We now know that the face value of the bond and the market price of the bond will be approximately equal if the coupon rate and the yield are the same. But what happens if the yields in the market start moving up. It could be due to rising inflation, expected rate hike by the RBI, expect Fed rate hike, liquidity shortfall etc. Let us look at the impact on price when the yields go up by 100 basis points. Check the table below.

Inputs

Rate 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

Outputs

Discount Rate / Period (RATE)

4.5%

Coupon Payment (PMT)

? 40

Calculate Bond Price 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

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

Bond Price

? 967.02

What do we see in the above table? The coupon rate is at 8% but the yields have gone up to 9%. This has led to a 1% gap between the coupon rate and the yield on the bond. As a result the bond price is down from Rs.1000 to Rs.967 or a fall of approximately 3.3%. Before we get into the reasons for this fall in bond price, let us look to increase the bond yields by another 100 bps to 10%. What is the impact now?

Inputs

Rate Convention: 1 = EAR, 0 = APR

0

Annual Coupon Rate (CR)

8.0%

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)

? 40

Calculate Bond Price 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

Cash Flows

? 40.00

? 40.00

? 40.00

? 40.00

? 40.00

? 40.00

? 40.00

? 1,040.00

Present Value of Cash Flow

? 38.10

? 36.28

? 34.55

? 32.91

? 31.34

? 29.85

? 28.43

? 703.91

Bond Price

? 935.37

What we get to see is that when the bond yield goes up by another 100 bps, the bond price is going down by another 3.3% to Rs.935.37. Again, this is not the market price but only the fair value of the bond. The moral of the story is that when the yield goes up, the bond prices go down. Here, the relationship is to the tune of 3.3 times i.e. a 1% rise in the rate is taking the bond price down by 3.3% each time. But why does this kind of negative relationship exist and why does the bond price fall each time the yield rises?

Let us say you are holding a bond paying a coupon rate of 8%. If the market yield goes up to 9% then your bond will continue to pay you only 8%. That means you are losing out on 1% yield. That means for a new investor coming into this bond, it does not make sense as the 8% yield is lower than the market yield of 9%. To compensate for that, the price will fall. Now what happens is that the investor in the bond will buy the bond at a discounted price in such a way that his YTM comes close to 9%. This will ensure that the bond remains attractive for investors. That is the reason, bond prices fall when the market yields go up.

We now know that the face value of the bond and the market price of the bond will be approximately equal if the coupon rate and the yield are the same. But what happens if the yields in the market start moving up. It could be due to rising inflation, expected rate hike by the RBI, expect Fed rate hike, liquidity shortfall etc. Let us look at the impact on price when the yields go up by 100 basis points. Check the table 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 Price 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

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

Bond Price? 967.02What do we see in the above table? The coupon rate is at 8% but the yields have gone up to 9%. This has led to a 1% gap between the coupon rate and the yield on the bond. As a result the bond price is down from Rs.1000 to Rs.967 or a fall of approximately 3.3%. Before we get into the reasons for this fall in bond price, let us look to increase the bond yields by another 100 bps to 10%. What is the impact now?

InputsRate Convention: 1 = EAR, 0 = APR

0

Annual Coupon Rate (CR)

8.0%

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)

? 40

Calculate Bond Price 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

Cash Flows

? 40.00

? 40.00

? 40.00

? 40.00

? 40.00

? 40.00

? 40.00

? 1,040.00

Present Value of Cash Flow

? 38.10

? 36.28

? 34.55

? 32.91

? 31.34

? 29.85

? 28.43

? 703.91

Bond Price? 935.37What we get to see is that when the bond yield goes up by another 100 bps, the bond price is going down by another 3.3% to Rs.935.37. Again, this is not the market price but only the fair value of the bond. The moral of the story is that when the yield goes up, the bond prices go down. Here, the relationship is to the tune of 3.3 times i.e. a 1% rise in the rate is taking the bond price down by 3.3% each time. But why does this kind of negative relationship exist and why does the bond price fall each time the yield rises?

Let us say you are holding a bond paying a coupon rate of 8%. If the market yield goes up to 9% then your bond will continue to pay you only 8%. That means you are losing out on 1% yield. That means for a new investor coming into this bond, it does not make sense as the 8% yield is lower than the market yield of 9%. To compensate for that, the price will fall. Now what happens is that the investor in the bond will buy the bond at a discounted price in such a way that his YTM comes close to 9%. This will ensure that the bond remains attractive for investors. That is the reason, bond prices fall when the market yields go up.