Answer: negative.

## Explanation **Duration Gap** is calculated as: **Duration Gap = Investment Horizon - Modified Duration** Given: - Investment Horizon = 7 years - Modified Duration = 7 years **Duration Gap = 7 - 7 = 0** However, the question specifies **"In a positive yield environment"**. This is a key detail because: 1. **Modified duration** measures price sensitivity to yield changes, assuming a parallel shift in the yield curve 2. In a **positive yield environment** (upward sloping yield curve), the bond's **effective duration** (considering yield curve shape) will be **less than** the modified duration 3. This is because in a positive yield environment, longer-term yields are higher, and as time passes, the bond's cash flows are discounted at progressively lower yields (moving down the yield curve) Therefore, the **effective duration** < **modified duration** = 7 **Duration Gap = Investment Horizon - Effective Duration** **Duration Gap = 7 - (Effective Duration < 7) = Positive value** Wait, let me reconsider this carefully. Actually, the duration gap is: **Duration Gap = Macaulay Duration - Investment Horizon** But modified duration = Macaulay Duration / (1 + y) Given modified duration = 7, and assuming typical yields, Macaulay Duration would be slightly higher than 7. However, the key insight is: - If **investment horizon** equals **duration**, the investor is immunized against interest rate risk - If investment horizon > duration, the investor has a **positive duration gap** (exposed to reinvestment risk) - If investment horizon < duration, the investor has a **negative duration gap** (exposed to price risk) In this case: - Investment horizon = 7 years - Modified duration = 7 years (Macaulay duration would be > 7) - Therefore, investment horizon < Macaulay duration - This creates a **negative duration gap** **Correct answer: A (negative)** **Why not zero?** Because modified duration (7) is not equal to Macaulay duration. Modified duration = Macaulay Duration / (1 + yield). Since yield > 0 in a positive yield environment, Macaulay Duration > Modified Duration = 7. Therefore, investment horizon (7) < Macaulay Duration, resulting in negative duration gap. **Why not positive?** Because the investment horizon is shorter than the bond's Macaulay duration, not longer.

Author: LeetQuiz .