A 5-year corporate bond has a Macaulay Duration of 4.20 years and a Yield to Maturity (YTM) of 5.0% per annum. What is the Modified Duration of the bond, and how is it interpreted?

[ A ]Modified Duration is 5.25 years; indicating that the bond will mature in exactly 5.25 years.

[ B ]Modified Duration is 0.21 years; indicating that the bond carries zero interest rate risk.

[ C ]Modified Duration is 8.40 years; indicating that the coupon rate will double when interest rates rise.

[ D ]Modified Duration is 4.00 years (4.20 / 1.05); indicating that the bond's market price will change by approximately 4.0% for every 1.0% shift in market interest rates.[ CORRECT ]

Takeaway

Option D is correct: Modified Duration is 4.00 years (4.20 / 1.05); indicating that the bond's market price will change by approximately 4.0% for every 1.0% shift in market interest rates.

Derivation

Modified Duration measures the percentage price sensitivity of a bond to changes in interest rates. Formula: Modified Duration = Macaulay Duration / (1 + YTM). Given: Macaulay Duration = 4.20 years, YTM = 5.0% (0.05). Modified Duration = 4.20 / (1 + 0.05) = 4.20 / 1.05 = 4.00 years. This means that if market yields change by 100 basis points (1.0%), the bond's price will move inversely by approximately 4.0%. This tests the mathematical calculation and economic interpretation of duration. The common error is multiplying duration by YTM or confusing it with nominal maturity.

Why the others fail

A — Modified Duration is 5.25 years; indicating that the bond will mature in exactly 5.25 years.

5.25 years is an arithmetic error resulting from multiplying Macaulay duration by 1.25 rather than dividing by (1 + YTM).

B — Modified Duration is 0.21 years; indicating that the bond carries zero interest rate risk.

0.21 years incorrectly divides Macaulay duration by 20 rather than applying the standard (1 + YTM) denominator.

C — Modified Duration is 8.40 years; indicating that the coupon rate will double when interest rates rise.

8.40 years doubles the duration arbitrarily; Modified Duration measures price sensitivity, not coupon adjustments.