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?

$$Futures value= 267+103(1.0042)^{3/12}+56(1.0042){3/12}-(13+13+1.3)$$ Can you please give me a hint to solve this question?

  • 1
    $\begingroup$ Your formula does not appear to make sense. Why is $13 subtracted twice? Furthermore, what is weighting scheme for the index? In any event, I believe that you just subtract the discounted value of dividends that an index holder would receive. $\endgroup$ – Brian Romanchuk May 21 '20 at 15:30
  • $\begingroup$ I am exactly not sure. Just I predict. Please can you show me how to write correct equation? Please font calculate. Just how can insert these values into the equation? @BrianRomanchuk $\endgroup$ – B11b May 21 '20 at 20:21
  • $\begingroup$ I will be happy if you show me a way dear @BrianRomanchuk $\endgroup$ – B11b May 21 '20 at 21:43

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