Suppose you have two bonds with 3 years to maturity. Both bonds pay semi-annual coupon and have par values of $1,000. One pays coupon at a rate of 5% and the other pays coupon at a rate of 6%. YTM for both bonds is 5.5%.
a. Which bond is going to be more sensitive to interest rate changes? (Hint: Calculate the percentage price change of the bonds when YTM increases by 1% and YTM decreases by 1%)
b. What can you say about the relationship between coupon rate and interest rate movement from what you observe about price changes of the above bonds?