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CMA Final · Strategic Financial Management · Forwards and Futures

Nifty spot is 22,000. The risk-free rate is 9% per annum and the index dividend yield is 3% per annum, both continuously compounded. The 3-month Nifty futures trades at 22,400. Take e^0.015 = 1.0151. What is the arbitrage position and approximate profit per unit of index?

Sell the overpriced futures and buy the index in the spot market, earning about Rs 67 per unit. The fair futures price is 22,000 times e to the power 0.015, about 22,332, which is below the quoted 22,400, so the futures is rich.

  1. ABuy futures, sell spot; profit about Rs 400
  2. BSell futures, buy spot; profit about Rs 67Correct
  3. CBuy futures, sell spot; profit about Rs 67
  4. DNo arbitrage; futures is fairly priced

Explanation

Fair futures = 22,000 x e^((0.09-0.03) x 0.25) = 22,000 x 1.0151 = 22,332.2. The actual price of 22,400 is higher, so futures is overpriced: sell futures and buy spot. Profit = 22,400 - 22,332.2 = about Rs 67.8, i.e. approximately Rs 67. Rs 400 ignores the cost of carry.

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