Question

1. 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.
   1. Define interest rate risk.   

b.Proof that Bond A has higher interest risk than bond B.

Answer 1

A) A fundamental principle of bond investing is that market interest rates and bond prices generally move in opposite directions. When market interest rates rise, prices of fixed-rate bonds fall. this phenomenon is known as interest rate risk.

If two bonds offer different coupon rates while all of their other characteristics (e.g., maturity and credit quality) are the same, the bond with the lower coupon rate generally will experience a greater decrease in value as market interest rates rise. Bonds offering lower coupon rates generally will have higher interest rate risk than similar bonds that offer higher coupon rates.

Lower fixed-rate bond coupon rates -->higher interest rate risk

Higher fixed-rate bond coupon rates --> lower interest rate risk

For example, imagine one bond that has a coupon rate of 2% while another bond has a coupon rate of 4%. All other features of the two bonds—when they mature, their level of credit risk, and so on—are the same. If market interest rates rise, then the price of the bond with the 2% coupon rate will fall more than that of the bond with the 4% coupon rate. remember:

Lower market interest rates-->higher fixed-rate bond prices-->lower fixed-rate bond yields--> higher interest rate risk to rising market interest rate.

B) A bond’s maturity is the specific date in the future at which the face value of the bond will be repaid to the investor. A bond may mature in a few months or in a few years. Maturity can also affect interest rate risk. The longer the bond’s maturity, the greater the risk that the bond’s value could be impacted by changing interest rates prior to maturity, which may have a negative effect on the price of the bond. Therefore, bonds with longer maturities generally have higher interest rate risk than similar bonds with shorter maturities.

Longer maturity-->higher interest rate risk

Shorter maturity ---> lower interest rate risk

To compensate investors for this interest rate risk, long-term bonds generally offer higher coupon rates than short-term bonds of the same credit quality.

Longer maturity --> higher interest rate risk --> higher coupon rate

Shorter maturity --> lower interest rate risk --> lower coupon rate

From this it is clear that Bond A is more riskier than Bond B