Solutions Students
Problems and Solutions
1
CHAPTER 1—Problems
1.1 Problems on Bonds
Exercise 1.1
On 12/04/01, consider a fixed-coupon bond whose features are the following:
•
face value: $1,000 coupon rate: 8%
• coupon frequency: semiannual
• maturity: 05/06/04
•
What are the future cash flows delivered by this bond?
Solution 1.1
1. The coupon cash flow is equal to $40
8% × $1,000
= $40
2
It is delivered on the following future dates: 05/06/02, 11/06/02, 05/06/03,
11/06/03 and 05/06/04.
The redemption value is equal to the face value $1,000 and is delivered on maturity date 05/06/04.
Coupon =
Exercise 1.3
An investor has a cash of $10,000,000 at disposal. He wants to invest in a bond with
$1,000 nominal value and whose dirty price is equal to 107.457%.
1. What is the number of bonds he will buy?
2. Same question if the nominal value and the dirty price of the bond are respectively $100 and 98.453%.
Solution 1.3
1. The number of bonds he will buy is given by the following formula
Number of bonds bought =
Cash
Nominal Value of the bond × dirty price
Here, the number of bonds is equal to 9,306 n= 10,000,000
= 9,306.048
1,000 × 107.457%
2. n is equal to 101,562 n= Exercise 1.4
10,000,000
= 101,571.31
100 × 98.453%
On 10/25/99, consider a fixed-coupon bond whose features are the following:
•
face value: Eur 100
2
Problems and Solutions
•
coupon rate: 10% coupon frequency: annual
• maturity: 04/15/08
•
Compute the accrued interest taking into account the four different day-count bases: Actual/Actual, Actual/365, Actual/360 and 30/360.
Solution 1.4
The last coupon has been delivered on 04/15/99. There are 193 days between
04/15/99 and 10/25/99, and 366 days between the last coupon date (04/15/99) and the next coupon date (04/15/00).
•
The accrued interest with the Actual/Actual day-count basis is equal to Eur
5.273
193
× 10% × Eur 100 = Eur 5.273
366
•
The accrued interest with the Actual/365 day-count basis is equal to Eur 5.288
193
× 10% × Eur 100 = Eur 5.288
365
1
CHAPTER 1—Problems
1.1 Problems on Bonds
Exercise 1.1
On 12/04/01, consider a fixed-coupon bond whose features are the following:
•
face value: $1,000 coupon rate: 8%
• coupon frequency: semiannual
• maturity: 05/06/04
•
What are the future cash flows delivered by this bond?
Solution 1.1
1. The coupon cash flow is equal to $40
8% × $1,000
= $40
2
It is delivered on the following future dates: 05/06/02, 11/06/02, 05/06/03,
11/06/03 and 05/06/04.
The redemption value is equal to the face value $1,000 and is delivered on maturity date 05/06/04.
Coupon =
Exercise 1.3
An investor has a cash of $10,000,000 at disposal. He wants to invest in a bond with
$1,000 nominal value and whose dirty price is equal to 107.457%.
1. What is the number of bonds he will buy?
2. Same question if the nominal value and the dirty price of the bond are respectively $100 and 98.453%.
Solution 1.3
1. The number of bonds he will buy is given by the following formula
Number of bonds bought =
Cash
Nominal Value of the bond × dirty price
Here, the number of bonds is equal to 9,306 n= 10,000,000
= 9,306.048
1,000 × 107.457%
2. n is equal to 101,562 n= Exercise 1.4
10,000,000
= 101,571.31
100 × 98.453%
On 10/25/99, consider a fixed-coupon bond whose features are the following:
•
face value: Eur 100
2
Problems and Solutions
•
coupon rate: 10% coupon frequency: annual
• maturity: 04/15/08
•
Compute the accrued interest taking into account the four different day-count bases: Actual/Actual, Actual/365, Actual/360 and 30/360.
Solution 1.4
The last coupon has been delivered on 04/15/99. There are 193 days between
04/15/99 and 10/25/99, and 366 days between the last coupon date (04/15/99) and the next coupon date (04/15/00).
•
The accrued interest with the Actual/Actual day-count basis is equal to Eur
5.273
193
× 10% × Eur 100 = Eur 5.273
366
•
The accrued interest with the Actual/365 day-count basis is equal to Eur 5.288
193
× 10% × Eur 100 = Eur 5.288
365