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CMA Final · Strategic Financial Management · Interest Rate Derivatives

Aarav Ltd holds a bond portfolio of market value Rs 100 crore with modified duration 6. It plans to hedge against a rate rise using interest rate futures on a government bond whose futures price is Rs 105 per Rs 100 face value, contract size Rs 1 lakh face value (so value Rs 1,05,000), and modified duration of the underlying 4. Using the duration-based hedge ratio, how many contracts should be sold, approximately?

About 1,429 contracts should be sold. The duration-based hedge ratio equals portfolio value times its duration divided by the futures contract value times its duration: Rs 100 crore x 6 divided by Rs 1,05,000 x 4, which comes to roughly 1,428.6.

  1. A1,429Correct
  2. B952
  3. C1,000
  4. D1,500

Explanation

Contracts = (Portfolio value x portfolio duration) / (futures value x futures duration) = (100,00,00,000 x 6) / (1,05,000 x 4) = 600,00,00,000 / 4,20,000 = 1,428.6, about 1,429. 952 uses the duration ratio inverted (4/6 x 1,428). 1,000 ignores both duration and price. 1,500 comes from using face value Rs 1 lakh with durations 6/4 (1,000 x 1.5).

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