# Value (long position on equity index)

Could someone tell me why is the Value of the long position on an equity index equal to (S / (e^dividend yield)) - (FP / e^risk free rate))? *I’ve slightly slightly simplified the formula.

just gotta subtract the continuously compounded div yield, because dividends on indices are “continuous” because it’s an index not a single stock. So it’s just spot-PV divs minus PV future price, the price we locked in at. Hence we want that spot price to go up and be greater than FP if we are long it

Why don’t we divide both by (e^risk free rate - dividend yield)? As another example so I can get my head around this, what is the reason why the Value of the long position on a currency forward contract is equal to (S / (1+risk free rate in FC)) - (F / (1+risk free rate in DC))?

because you aren’t PV-ing the current spot price, you are just taking out the dividends. But you have to PV the forward price you locked in at to bring it back to the spot date (now). The way they do currency forwards is confusing. Give me your email and i’ll show you a better way.

Cheers, its marcfa at gmail

Hey AndrewUNH, I’ve been having some trouble wrapping my head around the currency forwards as well. Go you think you could froward that email to me too? jdadoun@gmail.com Much appreciated!

Sorry head is fried after a day of MCQ’s. My e-mail is markcfa at gmail

These formulas just look weird after they multiply things through. Just go back to first pricipal intuitive formulas, and it may be easier. Stock Index (1) F = S*e^(rt - dt); now we can divide both sides by e^rt, and get: Fe^-rt = Se^-dt So, now for value, just subtract the Fe^-rt from both sides Currency (2) F = S*[(1+r_dom)/(1+r_for)]; divide each side by 1+r_dom => F/(1+r_dom) = S/(1+r_for); now subtract the left from the right I always start with the intuitive formula before they monkey around with notation. Makes sense? If you don’t understand the original formula, then you need to start over with that understanding. If you get those, then the rest is just algebra. Good luck.