Answer: will be equal to modified duration if the yield curve is absolutely flat.

## Explanation Let's analyze each option: **Option A: "will be equal to modified duration if the yield curve is absolutely flat."** - **Correct**. For option-free bonds, when the yield curve is flat, effective duration equals modified duration. This is because effective duration uses actual price changes from yield curve shifts, while modified duration assumes a single yield change. With a flat yield curve, both approaches give the same result. **Option B: "measures interest rate risk for both parallel and non-parallel benchmark yield curve shifts."** - **Incorrect**. Effective duration specifically measures interest rate risk for **parallel shifts** in the yield curve, not non-parallel shifts. Non-parallel shifts require more sophisticated measures like key rate duration. **Option C: "is an estimate of the percentage change in bond price given a change in the bond's yield to maturity."** - **Incorrect**. This definition describes **modified duration**, not effective duration. Effective duration measures the percentage change in bond price for a given change in the **benchmark yield curve**, not the bond's specific yield to maturity. ### Key Concepts: 1. **Effective Duration**: Measures price sensitivity to parallel shifts in the benchmark yield curve, calculated as: \(\text{Effective Duration} = \frac{P_- - P_+}{2 \times P_0 \times \Delta y}\) Where \(P_-\) = price when yield decreases, \(P_+\) = price when yield increases, \(P_0\) = initial price, and \(\Delta y\) = change in yield. 2. **Modified Duration**: Measures price sensitivity to changes in the bond's own yield to maturity, assuming a flat yield curve. 3. **When they are equal**: For option-free bonds with a flat yield curve, effective duration = modified duration. **Correct Answer: A**

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