Question

Suppose the current annualized spot rates are as follows: 6 months 2% 12 months 4% 18 months 6% Assume semi-annual compounding and semi-annual coupon payment. An investor has an investment horizon of six months. She can invest her money in three ways. First, buy a 6-month zero-coupon bond with a par of $1000 and hold it until maturity. Second, buy a 12-month zero-coupon bond with a par of $1000 and sell it 6 months later. Third, buy a 18- month zero-coupon bond with a par of $1000 and sell it 6 months later.

(a) The investor expects that the spot rates will stay the same 6 months from now. Which investment strategy would the investor choose if she prefers a high expected holding period return? (10 points)

(b) Suppose 6 months later, the annualized spot rates are as follows: 6 months 8% 12 months 10% 18 months 12% Calculate the realized holding period returns for the three investment strategies. Which strategy has the highest realized holding period return? Is it the preferred strategy in (a) and why? (20 points)

Answer #1

(a) Since the period is 6 months for all the three options, it is preferrable to chose any option as the return is same for all the three options as described below:

Option 1: buy a 6-month zero-coupon bond with a par of $1000 and hold it until maturity.

Return after 6 months= 1000 + 1000 x 2% = 1000 + 20 = 1020

Option 2: buy a 12-month zero-coupon bond with a par of $1000 and sell it 6 months later

Return after 6 months= 1000 + (1000 x 4%/2)^2 = 1000 + 20 = 1020

Option 3: buy a 18- month zero-coupon bond with a par of $1000 and sell it 6 months later

Return after 6 months= 1000 + (1000 x 4%/3)^3 = 1000 + 20 = 1020

Since compounding is semi-annual, the return is same in all options. Hence any option is preferrable.

(b) Since maturity period is only 6 months, it is not an option even if rates increase after 6 months. The period of holding is only for 6 months and not beyong.

Consider the following spot rate curve:
6-month spot rate: 7%.
12-month spot rate: 9%.
18-month spot rate: 14%.
What is the forward rate for a one-year zero coupon bond issued
6 months from today? Equivalently, the question asks for
f21, where 1 time period consists of 6
months.

Suppose that 6-month, 12-month, 18-month, and 24-month zero
rates continuously compounded are 0.01, 0.01,0.04,and 0.01 per
annum, respectively. Estimate the cash price of a bond with a face
value of $1000 that will mature in 24 months pays a coupon of $87
per annum semiannually. Please write down the numerical answer with
two decimal points and no dollar sign.

1. Suppose that 6-month, 12-month, 18-month zero rates are,
respectively, 4%, 4.2%, 4.4% per annum, with continuous
compounding. Estimate the cash price of a bond with a face value of
100 that will mature in 18 months and pays a coupon of 2.00
semiannually.
Hint: the value of a bond should be the sum of the present value
of each cash flow. This bond has the following cash flow: $2.00 at
6 month, $2.00 at 12 month, and $102 at...

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...

Assume the current Treasury yield curve shows that the spot
rates for six months, one year, and one and a half years are 1%,
1.1%, and 1.3%, all quoted as semiannually compounded APRs.
What is the price of a $1000 par, 5% coupon bond maturing in
one and a half years (the next coupon is exactly six months from
now)

Pacific Airline wants to borrow $100,000 6 months later for 3
months with a Forward Rate Agreement. The following table shows
bond market information.
Maturity (month)
Zero Coupon Bond Price
3
0.988
6
0.971
9
0.953
12
0.933
(a) What is the forward rate of the FRA (effectively for 3
months)?
(b) Suppose 6 months later, the 3-month annualized spot rate is
5%. What is the settlement amount of the FRA if settle in
arrears?
(c) Instead of using an...

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(%)...

Assume the current Treasury yield curve shows that the spot
rates six months, one year, and one and a half years are 1%, 1.1%
and 1.3%, all quoted as semiannually compounded APRs. What is the
price of a $1,000 par, 5% coupon bond maturing in one and a half
year s (the next coupon is exactly 6 months from now)?

Price the following:
12-year, $1000 par value, 6% semi-annual coupon bond whose
current nominal yield-to-maturity (YTM) is 8%.
10-year, $1000 par value, 8% quarterly coupon bond whose current
nominal YTM is 7%.
30-year, $1000 par value, zero-coupon bond whose current nominal
YTM is 9.5%.
13-year, $1000 par value, 8% monthly coupon bond whose current
nominal YTM is 10%.
5-year, $500 par value, 8% semi-annual coupon bond whose current
nominal YTM is 8.25%

the 6-month,12-month,18- month, and 24- month zero
rates are4%,4.5%, 4.75% and 5% with continouus compounding .
what are the rates with semi annual compounding ?

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