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CFA Level I · CFA Level I Exam · Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives

An analyst prices a six-month forward on an equity index with a spot level of 2,000. The annual risk-free rate is 4% (discrete compounding) and the index pays dividends with a present value over the forward's life of 15.00. The no-arbitrage forward price is closest to:

The forward price is about 2,025. Subtract the present value of dividends (15) from the spot level to get 1,985, then compound at 4% for half a year (factor about 1.0198). Ignoring dividends would overstate the price at about 2,040.

  1. A1,985.00
  2. B2,025.30Correct
  3. C2,040.00

Explanation

F0 = (S0 - PV of dividends) x (1+r)^T = (2,000 - 15) x 1.04^0.5 = 1,985 x 1.019804 = 2,024.31. This rounds to about 2,024; the closest option is 2,025.30. Using 2,000 x 1.04^0.5 gives 2,039.6 (ignoring dividends), the 2,040.00 option. The 1,985.00 option omits financing.

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