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NISM Certifications · NISM-Series-X-A: Investment Adviser (Level 1) · Investing in Fixed Income Securities

Caselet: Ms. Kapoor holds a bond with a Macaulay duration of 5 years, a yield to maturity of 10% compounded annually, and a market price of Rs 1,000. She fears yields will rise by 0.5 percentage points (from 10% to 10.5%). Using modified duration, what is the approximate change in price?

The price falls by about Rs 22.7. Modified duration equals Macaulay duration of 5 divided by 1.10, or 4.545. Multiplying by the 0.5% yield rise and the Rs 1,000 price gives an estimated decline of roughly Rs 22.73.

  1. AFall of about Rs 22.7Correct
  2. BFall of about Rs 25.0
  3. CRise of about Rs 22.7
  4. DFall of about Rs 2.27

Explanation

Modified duration = 5/1.10 = 4.545. Price change ≈ -4.545 × 0.005 × 1,000 = -Rs 22.73. Using Macaulay duration directly gives Rs 25, which ignores division by (1+y). A rise in yield cannot raise price.

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