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CA Final · Advanced Financial Management · Security Valuation

Ganga Securities holds a bond priced at Rs 1,000 with a modified duration of 6 and a convexity of 50. Yields are expected to rise by 1 percentage point (0.01). Using both duration and convexity, with the convexity adjustment taken as 0.5 x Convexity x (change in yield)^2, what is the estimated new price?

The estimated price is Rs 942.50. Duration implies a 6% fall, while positive convexity adds back 0.25% (0.5 x 50 x 0.01 squared). The net fall of 5.75% takes the price from Rs 1,000 to Rs 942.50. Using duration alone would understate the price.

  1. ARs 942.50Correct
  2. BRs 940.00
  3. CRs 945.00
  4. DRs 937.50

Explanation

Duration effect = -6 x 0.01 = -6.0%. Convexity effect = 0.5 x 50 x 0.0001 = +0.25%. Net change = -5.75%, so the price = 1,000 x 0.9425 = Rs 942.50. Rs 940 ignores convexity. Rs 945 omits the 0.5 factor (+0.5%). Rs 937.50 subtracts the convexity adjustment instead of adding it.

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