Question

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(%)

1 3.0

2 4.0

3 5.0

What is the value (in January 2021) of the long position in the forward contract?

Answer #1

Bond price = Face value * e^{-(3 year zero rate * Time to
Maturity)}

Bond price = $1000 * e^{-(4% * 3)}

Bond price = $886.92

Future price = Bond price * e^{(1 year zero rate * Time to
Maturity)}

Future price = $886.92 * e^{(2% * 1)}

**Future price = $904.84**

2)

Zero coupon Bond price after 1 year after the change in term structure

Bond price = Face value * e^{-(2 year zero rate * Time to
Maturity)}

Bond price = $1000 * e^{-(4% * 2)}

Bond price after 1 year = $923.12

Value of Long position in Future contract = Future price - Bond price after 1 year

Value of Long position in Future contract = $923.12 - $904.84

**Value of Long position in Future contract**
**= $18.28**

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...

Suppose that zero interest rates with continuous compounding are
as follows:
Maturity (months)
Rate (% per annum)
3
3.0
6
3.2
9
3.4
12
3.5
15
3.6
18
3.7
Calculate forward interest rates for the second, third, fourth,
fifth, and sixth quarters.

The Term Structure
shows the following Spot Rates:
Maturity in years
1
2
3
4
5
spot rate in %
1.8
2.1
2.6
3.2
3.5
What is the implied 2-year forward rate two years from now? What
is the implied 3-year forward rate two years from now?

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...

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...

The term structure for zero-coupon bonds is currently:
Maturity (Years)
YTM(%)
1
5.0
%
2
6.0
3
7.0
Next year at this time, you expect it to be:
Maturity (Years)
YTM(%)
1
6.0
%
2
7.0
3
8.0
a. What do you expect the rate of return
to be over the coming year on a 3-year zero-coupon bond?
(Round your answer to 1 decimal place.)
b-1. Under the expectations theory, what yields to
maturity does the market expect to observe...

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...

The term structure is at with all spot rates equal to 20%. You
observe a two-year zero-coupon bond. The first derivative of the
bond price with respect to the yield, dP/dy, is -625. What is the
price of the bond?
A:$375.00
How to solve this?

The term structure for zero-coupon bonds is currently:
Maturity (Years)
YTM(%)
1
4.3
%
2
5.3
3
6.3
Next year at this time, you expect it to be:
Maturity (Years)
YTM(%)
1
5.3
%
2
6.3
3
7.3
a. What do you expect the rate of return
to be over the coming year on a 3-year zero-coupon bond?
(Round your answer to 1 decimal place.)
b-1. Under the expectations theory, what yields to
maturity does the market expect to observe...

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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