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I need a help for the following question:

A stock index is constructed by including only two stocks in the index. One of the stocks (Stock $1$) currently sells for $250$ dollar and the other stock (Stock $2$) sells for $187.5$. The current value of the index is $437.5$. Stock $1$ is expected to pay a dividend of $7.5$ in one months and Stock $2$ is expected to pay a dividend of $2.5$ in two months. A futures contract written on this index expires in three months. Currently, the finance cost of carry in the market is $0.75%$ per month. Calculate the theoretically fair value of this futures contract by assuming monthly compounding.

Here what i have done so far: $f_0(T)=437.5(1.0075)^{3/12}-7.5(1.0075)^{2/12}-2.5(1.0075)^{1/12}$ I think this is not true. Where do i make mistake? Should i use stock $1$ and stock $2$?

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  • $\begingroup$ If you want to be a stickler, you could answer that the value is zero, and that the strike will be X. If you then want to be an even bigger stickler, you can say that this assumes no margining, if there is margining, you need to factor in the cost of funding the margin acount less the interest recieved on the margin paid. Then on top of that you need to account for the value of the VaR that holding the future provides you (is it risk increasing or does it net off/hedge existing exposure?). These extra points clearly aren't the point of the question, but i think it's useful to understand. $\endgroup$
    – will
    May 24, 2020 at 12:36

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You must convert all cash and dividend streams into the index points . The current value of the index between stocks seems ok but the dividends need to be converted to index points.

Basically divide the dividends you’ve calculated by the index divisor. Then the calculation seems ok

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  • $\begingroup$ Conceptually that is right. The index divisor appears to be 1 in this case or am I looking at it incorrectly? $\endgroup$
    – nbbo2
    May 24, 2020 at 2:29
  • $\begingroup$ Hmm, it is a bit weird. I read it as a price weighted index but it appears to be a non weighted index. My original view was that as there were two stocks making up the index, the dividends must be turned into index points according to the value they bring to the index hence divide the dividends by 2 which would have been the divisor. $\endgroup$
    – JazKaz
    May 24, 2020 at 2:55

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