Assignment 2 Fixed Income

CHAPTER 4

2. Calculate the requested measures in parts (a) through (f) for bonds A and B (assume that each bond pays interest semiannually)

(A) What is the price value of a basis point for bonds A and B?

- Bond A

Price (8%) = $100

Price (8.01%)= $99.9819

PVBP = price (8%) – price (8.01%)

PVBP = 100-99.8919 = $0.0181 per $100

- Bond B

Price(8%) = $104.0554

Price (8.01%)= $104.0139

PVBP = price(8%) – price(8.01%)

PVBP = 104.0554 – 104.0139 = $0.0415 per $100

(B) Compute the Macaulay durations for the two bonds.

Bond A

At yield = 8%

t

CF

PVCF

t*PVCF

1

4

3.85

3.85

2

4

3.70

7.40

3

4

3.56

10.67

4

104

88.90

355.60

100.00

377.51

Dmac (Half year)

3.775091

Bond B

t

CF

PVCF

t*PVCF

1

4.5

4.33

4.33

2

4.5

4.16

8.32

3

4.5

4.00

12.00

4

4.5

3.85

15.39

5

4.5

3.70

18.49

6

4.5

3.56

21.34

7

4.5

3.42

23.94

8

4.5

3.29

26.30

9

4.5

3.16

28.45

10

104.5

70.60

705.96

104.06

864.53

Dmac (Half year)

8.308352

Dmac (year)

4.154176

(C) Compute the modified duration for the two bonds.

Bond A

Modified duration = Dmac(years) /(1+YTM/2) = (3.775091/2)/1.04 = 1.815 (years)

Bond B

Modified duration = Dmac(years) /(1+YTM/2) = 4.154176/1.04 = 3.9944 (years)

(D) Compute the approximate duration for bonds A and B using the shortcut formula by changing yields by 20 basis points and compare your answers with those calculated in part (c).

Approximate duration = (P_ - P+)/2P0(dy)

Bond A

Price changes when yield increases by 20 bps (P+)

= -PVBP*(change in yield) = -$0.0181*20 = -$0.3620

So, P+ = 100 – 0.3620 = $99.6380

Price changes when yield decreases by 20 bps (P_)

= -PVBP*(change in yield) = -$0.0181*(-20) = $0.3620

So, P- = 100 + 0.3620 = $100.362

The approximate duration = (100.362 – 99.638)/2*100*(0.002) = 1.81

Bond B

yield increases by 20 bps

= -PVBP*(change in yield) = 0.0415 *20 = -0.83

So, P+ = 104.0554 – 0.83 = 103.2254

yield decreases by 20 bps

= -PVBP*(change in yield) = -0.0415 *(-20) = $0.83

So, P_ = 104.0554 + 0.83 = 104.8854

The approximate duration = (104.8854 – 103.2254)/2*104.0554*(0.002) = 3.9885

The approximate durations are a bit lower than the duration calculated using the formula.

3. Can you tell from the following information which of the following three bonds will have the greatest

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