Explanation:

Over the six-month period from June 30th to December 31st, the average dividend yield is:

\bar q = \frac{4\%\times 4 + 7\%\times 2}{6} = 5\%

Using the cost-of-carry formula with continuous compounding:

F_0 = S_0 e^{(r-q)T}

where $S_0 = 2500$ , $r=3\%$ , $q=5\%$ , and $T=0.5$ . Thus:

F_0 = 2500\, e^{(0.03-0.05)0.5} = 2475.12

So the nearest theoretical futures price is $2,475.12.

718.1. Assume that the risk-free rate is 3.0% per annum with continuous compounding and that the dividend yield on a stock index varies throughout the year. In January, April, July, and October, dividends are paid at a rate of 7.0% per annum. In other months, dividends are paid at a rate of 4.0% per annum. Suppose that the value of the index on June 30th is 2,500. Which is nearest to the theoretical futures price for a contract deliverable on December 31st? (this question is inspired by Hull's EOC Problem 5.11)

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Last updated: April 18, 2026 at 11:32

$2,450.50

$2,475.12

$2,602.03

$2,708.22

Financial Risk Manager Part 1