Deck 2: Basics of Fixed Income Securities

Question 1

What is the price on a 5.75-year floating rate bond that pays a semiannual coupon (no spread)? We know the following:
a. There is a coupon bond paying 3% quarterly P (0, 0.25) = 100.0448.
b. Last quarter the semiannually compounded rate was 3%.

Answer 1

The price of the floating rate bond is 100.7895.

Question 2

What effect does inflation have on discount factors?

Answer 2

Higher inflation makes less appealing money in the future, so discount factors will go down.

Question 3

From the following data obtain the discount curve:
a. A zero coupon bond Pz(0, 0.5) = 99.20.
b. A coupon bond paying 3% quarterly P (0, 0.25) = 100.5485.
c. A coupon bond paying 6% quarterly P (0, 0.75) = 100.1655.
d. A coupon bond paying 5% semiannually P (0, 1) = 103.0325.

Answer 3

The discount factors are the following:

Question 4

A Treasury dealer quotes the following 91-day bill at a 3.956% discount. What is the price of the security?

Question 5

For the following scenario, check if there is a mispriced security:

Question 6

You have two coupon bonds with same maturity, one pays 5% semiannu- ally and the other 5% quarterly. Which one has a higher yield?

Question 7

What is the price on a 4.5-year ?oating rate bond that pays a semiannual coupon (no spread)?

Question 8

What is the price of a 0.75-year ?oating rate bond that pays a semiannual coupon equal to ?oating rate plus 2% spread? We know the following:

Question 9

For the following scenario, check if there is a mispriced security:
a. A zero coupon bond Pz(0, 0.5) = 99.00.
b. A coupon bond paying 6% quarterly P (0, 0.25) = 101.1955.
c. A coupon bond paying 4% quarterly P (0, 0.50) = 102.0830.
d. A coupon bond paying 7% semiannually P (0, 0.75) = 105.8440.

Question 10

Using the previous discount curve price the following: A 1-year coupon bond paying 4% quarterly.

Question 11

What is the price of a 0.5-year floating rate bond that pays a quarterly coupon equal to floating rate plus a 1% spread? We know the following:
a. There is a zero coupon bond Pz(0, 0.25) = 99.80.
b. There is a coupon bond paying 2% quarterly P (0, 0.5) = 100.3960.

Question 12

Can a bond be quoted in more than one interest rate?

Question 13

Do discount factors depend on compounding frequency? Why?

Question 14

For the following scenario, check if there is a mispriced security:
a. A coupon bond paying 1% quarterly P (0, 0.25) = 100.6498.
b. A coupon bond paying 4% semiannually P (0, 0.25) = 101.8980.
c. A coupon bond paying 3% quarterly P (0, 0.50) = 101.2978.
d. A coupon bond paying 5% quarterly P (0, 0.75) = 103.4425.
e. A coupon bond paying 4% semiannually P (0, 1.00) = 103.5880.

Question 15

For the following scenario, check if there is a mispriced security:
a. A zero coupon bond Pz(0, 0.5) = 99.50.
b. A coupon bond paying 3% quarterly P (0, 0.50) = 100.9948.
c. A coupon bond paying 5% quarterly P (0, 0.75) = 102.7288.
d. A coupon bond paying 2% semiannually P (0, 1.25) = 102.8720.
e. A zero coupon bond Pz(0, 1.25) = 98.4.

Question 16

Using the previous discount curve price the following: A zero coupon bond expiring at t =0.75.

Question 17

Using the previous discount curve price the following: A 9-month coupon bond paying 5% semiannually.

Question 18

Using the previous discount curve price the following: A 6-month coupon bond paying 7% semiannually.

Question 19

For the following scenario, check if there is a mispriced security:
a. A zero coupon bond Pz(0, 0.25) = 99.30.
b. A zero coupon bond Pz(0, 0.50) = 98.70.
c. A coupon bond paying 3% semiannually P (0, 0.50) = 100.1850.
d. A coupon bond paying 2% semiannually P (0, 0.75) = 101.4880.

Question 20

A Treasury dealer quotes the following 182-day bill at a 3.956% discount. What is the price of the security?