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.