Similarly, the reason why bonds with lower coupon rates have greater interest rate risk is essentially the same as above. The value of a bond depends on the present value of its coupons and the present value of the face amount. For two bonds with same time to maturity but with different coupon rates, then the value of the bond with lower coupon is proportionately more dependent on the face amount to be received at maturity. As a result, the value of the bond fluctuates more as interest rate changes. On the other hand, the bond with higher coupon has a larger cash flow early in its life, so its value is less sensitive to changes in the interest rate.

YIELD TO MATURITY

Most of the times, the information on bond's price, coupon rate, and maturity date are known in advance to the investors. The return the bond holders will earn from the bond can be assessed by evaluating the yield to maturity. Yield to maturity measures the rate of return on bond assuming it is held to maturity including the premium or discount to the face value. In other words, yield to maturity is basically the interest rate that equates the bond's future cash flows to its price.

The value of a bond with time to maturity of ‘t' years, a coupon amount of ‘C', and face value of ‘F'. If the price of the bond is ‘S', then

Solving the above equation for the unknown discount rate will give the yield to maturity.