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      Question

      A Portfolio Manager at a Mutual Fund is evaluating two

      bonds, Bond A and Bond B, both of which have the same Modified Duration of 7.5 years. However, Bond A has significantly higher Convexity than Bond B. If the market interest rates (YTM) decrease suddenly by 100 basis points (1%), which of the following outcomes is most likely?
      A Both bonds will increase in price by exactly 7.5%, as they have the same Modified Duration. Correct Answer Incorrect Answer
      B Bond B will experience a greater price increase than Bond A because lower convexity allows for faster price appreciation. Correct Answer Incorrect Answer
      C Bond A will experience a greater price increase than Bond B due to the positive contribution of higher convexity. Correct Answer Incorrect Answer
      D Both bonds will decrease in price, but Bond A will decrease less than Bond B. Correct Answer Incorrect Answer
      E The price change cannot be determined without knowing the specific coupon rates of the bonds Correct Answer Incorrect Answer

      Solution

      Modified Duration measures the linear relationship between price and yield. A 1% drop in rates suggests a 7.5% increase in price ( ). Duration underestimates the price increase when rates fall and overestimates the price decrease when rates rise.   However, the Price-Yield relationship is curved (convex), not a straight line. Bond convexity measures the non-linear, curved relationship between a bond's price and its yield, indicating how much a bond's duration changes as interest rates fluctuate. It acts as a second-order risk management tool, refining duration estimates to show that bond prices change at different rates depending on whether interest rates rise or fall.    A bond with higher convexity will always perform better than a bond with lower convexity (all else being equal) because:

      • When rates fall, the price rises more than duration predicts.
      • When rates rise, the price falls less than duration predicts

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