Question

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?

Answer #1

Annualized Forward rate of 2 years 2 years from now =((1+4 Year rate)^4/(1+2 Year rate)^2)^1/2-1 |

Annualized Forward rate of 2 years 2 years from now=((1+0.032)^4/(1+0.021)^2)^1/2-1 |

Annualized Forward rate of 2 years 2 years from now % = 4.31 |

Annualized Forward rate of 3 years 2 years from now =((1+5 Year rate)^5/(1+2 Year rate)^2)^1/3-1 |

Annualized Forward rate of 3 years 2 years from now=((1+0.035)^5/(1+0.021)^2)^1/3-1 |

Annualized Forward rate of 3 years 2 years from now % = 4.44 |

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...

Use the term structure below for
problems 1 – 2:
Maturity
Spot Rate
Forward Rate
1
4.0%
2
4.25%
3
4.75%
4
5.25%
5
6.0%
6
6.75%
Calculate the 1-year forward rate as quoted today (year zero)
for years 1, 2, 3, 4 & 5. Show each of the spot and
forward rates on the time line below. (For simplicity, you can use
annual compounding.)
0 1 2 3 4 5
6
|____________|____________|____________|____________|____________|____________|
Calculate the 2-year forward rate as quoted today (year zero)
in year 1....

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(%)...

Consider the following term structure:
Term Yield
1 1.5%
2 2.3%
3 3.5%
4 3.7%
Compute
the implied forward rate on a one-year security 1 year from now and
2 years from now. What is the economic interpretation
of these rates according to the pure expectations theory?
…according to the liquidity preference (modified expectations)
theory? Suppose that you believe that the actual future one-year
rates will be greater than the implied forward rates....

Consider the following spot and forward rates:
1 year spot rate = 4%
3 year spot rate = 5%
4 year forward rate 1 year from now= 6%
Calculate:
2 year forward rate 1 year from now?
2 year forward rate 3 year
Hint: Draw the timeline, plot the given rates
to the corresponding intervals and calculate the forward rate for
the blank interval.

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...

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...

An investor has the following information about a zero-coupon
bond curve: Years to maturity 1 2 3 4 Spot rates 3.23% 3.65% 4.05%
4.30% The investor enters into a 4-year interest rate swap to pay a
fixed rate and receive a floating rate based on future 1-year LIBOR
rates. If the swap has annual payments, what is the fixed rate you
should pay? Six months into the swap the term structure
is now: Years to maturity 0.5 1.5 2.5 3.5...

The current 2-year spot rate is 4% and current 5-year spot rate
is 5.5%. According to the pure expectation theory of the term
structure of interest rates, what is the forward rate for 1-year
securities beginning three years from today?
A) 6.44%
B) 7.79%
C) 8.23%
D) 9.58%

1.The spot rate of interest is defined by s(t) = .1(.9)t for t =
1, 2, 3, 4, 5. Find the present value of a 5-year annuity-due in
which the first payment is equal to $1000, and each subsequent
payment increases by 5% of the immediately preceding payment.
2.You are given the following term structure of spot interest
rates:
Term (in years) Spot interest rate
1 5%
2 5.75%
3 6.25%
4 6.50%
A three-year annuity-immediate will be issued a...

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