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CA Final · Advanced Financial Management · Security Valuation

A bond priced at ₹1,000 has a Macaulay duration of 4.2 years and a yield to maturity of 5% per annum (annual compounding). Using modified duration only, what is the approximate fall in price if the yield rises by 50 basis points?

The price falls by about ₹20. Modified duration is 4.2 divided by 1.05, which is 4.0. A 0.5% rise in yield then reduces the price by roughly 4.0 × 0.5% = 2%, or ₹20 on ₹1,000. Using Macaulay duration directly would overstate the fall.

  1. A₹20Correct
  2. B₹21
  3. C₹40
  4. D₹42

Explanation

Modified duration = 4.2 / 1.05 = 4.0. Percentage price change ≈ -4.0 × 0.5% = -2.0%, so the fall is 2% of ₹1,000 = ₹20. Using the Macaulay duration directly gives 2.1%, or ₹21, which ignores the division by (1 + y).

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