2. The following table shows four bonds, their coupon rates and their prices bef

Question

2. The following table shows four bonds, their coupon rates and their prices before and after an interest raterise of 1 basis point (0.01%) this morning. The columns with maturity and duration information inthe table were erroneously erased. Assume that the yield curve is flat (i.e. yields are the same for allbonds) and use annual compounding throughout. All bonds have face values of $1000. The onlything you remember about the last two columns is that all bonds have the same number of years to maturity. Your task is to fill in the last two columns with the correct information.

Explanation / Answer

Calculation of duration

Formula

New bond price after interest rate rise = Old Bond price – 0.01% * Duration * old bond Price

For Bond 1,

1245.06 = 1245.78 – 0.0001 * Duration * 1245.78

Or 1245.78 – 1245.06 = 0.0001 * Duration * 1245.78

Or 0.72 = 0.0001 * duration * 1245.78

Therefore Duration = 0.72/ ( 0.0001*1245.78) = 5.78

For Bond 2,

999.39 = 1000 – 0.0001 * Duration * 1000

Or 1000 – 999.39 = 0.0001 * Duration * 1000

Or 0.61 = 0.0001 * duration * 1000

Therefore Duration = 0.61/ ( 0.0001*1000) = 6.1

For Bond 3,

815.13 = 815.66 – 0.0001 * Duration * 815.66

Or 815.66 – 815.13 = 0.0001 * Duration * 815.66

Or 0.53 = 0.0001 * duration * 815.66

Therefore Duration = 0.53/ ( 0.0001*815.66) = 6.498

For Bond 4,

385.19 = 385.54 – 0.0001 * Duration * 385.54

Or 385.54 – 385.19 = 0.0001 * Duration * 385.54

Or 0.35 = 0.0001 * duration * 385.54

Therefore Duration = 0.35/ ( 0.0001*385.54) = 9.078

Time to maturity and duration is equal for a zero coupon bonds therefore for bond 4 we have time to maturity = 9.078 but it is given that time to maturity is same for all the four bonds

Therefore it is equal to 9.078

So the table is like this -

Bond

Coupon

Price before ($)

Price – After ($)

Time To maturity

Duration

1

14%

1245.78

1245.06

9.078

5.78

2

10%

1000.00

999.39

9.078

6.1

3

7%

815.66

815.13

9.078

6.498

4

0%

385.54

385.19

9.078

9.078

Bond

Coupon

Price before ($)

Price – After ($)

Time To maturity

Duration

1

14%

1245.78

1245.06

9.078

5.78

2

10%

1000.00

999.39

9.078

6.1

3

7%

815.66

815.13

9.078

6.498

4

0%

385.54

385.19

9.078

9.078

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