Bond duration!

Hi all, Can anyone enlighten me on the following statement" when yield decreases, bonds with higher duration will benefit more". I was thinking: yield decreases==> bond price increases==> reinvestment risk increases==> delay the repayment as long as it could, better==> lower coupon is better==> lowest coupon benefit most==> highest duration bond benefits most But somehow it is not totally convincing to me. Is there any flaw ? Also, if understanding duration as how long it takes the price of the bond to be repaid, then lower coupon bond will have higher duration. but if understanding duration as the sensitivity of price to the change in yield, i am kinda puzzled in explaining the relation between coupon rate & duration… Would like to know ur thoughts. Thanks a bunch!

Easiest way to think about is simply the definition as the sensitivity to the price of the bond with respect to a change in yield (interest rates). If yield decreases, price increases…therefore, the more sensitive the bond is to that decrease in yield, the higher the price increase. A bond benefits from a decreases in yield due to the increase in price, so the MORE sensitive it is to that change, the HIGHER the bond price will increase (and hence benefit) This question isn’t asking the relationship between coupon rate and duration, it’s asking the relationship between yield and duration… (yield being interest rate, NOT coupon rate) Hope this helps!

the duration measures how much the price of a bond will change with a 1% change in yield. -Duration*change in yield*100 = percent change in bond price. a duration of 5 means for a 1% change in yield, up or down, the bond value with approximately decrease (increase in yield) or increase (decrease in yield) by 5%. so you can see how a larger duration affects bond price, for the same change in yield, the larger duration bond will change by a greater percent. also duration underestimates price increases and magnifies price decreases without the convexity adjustment.

Higher duration bond: riskier bond, more sensitive to interest rate changes, its price changes more than that of a lower duration bond.