# Covered interest rate parity formula variations

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