# Equity Index Forward Valuation

Hi everyone, Could someone please explain me why in the forward valuation formula wih dividend we substract St by the present value od dividends ? Vt = (St - PVD) - FP/(1+RFR)^t-T

and for me it would be

Vt = St - FP / (1 + RFR)^t-T

For me the value of dividends is already inside the Forward price… which is the future value of So and the future value of dividends.

Many thanks

Any value equation is telling you what you will get. You will get S-X at maturity (and in the value equation, this is discounted back to now). You will not be getting any dividends issued between now and maturity, the current owner gets those! Lucky him/her!

Issuing a dividend will push the spot price down by roughly the size of that dividend. Basically, that portion of the underlying assets value seeps out of the asset into the hands of the holder. So when you get that asset at maturity, it won’t be worth the same as when you started the forward contract.

Since dividends are pretty predictable, you can work this into the contract and discount it back to now.

Thank you for the help, however, i recognize a good definition of what is the price of a forward, which i think i understand. My point is actually about the valuation : if we accounted for dividends in the Forward price as you said, so why do we account again in the valuation given that it is already in the forward price O.o ?

If we compute (So - Present value of remaining dividends) - FP discounted (= Discounted future value of So - discounted future value of dividends), so there is two times the dividends ! i really do not get it

For those who read this post i finaly understand the problem. Actually the equation So - X discounted gives a postiive valuation of the FP at To, which is not arbitrage free price of the forward. Actually the positive result is the PVDividend… so the FP discounted need to be compared to what the investor really target : a “stock without dividend”

so the formula is roughlty : (Stock without dividend) compared to (FP of the stock without dividend) and at To this valuation equal zero