 3-year, $1000 bond
with a 12% coupon rate? Assume annual coupon payments.
b. What is the yield-to-maturity for this bond?

1. The following is a list of
prices for zero-coupon bonds of various maturities. Calculate the
yields to maturity of each bond and the implied sequence of forward
rates.
maturity years: Price of bond
1 943.40
2 898.47
3 847.62
4 792.16
2. [Chapter 15] The current yield curve
for default-free zero-coupon bonds is as follows:
Maturity (Years): YTM%
1 10%
2 11%
3 12%
a. What are the implied
1-year forward rates?
b. Assume that the pure
expectations hypothesis of the term structure...

Estimate term structure of discount factors, spot rates and
forward rates by using data on five semi-annual coupon paying bonds
with $100 face value each: The bonds, respectively, have 1.25,
5.35, 10.4, 15.15 and 20.2 years to maturity; pay coupon at annual
rates of 4.35, 5.25, 6.25, 7.25, and 8.25 percent of face value;
and are trading at quoted spot market prices in dollars of 98.25,
99.25, 100.25, 101.25 and 102.25 . Specify the discount factor
function d(t) by a...

Estimate term structure of discount factors, spot rates and
forward rates by using data on five semi-annual coupon paying bonds
with $100 face value each: The bonds, respectively, have 1.25,
5.35, 10.4, 15.15 and 20.2 years to maturity; pay coupon at annual
rates of 4.35, 5.25, 6.25, 7.25, and 8.25 percent of face value;
and are trading at quoted spot market prices in dollars of 98.25,
99.25, 100.25, 101.25 and 102.25 . Specify the discount factor
function d(t) by a...

In January 2020, the term-structure of spot rates is as
follows
(with continuous compounding):
Maturity (years) Zero-rate(%)
1 2.0
2 3.0
3 4.0
(a) A 3-year zero-coupon bond has the face value of $1,000.
Consider a 1-year forward
contract on the zero coupon bond. What should be the forward
price?
(b)Suppose that an investor takes a long position in the above
forward contract. One year
later, in January 2021, the term-structure turns out to be as
follows:
Maturity (years) Zero-rate(%)...

Using the Expectations Theory of the term structure,
calculate the interest rates in the term structure for maturities
of 1 to 5 years for the following paths of one year interest rates
over the next five years. Explain for each what the yield curve
would look like.
3% 4% 5% 6% 7%
3% 2% 1% 1% 2%

Currently, in October 2020, the term-structure of spot rates is
as follows (with continuous compounding):
Maturity (years)
Zero-rate (%)
1
1.0
2
2.0
3
3.0
(a) Consider a 2-year forward contract on a zero-coupon bond.
This bond is risk-free and will pay a face value of $1,000 in year
3. What is the forward price? [6 points]
(b) Suppose that, in October 2020, an investor entered a long
position in the forward found in (a). One year later, in October...

You observe the following term structure of interest rates
(zero-coupon yields, also called "spot rates"). The spot rates are
annual rates that are semi-annually compounded.
Time to Maturity
Spot Rate
0.5
2.00%
1.0
3.00%
1.5
3.50%
2.0
3.00%
2.5
4.00%
3.0
4.50%
1. Compute the six-month forward curve, i.e. compute
f(0,0.5,1.0), f(0,1.0,1.5), f(0,1.5,2.0), f(0,2.0,2.5), and
f(0,2.5,3.0). Round to six digits after the decimal. Enter
percentages in decimal form, i.e. enter 2.1234% as 0.021234.
In all the following questions, enter percentages in...

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