In fact, duration not only gets impacted by the changes in the yield to maturity of the bond but also is useful in measure in measuring how the shifts in yields impact the price of the bond. But first let us take a base case for calculation of duration.

Inputs

Rate Convention: 1 = EAR, 0 = APR

0

Annual Coupon Rate (CR)

7.0%

Yield to Maturity (Annualized) (y)

8.0%

Number of Payments / Year (NOP)

2

Number of Periods to Maturity (T)

8

Face Value (FV)

? 1,000

Outputs

Discount Rate / Period (RATE)

4.0%

Coupon Payment (PMT)

? 35

Calculate Bond Duration using the Cash Flows

Period

0

1

2

3

4

5

6

7

8

Time (Years)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Total

Cash Flows

? 35.00

? 35.00

? 35.00

? 35.00

? 35.00

? 35.00

? 35.00

? 1,035.00

Present Value of Cash Flow

? 33.65

? 32.36

? 31.11

? 29.92

? 28.77

? 27.66

? 26.60

? 756.26

? 966.34

Weight

3.5%

3.3%

3.2%

3.1%

3.0%

2.9%

2.8%

78.3%

100.0%

Weight * Time

0.02

0.03

0.05

0.06

0.07

0.09

0.10

3.13

3.55

Duration

3.55

Modified Duration

3.41

Now let us assume that the YTM of the bond goes up sharply to 10% due to a rise in the CPI inflation rate in the economy? Let us check out the impact on the duration on the bond when the yield in the market increases by 200 bps.

Inputs

Rate Convention: 1 = EAR, 0 = APR

0

Annual Coupon Rate (CR)

7.0%

Yield to Maturity (Annualized) (y)

10.0%

Number of Payments / Year (NOP)

2

Number of Periods to Maturity (T)

8

Face Value (FV)

? 1,000

Outputs

Discount Rate / Period (RATE)

5.0%

Coupon Payment (PMT)

? 35

Calculate Bond Duration using the Cash Flows

Period

0

1

2

3

4

5

6

7

8

Time (Years)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Total

Cash Flows

? 35.00

? 35.00

? 35.00

? 35.00

? 35.00

? 35.00

? 35.00

? 1,035.00

Present Value of Cash Flow

? 33.33

? 31.75

? 30.23

? 28.79

? 27.42

? 26.12

? 24.87

? 700.53

? 903.05

Weight

3.7%

3.5%

3.3%

3.2%

3.0%

2.9%

2.8%

77.6%

100.0%

Weight * Time

0.02

0.04

0.05

0.06

0.08

0.09

0.10

3.10

3.53

Duration

3.53

Modified Duration

3.36

Because of the higher discount rate, the present value of the final redemption is lower as that gets distributed through the earlier distributions. That ensures that the duration falls marginally, when the yields in the market increase.

sara Kunjuanswered.In fact, duration not only gets impacted by the changes in the yield to maturity of the bond but also is useful in measure in measuring how the shifts in yields impact the price of the bond. But first let us take a base case for calculation of duration.

InputsRate Convention: 1 = EAR, 0 = APR

0

Annual Coupon Rate (CR)

7.0%

Yield to Maturity (Annualized) (y)

8.0%

Number of Payments / Year (NOP)

2

Number of Periods to Maturity (T)

8

Face Value (FV)

? 1,000

OutputsDiscount Rate / Period (RATE)

4.0%

Coupon Payment (PMT)

? 35

Calculate Bond Duration using the Cash FlowsPeriod

0

1

2

3

4

5

6

7

8

Time (Years)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Total

Cash Flows

? 35.00

? 35.00

? 35.00

? 35.00

? 35.00

? 35.00

? 35.00

? 1,035.00

Present Value of Cash Flow

? 33.65

? 32.36

? 31.11

? 29.92

? 28.77

? 27.66

? 26.60

? 756.26

? 966.34

Weight

3.5%

3.3%

3.2%

3.1%

3.0%

2.9%

2.8%

78.3%

100.0%

Weight * Time

0.02

0.03

0.05

0.06

0.07

0.09

0.10

3.13

3.55

Duration

3.55

Modified Duration

3.41

Now let us assume that the YTM of the bond goes up sharply to 10% due to a rise in the CPI inflation rate in the economy? Let us check out the impact on the duration on the bond when the yield in the market increases by 200 bps.

InputsRate Convention: 1 = EAR, 0 = APR

0

Annual Coupon Rate (CR)

7.0%

Yield to Maturity (Annualized) (y)

10.0%

Number of Payments / Year (NOP)

2

Number of Periods to Maturity (T)

8

Face Value (FV)

? 1,000

OutputsDiscount Rate / Period (RATE)

5.0%

Coupon Payment (PMT)

? 35

Calculate Bond Duration using the Cash FlowsPeriod

0

1

2

3

4

5

6

7

8

Time (Years)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Total

Cash Flows

? 35.00

? 35.00

? 35.00

? 35.00

? 35.00

? 35.00

? 35.00

? 1,035.00

Present Value of Cash Flow

? 33.33

? 31.75

? 30.23

? 28.79

? 27.42

? 26.12

? 24.87

? 700.53

? 903.05

Weight

3.7%

3.5%

3.3%

3.2%

3.0%

2.9%

2.8%

77.6%

100.0%

Weight * Time

0.02

0.04

0.05

0.06

0.08

0.09

0.10

3.10

3.53

Duration

3.53

Modified Duration

3.36

Because of the higher discount rate, the present value of the final redemption is lower as that gets distributed through the earlier distributions. That ensures that the duration falls marginally, when the yields in the market increase.