Equity Forward contract pricing?

CFA Level II Portfolio Management
#1

I thought i was sorted on this topic but i just confused with the answer on this question:

If index is 1,840 and the continuously compounded dividend yied is 3% and compounded risk free rate is 4% . What is the value of the index in 6 months.

My pricing fomula has always been: So x e ^(r-d)T = which gives me 1849.22. However the solution is 1848.50. Solution involves converting the risk free rate into log number first…this is where im getting wipped! Someone explain. Would the solution be different if the risk free rate is not compounded?

#2

Did they say “the continuously compounded risk-free rate”, or “the risk-free rate”?

I’d interpret the latter as the annual, effective rate, and that’s clearly what they used.

#3

Aha, the question says “the risk free rate compounded annually is 4%”. Do you think we should always convert the annual rate to continuous first as i have just noticed this today and then apply stock index future fomula???

#4

If it says compounded annually just use the standard annual formula with the rate and 6/12 months, no need to overcomplicate

#5

Because index forwards use continuous dividend rates, you need to use the continuous annual rate for consistency. It’s not a matter of overcomplicating it; it’s the way it’s done.

(Note: as a practical matter, the difference _ may _ be small enough that you’ll get closest to the correct answer either way. Unless, of course, they figure that using the annual rate is a common mistake and use it for one of the wrong answers. On balance, it’s probably better to do it correctly.)