Question

4. Consider two $1,000 par coupon bonds, A and B. Bond A has a coupon rate of 5% with ten-year maturity and bond B has a coupon rate of 8% with five years until maturity. a. Define interest rate risk. b. Proof that Bond A has higher interest risk than bond B.

Answer 1

Solution:-

(a)

The return that a series of bonds offer is determined by two factors which are as follows:

• Benchmark interest rates in the economy (also known as risk free rate)
• Risk profile of the bonds, including default risk, liquidity risk, etc

Higher the benchmark interest raes in an economy, higher would be the expected return from various bonds and vice-versa.

Interest rate risk refers to the risk that existing bonds are exposed to the change in benchmark interest rates in the economy. An increase in benchmark interest rates may render interest rate offered by the existing bonds non-competitive to the market. Let's understand with the help of an example:

Let's say the benchmark interest rate is at 3% and a bond is today issued offering interest rate of 5% considering its risk profile. Now, if the benchmark interest rates go up, the new bonds issued with similar risk profile to that of the existing bonds will have to offer a higher interest rate than the 5% the existing bonds offer. Thus, the interest rates offered by existing bond would become non-competitive to those of new bonds with similar profiles.

This risk of interest rates becoming non-competitive to the market is called interest rate risk.

(b)

The level of interest rate risk is dependent on the interest rates offered by the bonds as well as the maturity.

Higher the maturity of bonds, longer the period they are exposed to risk due to changes in benchmark interest rates and vice-versa. Therefore, the longer the maturity , the higher would be interest rate risk and vice-versa.

Higher the interest rate offered by bonds, lower the risk of exposure to changes in interest rates. This is simply because a bond with higher interest rate as compared to the other would get exposed to interest rate risk when benchmark rates go past a relatively higher level as compared to the lower interest rate bonds who will get exposed to interest rate risk much earlier when benchmark interest rates are at comparatively lower level.

Also the level of interest rate risk for bonds with lower interest rate is much higher as their interest rates become much more less competitive to the market as compared to bonds with higher interest rates.

In the given case, A has a longer maturity than B and also has a lower interest rate than B. Thus, A is more riskier than B.