Not sure if this is just me but could someone please shed some light on how this formula:
Ff/d= Sf/d * (1+if[Actual/360])/(1+id[Actual/360]))
evolves into the below?
Ff/d−Sf/d = Sf/d * (([Actual/360]/(1+id[Actual/360])) * (if−id).
Source: CFAI Econ pg.508
Yes, both are the same.
The second one solves for the forward premium or forward discount. I think many traders use quotations based on premiums or discounts on the spot exchange rate, so this formula may be used commonly.
Subtract by Sf/d on both sides and solve it. I’ll solve it for you - for now just ignore the day count convention for convenience.
Ff/d - Sf/d = [Sf/d * (1+if) / (1+id)] - Sf/d
Ff/d - Sf/d = Sf/d * [{ (1+if) / (1+id) } - 1]
Ff/d - Sf/d = Sf/d * [{ ( (1+if) - (1+id) ) / (1+id) }]
Ff/d - Sf/d = Sf/d * [(if - id) / (1+id)]
Now multiply by the day count frequencies respectively to get:
Ff/d−Sf/d = Sf/d * (([Actual/360]/(1+id[Actual/360])) * (if−id)
Hope it is clear!
Thank you for your response but I’m still lost =( How did you get -1 in the second line? And how did (1+id) end up in the numerator in line 3? I really hope I am not recalling some simple math formulas from that I haven’t used in years. Your help is much appreciated!
Simple math.
Sf/d is common to the first and second part of the RHS - Line 2. Its like "[2*(3/5)] - 2. It can also be written as 2*[(3/5) - 1]
Line 3 is LCM multiplication. In the above example its like 2*[(3-5)/5].
Write it on paper, it’ll be easier.
Remove the f/d (convention) too, to make it easier to see
F = S (1+if) / (1+id)
F/S = (1+if) / (1+id)
you now subtract one from each side and simplify …
F/S - 1 = (1+if) / (1+id) - 1
(F-S)/S = (1+if- (1+id)) / (1+id)
(F-S)/S = (if - id) / (1+id)
F-S = S * ( if - id ) / (1+id)
Thank you guys