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nism-series-xb-macaulay-duration-vs-modified-duration-formula[ INVESTMENT ADVISER (LEVEL 2) ]

A corporate bond has a Macaulay Duration of 6.6 years and an annual Yield to Maturity (YTM) of 10.0%. What is the Modified Duration of the bond?

[ A ]6.00 years [ Modified Duration = Macaulay Duration / (1 + y) = 6.6 / (1 + 0.10) ][ CORRECT ]

[ B ]6.60 years (Macaulay duration without yield adjustment)

[ C ]7.26 years (6.6 * 1.10)

[ D ]5.00 years

Takeaway

Option A is correct: 6.00 years [ Modified Duration = Macaulay Duration / (1 + y) = 6.6 / (1 + 0.10) ]

Derivation

Macaulay Duration measures the weighted-average time in years until a bond's cash flows are received, but it isn't directly usable as a price-sensitivity number. Modified Duration converts it into that usable metric by discounting for the current yield environment: Modified Duration = Macaulay Duration / (1 + y) = 6.6 / (1 + 0.10) = 6.6 / 1.10 = 6.00 years. This 6.00 figure is what actually predicts price behavior — a 100 basis point rise in yield produces an approximate 6.00% drop in the bond's price, and vice versa for a yield decline. The division by (1 + y) matters more at higher yield levels, since it shrinks the effective duration relative to the raw Macaulay figure, which is precisely the adjustment candidates often forget to apply.

Why the others fail

B — 6.60 years (Macaulay duration without yield adjustment)

Reports the raw Macaulay Duration figure directly without dividing by (1 + y), skipping the exact conversion step that yields the correct Modified Duration.

C — 7.26 years (6.6 * 1.10)

Multiplies Macaulay Duration by (1 + y) instead of dividing by it, which moves the figure in the wrong direction relative to the correct 6.00 years.

D — 5.00 years

Understates Modified Duration; dividing the 6.6-year Macaulay figure by (1 + 0.10) correctly yields 6.00 years, not this lower number.