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Interest rate risk addresses price sensitivity to changes in rates. For the bond holder it is the fall in price due to higher interest rates due to their inverse relationship. For a given maturity, a bond with a higher coupon will be less sensitive to an increase in price than a similar bond with a lower coupon . Since the spread between the lower coupon and interest rates is higher the discount factor is greater than in the case of the higher coupon so price is affected to a greater degree. Hope this helps.