The coupon is the rate of interest and it determines the rate at which you recover the bond value in terms of cash flows. Quicker the recovery of the bond investment via interest rates, lower is the duration. Consider the base case below.

Now let us assume a scenario wherein the coupon rate goes up from 8% to 10%? In this case, the coupon rate is up by 200 bps so the recovery of the bond investment will be faster leading to a lower duration. Let us look at the actual impact through the table below.

Inputs

Rate Convention: 1 = EAR, 0 = APR

0

Annual Coupon Rate (CR)

10.0%

Yield to Maturity (Annualized) (y)

9.0%

Number of Payments / Year (NOP)

2

Number of Periods to Maturity (T)

8

Face Value (FV)

? 1,000

Outputs

Discount Rate / Period (RATE)

4.5%

Coupon Payment (PMT)

? 50

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

? 50.00

? 50.00

? 50.00

? 50.00

? 50.00

? 50.00

? 50.00

? 1,050.00

Present Value of Cash Flow

? 47.85

? 45.79

? 43.81

? 41.93

? 40.12

? 38.39

? 36.74

? 738.34

#######

Weight

4.6%

4.4%

4.2%

4.1%

3.9%

3.7%

3.6%

71.5%

100.0%

Weight * Time

0.02

0.04

0.06

0.08

0.10

0.11

0.12

2.86

3.40

Duration

3.40

Modified Duration

3.26

As we can see in the above table, the bond duration comes down from 3.49 to 3.40 due to the increase in the interest rates. Faster the money is recovered either through coupons or through early prepayment of loans, lower is the duration of the bond.

The coupon is the rate of interest and it determines the rate at which you recover the bond value in terms of cash flows. Quicker the recovery of the bond investment via interest rates, lower is the duration. Consider the base case below.

InputsRate Convention: 1 = EAR, 0 = APR

0

Annual Coupon Rate (CR)

8.0%

Yield to Maturity (Annualized) (y)

9.0%

Number of Payments / Year (NOP)

2

Number of Periods to Maturity (T)

8

Face Value (FV)

? 1,000

OutputsDiscount Rate / Period (RATE)

4.5%

Coupon Payment (PMT)

? 40

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

? 40.00

? 40.00

? 40.00

? 40.00

? 40.00

? 40.00

? 40.00

? 1,040.00

Present Value of Cash Flow

? 38.28

? 36.63

? 35.05

? 33.54

? 32.10

? 30.72

? 29.39

? 731.31

? 967.02

Weight

4.0%

3.8%

3.6%

3.5%

3.3%

3.2%

3.0%

75.6%

100.0%

Weight * Time

0.02

0.04

0.05

0.07

0.08

0.10

0.11

3.03

3.49

Duration

3.49

Modified Duration

3.34

Now let us assume a scenario wherein the coupon rate goes up from 8% to 10%? In this case, the coupon rate is up by 200 bps so the recovery of the bond investment will be faster leading to a lower duration. Let us look at the actual impact through the table below.

InputsRate Convention: 1 = EAR, 0 = APR

0

Annual Coupon Rate (CR)

10.0%

Yield to Maturity (Annualized) (y)

9.0%

Number of Payments / Year (NOP)

2

Number of Periods to Maturity (T)

8

Face Value (FV)

? 1,000

OutputsDiscount Rate / Period (RATE)

4.5%

Coupon Payment (PMT)

? 50

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

? 50.00

? 50.00

? 50.00

? 50.00

? 50.00

? 50.00

? 50.00

? 1,050.00

Present Value of Cash Flow

? 47.85

? 45.79

? 43.81

? 41.93

? 40.12

? 38.39

? 36.74

? 738.34

#######

Weight

4.6%

4.4%

4.2%

4.1%

3.9%

3.7%

3.6%

71.5%

100.0%

Weight * Time

0.02

0.04

0.06

0.08

0.10

0.11

0.12

2.86

3.40

Duration

3.40

Modified Duration

3.26

As we can see in the above table, the bond duration comes down from 3.49 to 3.40 due to the increase in the interest rates. Faster the money is recovered either through coupons or through early prepayment of loans, lower is the duration of the bond.