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NISM Certifications · NISM-Series-VIII: Equity Derivatives · Basics of Derivatives

A stock trades at Rs 400 and the one-month futures is quoted at Rs 408. Assume the risk-free rate is 12% per annum with continuous compounding, ignoring dividends, and take e^0.01 = 1.01005 (one month = 1/12 year). Which statement is correct?

Fair value is 400 x e^0.01, about Rs 404.02. Since the futures trades at Rs 408, it is overpriced, so an arbitrageur would buy the stock and sell the futures (cash-and-carry) to lock in a riskless gain of roughly Rs 3.98.

  1. AThe fair futures price is about Rs 404.02, so the futures is overpriced and a cash-and-carry arbitrage is possibleCorrect
  2. BThe fair futures price is about Rs 404.02, so the futures is underpriced and a reverse cash-and-carry arbitrage is possible
  3. CThe fair futures price is about Rs 412.00, so the futures is underpriced
  4. DThe fair futures price is Rs 408, so no arbitrage exists

Explanation

Fair price F = 400 x e^(0.12 x 1/12) = 400 x 1.01005 = Rs 404.02. Market futures at Rs 408 exceeds this, so it is overpriced. The arbitrageur buys the stock, borrows at the risk-free rate and sells the futures, locking in about Rs 3.98. Reverse cash-and-carry would be used if the futures were underpriced.

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