The following is a mathematical reasoning: i worked out some calculations to compare a 9% 2-year annual coupon bond vs. a 2% 2-year annual coupon bond. consider that at a 5% discount rate, the price of the 9% coupon bond is approximately $107.43 while the price of the 2% coupon bond is $94.41. when the discount rate drops from 5% to 2%, the price of the 9% coupon bond rises by a little over $6 to $113.58. at the same time, the 2% coupon bond increases in price by approximately $5.59 to a price of $100.since the low coupon bond started at a much lower price, the dollar change means much more to that bond in percentage terms than the high coupon bond price change in percentage terms. other things being equal, this relationship doesnt change low coupon bonds are more volatile in price percentage change than high coupon bonds.
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