In fact, the impact of price changes due to shifts in yield is actually determined using the modified duration of the bond. Check the table below of a live bond with the calculation of duration where the yield is 150 bps above the coupon rate.

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

In the above case, the yield is 100 bps higher than the coupon rate. We know that when the coupon rate and the yield is the same then the price of the bond (present value of future cash flows) and the face value of the bond is the same. In the above case a 1% rise in the yield from 7% to 8% has, therefore, resulted in the bond prices falling by 3.4% from Rs.1000 to Rs.966. That effectively means that the fall in the bond price is 3.4 time the rise in the yield. That sensitivity of 3.4 is exactly captured by the modified duration. That is why modified duration is important because it helps you to understand the extent of price impact either ways as an outcome of shifts in yields. That is what the modified duration presents.

In fact, the impact of price changes due to shifts in yield is actually determined using the modified duration of the bond. Check the table below of a live bond with the calculation of duration where the yield is 150 bps above the coupon rate.

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

In the above case, the yield is 100 bps higher than the coupon rate. We know that when the coupon rate and the yield is the same then the price of the bond (present value of future cash flows) and the face value of the bond is the same. In the above case a 1% rise in the yield from 7% to 8% has, therefore, resulted in the bond prices falling by 3.4% from Rs.1000 to Rs.966. That effectively means that the fall in the bond price is 3.4 time the rise in the yield. That sensitivity of 3.4 is exactly captured by the modified duration. That is why modified duration is important because it helps you to understand the extent of price impact either ways as an outcome of shifts in yields. That is what the modified duration presents.