Why own long-term low-coupon bonds when interest rates are falling and own short-term high-coupon bonds when interest rates are rising?

Im assuming you are looking for an explanation of that paragraph, rather than an example of someone buying and selling bonds.when interest rates fall, bond prices rise. in order to take advantage of rising bond prices, an investor would want to own the most volatile combination of term and coupon. the more volatile the combination, the bigger the price change on the bond. from your text, you have learned that long-term bonds are more volatile in price percentage changes than short-term bonds. you have also learned that low coupon bonds are more volatile in price percentage changes than high coupon bonds. as such, the most volatile combination you can own is a long-term low coupon bond.the opposite holds true when interest rates are rising and bond prices are falling. in this circumstance, you would want to own the least volatile combination of term and coupon. the least volatile combination in terms of price percentage change would be short-term high coupon bonds.