we form a stock index by using only two stocks in the index.

One of the stocks is the Stock-A. The current selling price of the stock-A is 103 dollars and the second stock is the stock-B. The current selling price of the stock-B is 56 dollars.

The current value of the index is equal to 267 dollars. Stock-A pays a dividend of 13 dollars in 1 months.

Stock-B pays a dividend of 1.3 dollars in 2 months.

We form a futures contract written on this index expires in 3 months.

Currently, the finance cost of carry in the market is 0.42% per month.

How can we calculate the futures contract's theoretically fair value which is monthly compounding.

Should I use the formula $f(T)= S_{stock}(1+r)^T-D_T$ ?

I don't understand how can I use this formula when for two dividend payments and two different stocks exist?

Can you please give me a hint to solve this question?


1 Answer 1


$$ Futures Price = Spot Index Value + Finance Charges - Dividends $$ You need to convert everything into index points. Check this out: https://www.cmegroup.com/education/files/understanding-stock-index-futures.pdf

  • $\begingroup$ Hi, thanks for helping. I understand which formula that I use. That's, $$Futures Price = 267 + 103(1+0.0042)^{3/12} + 56(1+0.042)^{3/12} - (13 +13 + 1.3)$$ When I insert the values in the given formula, is this true? $\endgroup$
    – 1190
    May 20, 2020 at 23:31
  • $\begingroup$ n fact, I cannot adjust how to insert dividend payments into formula and adjust time(dates) @marain $\endgroup$
    – 1190
    May 21, 2020 at 8:55
  • $\begingroup$ Please can you show a little bit more details? $\endgroup$
    – 1190
    May 21, 2020 at 11:17

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