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