Let us take the example of the SBI (State Bank of India) bond. The bond is rated AAA which is the highest safety rating given by rating agencies. The terms of the bond are
Issuer: SBI
Rating: AAA
Issue date: 1st March 2016
Face value of the bond: Rs 100
Coupon rate: 8%
Coupon payable: Annually on 1st March every year
Amount payable on maturity: Rs 100
We will find out the relationship between bond maturity and interest rates by keeping the discount factor (prevailing interest rate in the market) constant and changing the maturity of the SBI bond. We will keep the discount factor constant at 8.5% and take three different tenors for the bond, three years, five years and ten years.
- SBI bond maturity: 3 years. Discount factor 7%
Bond price = Rs 102.62. The three year SBI bond with a coupon rate of 8% gains in value by Rs 2.62 for a 100bps (1bps=0.01%) fall in interest rates.
- SBI bond maturity: 5 years. Discount factor 7%
Bond price = Rs 104.10. The five year SBI bond with a coupon rate of 8% gains in value by Rs 4.10 for a 100bps fall in interest rates
- SBI bond maturity: 10 years. Discount factor 7%
Bond price= Rs 107.02. The ten year SBI bond with a coupon rate of 8% gains in value by Rs 7.02 for a 100bps fall in interest rates.
Tabulating the results of the change in bond prices with a change in maturity keeping the discount factor constant we see that bond prices show higher increase with an increase in maturity when interest rates fall.
The inverse is true when interest rates rise. Bonds with longer maturity see a sharper fall in prices than bonds with shorter maturity. Table 2 gives the prices of three, five and ten year maturity SBI bonds at a discount factor of 9%.
The higher the maturity of a bond, the more the rise or fall in price of the bond due to change in interest rates.
Two main concepts in fixed income are a) Bond prices change with change in interest rates and b) The extent of change in bond prices to interest rates depend on maturity of the bond. Using these two concepts, fixed income investors invest in short maturity bonds when interest rates rise and invest in long maturity bonds when interest rates fall.
