# Solutions Students

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

•

The accrued interest with the Actual/360 day-count basis is equal to Eur 5.361 193

× 10% × Eur 100 = Eur 5.361

360

There are 15 days between 04/15/99 and 04/30/99, 5 months between May and September, and 25 days between 09/30/99 and 10/25/99, so that there are 190 days between 04/15/99 and 10/25/99 on the 30/360 day-count basis 15 + (5 × 30) + 25 = 190

•

Finally, the accrued interest with the 30/360 day-count basis is equal to Eur 5.278

190

× 10% × Eur 100 = Eur 5.278

360

Exercise 1.8

An investor wants to buy a bullet bond of the automotive sector. He has two choices: either invest in a US corporate bond denominated in euros or in a French corporate bond with same maturity and coupon. Are the two bonds comparable?

Solution 1.8

The answer is no. First, the coupon and yield frequency of the US corporate bond is semiannual, while it is annual for the French corporate bond. To compare the yields on the two instruments, you have to convert either the semiannual yield of the US bond into an equivalently annual yield or the annual yield of the French bond into an equivalently semiannual yield. Second, the two bonds do not necessarily have the same rating, that is, the same credit risk. Third, they do not necessarily have the same liquidity.

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Problems and Solutions

Exercise 1.15 What is the price P of the certificate of deposit issued by bank X on 06/06/00, with maturity 08/25/00, face value $10,000,000, an interest rate at issuance of 5% falling at maturity and a yield of 4.5% as of 07/31/00?

Solution 1.15 Recall that the price P of such a product is given by P =F ×

nc

B

1 + ym × nBm

1+c×

where F is the face value, c the interest rate at issuance, nc is the number of days between issue and maturity, B is the year-basis (360 or 365), ym is the yield on a money-market basis and nm is the number of days between settlement and maturity....

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