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NISM Certifications · NISM-Series-X-A: Investment Adviser (Level 1) · Understanding Derivatives

Nifty spot is 22,000. The risk-free rate is 6% per annum (simple, annualised) and the index has no dividend yield. Using the cost-of-carry model with simple interest, what is the fair value of a Nifty futures contract expiring in 3 months (take 3 months as 0.25 years)? Nifty futures are trading at 22,400. Which statement is correct?

Fair value is 22,330 (22,000 x 1.015). Since futures trade at 22,400, they are overpriced by 70 points, so an arbitrageur would buy spot and sell futures (cash-and-carry) to lock in a riskless profit equal to the mispricing.

  1. AFair value is 22,330; futures are overpriced, so a cash-and-carry arbitrage (buy spot, sell futures) is possibleCorrect
  2. BFair value is 22,330; futures are underpriced, so a reverse cash-and-carry is possible
  3. CFair value is 22,660; futures are underpriced, so buy futures
  4. DFair value is 22,400; there is no arbitrage

Explanation

Fair value = 22,000 x (1 + 0.06 x 0.25) = 22,000 x 1.015 = 22,330. The market price of 22,400 is higher than fair value, so futures are overpriced. An arbitrageur buys the index basket in the spot market and sells futures, locking in about 70 points. Check: 22,400 - 22,330 = 70, a riskless gain over carrying cost.

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